Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes

Frequency domain based design methods are investigated for the design and tuning of fractional-order PID for scalar applications. Since Ziegler-Nichol's tuning rule and other algorithms cannot be applied directly to tuning of fractional-order controllers, a new algorithm is developed to handle the tuning of these fractional-order PID controllers based on a single frequency point test just like Ziegler-Nichol's rule for integer order PID controllers. Critical parameters of the system are obtained at the ultimate point and controller parameters are calculated from these critical measurements to meet design specifications. Thereafter, fractional order controller is obtained to meet a specified robustness criteria which is the phase-invariability against gain variations around the phase cross-over frequency. Results are simulated on a second -order plus dead time plant to demonstrate both performance and robustness.