Model Order Reduction Strategy for LTI Systems and Application to PID Controller Design

Abstract

The mathematical modeling of the real-time system results in large-dimensional ordinary or partial differential equations, which are challenging to employ for investigation and control synthesis. Finding a comparable system of the same kind in a lower-order dimension that can maintain the core characteristics of the higher-order system (HOS) is essential. This article discusses a novel technique for HOS’s reduced order approximation and control design. The proposed method modifies the Schur method for balanced truncation. The method circumvents the requirement of balancing transformation and steady-state gain (SSG) deviation as required in the truncated model reduction algorithm. The offered technique eliminates the SSG deviation without altering the dynamical behavior compared to the HOS by appending a gain enhancement factor to the numerator polynomial of the reduced system transfer matrix. The offered technique ensures that the reduced system retains the HOS stability, passivity, SSG, and all critical characteristics. The recommended method’s findings are compared to the outcomes of recently published work’s lower-order models. Further, using the proposed method, the reduced model has been used to design a PID controller for the flexible-missile control model and an automatic voltage regulator system. The controller produced using the simplified model provides almost the exact time domain specifications (TDS) as the controller made using the HOS, and its design is also relatively more straightforward. Step response and TDS assess lower- and higher-order controller performance.