Control Design - How to Tune Loops

SPECIAL REPORT

HOW TO TUNE

PID LOOPS

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How to tune PID loops Servo-motor Servo-motor applications ap plications and temperature-co temperature-control ntrol applications often need training after the auto-tune By Mike Bacidore, editor in chief

A Control Design reader writes: I often have difficulty tuning PID loops, especially for temperature control applications and servo-motor motion applications. If I use a temperature controller, the auto-tune built into the device often works well if I follow the manufacturer’s recommendations. However, if the temperature control or motion control is through a PLC or other advanced controller, it’s often a long training process to find the optimum coefficients for the proportional, integral and derivative of the control loop.

Whether I am controlling the temperature of my medical cleaning process skid or moving my servo-controlled three-axis gantry, if the process variable (PV), such as temperature or position, needs to change slowly, it’s easy. As soon as I need better performance, such as a fast change in temperature or position, or if dynamic loads are involved, my PID loops become unstable and oscillate or the t he process variable overshoots or undershoots the setpoint. I can’t afford to burn up the medical device I’m cleaning or have a spongy motion-control system that can’t snap to a position.

How do I achieve a quick-responding PID control loop that can handle dynamic changes to the process variable without chasing PID coefficients for days? What are some rules when designing the control system for these closed-loop control applications?

Where do I start and what are some best practices to get stability and optimal control in process-skid and motion-control applications from both a hardware and a PID tuning standpoint. What are some procedures to follow to help reduce PID-loop-tuning time? Any suggestions are appreciated?

How to tune PID loops

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How to tune PID loops Servo-motor Servo-motor applications ap plications and temperature-co temperature-control ntrol applications often need training after the auto-tune By Mike Bacidore, editor in chief

A Control Design reader writes: I often have difficulty tuning PID loops, especially for temperature control applications and servo-motor motion applications. If I use a temperature controller, the auto-tune built into the device often works well if I follow the manufacturer’s recommendations. However, if the temperature control or motion control is through a PLC or other advanced controller, it’s often a long training process to find the optimum coefficients for the proportional, integral and derivative of the control loop.

Whether I am controlling the temperature of my medical cleaning process skid or moving my servo-controlled three-axis gantry, if the process variable (PV), such as temperature or position, needs to change slowly, it’s easy. As soon as I need better performance, such as a fast change in temperature or position, or if dynamic loads are involved, my PID loops become unstable and oscillate or the t he process variable overshoots or undershoots the setpoint. I can’t afford to burn up the medical device I’m cleaning or have a spongy motion-control system that can’t snap to a position.

How do I achieve a quick-responding PID control loop that can handle dynamic changes to the process variable without chasing PID coefficients for days? What are some rules when designing the control system for these closed-loop control applications?

Where do I start and what are some best practices to get stability and optimal control in process-skid and motion-control applications from both a hardware and a PID tuning standpoint. What are some procedures to follow to help reduce PID-loop-tuning time? Any suggestions are appreciated?


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ANSWERS P IS FOR PROPORTIONAL BAND

Before beginning, adjust the set point (SP) to about 80% of the normal process setting.

First, determine what engineering units the tuning parameters use. This allows you to

1. Start with the proportional band at what-

understand if increasing or decreasing a

ever the default value is, or 50% of setting

parameter has a positive or negative effect.

range. 2. Set both the integral and derivative pa-

The P in PID is for proportional band. It is

rameters to zero.

also known as gain. Increasing the proportional-band setting decreases its effect

Wait a few minutes for the temperature to

on the loop. Whereas increasing the gain

stabilize. Note that it will not be at the set

parameter increases the effect. Proportional

point, generally lower.

band = 100/gain. Upset the loop by introducing loss either by I is for integral. This is the time parameter.

raising the set point 10% or removing heat

It is also known as reset. Increasing integral

through whatever method is practical. I

parameter increases the effect; decreasing

have used air guns; opened doors of furnac-

reset parameter increases the effect. Inte-

es; sprayed cold water from a garden hose;

gral = 1/reset.

turned off main-burner gas-supply valves; tripped circuit breakers. And I’ve even shov-

D is for the derivative parameter. It is also

eled snow onto rotary kiln infeed conveyors

referred to as rate. These terms act the

in an attempt to simulate process heat loss.

same: Increasing the value will increase the effect on the loop.

Observe the response. If the output slowly increases and the temperature does not

For both integral and derivative, the units of

oscillate, decrease (increase the effect) the

time must be understood, as well (millisec-

proportional band and repeat the upset.

onds or seconds).

Do this several times until you see a pronounced oscillation of the process variable;

A reasonably quick method to create a sta-

it still will not be at set point.

ble loop requires a process upset through heat loss. This method is used without the

Now, without disturbing the process, in-

process actually being in operation.

crease the integral term one step at a time,


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waiting a reasonable length of time after

what. I will give a simplified example of what

making a change until the temperature is

I mean by resolution of the control variable.

now oscillating around the set point. This oscillation may not be very noticeable, but

If the application is controlling the tem-

remember you are in a steady state condi-

perature in a small 5-ft-by-5-ft room, for

tion at this time.

example, and you try using a 500,000-Btu furnace as your control variable, then your

Next, upset the loop using whatever meth-

loop will never be stable. You will always

od available and observe the response. You

overshoot to an extreme oscillation around

can now add in a small amount of derivative

the set point because you have too coarse

term one step at a time after upsetting the

of a control variable.

process until there is acceptable perfor-

— Dan Michki, senior robotics/controls engineer,

mance. Decent enough control should now

East Balt Bakeries, www.eastbalt.com, Chicago

be occurring, allowing you to run the system under real process conditions.

EQUIPMENT, ALGORITHM, SAMPLE RATE

Further fine tuning is now performed with

First, know your equipment. Don’t try to

small changes to one parameter at a time

tune over an issue that is caused by faulty

and allowing sufficient time for the change

or erratic equipment. Make sure there are

to be observed. Try to operate the loop in

no external equipment problems causing

as many different process conditions as

issues in your PID control—for example, tun-

practical. Record all changes along with

ing a methane-powered generator with a

performance notes to aid in solving future

dirty methane supply or tuning a generator

problems.

on top of a governor. Also watch out for lag

— Mike Krummey, electrical engineering manager,

or dead time in your equipment, which can

Matrix Packaging Machinery, www.matrixpm.com

be caused by actuators or sensors that are slow to respond to dynamic changes. And,

NO DERIVATIVE VALUE

lastly, keep an eye out for external noise on

In my experience, using PID-loop function

your PV signal; use a filter whenever pos-

blocks in a PLC the first thing that I do is to

sible to be sure the feedback is pure.

remove the derivative value completely. I have yet to find an application where a de-

Next, know your algorithm. All controllers

rivative value was needed. The second thing

are not created equal, and most manufac-

to consider is the resolution of your control

turers have their own interpretation of the

variable. If the resolution is too high, then

PID equation. Look through the help file or

you will never get stable control, no matter

product documentation to determine which


4


version of the PID equation your control-

PID equation, Kr*(en – e(n-1)), Kr is the calcu-

ler is using. This will help you to determine

lated coefficient, but the gain is determined

the proper values for your coefficients. This

based on the error at the current time minus

also explains why the auto-tune works so

the error at the time before. So, with a calcu-

well with the temperature controller you

lated coefficient of 1, if the error goes from

mention. Using the manufacturer’s recom-

2 to 10, then the D term is 8; but, if the error

mendations, which are fine-tuned to the

then goes from 10 to 12, the D term is 2 with

manufacturer’s algorithm, will undoubtedly

the error still increasing. The D term dropped

produce better results.

to 2 because the error rate of increase slowed even though the error itself increased. On the

Set your sample rate. PID sample rate

flip side, with the goal of eliminating error as

identifies how often the instruction will

fast as possible, the derivative term can also

calculate a new output value. Make sure

become a hindrance. If the D term sees a

the rate at which you are calculating is

dramatic swing toward correcting the error, it

set appropriately. Setting the rate too

will mitigate the gain to avoid an overshoot,

low will cause your controller to miss

which could unintentionally cause an under-

important changes, and sampling too fast

shoot if not set properly. In other words, use

could cause instability in your integral and

the derivative term carefully and only when

derivative terms. Try to shrink the sample

absolutely necessary.

rate as much as possible, but, more impor-

— Bill Dehner, technical marketer, AutomationDirect,

tantly, keep that value constant.

www.automationdirect.com

As for the tuning itself, I’m not saying you

MULTIPLE PIDs

are trying to tune the values all at once, but

I mainly work with temperature controls, and

don’t. You’ll go insane. Instead, cancel out

each piece of equipment has a unique tem-

the integral and derivative, and focus on the

perature profile within the temperature zone.

proportional term first. Get the proportional

The battle of having a PID loop that reacts

value to a point where the system is correct-

quickly without overshooting is a common

ing quickly in the right direction. Then add

problem. In the aerospace-parts manufactur-

the integral term in and tune until you get the

ing industry, this overshoot is tightly con-

desired response in the low-error range. For

trolled via AMS 2750 requirements.

most systems the PI control is good enough, but if you need derivative control, remember

One of the easiest ways that I have found to

that the derivative is based on the rate of

help resolve this is with multiple PID loops.

change in the error, not the error itself. For

In the past, we just had a single PID for the

example, looking at the derivative part of this

controller, but more modern controllers are


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allowing multiple PIDs. This is achieved by

the flow of steam, the temperature drops.

setting a PID for a temperature range. This

The change in steam flow impacts the final

will allow you to have an aggressive PID and

steady state temperature of the exit steam.

not worry about the overshoot. Then, when

Processes such as this are relatively easy

you get closer to your setting, you can have

to tune using the basic tuning rules avail-

a PID that is less aggressive and will not

able. This type of process is also known as

overshoot. For example: I’m trying to heat

a self-regulating process.

a furnace to 1,200 °F at a ramp rate of 50 °F/ minute. We will use a PID setting for

An example of a semi-continuous tem-

0-1,100 °F; then there will be a different PID

perature control application would be

setting for the range from 1,101 °F and up.

temperature control of a furnace or batch

This will allow us to tune the 1,101 °F-and-up

reactor (Figure 2). To increase the tempera-

differently than we do the lower range. If

ture, the power to the heating element or

the first PID was used, then we would surely

flow of steam through the reactor jacket

overshoot. However, once the temperature

is increased. As the amount of heat to the

reaches 1,101 °F, then the second PID takes

vessel increases, the rate of temperature

over and controls less aggressively so that

change increases. By decreasing the heat

we don’t overshoot.

into the system, the temperature will still

— Scott Richardson, continuous improvement manager,

rise, albeit at a much slower rate. Note,

special processes

however, that turning off the heat completely won’t cause the vessel to start cool-

TEMPERATURE CONTROL

ing instantaneously. The dynamics between

CHALLENGES

the heating and cooling can be remark-

Temperature control applications can be

ably different. Additionally, the inertia of

broken into two main categories—fully con-

the heating processes is challenging. The

tinuous and semi-continuous (or batch).

walls of the vessels, or even the material

An example of a fully continuous tempera-

that is being heated, all absorb energy and

ture controller is a shell-and-tube heat

generally are slow to release the energy.

exchanger (Figure 1). In this application,

This presents a challenge. These semi-con-

the exit temperature is controlled by ad-

tinuous temperature control applications

justing the flow rate of heating fluid, such

are highly nonlinear both in terms of their

as steam, through the shell side. As the

operating range and in terms of their op-

flow of heating fluid is increased, the tem-

erating direction (heating versus cooling).

perature also increases until it eventually

Temperature control exhibits give-and-take

settles at a temperature well below that of

dynamics that practitioners must consider

the heating fluid. Similarly, by decreasing

in order to strike the proper balance.


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Warm Liquid Flow (L/min)

Cold Liquid Valve Position (%)

FULLY CONTINUOUS Figure 1: In this shell-and-tube-heat-exchanger application, the exit temperature is controlled by adjusting the flow rate of heating fluid, such as steam, through the shell side. (Source: Control Station) Steam Flow (lbs/hr)

Controller Output (%) Exit Temp (ºC)

Set Point (ºC) Header Pressure

Steam Supply Header

To understand the solution, one must un-

lating influence over time. The proportional

derstand how a PID controller reacts to

and integral terms drive the process toward

disturbances and set-point changes. Most

set point in order to eliminate error, and

PID controllers work using three corrective

they will not stop until the error is gone. The

forces: proportional, integral and derivative.

derivative term, on the other hand, does not

The proportional term simply adds a correc-

account for the value of error (if it’s large

tion term to the output based on the current

or small); it only accounts for the rate of

error (SP-PV). The integral term adjusts the

change of the error. If the error is chang-

output based upon how much error and for

ing quickly, the derivative term has a large

how long the error has persisted, accumu-

influence and works to prevent the error


7


Reactant Feed

Conversion (%)

Controller Output (%) Reactor Temp ( C) º

Steam to Jacket

SEMI-CONTINUOUS

from changing too quickly. When all three forces work together, you get a fast correction using proportional and integral driving the output to get the process variable to set

Figure 2: To increase furnace or batch-reactor temperature, the power to the heating element or flow of steam through the reactor jacket is increased. As the amount of heat to the vessel increases, the rate of temperature change increases. By decreasing the heat into the system, the temperature will still rise, albeit at a much slower rate. (Source: Control Station)

point, and the counteraction of the derivative pulling back on the correction once the process variable starts to change too rapidly.

Let’s focus on the modeling part first. For the sake of simplicity, we will stick to first

In most cases, the full PID algorithm is rec-

order models. Let’s look at an open-loop

ommended for semi-continuous type tem-

bump test of a semi-continuous furnace,

perature controllers.

like an annealing furnace (Figure 3), and examples of open-loop step tests for self-

There are many methods for tuning semi-

regulating and non self-regulating process-

continuous temperature controllers, and all

es (Figure 4). Notice that the temperature-

apply a similar approach: model the process

control example from the furnace doesn’t

to characterize its dynamics, and then use

really look like either of the models. In fact,

that model to calculate tuning values based

these types of semi-continuous temperature

on tuning correlations.

controllers are best represented by a hybrid


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IMPACT OF HEATING ELEMENT POWER ON TEMPERATURE OF FURNACE

FURNACE TEST Figure 3: In an open-loop bump test of a semi-continuous furnace, the temperature-control example doesn’t really look like either of the models. In fact, these types of semi-continuous temperature controllers are best represented by a hybrid of the two models. (Source: Control Station)

of the two models. That is a different topic

as a non-self-regulating process. Figure 5

for another time.

shows an integrating process applied to the initial dynamics. Since we only require the

In practice, you have two options. The tra-

initial dynamic response, the time required

ditional method to generate a model is to

for testing can be significantly reduced. The

do a step test in manual mode and wait for

integrating model parameters (K* Integra-

the process to complete its response. The

tor Gain and

challenge with this method is that it takes a

generated either with software or by hand

very long time for these types of processes

using the slope method detailed at www.

to steady out, if they ever do. The other op-

controldesign.com/controlguru.

p

Process Deadtime) can be

tion is to treat the initial process dynamics


9


Once a model has been generated, tuning

The biggest challenge with using an IMC ap-

correlations can be employed to generate

proach to tuning temperature controllers is

a set of tuning parameters without having

the selection of the closed-loop time con-

to trial-and-error tune. For this example, we

stant,

can use the internal model control (IMC)

da. This value represents the time needed

method to generate full PID Tuning values

for the process to reach 63% of a set-point

for an integrating process (See equation 1

change. The closed-loop time can be based

on the next page).

either off of a particular design objective or

SELF-REGULATING

c

, which is often referred to as lamb-

NON-SELF-REGULATING

SELF-REGULATING AND NON-SELF-REGULATING Figure 4: These examples show open-loop step tests for self-regulating and non-self-regulating processes. (Source: Control Station)

INTEGRATING PROCESS Figure 5: An integrating process is applied to the initial dynamics. Since we only require the initial dynamic response, the time required for testing can be significantly reduced. (Source: Control Station)


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IMC TUNING CORRELATIONS NON-SELF — REGULATING PROCESSES

EQUATION 1

EQUATION 2

EQUATION 3

on the process’ dynamics. An estimate for the closed-loop time constant for a non-

and with the goal of providing a quick

self-regulating process can be calculated

initial response with minimal overshoot.

by determining the amount of time that

This method has been used with success

it takes for the PV to change by 1% when

on furnaces, ovens, fermenters and batch

the controller output (CO) is changed by

reactors. In the end, there is always a

1%. Once this time is determined, it can be

trade-off between fast initial response and

multiplied by 0.63 to determine the amount

overshoot. Indeed, the PID controller of-

of time it takes to reach 63% of the 1% PV

fers a simple means for control that has its

change. A simple method for estimating

is

c

shown above in equation 2.

limitations, especially as the deadtime of the system gets very large or as nonlinearity increases. In those cases, a simple PID

Applying this method to the temperature

controller may not be adequate, and more

loop explored earlier, the closed-loop time

advanced forms of control such as adap-

constant is estimated above in equation 3.

tive PID, model predicative control or even fuzzy logic may be appropriate.

This method is designed to generate tuning parameters quickly, using minimal data

— Robert Rice, Ph.D., vice president of engineering, Control Station, www.controlstation.com


11


TAME THAT LOOP

thermal mass to overshoot the set point pri-

A major aspect of controlling both thermal

or to the sensor being able to respond (lots

and position control loops begins with mak-

of power, large lag, small thermal mass).

ing the loop as tame as possible. This starts

Such a configuration needs a very slow con-

at the system design stage.

trol response and gentle gains to keep from overreacting in the lag time. Moving the

For the thermal loops, limiting the lag time

sensor closer to the heater cuts the lag time

helps to reduce the overshoot. Time lag is

but may also blind the sensor to what is

a high (theoretically infinite) order system

happening at the load. Either experimenta-

but may be modeled reasonably by fewer

tion or modeling, or both, can help to locate

stages to get a reasonable approximation,

a reasonable sensor placement to minimize

as long as the pure lag time is not too

lag. Other solutions, such as heat pipes, may

long. Pure lag time, or transport time, is

also be used to reduce the lag and to make

the time between applying a pulse to the

the system closer to equal temperatures, if

input and seeing any change in the feed-

that is a critical need.

back sensor response. Additional sensors may also be used to limit There is a trade-off in selecting the physi-

heating to a reasonable level approximating

cal position of the temperature sensor with

the desired temperature while the main sen-

respect to the heating element and with

sor is slower responding but sensing nearer

respect to the controlled load zone. Re-

to the temperature control point (dual loop

member, the control loop tries to minimize

control). Alternatively, intermediate temper-

the error as seen by the sensor. If the sen-

atures may also be estimated, using a model

sor is too far from the load and too close

of the system, as well as the power being

to the heater, the response at the load can

driven into the system, but these both are

be slow and the sensor may not see varia-

well past the realm of a basic PID controller.

tions at the load; the loop will, however, be very easy to control. Place the sensor too

On several medical-application tempera-

far from the heater, and the lag time can

ture-control projects of which I have been

make overshoot very hard to avoid. Place

involved, PID was not an optimal control

the sensor on the other side of the thermal

strategy; a targeted control system design

mass away from the heater, and the prob-

was used instead to allow significantly better

lem only gets worse.

stability and response. The addition of a zero (lead = differentiation) into the integrator,

The overshoot can be particularly bad if the

plus an additional zero (differentiator) with

heater can supply sufficient heat into the

gain, gave a pair of zeros that were avail-


12


able to attract the poles of the system for

When handling larger inertial mismatches,

a stable, fast response. The control point

the system may be modeled at a mass-

stayed to within ~.01 °C (as measured with

spring-mass (rotary inertia, torsional

the control sensor), with a fraction of a sec-

spring, rotary inertia, to be more exact),

ond response time to transients. Air load on

which has an anti-resonance (both masses

the system from waving a piece of paper at

rotating in opposition and a resonance,

it were readily detected and rejected. One

which is approximately the motor mass

project used a heat pipe to equalize the tem-

and the spring working against the signifi-

perature over a fairly wide area that also had

cantly larger load inertia [series and paral-

variable thermal loads. Any cold spot tended

lel resonances, if you will]).

to condense the gas phase, quickly releasing heat into the colder area while not causing

This is actually the motor inertia, the spring

measurable changes to those regions al-

constant of any shaft and coupler, and the

ready at temperature.

load inertia. Most people will recognize a mass connected via a spring to a second

Knowledge about the system being con-

mass. The equations are the same, but many

trolled is of great help in determining the

did not see the math worked in rotary units

proper control approach. In the absence of

in basic physics.

a good model, a little experimentation as to the placement of your temperature feed-

Optimizing the mechanical system for fast

back device(s) can significantly make a sys-

response control also starts long before

tem easier to control. Apply a short pulse

tuning. Such factors as presence or absence

of power to the heater and then watch the

of gearheads, the degree of backlash and

response on a digital oscilloscope. You may

the style of motor couplers can significantly

want a second (temporary) sensor at the

change the settling time and can limit the

load to allow you to visualize the lag time

response of any best control method. Over

and filtering effects of the thermal circuit,

the years, I have moved well away from

both at the control sensor and at the load.

PID. We at QuickSilver Controls use posi-

For example, a slight overshoot at the

tion velocity integration acceleration (PVIA)

sensor may still produce an underdamped

due to the large range of loads it accom-

response at the region you are trying to

modates. The motor and its load may be

control. Even if you are using a straight PID

modeled as a torque source coupled to the

rather than an optimized controller, making

motor inertia, which is in turn, coupled to

the problem easier by proper sensor loca-

the load mass via a spring. The gain is the

tion selection will make for a much more

ratio of acceleration at the motor shaft and

stable and robust control system.

encoder to the input torque. The spring


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represents the shaft and coupling stiffness.

to anti-resonance frequency, causing a

At low frequencies, the motor will see the

greater change in gain for which the con-

combined inertias (Jmotor + Jload). The low

trol system will have to cope. Appropriate

frequency motion does not significantly

filtering, which is not present in a basic PID

excite the spring. The gain (acceleration

system, can shape the overall system re-

per torque) drops off with frequency. At

sponse to provide a robust and responsive

a certain frequency, the lag introduced by

system. From the design side, the use of an

the spring causes the load inertia to have

adequately stiff shaft and coupler can push

opposite phase to the motor inertia; that is,

the resonance frequencies higher to move

the motions will be in opposite directions.

them away from the range of frequencies

This is the anti-resonance frequency and

in which the motion is desired. Adding in-

corresponds to a local low point in gain/fre-

ertia to the motor, or very near to the mo-

quency point. As the excitation frequency

tor, can reduce the frequency ratio of the

further increases, the load inertia has less

resonance and anti-resonance frequencies,

and less motion relative to the motor, as the

reducing excess gain, which may cause

springiness of the coupling from the motor

trouble in simpler PID systems. Finally,

to the load inertia limits the acceleration

gearing may be used to reduce the load

of the load inertia. The slope of the gain/

inertia as seen by the motor to effectively

frequency plot doubles each octave in this

reduce the ratio of motor to load inertia.

frequency range. This gain increases until

This again limits the gain rise between

the spring constant of the shaft and coupler

anti-resonance frequencies and resonant

interacting with the motor inertia will cause

frequencies, which tames the system for

a maximum gain point called resonance.

simple PID controllers. Gearing reduces the

The peak in gain here may be very strong if

reflected inertia by the square of the gear

there is little damping in the system. Be-

ratio. The addition of a properly filtered ac-

yond this frequency, the motor inertia will

celeration estimate provides an electronic

dominate and the gain/frequency plot will

approximation of a viscous inertial damper,

again drop off by a factor of 2 for each oc-

which provides an additional damping and

tave. Note this is a simplified model; things

significantly boosts the phase margin over

can get much more interesting when more

a range of frequencies that can be as large

elements are considered and especially if

as two or three octaves. This may eliminate

there is any backlash in the system.

the need for tight notch filters, which may have issues as the load changes.

Increasing the relative inertia of the load compared to the motor inertia will cause

Finally, we use a patented interaction

a greater ratio of the resonance frequency

between the motor and the driver stage


14


to introduce additional damping into the

thicker shafts; solid anchors for the motor

system, by a combination of active and

and for the gearhead, if needed, to handle

passive methods, which further adds to

the reaction forces. This is missed more of-

the gain margin. As shipped, the system

ten than would be expected. Minimizing the

typically will operate open shaft to ap-

load where possible is also helpful.

proximately 5x motor inertia with minimal additional tuning. With about 10 minutes

Yes, there is expertise available to handle

of effort, a 100:1 inertial mismatch may be

more difficult control problems, but in a

easily obtained. According to varying lit-

large majority of the systems, a little effort

erature, PID is typically limited to less than

up front can make the control effort much

a 10:1 inertial mismatch.

easier, less expensive and more robust.

Using straight PID, it is important to be

Why lag is so bad: control systems are

aware that there are series and parallel

all about timely responses to measured

implementations, and various implemen-

stimulus. Lag increases uncertainty in

tations in between. The method of tun-

the system. Think about investing with

ing each of these significantly varies. The

information that is months or years old,

series implementation tends to have more

or driving watching a 10-second-delayed

tuning interactions but is more common of

video. It would be very difficult to respond

analog controllers.

to a light changing when you were already through it by the time you saw it change.

Remember, the first step is to start with

The control system has the same problem

an easily controllable solution. For ther-

if a heater has already supplied sufficient

mal, pick a sensor location without too

energy into a system to overshoot the set

much lag, if possible, and (almost) always

temperature by the time the sensor starts

between the heater and the region to be

to respond. In the absence of timely data, a

thermally controlled. Try to minimize lag

model of the system that gives a predictive

in the system, which includes both the

response may be needed, or the maximum

physical system and any computational

rate of power must be limited—driving re-

lag in the system, such as a slower or

ally slowly, in the comparison. Mathemati-

overtaxed PLC.

cally, lag degrades the phase margin of a system, forcing either lower gains or low

With mechanical systems, for fast respons-

stability margins (overshoot), or even os-

es, minimize the springiness and lost mo-

cillations (loss of stability).

tion in the system—tight and stiff couplers;

— Donald Labriola P.E., president, QuickSilver Controls,

lower backlash gearing, if needed; shorter,

www.quicksilvercontrols.com


15


START WITH THE LOOP

above the PV. If for some reason the ramp

Here are some techniques I have used in

is faster than the system can physically sup-

the past when a fast temperature ramp fol-

port, the output will be pegged and you are

lowed by minimal overshoot is desired.

out of control. At that point the SP will pull away from the PV. Having an outrun limit

Obviously a good understanding of how PID

means that when you regain control, your

loops work is essential (See www.innovative-

overshoot will be less severe than it would

controls.com/blog/basics-tuning-pid-loops).

have otherwise been, but it’s still better to keep the ramp slow enough to stay in con-

Use a ramping set point with an expo-

trol so that this never happens.

nential decay at the end to knock off the terminal elbow. That was a technique I

If, rather than controlling on the way up,

came across back in 2006 for exactly this

you want to heat up to the target as fast as

problem—a difficult temperature loop that

the system’s capacity will allow, an alter-

needed to ramp up quickly to a target

nate technique is to set up a learning sys-

set point, but not significantly overshoot

tem. This is something I did last year with

it. Ramping the set point at a proper rate

an oven system that had a huge latency; it

keeps the loop under control the whole

would continue heating up very significantly

way up, meaning your output is not

even after we cut the heating output. When

pegged. If it is pegged, the PV will lag, and

it’s time to heat, have your PID loop output

you are out of control, and it will overshoot

track its maximum. Then, when the PV gets

badly. The solutions are to either slow your

within x degrees of the target SP, cut the

ramp rate or add physical heating capac-

output track to zero and release the loop to

ity to achieve the desired rate. But, if you

automatic. You may need to hold the out-

ramp in control at a constant rate until you

put at zero for a few seconds before releas-

reach the target, then stop. The loop will

ing. Here’s the tricky part: Have a timer that

have settled controlling at a steady rise

runs for about 1.5 times as long as it takes

in temperature and will have a small but

that system to get to its maximum initial

avoidable overshoot when you switch to

overshoot. Capture the highest (smooth/fil-

the steady target set point. Instead, slow

tered) PV during that entire duration. When

the ramp at the end to knock the corner

the timer expires, automatically adjust the x

off the ramp-target transition, and you can

offset based on how much the PV overshot

consistently nail the target.

or undershot the set point so it hits it closer the next time. Have clamps on that x offset

SP outrun limits: program your ramping

so, if something odd happens, it will still be

set point to never be more than x degrees

reasonable the next time.


16


The other big technique here is to use

controller tune itself, occasionally adjusting

adaptive gain control. Use one set of tun-

the S curves in the servo controller.

ing parameters during the ramp, and then

— Chris Hardy, systems integration engineer,Cross

switch to a different set for the soak. I find

Integrated Systems Group, www.crossisg.com, CSIA

the above techniques usually eliminate the

(www.controlsys.org) member, Birmingham, Alabama

need for this, but in some systems it can be beneficial.

REMEMBER TO RECORD PAST SETTINGS

Derivative action is only useful when there

While PID loops make life easier by auto-

is a significant time delay from a step

mating process control functions, they also

change in output until the result of that

present challenges in a variety of applica-

change starts to be seen in the PV. Loops

tions to achieve optimal stability and con-

controlling variables such as flow, pressure,

trol. The following method can be applied

level speed, and position—where an output

across the board to improve loop tuning.

change affects the PV everywhere instantly—never need derivative. By contrast,

Before making any changes, be sure to

loops controlling variables such as tempera-

record the current PID settings. It is also a

ture, pH and other chemical concentrations

good idea to have a record of past set-

deal with fluids where the change in output

tings, stable or otherwise. Finally, check for

must be mixed, convected or transported

safety concerns.

from the point where the output affects the fluid to the measurement point. Those loops

The following steps are for a controller set

may benefit from derivative action. How-

to interacting type. Most controllers offer

ever, when manually tuning, I usually avoid

a choice.

using derivative, except as a last resort. 1. a. Turn integral to no integral action. These techniques also are covered in my

b. Turn the derivative time to as small a

loop tuning blog at www.innovativecon-

number as possible. These settings are

trols.com/blog/advanced-pid-loop-tuning-

often called Off.

methods.

2. a. Increase the gain in steps until the loop begins to cycle. This gain will be called

As for motion control, most of my experi-

Kcu.

ence is in process controls. But in my little

b. Record the period of cycling in min-

experience with servo controllers, I’ve

utes. Call this Pn.

always just sent the target position from the

c. Decrease gain to stable levels as soon

PLC to the servo controller and let the servo

as possible.


17


These readings are only estimates.

That usually provides some really good re-

3. Calculate Kc = Kcu/2 for aggressive loop

sults to start with.

tuning. 4. Calculate Kc = Kcu/4 for conservative tuning.

In general, I think full PID controllers are rather rarely used, but they have their place.

5. Ti (integral time in minutes) = 1.2Pn.

Obviously, the more elements you need to

6. Td (derivative time in minutes) = Pn/8.

control, the more difficult it becomes to find

7. Tf (Filter time) = Pn/8.

the optimal solution. — Marcel Voigt, senior solutions engineer,

If the process is not too noisy, it may be as

B&R Industrial Automation, www.br-automation.com

well to turn the filter off. To some degree, filter and derivative just offset each other.

5 TUNING TIPS This is a complex question in two parts—

For especially difficult cases, an experi-

process PID tuning for temperature and

enced expert consultant may be required

motion control PID tuning.

on-site. — Lee Payne, president, Dataforth, www.dataforth.com

The customer doesn’t give specifics about the system or mechanics. Thus, his difficulty

FOCUS ON PI

to be able to tune his system might come

Motion systems usually only use PI control-

from poor mechanics, inappropriate motor-

lers and add filters on top of it to filter out

and-gearbox sizing, the low bandwidth of

machine-specific interferences. If you have

his system, saturated amplifier or a number

a specific frequency, you could use a simple

of other things.

notch filter; for more challenging issues a biquad could get you some really nice results

For motion-control PID tuning, here are

and a better-performing motion system.

some general guidelines. 1. Always perform sizings to take in account

We have a built-in system that measures

the load to motor inertial mismatch, which

the system response and you can apply

is the most common problem and the

filter directly into the resulting bode plot.

source of loop instability. It will be hard to tune if this load inertia is too high.

As for temperature or other control loops,

2. Remove system backlash as much as pos-

we have similar functionality based on our

sible in the driven components. For exam-

mechatronics libraries. We can identify the

ple, use servo gearboxes with 16 arc-min

system the loop needs to control and apply

or less; and use backlash-free couplings,

default settings based on the identification.

low backlash nuts or belt and pulleys.


18


3. Use the step response method (command vs. response) to see how the system is re-

— Warren Osak, founder and CEO, Electromate, www.electromate.com

acting. This is commonly performed using an oscilloscope or is sometimes provided

MOTION PROFILE

with the controller manufacturer’s software.

Even though the control of temperatures

You need to see what you are doing; other-

and servo positioning both use PID, they are

wise, you are just shooting in the dark.

different animals. Both systems have to deal

4. Start tuning with integral gain at zero;

with inertia. In a temperature control sys-

increase proportional gain to get a bit of

tem there is thermal mass (thermal inertia).

overshoot response; and then adjust the

This mass is normally quite high and causes

derivative gain a bit at the same time to

a long lag between an output change and

damp the oscillations. Add integral gain

actually seeing a resultant. Normally this is

at the end to remove the static error.

many minutes. This is the time constant of

Think of it as a pyramid. The base of the

the system. In the case of heating a large

pyramid is KD; the middle of the pyramid

metal object such as an extruder barrel, we

is KP; and the top of the pyramid is KI.

will have a much higher time constant than

The KD (derivative gain) would have the

an air heating system where we are control-

highest value, followed by KP (propor-

ling a gas valve for a furnace. With a servo

tional gain) with a lower value, followed

system, the time constants are typically in

by KI (integral gain) with the lowest

the millisecond range. When we ask for mo-

value. Manual tuning is a trial-and-error

tion, we get a response very quickly.

process. For systems with underdamped conditions, increase KP and decrease KD

Most servo systems these days have the

in tandem. For systems with poor accu-

ability to generate their own gains. This

racy, gradually increase KI. For systems

is internally done by the system making

with high frequency ringing, increase KD.

several velocity changes, and as a result of

5. At all time, make sure the current output

those changes, it calculates the time con-

of the amplifier is not saturated; otherwise,

stant of the system. From that information,

this procedure is invalid, and tuning is im-

it will generate the gains.

possible. Saturated current can mean you are asking too much torque from the motor

In a servo control system, we normally gen-

and amplifier or you are asking for a speed

erate a motion profile for the velocity part

higher than what your system can achieve.

of the control. This can typically be done in

A deeper analysis of the complete system

the motion command and is normally trap-

might still be needed to help diagnose flaws

ezoidal or triangular. When we use a profile,

or weaknesses.

we don’t just command the system to jump


19


immediately to the new position, but to

allow it, depending on the amount of power

move to the destination with a velocity pro-

available and the mass of the system. Using

file. In the case of a trapezoidal profile, we

a profile doesn’t mean the system can’t be

cause the servo to ramp up to a constant

snappy; it just means that we are anticipat-

velocity, remain at that velocity for a pe-

ing the work needed to accelerate the mass

riod and then decelerate to zero. When we

ahead of time, which keeps the positioning

reach zero, we should be at our requested

system from having to make huge correc-

position. A trapezoidal profile accomplishes

tions during the move.

the requested motion. This keeps the servo from seeing a huge position error and thus

An example might be if we wanted to move

causing a large velocity command to the

our car exactly 50 feet ahead and stop. We

servo. This typically results in a quite large

wouldn’t tromp on the gas pedal to get

overshoot and most likely ringing badly

there. We would slightly accelerate, then

around the desired target point depending

hold and then decelerate. It’s a very basic

on how aggressive the gains are.

example, but relevant. — Doug Moldenhauer, senior controls engineer,

When using a profile move internally the

Optimation, www.optimation.us

servo sees a constantly increasing position set point throughout the whole position

LIMITED PID

move until it reaches the target. We can

PID is limited for these problems. On the

think of this as a virtual set point with a pro-

servo side, it is well documented that PID

file. When this is utilized, the servo doesn’t

cannot handle dynamic loads without

see the huge position error but follows the

changing gains. Most servo manufacturers

profile and just having to make minor veloc-

provide S-curve to reduce startup and shut-

ity/position corrections to stay on the pro-

down disturbance, gain adjustment for sys-

file. This allows the system to have higher

tems that have a load buildup or build down

gains for tight position control without

(such as a winder/unwinder), and adaptive

causing the excursions that would normally

controls based on speed or operating vari-

result from those higher gains. This is like

ables. Some use alternate control loop strat-

making thousands of very small moves

egies, such as entering time constants and

continuously until the target is reached.

inertia instead of proportional and integral

The profile’s acceleration and deceleration

values. Or fuzzy logic and neural networks

slopes will be dependent on the mass and

are good options for very dynamic loads.

inertia of the system. Just because it’s a servo doesn’t mean it can snap to a com-

On ovens, temperature gets challenging

manded position, as physics just won’t

if there is a large thermal mass or signifi-


20


cant multi-zone influence. The ways out of

and we have a model of the controller from

this one are using derivative, which I could

the manufacturer’s instructions. Then we

never figure out; using cascade control if

only need a little math to back-calculate

there are other temperature zones; or using

what parameters to use in the controller.

model predictive or neural networks as is done on glass furnaces or high-end building

If the process is self-regulating (like some

HVAC systems.

temperature processes), then lambda tuning means the loop will not oscillate and

The problem is that the question is how to

the temperature will make a first-order ap-

tune PID, and these answers suggest not to

proach to the set point, with a time con-

use PID or to put a layer above it.

stant (lambda) that you choose. This aligns

— Mike Triassi, business development manager,

perfectly with your goal.

Optimation, www.optimation.us

If the process is integrating (like some other

LAMBDA TUNING

temperature processes), then any standard

For the temperature applications, I can

PI or PID controller will give a temperature

answer, having done this in 12 pharmaceu-

overshoot on set-point steps. Lambda tun-

tical or biotech plants. I believe a similar

ing still means the loop will not oscillate,

approach will help with the motion control

and you choose a response time (lambda).

applications. The PID tuning is part of a

But to prevent the overshoot, you need a

specialty that we call “control performance”

little more math to choose an alternate PID

in Emerson. It’s part because you can only

algorithm, a set-point filter or a helpful non-

tune the controller after you make every-

linearity in the process or controller.

thing else right in the loop—the control valve or slave flow loop, the process sen-

You can read my white paper on lambda tun-

sor/transmitter and the controller configu-

ing at www.controldesign.com/lambdatuning.

ration including choice of PID algorithm.

— Mark Coughran, senior process control consultant, Emerson Process Management,

Instead of chasing PID coefficients for days,

www.emersonprocess.com

we use a synthesis method called lambda tuning. Our overall model of the loop has

AGGRESSIVE TUNING

a model of the process and a model of the

Unfortunately, I do not have 3D (or three-

controller, wired as a feedback system.

axis, robotic) servo-motion-control experi-

Synthesis means we know how we want the

ence and cannot provide guidance on that

loop to perform; we can measure how the

application. However, some of the issues

process responds to the controller output;

posed are fairly common among customers.


21


There is no magic bullet for quick response

log the data in a .txt or .csv file with the time,

over a wide operating envelop. End users

SP (set point: the target or goal value of the

have to consider the critical parameters. Is

process), PV (the process variable) and MV

it OK to overshoot a process limit, or does

(the manipulated variable: the control output)

that create too much risk? If overshooting is

listed in columns. This data can also be dis-

OK, then you can use more aggressive tun-

played and graphed using a spreadsheet.

ing; if there is too much safety or cost risk, then the loop should be de-tuned or have

Next, determine if you have a non-integrat-

an over-damped response, characterized

ing (velocity or temperature) system or

as a “conservative” response. If a loop is

an integrating system (position or level).

tuned aggressively, with an under-damped

Some systems have one, two or more poles.

response, then it can easily exhibit the be-

Some of these poles are real, but if there

havior described by the reader’s remark, “if

are two or more there can be complex

dynamic loads are involved, my PID loops

poles that will cause oscillations even when

become unstable and oscillate.” I modi-

driven open-loop (with no feedback). Try to

fied a basic tuning presentation I created

estimate the open-loop parameters by the

with Nathan Lichti of Apache to provide

response to some form of open-loop excita-

simple visual guidance in tuning loops or in

tion. Each different type of open-loop sys-

trial-and-error adjustments once standard

tem has a set of equations that can be used

methods are used for tuning. I believe this

to calculate the closed-loop gains. Acker-

presentation (www.controldesign.com/pid-

mann’s formula is a good way to calculate

tuningbasics) will provide a good guide to

closed-loop gains for motion systems. The

understanding PID tuning basics.

internal model control (IMC) method is

— Gene Chen, DCS/safety systems product manager,

good at calculating gains for temperature

North America Yokogawa of America,

control, if the plant parameters are known.

www.yokogawa.com/us

Ackermann’s formula is basically a pole-

KNOW YOUR SYSTEM

placement algorithm. If all the poles are

You can’t control what you don’t under-

placed on the real axis in the z or s domain,

stand unless one uses a lot of trial and error.

there will be no overshoot or oscillations.

Therefore, the first thing to do is identify

Ackermann’s formula calculates 1 gain for

the system by determining the general sys-

every pole in the open-loop system, plus

tem type and estimating the parameters.

one more if an integrator gain is used. For example, a simple motor-control system

In this exercise, the engineer records how the

has a gain and a time constant. The time

system responds to stimulus. It is helpful to

constant determines the location of the


22


open-loop system’s single pole. However,

In short, know your system’s basic transfer

if the motor is going to be used for posi-

function. Use graphs or trend plots to esti-

tion control, then the system has another

mate the open loop parameters. Use the ap-

pole for integrating the velocity to position.

propriate algorithm for calculating the closed

Finally the integrator in the PID adds an-

loop gains so the closed loop poles are on or

other pole so a simple closed-loop position

close to the real axis, and have realistic ex-

control system has three poles. Therefore,

pectations on how fast the response can be.

three gains (P, I and D gains) are required

— Peter Nachtwey, president, Delta Computer Systems,

to place the three poles in the s plane.

www.deltamotion.com

There are limitations. The controller can

STEADY STATE

only output a maximum of ± 100%. Low-res-

The nature of the control loop must be un-

olution feedback and sample jitter can se-

derstood before tuning. Is it self-regulating or

verely limit the usefulness of the derivative

integrating? In a self-regulating process, the

gain. There are also limitations on power.

process variable will typically reach a steady

There may not be enough power to acceler-

state value for a given controller output, such

ate or decelerate as quickly as desired. This

as flow control. In an integrating process, the

is easy to determine by looking at a trend

rate of change of the process variable will

plot. If the MV saturates during acceleration

typically remain constant for a given control-

or deceleration, the acceleration or decel-

ler output—for example, manipulating an

eration ramps must be made longer. Tuning

inflow or outflow valve to a tank when the

will not help this. In fact while the control

process variable is tank level. The two types

output is saturated (at its maximum value),

of processes have different tuning rules.

the system will behave like an open loop system. As pointed out, using ramps (as op-

The tuning goal must also be clear. Is it to

posed to simple on/off controls) makes tun-

reach set point as quickly as possible or to

ing easier. Motion control systems should

ensure there is no overshoot? Ensure that

always use ramps to keep the control out-

the tuning parameters selected align with

put from saturating. Another limiting factor

the desired outcome. There is also tuning

is deadtime, which is the time between the

software available to assist in identifying

control output changes and when the PV

processes and tuning PID controllers.

starts to respond. It is unrealistic to expect a temperature system to reach an SP within

Whether tuning manually or with software,

the longer of five times the dead time or

the process should be in a steady state pri-

five times the plant time constant without

or to bumping the process. Also, the tuning

oscillating using just a simple PID.

procedure should be performed at or near


23


the expected process operating point. If the

troller is designed to solve a difficult con-

process operates over a wide range and is

trol problem. For instance, the nonlinear

not linear, tuning parameters may need to

MFA controller can control various types

be calculated for other operating ranges

of extremely nonlinear processes in differ-

and the tuning parameters can be sched-

ent industries and applications. Each MFA

uled based on the current operating range.

controller is like a specifically developed

— Paul Wentzell, global process technical consultant,

medicine to cure one specific ailment. For

Rockwell Automation, www.rockwellautomation.com

the user, it is an effective yet easy-to-use controller. Therefore, large deployment

MODEL-FREE ADAPTIVE CONTROL

is more likely. For instance, the Siemens

Since you are providing mission-critical sys-

Apogee building automation system has

tems, I suggest that you solve the PID tun-

embedded MFA controllers to control

ing problems with a systematic approach.

temperature, flow, pressure and humidity,

There are mainly three control methods that

with no controller tuning required. Na-

have achieved commercial success on the

bors Industries use MFA controllers for its

market: PID, model-based control (MBC)

DrillSmart auto-drilling systems.

and model-free adaptive (MFA) control. 1. PID is a “one algorithm fits all” method.

PID is used for a large variety of processes

Inevitably, its capability is limited. In other

where no detailed process info is required

words, PID is more like a general-purpose

(black box). Model-based control is well-

medicine, except there is no way for one

suited for controlling a process where

medicine to effectively cure all illnesses. So,

detailed knowledge is available (white box).

PID tuning difficulties can be fundamental,

MFA is suitable for controlling processes

especially for those loops where PID won’t

with qualitative process knowledge but no

work well, no matter how you tune it.

detailed process models are available (gray

2. Model-based control is more like a “one

box). In addition, the process dynamics can

algorithm fits one system” method. If the

have significant variations. Many industrial

process dynamics do not change fre-

processes are gray boxes that have fre-

quently and the process model can be

quent load, fuel, and dynamic changes.

well-maintained, model-based control can provide excellent performance. However,

For your medical-device and motion-control

since it is so specialized and has a poten-

applications, embedded MFA control soft-

tially high installation and maintenance

ware may be required, depending on your

cost, large deployment is difficult.

control system platform.

3. MFA control takes a “one algorithm solves one problem” approach. Each MFA con-

— Dr. George S. Cheng, CEO, CyboSoft and CyboEnergy, www.cybosoft.com.


24


INERTIA RATIO

changed with the digital control algorithm.

When optimizing PID control loops, or even

I/O processing needs to occur at well-timed

starting the process of creating a mo-

intervals, or else you’ll experience jitter ef-

tion system that requires precise PID loop

fects that end up appearing like noise on

control, the most important starting point is

your I/O. The timing is also important in

to size the application appropriately, aim-

terms of programming difference equa-

ing for a 5:1 inertia ratio. As a result, tuning

tions (filters, PID) whose coefficients can be

time can be drastically reduced, particularly

calculated off-line and applied with predict-

when using a PC-based control system. Ad-

able performance. Reconstruction of sig-

ditionally, choosing a robust drive system

nals sampled on an irregular basis has been

and servo motors goes a long way toward

researched and studied, but best avoided

simplifying the tuning process.

when trying to do simple and more practical applications like what I think you are

Other helpful features to look for in a con-

trying to do.

trol platform, in order to streamline PID tuning, are integrated analytics and moni-

I recently saw a PLC that didn’t bother to

toring tools. In conclusion, users should

try to execute programs or process I/O at

seek out system-integrated tools that pro-

regular time intervals. It just ran programs

vide more features and functionality in one

as fast as it possibly could. Timing changed

place. One must also seriously consider the

depending on paths taken in the program

efficiencies and savings that can be gener-

and also changed as the program grew or

ated from drive configuration and tuning

shrunk. Imagine what the result of integrals

via a central PC-based controller rather

and differentials would look like if your time

than via the individual drives.

delta is constantly changing. I watched a

— Matt Prellwitz, drives technology application special-

colleague maintain the PID parameters as

ist, Beckhoff Automation, www.beckhoff.com

the program evolved. A lot of the “tuning” unfortunately had nothing to do with the

CONTROLLER, PLANT

dynamics of the plant or feedback control-

AND PERFORMANCE

ler; it was just dealing with fundamental

One topic mentioned was performing feed-

processing issues.

back control with a PLC. Be forewarned that there are a number of PLCs out there

I’m not saying all PLCs behave like this.

that have not been designed with real-time

Some do a good job with real-time pro-

control/processing in mind. Some thought

cessing. I only bring this up because this

needs to be applied to how inputs and

alone could be a big contributor to some

outputs are sampled and released and ex-

of your struggles. Read up on these topics


25


and arm yourself with tough questions for

order (power applied to a heating element

your PLC supplier.

causes thermal energy to increase at some rate) and an electric servo is a good ex-

There were some examples provided for

ample of second order (current, or torque

different types of systems to which control-

input to the motor accelerates the axis

lers can be applied, which in control theory

position). This is good to know because

is commonly referred to as a “plant.” A

it can be mathematically shown that PID

plant is a generic term for a dynamic sys-

rarely makes sense for a first order system

tem whose states (or process variables) you

(PI is much more applicable; leave the D

want to control. It has causal relationships

set to zero). In the second order case, PID

between the inputs you drive and its resul-

is essential for stability purposes.

tant states that can be directly or indirectly measured and hopefully controlled. It can

The next property is linearity. It’s not

be a heating or cooling element applied to

always the case that 10% control input re-

air. It could be an electric servo motor driv-

sults in 10% rate of change of plant output

ing a robot or gantry axis. It could be an hy-

and that 90% input equates to exactly 90%

draulic valve that’s driving position, speed

output rate of change. If this isn’t the case,

or force output of an hydraulic cylinder. It’s

it’s sometimes useful to understand this

my opinion that not enough time and at-

and compensate your PID with gain sched-

tention is spent understanding a plant. Too

ules, or just scale the output of the PID

often, I’ve seen a PID controller arbitrarily

with lookup tables, so your PID output has

applied to a plant, followed by lengthy

as much of a linear relationship with plant

trial-and-error tuning sessions. A little bit of

output as possible. This will make your

attention to the plant model can make this

controller respond much more consistently

process simpler and less time-consuming.

with respect to different inputs.

I’ll go through a few of the more important properties I think someone should under-

Another property is dynamic response. If

stand about a plant.

you apply 10% control input, and it takes a few seconds for the plant to start to change

First property is order. For a first order

its outputs, then you are dealing with a

system, the control input influences the

plant that has low open-loop bandwidth

first derivative, or rate of change or the

with no potential for fast (but still stable)

plant output. In a second order system,

closed-loop response. A good rule of thumb

the control input influences the second

is a plant needs to respond four to five

derivative of the plant output. A tempera-

times faster than the desired response of

ture controller is a good example of first

the closed-loop system. If the plant can’t


26


meet these criteria, then you will have a lot

For stability, this needs to be proven by

of trouble achieving your control goals.

thorough testing. Step response testing is a very common method for testing and is no

The last pointer I have on this is paying

doubt useful. I like testing with dynamic in-

attention to units. If you can scale control

puts. Drive your PID input with a sine wave

inputs so they are using the same units as

and vary the frequency once. If you see the

the plant outputs, then you’ll find PID tuning

output moving at a much larger amplitude

to be fairly consistent from one application

than the input, you’ve found a resonance

to another. Let’s say the process variable is

and potential area of instability. Another

in x units. If I scale the control input to be

thing to watch for is when the output is

in units of x units/second, then I know right

moving at full amplitude of the input, but is

away that a Kp of 2*PI radians (1Hz) will get

lagging by a half wavelength or more; then

me very close to a 1-second response.

your controller tuning lacks margin and could potentially go unstable.

There was mention of tracking performance, stability and robustness to changing loads.

In terms of robustness to part variation or

These are all important properties of a good

load changes, this again can only be proven

controller and very much in line with differ-

through testing. Pick extreme operating

ent measures we use to specify and validate

points to test your controller. If the control-

controllers. I’ll mention right away that trying

ler is too sluggish at one operating point

to score high marks on all of these topics is

and marginally stable at the other extreme,

not easy to do with just a PID controller.

this is a clear indicator that you will need more than a PID to control the system to

In terms of tracking, I’d suggest reading

desired specifications.

a little bit about feed-forward control. If you have some a priori knowledge of how

One last comment on PID coefficients: They

to drive control inputs to achieve desired

work together to define the poles of your

outputs, put that knowledge in your control

system defined by your closed-loop transfer

algorithm and let the PID do the rest of the

function. The location of these poles tells a

control for you. If you know x amount of

lot about how responsive, stable or unstable

current applied to a heater will eventually

a system can behave. If you tune a Kp that

get you to a steady state fluid temperature,

gets you close to the responsiveness you

then just add that current to the output of

need, but then start tuning a Ki to improve

the PID. The PID has less work to do and

steady state error and then find the system

can now focus on compensating for distur-

starts to resonate a little bit, it might be

bance inputs or load changes.

worth your while to increase Kp rather than


27


back off on Ki. When you change one coef-

That being said, what can we do when an

ficient, it’s likely you will need to scale the

auto-tune feature is not good enough or not

others, as well.

available?

— Jason Kraft, engineering specialist, controls, Eaton, www.eaton.com

Once the auto-tune feature is complete, methodically write down the values of the

DEDICATED TO CONTROL

PID and feed-forward parameters, plus any

First, if the controller has an auto-configure

auto-filtering parameters/values established

and/or -tune feature, by all means use it. To-

by the auto-tuner.

day’s tuning technology is greatly enhanced over just a few years ago and the auto-tune

From this point it’s important to remember

feature can automatically adapt to, say, a

what these specific parameters do.

given motor-drive mechanism, without a decrease in performance in many applications;

Proportional (P) gain is the amount of con-

and, in other applications, it can get you to

trol variable (CV) response action propor-

a working baseline much more quickly than

tionally presented against the error signal

starting from scratch. There are many differ-

determined by the difference of the mea-

ent versions of PID control and PID topolo-

sured process variable (PV) and the com-

gies found in temperature controllers that

mand/set point (SP). For unity gain, the PV

are not normally the same as used for mo-

range is set directly proportional to the CV

tion control. For the purposes of this answer,

range (Figure 6).

motion control examples are utilized. Integral (I) gain is the amount of control It has been my experience that control

variable (CV) response action presented

loops needing fast dynamic response, such

against the accumulated error over time

as motion control, require their own dedi-

(error/ _time); thus presenting a propor-

cated controller, whether a PLC is utilized

tional CV output signal as a function of its

or not; and, even with this, there are times

gain setting depending on the amount of

that signal/feedback latency can have sig-

error and length of time the error is pres-

nificant detrimental effects, depending on

ent. Integral gain presents phase lag into

the components selected and/or how they

the system, which is important to remember

were chosen to work together. Additionally

when instability is an issue.

if you can only view the outside loop (position-loop) response, you are basically in

Derivative (D) gain is the amount of control

the dark as to what is happening within the

variable (CV) response action presented

internal control loops (current and velocity).

against the rate of change of the error


28


PROCESS VARIABLE (PV) RESPONSE WITH DIFFERENT PROPORTIONAL GAINS

Underdamped Critically damped

Overdamped

Step Command

TIME

HOW MUCH DAMPING? Figure 6: Proportional (P) gain is the amount of control variable (CV) response action proportionally presented against the error signal determined by the difference of the measured process variable (PV) and the command/set point (SP). (Source: Kollmorgen)

( _error/ _time); thus presenting a pro-

amplifier or summing circuit/algorithm, and

portional CV output signal as a function of

goes directly into the pre-amp stage driving

its gain setting depending on how fast the

the power devices, presenting a phase lead

error is changing.

into the system. The feed forward signal presents power to the motor to counter the

Feed forward gain is a non-error-based sig-

damping effect of the acceleration of mass

nal that jumps ahead with a predefined sig-

and thus provides a pre-determined phase

nal, based on a measured disturbance and/

lead control response.

or command change. When utilized with a closed-loop system, the signal typically jumps over several hardware/algorithm control blocks, such as PID blocks, filters,

Signal filtering, whether utilized in the forward control path or feedback signal, is generally used to smooth out the over-


29


all system response by reducing electrical

If your auto-tuner has established filter

feedback noise, audible noise, high-frequen-

settings within the control loops, let them

cy noise and system resonances/harmonics.

be; establishing filter types and frequencies by manual examination is beyond the

Even with a good understanding of how

scope of the writ; and generally a good

these control blocks work, for any spe-

auto-tuner will be able to determine the

cific controller it can become daunting to

needed filter settings.

explain what adjustment needs to be made for a specific topology’s desired response,

If slight methodic gain tweaking does not

as compared to some measured step re-

get you within acceptable parameters,

sponse, due to the different interactions

one way to proceed is to basically start

and interdependencies of the responding

from scratch except for the auto-tuner

PID algorithms with a fixed or varying load.

filter settings; let them be, at least for the

P, I and D algorithms can be designed in

first attempts.

series, in parallel or in some combination of series and parallel, with each control-de-

A fresh start: For servo-motor systems we

sign technique presenting a different style

often talk in terms of three different control

CV response against a fixed or varying

loops: I-loop (current loop), vel-loop (veloc-

load, disturbance or command. Your tuning

ity loop) and position loop.

method can also vary as a function of the specifications of the process/work being

The I-loop is the innermost loop and fastest

accomplished, all presenting multiple ways

of the three. The I-loop is active when the

and priorities to optimally tune a servo

controller is in a current/torque mode, ve-

controlled load.

locity mode or position mode. The current gain setting is normally pre-calculated from

With the basic definitions in mind with

such parameters as motor inductance and

your specific process, it may be reason-

resistance. It will likely also have integrators

able to tweak some of your gains up and

to help to compensate for PWM dead time

down slightly to get a feel for how the

among other things. In most cases you will

system response changes. If applicable, it

not need to adjust these settings, and, if one

is best to examine the vel-loop step input

does, it typically should be done in conjunc-

response first and separate, from the posi-

tion with the manufacturer’s post applica-

tion loop, if there is a position loop. Me-

tions department / instructions. For exam-

thodically write down the values, record

ple, when a servo-motor controller’s I-loop

what happens and accordingly make slight

is set too high, it will often display itself with

changes in the gain settings.

a load noise coming from the motor that a


30


change in vel-loop gain cannot reconcile;

tional gain until you have approximately 10-

and this instability may only manifest itself

15% (no more than 15%) with an undershoot

at specific currents and/or speeds. For this

of approximately 3-5% (no more than 5%).

type issue, the I-loop gain setting can typically be reduced 10-15% without affecting

The step response may identify oscillations,

the system performance.

resonance and/or harmonics that will need filtering or source identification to achieve

The vel-loop is the second fastest of the

desired response goal. This is beyond the

three and for many the most troubling to

scope of this brief write-up.

compensate or fine-tune. Even if the system is going to be run in position-loop mode, the

Repeatedly provide a velocity step input

vel-loop needs to be properly compensated

command to determine the velocity (CV)

first for the system to act at optimum levels.

response, and increase the vel-loop’s integral gain until any steady-state error has

The vel-loop is active when the controller is

been reduced to zero.

in a velocity mode and position mode. The Integral function presents phase lag to In order to compensate/tune the vel-loop,

your system, which increases risk of insta-

provide a step input to determine its step

bility; you do not want any more vel-loop

response; then from the CV velocity re-

integral gain than it takes to reduce the

sponse, adjust and fine tune the vel-loop’s

steady-state error within acceptable levels.

proportional, integral and derivative gains. Too much velocity overshoot and audible

When the position-loop is to be closed,

noise—objectionable oscillations creating

many engineers prefer to zero or minimize

humming, buzzing—are signs that a gain

vel-loop integral gain and allow the position-

limit has been reached; back it off slightly.

loop integral gain to dominate, creating a stiffer system. My recommendation is to find

With the controller in its velocity mode, set

the preferred setting for the vel-loop integral

all vel-loop gains—proportional, integral and

gain, even if the controller is to be used in

derivative—to zero. Utilize filters as set by

position mode, for possible reference.

the auto-tuner; if there is no auto-tuner set filters to zero.

Repeatedly provide a velocity step input command to determine the velocity (CV)

Repeatedly provide a velocity step input

response, and increase the vel-loop’s de-

command to determine the velocity (CV)

rivative gain until the desired high speed PV

response, and increase the vel-loop’s propor-

response is achieved.


31


If the response looks good, do not add in any derivative gain; if the response appears to be

Make step command

not fast enough, add as little derivative gain as possible to achieve your fast-response goal.

Though velocity feed forward is not a function of the closed-loop system, it is based

Does the motion oscillate or make noise?

NO

Turn up Kd

YES Turn down Kd by 2/3

on the measured amplitude of change (disturbance and/or command) to present

Make step command

a pre-defined (open-loop-type) response, similar to a derivative function; thus if your system has velocity feed forward capability, it may be important to consider its gain setting as a function of the load type. Even

Is the overshoot more than half of your overshoot spec?

NO Turn up Kp

YES Make step command

if only for experimentation, it may be desirable to reduce your velocity feed forward gain to possibly one-third or less of its perceived ideal gain setting—direct drive, fixed load—when there is compliance and/

Is the overshoot more than your spec?

NO Turn up Ki

YES Set the Integral Limits

or backlash within the system. Remember that a positive phase shift is presented by

Done

the velocity feed forward gain; typically you don’t want to add any more positive feed forward than it takes to offset phase lag from the integrator, and filters if required, over the speed range of the axis.

TUNING METHOD Figure 7: Kd = Derivative Gain; Kp = Proportional Gain, Ki = Integral Gain. (Source: Kollmorgen)

It is most desirable to have your feed for-

gain are changed/updated, the proportional

ward parameter and derivative gain set

and integral gains need to be retuned for

before tuning proportional and integral

their optimum performance (Figure 7).

gains based on a step response. However, unless the user has significant experience

When using this tuning method, be sure

with a particular controller and subject PV

that the command output is not clipping

load, it is unlikely the values will be set close

the step command. If the command output

enough on the first try. When either the

does clip the step command, you have a

feed forward parameter and/or derivative

nonlinear system. If the system is nonlinear,


32


the generalizations made on this page may

VALIDATION

not apply. If you are determined to tune

Tuning a PID control can be quite challeng-

despite the nonlinearities, make sure that

ing, especially when you take into account

there is a repeatable way to generate the

load changes and nonlinearities of your

nonlinearities, as well as the ability to try

system. Basically, the optimal tuning of

many different scenarios.

a PID control requires not only a deeper knowledge of the system in question, but

The position-loop when utilized is the slowest

also a more in-depth knowledge of existent

of the three. The position-loop is only active

techniques for PID tuning. However, there

when the controller is in its position Mode.

are some heuristics that you can use to bet-

The position-loop’s capability is a function of

ter define PID tuning.

the vel-loop compensation. A bad vel-loop = a non-optimized position-loop.

Know your system: The first thing you have to do before controlling a system is know

In order to tune the position-loop, present

how it should behave. This can start by veri-

repeating positon commands under a defined

fying the existent literature that can provide

move and adjust for position-loop propor-

you with mathematical models of your sys-

tional gain for the desired response—quick re-

tem. This process can be very time-consum-

sponse with some overshoot before settling,

ing, but it will give you the insight of differ-

no-overshoot (overdamped), minimum set-

ent nonlinearities that could influence the

tling time—based on the axis’ criteria/specifi-

response, especially when trying to achieve

cations. If the axis’ criteria demands minimal

optimal control. You don’t need to model

position error (PE) while holding position or

every single detail. For control process, we

during a specific motion profile segment, one

are really interested around the frequency

may wish to try introducing integral gain to

that could invert the feedback loop signal

the position-loop. This will often mean the re-

(also known as phase margin crossover fre-

moval or significant reduction of the vel-loop

quency), and there is where you really have

integral gain. Position-loop derivative gain is

to be accurate. So, simple approximations

not typically utilized.

for first-order model with delay could be enough to model your system. Sometimes,

After tuning, if your PE looks like noise, you

your model is a series of rules or an input-

know you have a good compensation for

output mapping that was obtained empiri-

most applications; but this is not always

cally, but you know how it behaves.

possible for many reasons. — Hurley Gill, senior systems and applications engineer, Kollmorgen, www.kollmorgen.com

Validate the model of your system: After you have an understanding of how your


33

Control Design - How to Tune Loops

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