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PID controller design of nonlinear systems using an improved particle swarm optimization approach. (English) Zbl 1222.90083
Summary: An improved particle swarm optimization is presented to search for the optimal PID controller gains for a class of nonlinear systems. The proposed algorithm is to modify the velocity formula of the general PSO systems in order for improving the searching efficiency. In the improved PSO-based nonlinear PID control system design, three PID control gains, i.e., the proportional gain $$K_{p}$$, integral gain $$K_{i}$$, and derivative gain $$K_{d}$$ are required to form a parameter vector which is called a particle. It is the basic component of PSO systems and many such particles further constitute a population. To derive the optimal PID gains for nonlinear systems, two principle equations, the modified velocity updating and position updating equations, are employed to move the positions of all particles in the population. In the meanwhile, an objective function defined for PID controller optimization problems may be minimized. To validate the control performance of the proposed method, a typical nonlinear system control, the inverted pendulum tracking control, is illustrated. The results testify that the improved PSO algorithm can perform well in the nonlinear PID control system design.

##### MSC:
 90C59 Approximation methods and heuristics in mathematical programming 37N35 Dynamical systems in control 93C95 Application models in control theory
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##### References:
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