Particle Swarm Optimization for Tuning Three PID Parameters

Particle Swarm Optimization (PSO) is a population-based intelligent optimization method particularly suitable for automatic tuning of PID controller parameters (proportional Kp, integral Ki, derivative Kd). Its core concept simulates bird flock foraging behavior to iteratively search for optimal solutions.

Implementation Approach Analysis Particle Encoding: Each particle represents a set of PID parameters (Kp, Ki, Kd). During population initialization, multiple parameter combinations are randomly generated using code like: particle_position = [random(Kp_range), random(Ki_range), random(Kd_range)]. Fitness Function: Typically employs error metrics from system step responses (such as ITAE, ISE) to evaluate each parameter set's control performance, implemented as: fitness = calculate_ITAE(step_response). Velocity Update: Particles adjust their "flying" direction based on personal historical best and global best positions, incorporating inertia weight to balance global and local search capabilities using: velocity = w*velocity + c1*rand()*(pbest-position) + c2*rand()*(gbest-position). Termination Criteria: The algorithm stops when reaching maximum iterations or fitness convergence, outputting the global best parameters through: if (iteration > max_iter OR fitness_change < tolerance) return gbest_params.

Advantage Analysis Compared to traditional trial-and-error methods, PSO avoids local optima traps No requirement for precise mathematical models, suitable for nonlinear systems Simple algorithm structure facilitates embedding into actual control systems

Extension Applications Can integrate adaptive inertia weights or hybrid genetic algorithms to further improve convergence speed Applicable for cooperative optimization of multivariate PID systems through multi-dimensional particle encoding