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Novel Technique for PID Tuning by Particle Swarm Optimization S. Easter Selvan Sethu Subramanian S. Theban Solomon
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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
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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
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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
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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
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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
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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
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Experimental Results
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Experimental Results cont.
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System Response Comparison Ziegler Nichols MethodPSO Method
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Swarm Behavior in PI Controller Surface PlotParticle Settlement
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PSO Results Initial PopulationUnbiased Search Result
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PSO Results cont. Unification of ClustersBest Particle
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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
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