P - I and I - P Controllers In A Closed Loop For DC Motor Drives

F. I. Ahmed A. M. El-Tobshy Professor of Power Electronics

Faculty of Engineering, and Vice-president of Cairo University, Cairo, EGYPT

Professor of Power Electronics, Faculty of Engineering, Cairo University

Cairo, EGYPT

A. A. Mahfouz Assistant Professor of Power Eiectronics

Faculty of Engineering Cairo University Cairo, EGYPT

Fax: +202-5723486, Phone: +202-5613 156 E-mail: elkousy @ Cairo. eun.eg

Abstract-The traditional Proportional-Integral ( P - I ) controller, which has been widely used for the speed control of dc motor drives, has been compared with the relatively new Integral-Proportional ( I - P ) controller which first discussed in the year of 1978. This paper presents some improvements in this important field of industries. Theoretical studies for ( P - I ) and ( I - P ) controllers in the S-domain are presented, and the transfer functions for both are derived. Simulation results due to step response in S-domain and Z-domain are presented for both controllers. Experimental studies are discussed in detail. The performance of the two controllers due to step input reference and their behavior to sudden change in reference speed and sudden change in load are discussed. The simulation and the experimental results indicate the superiority of ( I - P ) controller over ( P - I ) controller.

I. INTRODUCTION

A variety of engineering applications, such as: material conveyors, paper mills, transportation systems etc., require very accurate speed tracking, fast response and high precision. For many years, dc motor drives have been widely used in such applications, and in spite of the fact that ac motors are rugged, cheaper and lighter, dc motor controlled by a thyristor converter is still a very popular choice in particular applications. In spite of the fuzzy logic is getting emphasis in process control applications [ 11, [2], the conventional controllers [3] - [5] are an option in applications where low cost is the primary concern. The proportional-integra1 ( P - I ) is one of the conventional controllers and it has been widely used for the speed control of dc motor drives. The major features of the ( P - I) controller are its ability to maintain a zero steady-state error to a step change in reference and its simple and straight- forward microprocessor implementation. On the other hand ( P - I ) controller has some disadvantuges: the undesirable speed overshoot, the sluggish response due to sudden change in load torque and the sensitivity to controller gains K, and K,.

M. M. S . Ibrahim Ph.D. Candidate of Power Electronics

Faculty of Engineering Cairo University Cairo, EGYPT

Fax: +202-3608453, Phone: +202-3483986

0-7803-3823-5/97/$10.000 1997 IEEE 61 3

Takahashi, Harashima and Kondo [6] suggested a new method of control called integral-proportional ( I - P ) as a trial to solve the main problems of ( P - I ) controllers. This paper discusses the two controllers theoretically and experimentally as applied in speed control of dc motor of 0.5 kW, and it finds some improvements in this field. Experimental work has been carried out to verify the theoretical results.

11. MATHEMATICAL MODELS

The ( P - I ) controller has a proportional as well as an integral term in the forward path, the block diagram with a ( P - I ) controller for a dc motor drive is shown in Fig. 1. The integral controller has the property of making the steady-state error zero for a step change, although a ( P - I ) controller makes the steady-state error zero, it may take a considerable amount of time to accomplish this. Fig. 2 shows ( I - P ) controller along with a dc motor drive, where the proportional term is moved to the feedback path and it acts like a feedback compensation. The analysis in S- domain is discussed in this section to study the transient and the steady-state behavior for both controllers.

+

Fig. I . Block diagram with P - 1 controller

PCC-Nagaoka '97

Fig. 2. Block diagram with I - P controller

A. P - I Controller

The closed loop transfer function between the output C(S) and the input R(S) is given in (1).

Where Ki and K, are the integral and the proportinnal gains of ( P - I ) or ( I - P ) controller, T, is the mechanical time constant of motor, and K, is the motor gain constant.

The transfer function between the output C(S) and the load torque disturbance TL(S) is given in (2).

From (1) and (3), (P - I ) and ( I - P ) controllers have the same characteristic equations, and it can be seen that the zerb introduced by the (P - I ) controller is absent in the case of the ( I - P ) controller. Therefore the overshoot in the speed, for a step change in the input reference R (S), is expected to be smaller for the ( I - P ) control. Equations (2) and (4) are exactly the same, therefore, the response to a load disturbance is expected to be very similar for both ( P - I ) and ( I - P ) controllers.

111. SIMULATION RESULTS

Simulation studies are made due to step input reference in the S-domain and Z-domain. Appendix I shows the parameters of the motor used for the simulation studies. Fig. 3 shows ( P - I ) and ( I - P ) controllers due to step input reference at 5 < 1 : the overshoot for ( P - I ) controller is equal to 34.8%, while for ( I - P ) controller is 27.2%. The settling time for ( P - I ) is 0.375 s, while for ( I - P) is 0.455 s. It is clear that ( I - P ) has longer delay time. Table I summerizes the results for the two controllers in digital

A+ P - I I

0 0.5 1 1.5 2 Time(s)

B. I - P Controller Fig. 3. P - I and I - P controllers step response

( < I , K p = 1.5, KI = 30.

The closed loop transfer function between the output C (S) and the input R (S) is given in (3).

The transfer function between the output C(S) and the torque disturbance T L (S) is given in (4).

TABLE I

DIFFERENT GAIN FACTORS PERCENTAGE OVERSHOOT AND SETTLING TIME USING

Gain % Overshoot Settling time (s) Ks Kn P - I I - P P - I I - P

1 2.36 20.45 4.55 0.36 0.5 0.5 3 3.4 0 0.36 0.6 1 0.3 3.5 0 0 0.18 1.07 5 3 40.3 26.3 0.13 0.13

1.5 3 48 5.77 0.25 0.25 K,a 2.04 0 0 0.035 0.03

, ..... .. ......... ............... .......................................................................................................................... ............................. .. ....

'K, = 0.714 for ( P - I ) and 2.5 for ( I - P ), these are optimal values, which depend on the closed loop transfer functions [8].

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1V. EXPERIMENTAL WORK

A. System Description

For the experimental work a closed-loop system is built which consists of : 0.5 kW dc motor-generator separately excited, the parameters of the motor are in AppendixI, tacho-generator 0.06 Vlrlmin as a feedback voltage, a powerful data acquisition instrument 12 bit resolution, and a personal computer AT 80286. A fully-controlled thyristors bridge is also built where the firing angle is controlled using Relative Firing Angle Method, with this method the firing angle is controlled by lenghtening or shortening the interval between two successive thyristors triggerings [7]. Fig. 4 shows the schematic diagram of experimental set up.

B. Program and Flowchart

The main program is written in C language and is linked with the assembly program which controls the firing angle a . The program can be described using the following steps:

1. P - I or I - P controller is selected using a menu, then the coefficients K, and Ki are entered via the keyboard.

2. The program starts to read using the analog to digital card, the reference and the error values.

3. Depending on the controller type, the output voltage from controller is calculated.

4. Cos c1 is calculated using an interpolating, polynomial, and from the look-up table the angle c1 is known and using a programmable peripheral interface, the assembly program reads the value.

start J

Firing angle (a) = 52 O

Average armature voltage = 60 V

1 1. Choose controller type. 2. Select K, and K,. +

I . Using A B , read the error and the reference values.

and the integral part of the controllers,.

and the average current using motor

2. Calculate the output speed in volts,

3 . Calculate the instantaneous

equations. % t 1. Calculate the controllers

2. Using curve fitting, get cos a and from look-up table find a in degree.

3 . Using the assembly program read the new value of a.

I

outputs.

v Save the current screen to a data file.

Fig. 5. Main flowchart

Fig. 5 shows the main flowchart of the program.

Limitation of current using dc motor equations

1 ontroller Program elative Firing Scheme

AD-ADDA- 12 \ Card.

12-Bit D/A and using “C”- Language using Assembly AID Language

angle t Tachometer

feedback voltage

Fig. 4. Schematic diagram of experimental set up.

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C. Experimental Results

83I

Theoretical studies as a primarily step are made to choose the suitable coefficients K, and K, [8]. The sampling rate T affects the time response because it depends upon the execution time of program and the speed of computer used. Using the same conditions for both controllers: e.g. , gain coefficients, reference voltage and required output speed, the performance of both controllers are studied. Fig. 6 and Fig. 7 show the speed time response for ( P - I ) and ( I - P ) controllers due to step response, Fig. 8 and Fig. 9 show the instantaneous current time response of both controllers ( P - I) and (I - P). Table I1 summerizes the differences between the two controllers at required speed equal 600.79 dmin, where (I - P ) controller has smaller overshoot and a very fast response and thus the starting current is limited. The performance of sudden change in reference speed and sudden change in load are tested experimentally for both controllers. Fig. 10 and Fig. 11 show the instantaneous current time response due to sudden change in reference speed, ( P - I ) controller has a fast response and a large overshoot in current occurs. Fig. 12 and Fig. 13 show the speed response due to sudden change in load, for ( P - I ) controller, the time to reach the steady state condition is 8.9 s and the settling time T, is 7.4 s [9], while for ( I - P ) controller the time to reach the steady-state condition is 5.36 s and the settling time T, is 4.63 s.

I

TABLE I1 COMPARISON BETWEEN P - I AND 1 - P CONTROLLERS DUE

TO STEP RESPONSE

Performance characteristics P - I I - P Starting current at rated voltage 13OV 1.2 A 0.8 A Steady-state speed 488.33 r/inin 558.33 r/min Percent maximum overshoot 34. I 3 21.79 Settling time 1 1.23 s 0.729 s

....... ... . . . . ................................................................................... ... , , ....... ..................... ......... , , , , , , , , , , .., , ........... ...........,.

3

Fig. 7. I - P Speed response K, = 3 , K, = 5

Y 5 0.4

0.2

Time ( S )

Fig. 8. P - I Instanteneous current response. K,= 3 , K, = 5

Time (S)

Fig. 6 P - I Speed response. K,= 3 , K , = 5

Time (St

Fig. 9. I - P Instanteneous current response K, = 3 , K, = 5

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Fig. 10. P - I Instanteneous current response due to sudden change in reference speed.

K, = 3 , K, = 1.5

1.8 T

1.6 1.4

- 1 0.8

6 0.6

3 1.2

E

Time (S)

Fig. 1 1. I - P Instanteneous current response due to sudden change in reference speed.

K, = 3 , Ki = 1.5

Fig. 13. I - P Speed response due to sudden change in load

Kp = 3.5 , K, = 0.3

V. CONCLUSIONS

The project is intended to demonstrate ,the successful application of ( I - P ) controller to a phase-controlled converter dc separately excited motor-generator system. ( I - P ) controller's performance was compared with that of conventional ( P - I ) system. ( I - P ) controllers show some important advantages: the overshoot in speed is limited, thus the starting current overshoot is reduced. Also, using the suitable coefficient gains, ( I - P ) controllers offer a good load recovery characteristics. Analysis in S-domain and Z- domain shows the advantages of ( I - P ) controller. Thus ( I - P ) can be implemented using analog components. Analog ciruits are still required where: the low cost is required, the experience for high technology is not necessary, or where the replacement for modern control is difficult. Moreover, the simulation and experimental studies clearly indicate the superior performance of ( I - P ) controller, becauseit is inherently adaptive in nature. From the above derivation ( I - P ) controllers can replace ( P - I ) for the speed control of dc motor drives.

VI. FUTURE RECOMMENDATIONS

0 g $ : g w g p The wide advances of computers and software languages will make the controllers' algorithm much easier to implement, the sampling timt: and the execution time can be reduced. Using ( I - P ) controller as a current feedback loop may give good controlling results. The experimental set up can be used to test the ( I - P ) self-tuning adaptive controller and the ( I - P ) adaptive variable gain controller. Also ( I - P ) impulse response can be tested experimentally. To prove the simplicity of ( I - P ) controller, a comparatively study is already started between ( I - P ) and fuzzy controller.

N O 0 0 m a Q q E L 8 m - - N N % G a - - - "

"e 6)

Fig. 12. P - I Speed response due to sudden change in load.

K, = 3.5 , K, = 0.3

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VII. ACKNOWLEDGMENT [2] N. Manaresi, R. Rovatti, E. Franchi, R. Guerrieri, and G. Baccarani, "Automatic synthesis of analog fuzzy controllers: a hardware and software approach," IEEE Truns. Industrial Electrorzics. vol. IE-43, no. I , February 1996, pp. 217-225.

The authors wish to express their gratitude to the staff of Power Electronics Laboratory, Faculty of Engineering, [31 R. Moffat, Paresh C. Sen, R. Younker, and Mohamed M. Bayoumi, Cairo University, Egypt, for their encouragement and "Digital phase-locked loop for induction motor speed control,"

IEEE Trans. Industry Applicutions. vol. IA- 15, no. 2, MarcMApril 1979, pp. 176-182. assistance in the laboratory work.

Motor's Parameters

VIII. APPENDIX I [4] KiyosHi OHishi, Masato Nakao, Kouhei Ohnishi, and Kunio

Miyachi, "Microprocessor-controlled dc motor for load-insensitive position servo system," IEEE Truns. Industrial Electronics, vol. IE- 34, no. I , February 1987, pp. 44-49

[5] M. OKyay Kaynak, Fumio Harashima and Seiji Kondo, The motor used in this experiment is dc separately "Microprocessor controlled position servo system with a sliding

excited, rating 0.5 kW at rated voltage 220 V, Bnd the motor's parameters are as follows:

mode," in Proceedings of the 1982 Microelectronics in Power Electronics und Electric Drives Conference, ETZ, Darmstadt, West Germany, pp. 273-279.

Armature resistance = 7.72 R [6] 0. Kaynak. A. D. Abbaszadeh and S. Nazlibilek,"Digital speed Armature inductance = 0.16273 H control system with integral-proportional control," IFAC Conrrol in

Power Electronics and Elecrrical Drives, Lausanne, Switzerland, 1983, pp. 501-506. Back e.m.f constant = 1.25 Vlradls

Mechanical inertia = 0.0236 Kg ' mz Friction coefficient = 0.003 N ' m/rad/s [7] Guy Olivier, Victor R. Stefanovic, and Georges-Emile April, Rated armature current = 2.7 A "Microprocessor controller for thyristor converter with an improved

power factor, '' IEEE Trans. Industrial Electronics und Con fro1 Instrurnentution, vol IECI-28, no. 3, August 1981, pp. 188.194. Speed = 1500dmin

IX. REFERENCES [8] Fang L. Luo and Roland J. Hill, "Fast response and optimum

regulation in digitally controlled thyristor converters," IEEE Truns Indusrrv Applicafions, vol. IA-22, no. 1, January/ February 1986, . . .

pp. 10-17. [ l ] Gilbert0 C. D. Sousa, and Birnal K. Bose, "A fuzzy set theory based

control of a phase-controlled converter dc machine drive," IEEE Truns. Industrj Applicafions, vol. U-30, no. 1 , January/February 1994, pp. 34-43.

[9] Benjamin C. Kuo, Aurornutic Control Systenzs, New Delhi: Prentice- Hall, 1983, p. 327.

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