Optimal control of multi-axis robotic system using Particle Swarm Optimization

Abstract

Optimization is a mathematical technique that concerns the finding of maxima or minima of functions in some feasible region. There is no business or industry which is not involved in solving optimization problems. A variety of optimization techniques compete for the best solution. Particle Swarm Optimization (PSO) is a relatively new, modern and powerful method of optimization that has been empirically shown to perform well on many of these optimization problems. This paper presents an application of `Particle Swarm Optimization (PSO)' for tuning the parameters of PID controller to achieve system stability. Here the system is two axis robotic arm. PSO algorithm will search for best possible PID controller parameters within its three dimension space of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> . Optimization of peak overshoot (M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ) and settling time (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ) is achieved by using a multi-purpose performance criterion (MPPC). The system is stabilized by minimizing the performance criterion. This paper presents simulation results using MATLAB Simulink to demonstrate tuning of PID controller using PSO along with MPPC gives minimum M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> and t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> .