Identification and PID Control for a Class of Delay Fractional-order Systems

In this paper, a new model identification method is developed for a class of delay fractional-order system based on the process step response. Four characteristic functions are defined to characterize the features of the normalized fractional-order model. Based on the time scaling technology, two identification schemes are proposed for parameters' estimation. The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly. The other scheme employs optimal searching method to adjust the fractional order for the best model identification. The proposed two identification schemes are both applicable to any stable complex process, such as higher-order, under-damped/over-damped, and minimum-phase/nonminimum-phase processes. Furthermore, an optimal PID tuning method is proposed for the delay fractional-order systems. The requirements on the stability margins and the negative feedback are cast as real part constraints (RPC) and imaginary part constraints (IPC). The constraints are implemented by trigonometric inequalities on the phase variable, and the optimal PID controller is obtained by the minimization of the integral of time absolute error (ITAE) index. Identification and control of a Titanium billet heating process is given for the illustration.