DESIGN AND IMPLEMENTATION OF A PID CONTROLLER ANALOG FOR UNIVERSAL MOTOR Jhon Alexander Acevedo Diaz, Freddy Muñoz Enrique Barragan. Students from IX Semester University of Cundinamarca Faculty of Electronic Engineering
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Abstract: In this paper a PID controller for a universal motor, place to see how this type of controllers, the simplest being can reach control system optimally, based on the parameters as designer wants obtained, this in order to make the end of the course a comparison of these drivers with respect to a fuzzy control. I. INTRODUCTION Regarding the issue is control, the controller easier to design and implement control is ON / OFF, however this type of control is not to adequate for most systems, that is why most often spoken of PID controllers because they are simple, practical and very effective. One advantage of the control is that there is great variety of techniques to carry out the design mimes, in this case we speak of the PID as very simple to design drivers, however there are other control techniques such as be compensating, adaptive control networks Neural, fuzzy control and combinations them, although often with just enough Simple PID, but you cannot always fix everything a controller of this type II. APPROACH For this laboratory has been defined that conduct a PID controller for a universal motor, this engine will have to work connected directly to the network power, i.e. it will work in the AC mode. The overall
system diagram is what is It aims to reach is as follows
Figure 1: general block diagram of the system III. PRACTICE DEVELOPMENT To begin the design of the controller, which first must be obtained is the function of transfer system, however for this we that identify the linearity of the system, i.e. there to determine what part or part until the system is linear and based on this work the system within this range, this is done because as know, a PID controller only works for linear systems. To carry out the test and can determine the reaction curve of the plant is taken into Consider the following block diagram.
Figure 4 is a functional block diagram of the loop plant closed.
Figure 2: Block diagram of the open loop system. For a better understanding of what to do for obtaining said parameters in Figure 3 the functional diagram of the system is presented in loop opened.
Figure 3: Functional Block Diagram loop system opened The figure above is the plant in open loop and this is the representation of the plant itself when the characteristic curves of the same are made. To complete the closed loop only needs the adder between the measurement provided by the sensor and the point reference and control system "PID" which receives as input the sum between the reference point and sensor signal, and transmits a signal as such for control plant. Note in Figure 4 the functional block diagram of the closed-loop plant
A. System Linearity The first thing to look at is the linearity of Mr. and whether the entire system (Figure 3) to determine if the system is linear or range of linearity, has entered an input voltage actuator gradually to observe the voltage and output data obtained are presented in Then in the following table Vin PWM 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4
Vout F/V 0.58 1.9 3.1 3.8 4.3 4.6 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.8
Table 1 Relationship between input voltage output voltage Vs for determine the range of linearity of the system Based on the above table was obtained as follows graphic:
3.2 7600 3.4 7600 3.6 7600 3.8 7600 4 7900 Table 2:Relationship between input voltage output Vs RPMs for determining the rotational speed versus voltage Based on the above table was obtained as follows graphic Figure 5: Relationship Vs input voltage to output voltage determine the range of linearity of the system As could see both Figure 5 and Table 1, the system is linear over a very small range so which means that you can only work with a step of 1.2V to 2.2V, however this did you can have a good analysis. Also another important parameter to determining engine speed is relative of entered voltage because what matters to a user is controlling a particular speed engine, which is why we also made a relationship between input voltage and RPMs that delivers the engine, the results can be seen below in Table2. Vin PWM 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0
RPM 980 3000 5000 6300 7100 7600 7600 7600 7600 7600
Figure 6 Relationship between input voltage output Vs RPM determining the rotational speed versus voltage
As seen in the previous figure also the voltage / RPM regarding the small range of linearity of the system because the engine is not largely linear, therefore there is nothing to do because the nature of the plant is that so much work is required just that little range B. Transfer function of the system Once determined the range of work is continued obtaining a transfer function System as PID controller cannot performed
if not have this function, i.e. the function transfer of the plant is the parameter most important in this type of controllers. For this function must be obtained curve reaction of the plant in the same way that determine the linearity of the system, except that you must performing an instantaneous voltage change, in other words must generate a unit step voltage at the input of the actuator. Once this is done, is obtained the curve shown in Figure 7. For the transfer function by reaction curve, the first thing you have to is whether the system is first or second order. At first glance (Figure 7) the system seems to first order, however, may be a system second-order damped. To determine the order of the system is used the Van Der Grinten method which is based on find a constant "a" and compare. To this has filtered signal and adjusted the curve to the point. Reference 0-0, on this basis is obtained as shown in Figure 8
Figure 8: Van Der Grinten method applied to the curve Motor reaction The method used to determine the function of transfer takes into account the following criteria
Where
Taken into account the above equations and Figure 8 is determined as follows.
Figure 7: curve reaction to a unit step (1.2VA 2.2v)
Kp=3.839
(5)
a*Kp=0.933
(6)
Figure 9: Comparison Real Vs curve transfer function mathematically found second order.
With the result obtained mathematically a very good result compared to the curve actual reaction (see Figure 9), however looking for something a little more precise, which is why it has "Tuned" the transfer function to be very similar to the real, accordingly function transfer that will work is shown in equation (17), the graphic shown in Figure :
Figure 10: Comparison Real Vs curve transfer function second order found for practice
C. Transfer function of the system To start with the design of the PID controller, first you have to observe and analyze is the behavior of the closed-loop system so know the system and define the design parameters to proceed to the implementation of control. In the Figure 11, one can observe the behavior of system
closed loop to a unit step in This case arises that a time stabilization (Te) of 0.224 seconds, envelope peak(Sp) of 0% and steady-state error (Ess) of 20%
controller that has yielded an Sp 0% a Te of 0.164 seconds and Ess 0% that was what I was looking for, plus the output the controller has an amplitude less than 5V and that you are using a micro-controller for actuator (PWM synchronized with the network). According to that in Figures 12 and 13 shown described
Figure 11: Behavior of the closed-loop system to a unit step input.
D. Design Criteria According to the above the following defined design criteria: Te = approximately equal (the system reacts fast) Sp = 0% (this criterion is to be maintained) Ess = 0% (this is the most important and the system Driverless closed loop has an error of 21%)
Figure 12: System with PID controller tuned according design parameters
As you can see the closed-loop system has good results, however the only downside is the steady-state error, which is why all that you want to change in the design parameters is this. E. Design of PID controller Once done all the above can be further Controller design, for ease of obtain the parameters of the PID was used PID Windup tool and through a small tuning a
Figure 13 Output of the PID controller tuned Below in Figure 14 is shown one comparison of the system with and without driver
Figure 1: System response with and without the controller Tuned PID
Driver settings are: P = 1.7 I = 1.7 / 0.32 = 5.31 D = 1.7 * 0.005 = 0.0085 Thus concludes the controller design, the next step is the implementation and realization of the test.
Given the equation of a PID controller
The transfer function is organized so that these values correspond to equation (22).
F. Implementation of PID controller For the implementation of the controller is used circuit shown below:
Thus it must be to determine P, I and D The following equations are used.
Figure 15 Electrical circuit implementing the PID controller
However, the transfer function is negative therefore necessary to place an inverter circuit departure. Thus the resistance values and capacitances for the values of P, I and D
Transfer function of the circuit given by:
for
according controller design that are given above by: R1= 664.9 KΩ; R2= 532Ω; C1= 9.4UF; C2= 4.7uF G. Analysis of the results Once the closed loop with the controller was performed the same test at the beginning of the document is mean observed system behavior before a unit step, then shown the result obtained
Elements have a margin of error and in a system like this, a slight variation of these elements may represent a significant change respect to the output to be obtained. Also worth to carry out tests disturbances, this time is applied a power to the motor rotor thus obtained the following result.
Figure 17 Output voltages applied to a disturbance in the motor rotor
Figure 16 output voltage with respect to a unit step applied at the input.
As can be seen in the figure above the result is not exactly as expected since it has an envelope peak that had not been contemplated of approximately 30% and has a longer stabilization 0.5 seconds, however was achieved reduce the steady-state error to 0% which is the most important thing in this type of system, the output voltage follow the reference or desired value. Faults that may be obtained at the values used for capacitors, resistors and operational amplifier because as you know these
Applying this perturbation was quite large As can be seen, the system is returned to stabilize while when applied the step, you can also see about having a peak almost equal to that of Figure 16, can therefore say that the system reacts in a way appropriate to a disturbance. Thus development ends and although the practice is not in practice was able to obtain the desired results the simulation, the controller obtained is acceptable. IV. CONCLUSIONS The design of PID controllers is a task relatively simple but it can get to be tedious, mostly when tuning the controller to function as desired, without But it is more
complicated to carry design reality and that often does not get the intended results with the simulation as was in this case because it inconveniences occur in practice as it is the noise generates the motor, the tolerance of the elements, eddy current, working range of elements, among other factors, therefore it should be very careful when implementing to achieve as much as possible to minimize these factors unwanted Bibliography [1] Richard C. Dorf, Robert H. Bishop, Systems Modern Control, tenth edition, Pearson, 2005. [2] Virginia Mazzone, PID controllers, Control Auto 1, Automation and Control National University of Quilmes, March 2002 available on the website:http://www.eng.newcastle.edu.au/jh b519/teaching/ca ut1 / Notes / PID.pdf [3] Ing. Améstegui Mauricio Moreno, University Mayor De San Andres La Paz Bolivia, notes PID control, pdf file, available on the website internet:http://jvr33.free.fr/pdf_laser/03_ele ctronique/Control % 20Pid.pdf
