Trajectory Control of DC Shunt motor by NARMA Level-2 Neuro Controller Sudarshan K. Valluru, MadhusudanSingh Department of Electrical Engineering Delhi Technological University Delhi-110042, India E-mail:
[email protected],
[email protected]
Abstract— This paper proposes an intelligent speed controller to the trajectory control of shunt-connected DC motor based on Nonlinear Autoregressive Moving Average Level-2(NARMA L-2) technique. By adjusting the weights of a neural network with respect to variation between the actual speed and command speed the armature rotor speed is tracked. Based on the dynamic mathematical model of motor, PID and NARMA L-2 controller responses are analyzed. The speed response of motor is observed by giving reference inputs as speed and load torque in terms of step variation. By comparing the motor response of conventional PID and NARMA L-2 neuro controller, it was observed that NARMA L-2 neuro controller exhibits better performance in terms of settling time, peak over shoot, steady state error. Keywords—Nonlinear dynamical system; System identification; DC shunt motor system; PID controller; NARMA L-2 controller.
I.
INTRODUCTION
The DC shunt motor has been widely used in many industrial applications, where it is necessary for continuous speed variation of rotating system in order to perform certain functions. Many typical examples are found in electric vehicles, robotic manipulators, rolling, milling, cutting and threading of steel mills due to precise, and continuous control characteristics[1]. A DC Motor in which the field circuit is connected in parallel with the armature circuit and excited with voltage source is denoted as shunt connected DC motor. In commercial practice shunt motors are the most widely used in situations of linear torque-speed characteristics, constant controllable speed over load variations and not sever starting conditions. Generally the shunt motor is exhibits nonlinear degree of magnetization, so the nonlinearity makes the system complicates their use in automatic speed regulation. As per the control of DC motor there are several methods to control the speed and position. The persistence of motor speed controller is to supply desired voltage signal according to demanded speed at that instant. Conventionally rheostatic speed control method was commonly used for the integral horse power dc motors. However due to the recent developments of static power converters, leads to an enhancement in the performance of DC motors in terms of controllability, cheapness, higher efficiency, and higher current carrying capabilities. The proportional integral- derivative (PID) controller is one of earliest desired control strategy to achieve torque-speed characteristics. The 978-1-4673-8587-9/16/$31.00 ©2016 IEEE
desired torque-speed characteristics could be achieved if the dynamic model of the system should be as exactly known at all the parameter variations. The performance of the PID is poor if there is a system parameter variation. Due to this drawback, the neural network controllers are effectively introduced in nonlinear dynamical systems and exhibits improved performance in recent past[2]. The neural network controllers are very promising in nonlinear dynamical system identification and control due to the learning capability, immense parallelism, fast adaptation and computation, inherent approximation of wide nonlinear functions, and high degree of tolerance. The NARMA method which stands for nonlinear auto regressive moving average with exogenous input– output behaviour of nonlinear dynamic system in a neighbourhood of the equilibrium state[3]. However, due to nonlinearities, it is relatively difficult to implement for control systems in real time. To solve the computational problems related to use of neural network in advanced control of electrical machines, two versions of NARMA such as NARMA-L1 and NARMA-L2 are recommended. The latter is further suitable to implement practically by using multi-layer neural networks due to the advantages such as the training is straight forward because the controller is simply rearrangement of neural network plant model. The plant model is trained offline by batch form and there is no separate dynamic training for the controller[4]. Alternative advantage is only online computation is forward passed through neural network controller[5]. The novelty of this paper is to use NARMA-L2 for dc shunt wound motor control. This paper is organized in five sections commencing from introduction followed by section II which analyses dynamic modelling of DC shunt motor. In section III presents PID controller investigations. Section IV discussed implementation of NARMA L-2 controller for regulation DC shunt motor. Section V presents the comparative analysis and with conclusion. II.
MODELLING AND DYNAMICS OF DC SHUNT MOTOR
The goal in the development of the mathematical model is to relate the voltage applied to the armature to the speed of the motor. Two differential equations can be developed by considering the electrical and mechanical characteristics of the
system[6]. The equivalent electrical circuit of a dc shunt motor is illustrated in Fig. 1. The notations of the quantities mentioned TABLE I.
Control Signal from NARMA L2 Neuro controller
PERFORMANCE VALUES OF CONTROLLERS
200
Parameters Controllers
150
Settling Time(sec)
Peak overshoot
Steady state error
PID
4.99
6.7
0
NARMA L-2
0.56
5.4
0.8
Control Input
100
REFERENCES 50
[1]
M. B. John Chaisson, “Nonlinear Control of Shunt DC Motor,” IEEE Trans. Automat. Contr., vol. 38, no. 11, pp. 1662–1666, 1993.
[2]
M. R. Faieghi and S. M. Azimi, “Design an optimized PID controller for brushless DC motor by using PSO and based on NARMAX identified model with ANFIS,” in 12th International Conference on Computer Modelling and Simulation, 2010, no. 1, pp. 16–21.
[3]
K. H. Chon and R. J. Cohen, “Linear and nonlinear ARMA model parameter estimation using an artificial neurol network,” IEEE Trans. Biomed. Eng., vol. 44, no. 3, pp. 168–174, 1997.
[4]
Sudarshan K. Valluru, Rao Introduction to Neural Networks, Fuzzy Logic, Genetic Algorithm, 2nd Reprin. Mumbai: Jaico Publishing House, 2011.
[5]
O. Nelles, Nonlinear System Identification, 1st ed. Chichester, West Sussex,United Kingdom: John Wiley & Sons, Ltd, 2013.
[6]
A. D. Kourosh Sedghisigarchi, Amer Hasanovic, AliFeAliachi, “Evaluation of Three Algorithms for Nonlinear Control of a DC Shunt Motor,” in Proceedings of the 33rd Southeastern Symposium onSystem Theory, 2001, pp. 407–411.
[7]
M. T. Hagan, H. B. Demuth, and O. D. E. Jesús, “An introduction to the use of neural networks in control systems,” Int. J. Robust Nonlinear Control, vol. 12, no. 11, pp. 959–985, 2002.
[8]
Sudarshan K valluru, Madhusudan Singh,Kumar “Implementation of Narma-L2 Neurocontroller For Speed Regulation of Series Connected DC Motor,” in IEEE 5th India International Conference on Power Electronics, 2012, pp. 1–7.
[9]
S. K. Pradhan, B. Subudhi, “Nonlinear Adaptive Model Predictive Controller for a Flexible Manipulator : An Experimental Study,” IEEE Trans. Control Syst. Technol., vol. 22, no. 5, pp. 1754–1768, 2014.
[10]
Sudarshan K valluru, Madhusudan Singh B. Bhushan, and B. Sreevidya, “Comparative Analysis of PID, NARMA L-2 and PSO Tuned PID Controllers for Nonlinear Dynamical System,” J. Autom. Syst. Eng., vol. 9, no. 2, pp. 94–108, 2015.
0
-50 0
10
20
30
40
50
Time(Sec)
Fig.13 Control signal of NARMA L-2 controller Shunt motorresponsewith NARMA L2 neuroController
100 Response Reference trajectory
Closed loop response of DC shunt motor
90
80
70
60
50
40
30
20 0
10
20
30
40
50
Time(Sec)
Fig.14. Closed loop response of DC shunt motor with NARMA L-2 controller
III.
CONCLUSION
To demonstrate the performance in terms settling time, peak over shoot and steady state error for the implemented controllers such as PID and NARMA L-2 are carried on DC shunt motor with step changes in reference speed is given in table II. The conventional PID and NARMA-L2 controllers have been successfully developed to control the speed of a DC shunt motor. Simulation results show effectiveness of these two controllers for dealing with the motor system with nonlinearity under wide dynamic operation regimes. In comparison with the PID controller, the NARMA L-2 controller has less overshoot and admirable speed tracking performance.
