Modelling and Control of Ball and Beam System using Coefficient Diagram Method (CDM) based PID controller

Abstract

This paper introduces a design methodology of a PID controller for an unstable ball and beam system based on Coefficient Diagram Method (CDM). Ball and beam system is a non-linear, unstable, double integrating system which is widely used as a bench mark control setup for evaluating various control strategies. Many PID controller design is developed for stable system however it is very less common for double integrating unstable system. Co-efficient Diagram Method (CDM) is one of the recently developed controller design methodology based on algebraic approach. With CDM, it is easy to realize a controller under the conditions of stability, robustness and time domain performance. In this paper, CDM based PID (CDM-PID) controller parameters are computed based on the dynamics of ball and beam system which is developed using Euler – Lagrangian Approach. To evaluate the performance of proposed CDM-PID controller, set-point tracking and disturbance rejection analysis of ball and beam system are carried out through simulation runs in MATLAB-SIMULINK platform. The results are compared with the conventional Ziegler Nicholas – PID (ZN-PID) controller in terms of Error indices (Integral Squared Error (ISE) and Integral Absolute Error (IAE)) and Quality indices (Rise time (t_r), Settling time (t_s) and Maximum peak overshoot (%M_p)). The results reveal that the CDM-PID controller maintains good stability of the ball's position with reduced percentage of error than ZN-PID controller.