By D.K. Jana, AM(PS),BkTPP AM(PS),BkTPP,, WBPDCL WBPDCL
P I D CONTROLLERS CONTROLLER S
In Power Plants, Plants, process process variables variables like pressure, pressure, temperature temperature,, flow, flow, level and chemical analysis are required to follow some desired value. It would be possible to control the process more efficiently by use of some form of automatic control. Proportion Proportional al (P), Proportional plus integral (PI) and Proportional plus integral plus derivative (PID) Controllers are used used to generat generatee a correct correction ion signal signal to the final contro controll elements elements (Control (Control valve) valve) to eliminates the error (error error (error actual value ! set value). " controller controller is called direct acting if its output increases when its measurement measurement rises and the controller is called reverse acting, if its output decreases when its measurement rises. #here are several basis of modes of control $% (&) (&) Prop Propor orti tion onal al con contr trol ol'' () () Inte Integr gral al cont contro rol' l' () () Deri Deriva vati tive ve cont contro rol' l' (*) Propor Proportio tional nal plus plus integr integral al contro control' l' (+) Propor Proportio tional nal plus plus deriva derivativ tivee contro control' l' () Propor Proportio tional nal plus plus integ integral ral plus plus deriva derivativ tivee control control'' -arious combination of this basic mode may be employed to suit the plant characteristics. Proportional control : #he proportional proportional control is directly related to the error or deviations signal. Proportional controller continuously ad.ust the manipulated variable so that the input to the process is appro/imately in balance with the processed demand . #he equation describes the operation of the proportional controller is 0 &44 m 1 p2 3b / 2 3 b P5 where m the output signal of the controller' 1 p proportional sensitivity or gain of the the controller' controller' &446P5' 2 the deviation from set point or, error' b controller output with 7ero error' P5 proportional band
#he proportional controller responds only to the present . It cannot consider the history of the error or the possible future consequences of an error trend, it simply the responds the present value of the error . It responds to all errors in the same manner in proportionate to them. 8hen a small error results in a large responds, the gain (1p) is set to be large or the proportional band is set to be narrow . Inversely, when it takes a large error to cause a small responds the controller is set to have a small gain (1p) or a wide proportional band . If the deviation is increasing rapidly the controller will apply correction rapidly . If the load changes or coming disturbances, the measured value will deviate from desired value and the controller output varies proportionately in an attempt to correct for this deviation . If the deviation is within the range, the controller will assume a position or equilibrium and the measured variable
again be under control but a different value . #he amount of controlled measured value deviates from the desired value is the 9:;; <2#=, and its depends on the amount of load change . Pneumatic proportional controller is designed by the flapper % no77le and proportional bellow arrangement. #o correct the 9:;; <2#= the relative positions of the desired value and proportional band must be altered. "dvantage $ Can give steady control' Disadvantage $ (a) 9:;; <2#= presents' (b) #oo narrow a proportional band can cause of hunting' >sed where load changes are small and 9:;; <2#= can be tolerated'
Integral control : #his mode is called 9?2<2#= mode of control because after a load change it returns the control variable to set point and eliminates the 9:;; <2#= which the plain proportional controller would leave. #he mathematical e/pression of this integral control is t m &6#i ∫ 2 dt 3 b 0 4
where #i the integral time setting of the controller which is called 9?2<2# #I@2=. #he integral mode has been introduced in order to eliminate the 9:;; <2#= which plain proportional control can not be removed . #he reason proportional control must result in an 9:;; <2#= is because it disregards the past history of error . #he integral control, on the other hand continuously looks at the total past history of the error by continuously integrating the area under the error curve and eliminate the 9:;;<2#= by forcing the addition or removal of mass or energy which should have been added or removed in the past.
: 2liminate the=:;; <2#=' "dvantage Disadvantage : #his control action is slow speed with response of the load change' Derivative Control : #he derivative action the controller is not influenced by the desired value but changes in accordance with direction with rate of change of deviation . If the change in the variable is a certain step movement, the controller will changes with ramp by an amount proportional the rate of change of deviation until stop the rate of change of deviation . #he derivative mode anticipates its future state and acts on that prediction. 8hereas the proportional mode considered the present state of the process error and the integral mode looks at its past history. #he equation of controller output in derivative mode (rate) is m #d (d2 6 dt )3b where #d derivative time d2 6 dt rate of error change in percent per second or minute' b controller output with no error change'
8hen the error changing rapidly the controller can anticipate what action is needed for more correction. #his corrective action based on the rate of change of error . In the starting portion of the curve, the error is changing and the derivative action signal is transmitted to the valve . #he unit of the derivative setting is the derivative time (#d) .
In the middle portion of the curve where the error is constant the derivative contribution to the output signal to the valve is also 7ero . :n the right of the curve the error is still positive, the derivative action is already negative as it is anticipating the future occurrence where the loop might overshoot in the negative direction and is correcting for that . "dvantage : Can anticipate what the control condition is going to do' Disadvantage : Aong recovery time slow to respond to rapid changes'
Proportional plus Integral : #he combination of proportional action and integral action is called PI Controller . #he mathematical e/pression for PI controller is m 1p B23&6#i ∫ 2 dt 3 b where m Controller output 1p Proportional gain 2 2rror signal #i Integral time setting of the controller b Controller output with 7ero error
In PI controller the error signal generated from disturbance has two terms, a straight proportional signal and a signal which is a scaled time integral .
PD controller : #he combination of proportional plus derivative control is called PD controller' #he equation of for a PD controller can be written as m 1p B 23# d d26dt) 3 b'
"dvantage $
change progresses at a constant rate the deviation action remains constant' #he graph showing in fig%'& G '' t
#he output of the PID Controller is m 1 p B23&6#i ∫ 2 dt 3 #d(d26dt)3 b 4
where #d derivative time constant' d26dt rate of change of error or deviation' "dvantage $
sed in the process industry to control slow variables' Electro Pneumatic (I/P Converter : "n 2lectro Pneumatic converter converting the electrical signal to pneumatic signal by flapper no77le device or force balance device. #his mechanical movement is normally achieved by 2lectro magnetic mechanism and ensures the pneumatic signal pressure 4' to &'4 1g6cmH . #he supply air pressure for this device is &'+ 1g6cmH and the current applied to the coil is * to 4m" resulting the pneumatic output pressure is 4' to &'4 1g6cmH via restriction and flapper no77le arrangement . #he permanent magnet and the amount of current applied to the coil controls the gape between no77le and flapper resulting the pneumatic output pressure increases or decreases between 4' to &'4 1g6cmH .
&'+ kg6cm
Ainear part &'4 Pressure kg6cm 4'+
4 4
&4
4
4
*4
+4
Dist' between flapper G no77le Control of outlet pressure is achieved by variation of pressure in the control volume' #he steady state position of the pistons is such that both v6v s are closed, thus minimising the air consumption' Increasing the control volume pressure causes the pistons to move downwards, opening the inlet v6v '
point at a frequency of &4h7' #he magnitude of this oscillation is too small to affect v6v actuators' #he pressure signal produced is compared with the demand current signal to produce an error signal' #he width of the pulse sent to the reede/ is proportional to this error signal' If the outlet pressure falls or the signal current rises then the length of the pulse increases causing the pressure in the control volume to rise and vise versa'' If the outlet pr' falls or the signal current rises then the length of the pulse sent to the reede/ increases causing the average pressure in the control volume to rise' #his causes air to be supplied to the load to increase the o6l pressure' "s the outlet pr' rises the width of the reede/ pulse decreases until the state of balance is achieved' Conversely if the o6l pr' rises or the signal current falls the width of the pulse sent to the reede/ is decreased allow the control volume pr' to fall and open the relief v6v' "s the o6l pr' falls the reede/ pulse width is gradually increased until the state of balance is achieved' 8hen the signal current falls or is reduced below about m" the reede/ is unable to open and the pr' falls to a low value due to the bleed, thus ensuring fail safe operation' In normal operation the reede/ v6 can be heard to click at a constant rate of &47' #he diagram shown in fig% '*'
Positioner : #he positioner is a high gain proportional controller G the primary function of a positioner is to ensure that the control valve plug position is always directly proportional to the controller output pressure 4' to &'4kg6cm, regardless of gland fiction, actuator hysteresis, off balance of forces on the valve plug etc' . #he controller output signal does not directly actuate the valves stem but is fed to a bellows or diaphragm unit, which is connected to the flapper% no77le or spool valve system . "ssume that the system is in equilibrium and then the controller output increases slightly. #he flapper is moved towards the no77le and the variable output pressure begins to increase . #his output pressure continues to increase until the valves spindle moves, mechanical feed back (cam arrangement) then restores the equilibrium . #hus the force applied to move the valves spindle is sufficient to overcome the effect of all forces .
PNE!"#TIC #CT!#TOR: "n actuator is that portion of a valve that responds to the applied signal and causes the motion resulting in modification of fluid flow' #hus an actuator is any device that causes the valve stem to move' It may be a manually positioned device, such as a hand wheel or lever' #he manual actuator may be open%closed, or it may be manually positioned at any positioned between fully open and fully closed' :ther actuators are operated by compressed air, hydraulics, and electrically' Pneumatic actuators to an air signal moving the valve trim into a corresponding throttling position' Diaphragm6spring type and Piston type actuators are used for moving the valve to any position from fully open to fully close or fully close to fully open' In a spring and diaphragm actuator, variable air pressure is applied to a fle/ible diaphragm to oppose a spring' #he combination of diaphragm and spring forces acts to balance the fluid forces on the valve' In a piston actuator, a combination of fi/ed and variable of air pressure is applied to a piston in a cylinder to balance the fluid forces on the valve'
assists valve closure' 2/cluding of springs, there two variations of piston actuators0 cushion loaded and double acting' In the cushion loaded type, a fi/ed air pressure, known as cushion air pressure, is opposed by a variable air pressure and is used to balance the fluid forces on the valve' It is necessary to have a single acting positioner to move the valve' In the double acting type, two opposing variable pressures are used to balance the fluid forces on the valve by using the positioner' #his positioner has two variable air pressure outputs, one connected above the piston and the other below' In rotary type double acting piston actuator operate at higher air pressures and can provide higher torques, suitable for large ball or butterfly valves' In connection with the performance of these actuators, an analysis is presented of the various forces positioning the plug, including diaphragm, spring and dynamic forces generated by the forces fluid' "n understanding of the interrelationships among these forces will allow the reader to properly si7e these actuators and make the correct spring selection' 5oth the spring and diaphragm and the piston type actuator produce linear motion to move the valve'
"ir pr' "ir pr' "ir pr' "ir pr'
Constan "ir pr'
"ir pr'
Pr' balance diaphragm actuator
Double acting Piston actuator
Diaphragm actuator
way output%&
vairable air
way output%
;orce side%&
;orce side %
2/haust out%&
@ain air supply in
2/haust out%
Positioner with spool ;ig%'
spool
Power supply G control electronics
4* ! 4 m"
Control signal
Comparators G Ao ic
Pr' feedback signal
?eede/ driver ckt' Pulse width modulated signal
I6l ?eede/
4' mm restriction
Control pressure
"ir supply
2/haust
P?' <2J<:?
PJ2>@"#IC ?2A"K
2A2C#?: % PJ2>@"#IC C:J-2?#2? ;ig ! '*
"ir pressure outlet
Proportional 5and $ #he proportional is e/pressed as a percent of span, but it may also be e/pressed as controller gain in other' Proportional band and controller gain are related inversely by the equation, &44L LP'5' ain
&44L
-6Posn'
+4L
4L 4
<'P +4 Jarrow P'5' &44L P'5'
Controlled variable &44
If the proportional band is reduced to 7ero, the result would be 9:J%:;;= control'
Control variable
#ime
Controller output PGI D P
#ime Proportional plus Integral and Derivative
$ig%&.'
#otal PGI correction
2rror (2)
Correction(m)
Derivative contribution Integral correction
"
5
C 2rror(2)
:
2 #d
; time PID control $ig% &.&
Proportional "ction $ Curve :5CD , Integral "ction $ Curve : to ' Derivative "ction $ Curve "52;D'
Proportional correction
D
;eedback control (CLOSE LOOP $ " control algorithm looks at the desired value, the actual value and possible outside disturbances effecting the plant and on the basis of these observations ad.usts the plant actuators to bring the process variable to the desired value' #he control algorithm has to cope with two circumstances' #he desired value may be changed continuously or the process variable itself may be affected by disturbances' In many analog system, a variable such as temp', press', level, flow is required to be kept automatically at some preset value' It works well as a regulator to maintain a desired operating pt' by compensating for various disturbances'
;eed forward (:pen loop) control $ ;eed forward control is another basic technique used to compensate for uncontrolled disturbances entering the system' In this system, the control action is based on the state of a disturbances input without reference to the actual system condition' ;eed forward control is much faster correction than feedback control, and in the ideal case, compensation is applied in such a manner that the effect of disturbances is never seen in the process output'