Analytical Tuning Rules for Cascade Control Systems Based on Fractional-Order PI Controller in Frequency Domain

A design method for a cascade control system is proposed in this paper. To deal with delay times in most of process control systems, the Smith predictor is also suggested in the control structure to eliminate a delay term in closed-loop systems. The classical proportional-integral (PI) and the fractional-order PI controller are adopted for the inner loop and the outer loop respectively. The analytical tuning rules are derived based on frequency domain and also using the direct synthesis method for improving the performance for both disturbance rejection and set-point tracking problems. An illustrative example is considered to confirm the effectiveness of the proposed algorithm. In addition, the robust stability of the fractional-order system is also carried out to demonstrate that the proposed fractional-order PI controller can hold well the robustness against perturbation uncertainties in the process models.