Hybrid Fractional-order PI-PD Controller Design with Indirect Design Approach

In this article, a Hybrid controller structure with fractional order Proportional Integral (PI) and Integer order Proportional-Derivative (PD) controller is proposed (FOPI-PD) for stable and unstable first-order processes. The proposed controller structure consists of a Feed-forward fractional order PI controller and Feedback integer order PD controller. The Proportional Derivative controller in feedback gives a better regulatory response as compared to the Feed-forward PD controller; and the fractional-order PI Controller in feed-forward helps to achieve the better Servo response. Analytical tuning rules are proposed for the FOPI-PD controller with the help of Gain and Phase Margin analysis. After that, the proposed controller is further fine-tuned with the Fractional Indirect Design approach-2 to mitigate the mathematical approximation errors and improve the performance of the proposed controller. Additionally, it is shown that the robustness of the FOPI-PD controller can be adjusted with a single variable in a given range. The proposed controller is validated with the help of the MATLAB simulation examples on the First-order Stable and Unstable processes.