Optimum Weight Selection Based LQR Formulation for the Design of Fractional Order PI{\lambda}D{\mu} Controllers to Handle a Class of Fractional Order Systems

摘要

A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) andIntegral of Squared Controller Output (ISCO) minimization based time domainoptimal tuning of fractional-order (FO) PID or PI{\lambda}D{\mu} controller isproposed in this paper with a Linear Quadratic Regulator (LQR) based techniquethat minimizes the change in trajectories of the state variables and thecontrol signal. A class of fractional order systems having single non-integerorder element which show highly sluggish and oscillatory open loop responseshave been tuned with an LQR based FOPID controller. The proposed controllerdesign methodology is compared with the existing time domain optimal tuningtechniques with respect to change in the trajectory of state variables,tracking performance for change in set-point, magnitude of control signal andalso the capability of load disturbance suppression. A real coded geneticalgorithm (GA) has been used for the optimal choice of weighting matrices whiledesigning the quadratic regulator by minimizing the time domain integralperformance index. Credible simulation studies have been presented to justifythe proposition.