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 U+02BC 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 U+002F over-damped, and minimum-phase U+002F 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 U+0028 RPC U+0029 and imaginary part constraints U+0028 IPC U+0029. 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 U+0028 ITAE U+0029 index. Identification and control of a Titanium billet heating process is given for the illustration. © 2014 Chinese Association of Automation.

Robust Stabilizing Regions of Fractional-order PI~λ Controllers for Fractional-order Systems with Time-delays

This study focuses on a graphical approach to determine the robust stabilizing regions of fractional-order PIλ（proportional integration） controllers for fractional-order systems with time-delays. By D-decomposition technique, the existence conditions and calculating method of the real root boundary（RRB） curves, complex root boundary（CRB） curves and infinite root boundary（IRB）lines are investigated for a given stability degree. The robust stabilizing regions in terms of the RRB curves, CRB curves and IRB lines are identified by the proposed criteria in this paper. Finally, two illustrative examples are given to verify the effectiveness of this graphical approach for different stability degrees.