Nonlinear Control of a DC Motor Siti Hawa Abu-Bakar School of Engineering and Built Environment, Glasgow Caledonian University, United Kingdom Universiti Kuala Lumpur – British Malaysian Institute, Malaysia E-mail: sabuba10@gcu.ac.uk/hawa012@gmail.com Firdaus Muhammad-Sukki School of Engineering and Built Environment, Glasgow Caledonian University, United Kingdom Faculty of Engineering, Multimedia University, Malaysia Khairil Anuar Faculty of Engineering, Multimedia University, Malaysia Abdullahi Abubakar Mas’ud School of Engineering and Built Environment, Glasgow Caledonian University, United Kingdom Abstract—This paper deals with a nonlinear system where an online nonlinear control is applied to a DC motor. First, nonlinear model of the motor is explained. Next, based on the model, the nonlinearity is simulated using MATLAB. The simulations were on two nonlinearities, ideal relay and relay with hysteresis. To further investigate the relay with hysteresis, the implementation of the LabVIEW program is presented to verify the results obtained from the MATLAB simulations. It was found that experiments show good agreements with the simulation results. Keywords— DC motor, nonlinear control, relay. I. INTRODUCTION For linear systems, there are many well-established control techniques, for example root-locus, Bode plots, Nyquist criterion, state-feedback, pole-placement etc. [1]-[4]. But for nonlinear system, it is much more complex. The objective of this project is to analyse and design a way of controlling the motor using on-line nonlinear control. In this particular project, a relay with hysteresis was chosen as the nonlinear controller. II. NONLINEAR MODEL OF THE SYSTEMS Consider theoretically the system in Fig. 1 having the relay with hysteresis of gain 1  D and width 5 . 0  h as illustrated in Fig. 2. Fig. 1: Circuit using Relay with hysteresis as controller. Fig. 2: Relay with hysteresis The parameters of A, B and C in Fig. 1 were determined from experiments [1] and the values are           389 . 3 0 1 0 A ,          656 . 20 0 B and   1405 . 0 0  C . The transfer function is defined as: B A sI C s G L 1 ) ( ) (    (1) and based on the values obtained earlier, the transfer function for the system is calculated to be s s s G L 389 . 3 656 . 20 ) ( 2   . To be able to analyse this system, a few assumptions are made, which are:  No input, 0 ) (  t r  Linear part (motor) act as a low pass filter, that is, higher order harmonics are damped.  Nonlinearity does not generate subharmonics  Nonlinearity is symmetric  Nonlinearity does not depend on frequency  Assume that the error signal, ) cos( ) ( t E t e   The authors would like to thank Yayasan TM and Majlis Amanah Rakyat Malaysia for funding this study. Thanks are due to Dr JC Allwright for supervising this project. 978-1-4673-4691-7/13/$31.00 ©2013 IEEE 2013 IEEE Conference on Sustainable Utilization and Development in Engineering and Technology 37