Stability analysis and design of integrating unstable delay processes using the mirror-mapping technique

• Using the all-pole Pade approximation to tackle the time delay term.
• The mirror mapping technique and CGSA are original works of the authors, and two CGSA based controllers are developed for the integrating unstable process in this paper.
• The exact stabilization analysis is discussed using the Nyquist criteria.

Robustness analysis and design for the integrating unstable delay systems are discussed in this note. The Nyquist criteria have established the exact stability margin of the novel robust control scheme, which is meaningful in the process control practice. Comparing with the existing results, the control law is designed based on the delay-approximated model (using the all-pole Padé approximation). The unstable system was mirror mapped into a minimum-phase system and then the control law was derived by the closed-loop gain shaping algorithm (CGSA). In addition, a small constant δ was introduced in the algorithm to prevent the integral cancellation limitation, which is inherent in the CGSA. The proposed scheme obtains several advantages: a concise design procedure and easy to implementation due to the simple unit feedback structure. The comparative analysis with respect to recently successful works illustrates a substantial improvement in the performance-robustness tradeoff.