Novel Technique for PID Tuning
by Particle Swarm Optimization
S. Easter Selvan
Sethu Subramanian
S. Theban Solomon
Introduction
• 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.
Proposed Features in PSO
1. Unbiased search for optimal solution.
2. Unifying the clusters in the potential space.
3. Fine search – selection of the fittest particle.
Generation of Solution Space
• Feasible set of Kp, Ki, Kd values generated based
on Ziegler Nichols method and Nyquist criteria.
• Solution space populated with particles in random
positions.
Unbiased Search
• 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.
Cluster Unification
• 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.
Selection of Best Particle
• 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.
Experimental Results
Experimental Results cont.
System Response Comparison
Ziegler Nichols Method
PSO Method
Swarm Behavior in PI Controller
Surface Plot
Particle Settlement
PSO Results
Initial Population
Unbiased Search Result
PSO Results cont.
Unification of Clusters
Best Particle
Conclusion
• 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.