A model-free fractional-order PID tuning method based on an improvement of particle swarm optimization

Abstract

In recent times, applications of Fractional Calculus have gained importance in various areas of science and engineering. In the realm of control engineering Fractional Calculus started to draw the attention of researchers a decade ago with its most common application, namely Fractional-Order PID control, in contrast to its integerorder counterpart, it provides more flexibility in PID controller design applications with having integral and derivative actions of arbitrary order. However, classical PID tuning methods become inapplicable. The closed-loop system behavior exhibits sensitivity especially depending on the order of the derivative action. This behavior leads to use derivative-free stochastic optimization techniques rather than deterministic search methods. The trend of biologically-inspired computational approaches brought forth many heuristic optimization techniques. Among the most popular ones one can count evolutionary algorithms and swarm algorithms. Given an assessable objective function to be optimized, PSO technique can be used as a model-free optimization method that belongs to the "blind search" category. The innovation in this study is an improvement in this technique that combines the "blind search" inherent to PSO with "knowledge- supported search" in cases where some systematic knowledge about the optimization problem is available. This study proposes a model-free fractional-order PID controller tuning method which is Knowledge-Supported Particle Swarm Optimization (PSO) technique, sug- gesting a different combination of classical PID tuning approaches and stochastic optimization approaches. The stochastic method will be based on the socalled Particle Swarm Optimization (PSO) Technique, which is becoming a popular design method ever since it was introduced. In this study Knowledge-Supported Particle Swarm Op- timization (PSO) technique is used for fractional-order PID controller tuning based on the design specifications maximum percentage overshoot, rise-time, settling-time, and steady-state value. Constructed objective function for optimization which yields a possible solution to the design problem is optimized using popular Particle Swarm Optimization and systematic knowledge about PID controllers. With the help of examples the superiority of the proposed method to classical PSO algorithm is presented.