A new Fractional Order Proportional-Integral (FOPI) controller is proposed in this paper for process control systems. This is achieved by extending the Biggest Log-modulus Tuning (BLT) method of designing conventional PID controllers to tuning FOPI controllers for multivariable processes. Unlike the conventional PID case, internal model control (IMC) method is first used to design the FOPI controller and obtain preliminary values of controller parameters. This yields simple formulae for setting controller gains. Thereafter, the FOPI controller gains are adjusted using a single detuning factor (F) until a biggest log modulus of 2N dB is obtained where N is the number of loops. Extended simulation studies show that good compromise between performance and robustness can be achieved for multiloop process control applications with the proposed FOPI controller.
A new method of designing fractional-order predictive PID controller with similar features to model based predictive controllers (MPC) is considered. A general state space model of plant is assumed to be available and the model is augmented for prediction of future outputs. Thereafter, a structured cost function is defined which retains the design objective of fractional-order predictive PI controller. The resultant controller retains inherent benefits of model-based predictive control but with better performance. Simulations results are presented to show improved benefits of the proposed design method over dynamic matrix control (DMC) algorithm. One major contribution is that the new controller structure, which is a fractional-order predictive PI controller, retains combined benefits of conventional predictive control algorithm and robust features of fractional-order PID controller.
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 just like Ziegler-Nichol's rule for inter order PID. Critical parameters of the system are obtained at the ultimate point and the controller parameters are calculated from these critical measurements to meet design specifications. Thereafter, fractional order 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 second-order plus dead time plant to demonstrate both performance and robustness.
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