Design of Digital Pole placement Controller for a Ball & Beam system

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GRD Journals | Global Research and Development Journal for Engineering | International Conference on Innovations in Engineering and Technology (ICIET) - 2016 | July 2016

e-ISSN: 2455-5703

Design of Digital Pole Placement Controller for a Ball & Beam System 1S.

Nagammai 2S. Latha 1 Department of Electronics and Instrumentation Engineering 2Department of Electrical and Electronics Engineering 1 K.L.N. College of Engineering, Pottapalayam, Sivagangai 630612, India 2Thiagarajar College of Engineering, Madurai 625015, India Abstract The Ball and Beam system is a nonlinear unstable system due to this property it is used as a bench mark problem for many researchers. The proposed work focuses on the design of a digital pole placement controller for a Ball and Beam system (BBS) connected with servo motor which is an open loop unstable system due to the presence of multiple poles at the origin. A one degree of freedom (DOF) and 2-DOF digital pole placement controller is designed using the discrete transfer function for the specified constraints namely peak overshoot and rise time. The digital controller designed is capable of providing system stability and also provides good set point tracking and disturbance rejection. The simulation result shows the feasibility of using the proposed controller for control of an unstable Ball and Beam system. Keyword- BBS, 1 DOF Controller, 2 DOF Controllers, Pole Placement __________________________________________________________________________________________________

I. INTRODUCTION The BBS mimics the real control problems namely stabilization of an airplane during landing, rocket and aircraft vertical takeoff. The BBS has two degrees of freedom namely rolling of the ball back and forth on the beam, and the other is beam rotation. It has nonlinear dynamics and under-actuated characteristics. The nonlinear property becomes insignificant when the beam deflects a small angle from the horizontal position which leads the mathematical modelling simpler. It is an ideal example for examining the performance of classical, modern and advanced control theory. Many researchers have done work on this laboratory test bench. Hauser et al proposed feedback linearization controller [1]. Pang et al designed a Linear Quadratic Regulator (LQR) for stabilization [2]. H.Verrelst et al used Neural Network for stabilization of BBS [3],S.K Oh et al proposed Fuzzy based cascade control [4] and Chang et al designed a tracking control strategy using a fuzzy sliding-mode controllers [5]. Further all the intelligent controllers are knowledge based and the stability of the system is not guaranteed. In this proposed work controller is designed for positioning and stabilization of the ball along the beam by manipulating the voltage applied to the servomotor. Thus the system under consideration is a single input single output system (SISO). The paper is organized as follows. Section II gives details about the mathematical modelling of BBS and servomotor. In Section III the concepts of 2 DOF pole placement controllers is presented. In Section IV the design of pole placement controller for a desired specification is discussed. The simulated results are given in section V. Finally conclusion is given in section VI.

II. MATHEMATICAL MODELLING A. Modelling of Ball and Beam System

Fig. 1: Schematic of ball and beam system

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