Novel Technique for PID Tuning by Particle Swarm Optimization S. Easter Selvan Sethu Subramanian S. Theban Solomon

PARTICLE : Volume-less individual; conditionally dislodged in search space. SWARMING : Behavior of organisms in search of conducive environment for sustenance. APPLICATION : Tuning PID controller by globally best solution. Introduction

1.Unbiased search for optimal solution. 2.Unifying the clusters in the potential space. 3.Fine search – selection of the fittest particle. Proposed Features in PSO

Feasible set of Kp, Ki, Kd values generated based on Ziegler Nichols method and Nyquist criteria. Solution space populated with particles in random positions. Generation of Solution Space

Each particle dislodged randomly by fixed step size. If cost favorable – proceeds in same direction Else returns to previous position; attempts random directions with increased step size. Initially coarse search; towards end finer search. Unbiased Search

Particles settle in clusters at locations of favorable costs. CASE I : Best particle in major cluster. CASE II : Best particle in minor cluster. Cluster with best particle drags the rest based on Euclidean distance – thereby unifying clusters. Cluster Unification

Particles assume virtual spheres whose radius is distance between best particle and themselves. Particles radially move in search of cost better than best particle’s cost. If better one found - virtual spheres updated. Else search continues until absorbed by best particle. Search terminated when majority absorbed. Selection of Best Particle

Experimental Results

Experimental Results cont.

System Response Comparison Ziegler Nichols MethodPSO Method

Swarm Behavior in PI Controller Surface PlotParticle Settlement

PSO Results Initial PopulationUnbiased Search Result

PSO Results cont. Unification of ClustersBest Particle

80% of tested cases form distinct clusters - faster convergence. Extremely low settling time obtained by PSO compared to Ziegler-Nichols method. Improper valley formation due to cost function leads to slow convergence. Conclusion