An Adaptive, Robust control of DC motor Using Fuzzy ... - IEEE Xplore

2012 IEEE International Conference on Power Electronics, Drives and Energy Systems December16-19, 2012, Bengaluru, India

An Adaptive, Robust control of DC motor Using Fuzzy-PID controller Rishabh Abhinav

Satya Sheel, Senior Member, IEEE

Electrical & Electronics Engineering Department Galgotias College of Engineering & Technology Greater Noida, India e-mail: [email protected]

Vice-President, Academic-Affairs University of Petroleum and Energy Studies Dehradun, India e-mail: [email protected]

Abstract— DC motor is the most common choice if the wide range of adjustable speed drive operation is desired. In many studies, the DC motor controllers have been implemented without considering the final control element (FCE), leading to a non-realistic performance. In this paper, the authors have suggested a new approach to obtain the adaptive and robust control of DC motor. Buck converter, driven by high frequency PWM signals obtained from PID controller has been chosen as FCE in this study. ZieglerNichols method is applied to the combined system of dc motor and buck converter, to get the initial settings of PID controller. Using fuzzy logic, these settings are online updated corresponding to the changes that may occur during system operating conditions. Also, this approach has a robust performance against disturbance/parameter variations. The buck converter has been simulated using sim-power system library of MATLAB. Comparative results have been shown for PID controller and adaptive fuzzy-PID controller for both tracking and regulatory type of control problems to obtain excellent performance with no steady state error.

converter is obtained by considering a small linear region near its operating point. A practical model of buck converter is implemented using Sim-Power library of MATLAB. The dynamics of speed sensor is also considered for more realistic performance. ZieglerNichols tuning method is applied to get the initial settings of PID controller. Then fuzzy logic is used to update these controller settings on-line, corresponding to the changes that may occur in the system operating conditions. Both tracking control and regulatory control problems have been considered for simulation purpose. This configuration of controller has also been observed for robust performance against parameter variations and uncertainties. The simulation work has been carried out in MATLAB/SIMULINK. The overall concept of the control scheme can be explained in the block diagram shown in Fig. 1.

Keywords— DC motor, buck converter, adaptive, PID, fuzzyPID

I. INTRODUCTION DC motors are controllable over a wide range with stable and linear characteristics. Therefore, they are the most common choice in the industries for both constant speed and constant load operations [1, 2]. Separately excited DC motors are most suited for tracking control problems [3]. In [4, 5], authors have suggested various control strategies for dc motor using PID and fuzzy-PID controllers. In [6], fuzzy-PID control techniques have been discussed in detail with examples. In [7], various techniques for self-tuning PID controllers have been discussed. In [8], authors have suggested optimal and robust control of dc motor under parameter variations. In this study, the inaccuracies noted in earlier studies have been considered and an adaptive, robust Fuzzy-PID controller has been developed. A separately excited DC motor, driven by buck converter has been considered for the study. The dc motor model is developed using the dynamic equations and the speed to voltage transfer function is obtained. The transfer function of the buck

978-1-4673-4508-8/12/$31.00 ©2012 IEEE

Figure 1

Block diagram of proposed Fuzzy-PID controlled, buck converter driven DC motor

The paper is organized as follows: Second section outlines the design of buck-converter being used as the final control element for the chosen dc motor. In section III the dc motor transfer function model and PID gain settings are obtained using Z-N method. Section IV presents the design of fuzzy logic based PID controller for the overall dc motor drive. The simulation results are presented in section V and conclusions are brought out in section VI.

II.

BUCK CONVERTER DESIGN

A buck converter is a dc-dc step down converter. It consists of dc input voltage source Vd, controlled switch S, diode D, filter inductor L, filter capacitor C, and load resistance R. The circuit diagram of a buck converter is shown in the Fig. 2.

The speed of motor can be expressed as a function of input voltage and load torque as follows [11]: ߱௠ ሺ‫ݏ‬ሻ ൌ ܸሺ‫ݏ‬ሻ

Where, IJୟ ൌ

Figure 2

Circuit diagram for Buck converter

The design of buck converter is based on the output voltage (V), maximum allowed ripple in the output voltage (ᇞVc) and maximum allowed ripple in the output current (ᇞIL) [9]. The buck converter parameters i.e. inductance and capacitance can be derived as: ൌ

ୢ ሺͳ െ ሻ ୢ ሺͳ െ ሻ  ൌ ˆο ୐ ͺˆ ଶ οେ

Based on the specifications to be met, following values have been taken: Vd = 480V

D= 0.5

f = 10 KHz

ο ୐ ൌ ͲǤͲͷ’

οେ ൌ ͲǤͷ ‘Ž–•

The values of inductor and capacitor are calculated as: L = 240 mH C = 1.25 μF Using small signal model of the converter [10], the control transfer function can be obtained as: ˜ොሺ•ሻ ൌ †෠ሺ•ሻ

III.

ୢ  • ͳ •ଶ ൅ ൅  

DC MOTOR TRANSFER FUNCTION

A separately excited DC motor has been considered with the assumptions as field is maintained constant and the effect of armature reaction is neglected.

Figure 3

Separately Excited DC motor

୐౗ ୖ౗

ሺ‫ ܭ‬Τܴ௔ ሻ ߬ ͳ ቃ ‫ ܬ‬ቂ‫ ݏ‬ଶ ߬௔ ൅ ‫ ݏ‬ቀͳ ൅  ௔ ቁ ൅ ߬௠ଶ ߬௠ଵ ͳ ൅ ‫߬ݏ‬௔ െ ܶ௅ ሺ‫ݏ‬ሻ ߬ ͳ ‫ ܬ‬ቂ‫ ݏ‬ଶ ߬௔ ൅ ‫ ݏ‬ቀͳ ൅  ௔ ቁ ൅ ቃ ߬௠ଶ ߬௠௟ ୎

୎ୖ౗

୆

మ ౗ ା୏ ሻ

ǢIJ୫ଵ ൌ ǢIJ୫ଶ ൌ ሺ୆ୖ

For the conduct of a case study of the performance of the proposed fuzzy-PID approach, a separately excited dc motor with following ratings and specifications has been used in simulation. TABLE I. DC motor Ratings and Specifications

Rated Power Rated Voltage Rated Speed Rated Torque, TL Moment of Inertia, J Coefficient of Viscous Friction, B Armature Resistance, Ra Armature Induction, La Torque Constant, K

5 HP (3.73 KW) 240 V 1750 rpm (183.26 rad/s) 20.345 N-m 0.2215 Kg/m2 0.002953 N-m-sec 0.2592 ȍ 0.028 Henry 0.002953 V/rad/sec

The transfer function of speed sensor has been considered as: ͳ ሺ•ሻ ൌ ͳ ൅ •ɒ where, IJ = Sensor time constant = 0.05 sec The overall transfer function of the system has been obtained by combining the transfer functions of dc motor, buck converter and speed sensor. Ziegler-Nichols tuning method has been applied to the combined transfer function to get the initial settings of the PID controller. The three parameters KP, KI and KD are obtained using the PID tuning software developed by Sheel and Gupta [12]. IV.

DESIGN OF FUZZY-PID CONTROLLER

The fuzzy logic is used to update these settings online, corresponding to the changes that may occur in the system operating conditions. This configuration of controller has also been observed to have robust performance against parameter variations and uncertainties. The philosophy of generating rules for fuzzy-PID can be different according to the requirement. Here these rules have been created by considering the concept given by Kha and Ahn [13], in which the rule surfaces are given for PID tuning. Using these rules, the fuzzy rule tables have

been developed. The inputs of the fuzzy logic are the speed error (E) and derivative of error (ED). Using these inputs and after applying the fuzzy rules, it provides the outputs οKP, οKI and οKD, which are used to update the PID controller gains online. A total of 49 rules have been used in this study. Each rule uses an If – Then logic of the following form: If E is PM (positive medium) and ED is PL (positive large) then οKP is PS (positive small), οKI is NM (negative medium) and οKD is ZE (zero).

Figure 4

Membership function for E and ED

Table II-IV show the fuzzy rules for οKP, οKI and οKD. TABLE II. Rules for incremental change in KP

E/ED

NL

NM

NS

ZE

PS

PM

PL

NL

PL

PL

PL

PL

PL

PL

PL

NM

PS

PM

PM

PM

PM

PM

PS

NS

ZE

ZE

PS

PS

PS

ZE

ZE

ZE

NL

NS

ZE

ZE

ZE

NS

NL

PS

ZE

ZE

PS

PS

PS

ZE

ZE

PM

PS

PM

PM

PM

PM

PM

PS

PL

PL

PL

PL

PL

PL

PL

PL

TABLE III Rules for incremental change in KI

E/ED

NL

NM

NS

ZE

PS

PM

PL

NL

NL

NL

NL

NL

NL

NL

NL

NM

NL

NL

NL

NL

NL

NM

PM

ZE

NM

NL

NM

ZE

PM

PL

PM

PS

NL

PS

PM

PL

PM

ZE

NM

NL

NM

ZE

PM

NM

NL

NL

NL

NL

NL

NM

NL

NL

NL

NL

NL

NL

NL

NM NS ZE PS PM PL

TABLE IV Rules for incremental change in KD

E/ED NL NM NS ZE PS PM PL

Figure 5

Membership function for οKP,

Fig. 4 and 5 show the triangular membership functions assigned to input and output variables. The output variables οKP, οKI and οKD are de-normalized to fit in the desired range of control action. The final control action is achieved by the following equations: KP1 = KP + οKP KI1 = KI + οKI KD1 = KD + οKD where, KP, KI, KD are the initial values of gain parameters obtained from Z-N method, οKP, οKI, οKD are fuzzy outputs; and KP1, KI1, KD1 are the settings of the PID controller being updated online corresponding to the changes that occur during the system operation. The output of the PID controller is given by: —ሺ–ሻ ൌ  ୔ଵ Ǥ ‡ ൅  ୍ଵ න ‡†– ൅  ୈଵ Ǥ ‡ሶ ൅ —ሺͲሻ where, u(0) = initial controller output when system was under steady state. The output of the controller is

saturated in the range of 0 to 1 which corresponds to the duty ratio of the buck converter. V.

NL

NM

NS

ZE

PS

PM

PL

NL

NL

NL

NL

NL

NL

NL

ZE

NS

NM

NM

NM

NS

ZE

PS

ZE

ZE

ZE

ZE

ZE

PS

PL

PL

PM

PS

PM

PL

PL

PS

ZE

ZE

ZE

ZE

ZE

PS

ZE

NS

NM

NS

NM

NS

ZE

NL

NL

NL

NL

NL

NL

NL

οKI and οKD

SIMULATION RESULTS

The motor considered in section III has been simulated in MATLAB/SIMULINK for tracking control as well as regulatory control. Motor is started normally under full load, by using the starter to keep the starting current within limits of safety and when motor achieves steady state; the controller is switched-in. Simulation results have been obtained for േͷΨ and േͳͲΨ step change in reference speed in case of tracking control and േͷΨ and േͳͲΨ in load torque in case of regulatory control. Results have also been obtained for േʹΨ variation in motor parameters such as armature resistance and armature inductance.

2000

2500

1950

Fuzzy-PID

Fuzzy -PID PID

1900

M o to r S p e e d (r p m )

M o to r S pe e d (r p m )

2250

PID

1850 1800

2000

1750 1700

1750

1650

1500

1

Figure 6

1.05

1.1

1.15

1.2 1.25 Time (sec)

1.3

1.35

1.4

1.45

1.5

1600

1.1

1.15

1.2 1.25 Time (sec)

1.3

1.35

1.4

1.45

1.5

2000

1900

Fuzzy-PID PID

1900 S p e e d (r p m )

M otor S p e ed (r pm )

PID Fuzzy-PID

1800

1800

1700

1700

1600

1

Figure 7

1.05

1.1

1.15

1.2 1.25 Time (sec)

1.3

1.35

1.4

1.45

1600

1.5

Motor speed for -5% change in reference speed

1

1.05

1.1

1.15

1.2 1.25 Time (sec)

1.3

1.35

1.4

1.45

1.5

Figure 11 Motor speed for -10% change in load torque

2500

1800

Fuzzy-PID

M o to r S p e e d (r p m )

2250

Fuzzy-PID

1780 M o to r S p e ed (rp m )

PID

1760

2000

1740

1750

1,500

1.05

Figure 10 Motor speed for +10% change in load torque

2000

1500

1

Motor speed for +5% change in reference speed

1720

1

1.05

1.1

1.15

1.2 1.25 Time (sec)

1.3

1.35

1.4

1700

1.45

Figure 8. Motor speed for +10% change in reference speed

1

1.05

1.1

1.15

1.2 1.25 1.3 1.35 1.4 1.45 Time (sec) Figure 12. Motor speed with +2% variation in armature resistance and inductance

1800

2000 1900

M o to r S p e e d (r p m )

M o to r S p e e d (r p m )

Fuzzy-PID

1780

Fuzzy-PID PID

1800

1760

1700 1600

1740

1500

1720

1400 1300 1 Figure 9

1.05

1.1

1.15

1.2 1.25 1.3 1.35 1.4 1.45 Time (sec) Motor speed for -10% change in reference speed

1.5

1700

1

1.05

1.1

1.15

1.2 1.25 Time (sec)

1.3

1.35

1.4

1.45

1.5

Figure 13. Motor speed with -2% variation in armature resistance and inductance

Tables V and VI show the comparative analysis of time domain performance of both PID and fuzzy-PID controller TABLE V. Comparison of results for PID and Fuzzy-PID controller for Tracking Control Change in Reference Speed PID Percentage Fuzzyovershoot PID PID Rise time Fuzzy PID PID 2% Settling Fuzzytime PID

+5%

-5%

+10%

-10%

4.08

2.7

10.2

4.21

3.29

2.2

6.83

3.14

0.0426s

0.0513s

0.0384

0.0584s

0.0315s

0.0493s

0.0295s

0.0487s

0.0612s

0.0235s

0.0834s

0.0738s

0.0492s

0.0156s

0.0824s

0.0463s

TABLE VI. Comparison of results for PID and Fuzzy-PID controller for Regulatory Control

Change in Load Torque Percentage overshoot Load disturbance Rejection time

VI

+5%

-5%

+10%

-10%

PID

0.77

0.92

1.08

1.17

FuzzyPID

0.6

0.72

0.54

0.88

PID

0.041s

0.048s

0.055s

0.052s

FuzzyPID

0.032s

0.035s

0.045s

0.048s

CONCLUSION

Table V and figures 6-9, and Table VI and figures 10-13 show the comparative results for PID and fuzzy-PID controllers, both considered for tracking and regulatory control problems respectively. The performance of fuzzyPID controller is observed to be better than the conventional PID controller as the proposed controller results in smaller overshoot in the system and the response also settles faster. In tracking control problems, zero steady state error is achieved with the proposed fuzzy- approach. In regulatory type of control problem also, the overshoot is minimum. The fuzzy-PID controller is also observed to be more robust, against parameter variations as it does not allow the system to deviate from its reference value. In this case, the overshoot is less than 1% of the steady-state value. With the number of studies conducted for different conditions for both types of control problems, with control hardware implemented at component level simulation, it is concluded that, the proposed fuzzy-PID controller efficiently controls the buck-converter driven dc motor. Due to its adaptive nature, it improves the closed loop performance of the dc- drive considered with robustness also achieved.

REFERENCES [1] Thadiappan K and Bellamkonda R, “A fast-response DC motor speed control system”, IEEE Transactions on Industry Applications, vol. IA-10, no. 5, September/October 1974, pp. 843-851. [2] Sheel S, Chandkishore R. and Gupta O., “Speed control of DC drive using MRAC technique”, International Conference on Mechanical and Electrical Technology, 10-12 September, 2010, Singapore, pp. 135-139. [3] Weerasooriya S and Sharkawi M.A., “Development and implementation of self-tuning controller for DC motor”, IEEE Transactions on Energy Conversion, vol.5, no.1, March 1990, pp. 122128. [4] Mountain Jeffrey R., “Fuzzy logic motor speed control with realtime interface using an 8-bit embedded processor”, 42nd South Eastern Symposium on System Theory, March 7-9, 2010, Tyler, Texas, USA, pp. 307-312. [5] Muruganandam M. and Madheswaran M, “Modeling and simulation of modified fuzzy logic controller for various types of DC motor drives”, International Conference on Control, Automation, Communication and Energy Conservation -2009, 4th-6th June 2009, Perundurai, Tamilnadu, pp. 1-6. [6] Mann G K I, Hu B G, and Gosine R G, “Two-level tuning of fuzzy PID controllers”, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, vol. 31, no. 2, April 2001, pp. 263269. [7] Kumar V and Mittal A. P., “Parallel fuzzy P + fuzzy I + fuzzy D controller: Design and performance evaluation”, International Journal of Automation and Computing, vol.7, no. 4, November 2010, pp. 463-471. [8] Lee C. K. & W. H. Pang, “Adaptive control to parameter variations in a DC motor control system using fuzzy rules”, Intelligent Systems Engineering', 5-9 September 1994, Conference Publication No. 395, IEE, pp. 247-254. [9] Rashid M H, “Power Electronics Circuits, Devices and Applications”, Third Edition, Prentice Hall, 2003, pp. 186-190. [10] A. Simon, O. Alejandro, Power-Switching Converters, Chapter-6, continuous-time modeling of switching converters, Third Edition, CRC Press, 2010. [11] Dubey G. K., “Fundamentals of Electrical Drives”, Second Edition, Narosa Publishing House, (2001), pp. 75-76. [12] Sheel S and Gupta S, “Advanced techniques of PID controller tuning–development of a toolbox”, First International conference on Control, Instrumentation and Mechatronics CIM ‘07 at Persada Johor, Malaysia. [13] Kha N. B. and Ahn K. K, “Position control of Shape Memory Alloy actuators by using self tuning Fuzzy PID controller”, First IEEE Conference on Industrial Electronics and Applications, 2006, Singapore, pp. 1-5.