Particle Swarm Optimization (PSO) Algorithm

Particle Swarm Optimization (PSO) is a population-based optimization algorithm inspired by the social behavior of bird flocks or fish schools, designed to solve complex optimization problems. In control engineering, it is commonly applied for PID parameter optimization, enabling rapid convergence to near-optimal solutions. The algorithm operates by maintaining a swarm of particles where each particle represents a candidate solution moving through the search space.

The core concept of PSO involves guiding the search direction through a combination of individual and collective experiences. Each particle adjusts its velocity and position based on its personal historical best position (pbest) and the global best position (gbest) found by the entire swarm. In PID optimization, PSO treats the three parameters—Kp, Ki, and Kd—as dimensions of a particle. Through iterative updates using velocity and position equations (e.g., v_i(t+1) = w*v_i(t) + c1*r1*(pbest_i - x_i(t)) + c2*r2*(gbest - x_i(t))), the algorithm refines parameters to achieve an ideal system response. Key functions in implementation include fitness evaluation (e.g., ITAE, ISE metrics) and boundary handling for parameter constraints.

Compared to traditional trial-and-error methods or gradient descent, PSO offers advantages such as parallel search capability, avoidance of local optima, and no requirement for gradient information. This makes it particularly suitable for PID tuning in multimodal or nonlinear systems. In practical applications, hyperparameters like inertia weight (w) and learning factors (c1, c2) must be carefully configured to balance exploration and exploitation. Code implementation typically involves initializing particle positions/velocities, iteratively updating pbest/gbest, and applying convergence criteria (e.g., maximum iterations or fitness threshold).