Multi-Objective Step Response Shaping via the Fractional-Order Proportional-Integral-Derivative Controller

A well-known problem in control system design and analysis is the shaping of the unit step reference response of a system to produce desired transient characteristics for various system references. The necessity of having fast, accurate, and stable control systems for a large number of practical applications has created the need for advanced control methods. In this regard, the development of fractional-order controllers has received considerable attention from the control community. Many papers and books on the topic of fractional-order systems have been published, which also include the usefulness of fractional calculus in the area of controllers. The fractional order proportional integral derivative controller is proven to be versatile, and its design can be obtained for any given target step response. A sufficiently large number of response characteristics, such as performance, phase margin, immunity to plant modeling, and robustness, can be adjusted by means of five tuning parameters. The control strategy of this paper focuses on developing a fractional order proportional integral derivative controller, which aims at overcoming the infeasibility of the controller to satisfy the conflicting goals of go-to speed and settling time in the traditional PID controller. The controller design has two main goals: one is to satisfy system stability, while the other is tuning the overshoot and the settling time. In this direction, the genetic algorithm is implemented. The results are presented through an illustrative example.