Design of Robust Integer/Fractional Order PID Controller Based on Bode’s Ideal Transfer Function and H-Infinity Robust Performance Condition

In this paper, we proposed a new fitness function that is minimized by optimization algorithms to tune the parameters of the integer/fractional order PID (proportional-integral-derivative) controllers. The fitness function has been designed by combining H-$\infty$ robust performance condition constraint and Bode’s ideal transfer function as a reference model. Two weighting functions have been used for robust performance condition; multiplicative uncertainty weighting function as a fixed parameters structure, and performance weighting function both as a fixed parameters structure, and optimized adjustable parameters structure. The parameters of the Bode’s ideal transfer function are selected based on desired time response specifications. The particle swarm optimization (PSO) algorithm has been used as an optimization tool to minimize the proposed fitness function to tune the parameters of integer/fractional order PID controllers. The parameters of the controllers are obtained for the given second-order transfer function system as an example. The performance of the systems with obtained controllers has been compared in terms of the reference tracking ability, disturbance rejection capability, and robustness performance against parameter changes in the system. The simulation results have revealed that the proposed fitness function can be used with the aim to tune the parameters of the robust fixed structure controllers such as integer/fractional order PIDs by using any optimization algorithm while retaining the H-$\infty$ robust performance condition.