Design of FOPID controller for higher order MIMO systems using model order reduction

Designing a controller for higher-order system is tough, as the system order grows, mathematical analysis gets more complicated and time-consuming. As a result, it is preferable to reduce higher-order systems to lower-order systems. A new stability preserving order reduction approach is proposed in this paper for the reduction of higher order multi input multi output (MIMO) continuous time systems. With the help of bilinear transformation technique, the proposed method becomes more flexible compared to available conventional methods. It is a one to one transformation from s-domain to z-domain and vice-versa. This method is free of aliasing effect. This method always generates stable reduced order models for stable high order systems which can be used for the stability analysis and design of high order MIMO continuous time systems. The method is extended for the design of proportional integral derivative (PID), fractional order PID (FOPID) controllers tuned by Genetic Algorithm (GA). From the results, it can be observed that GA tuned FOPID gives less settling time than the GA tuned PID and auto tuned PID.