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

TL;DR

This paper introduces a novel LQR-based method for optimally tuning fractional-order PID controllers using a weighted cost function, improving response characteristics for sluggish and oscillatory fractional systems.

Contribution

It presents a new LQR-based tuning approach incorporating a weighted cost function for fractional PID controllers, with genetic algorithm optimization of weighting matrices.

Findings

Enhanced control performance for fractional systems with sluggish responses

Improved disturbance rejection and set-point tracking

Effective optimization of controller parameters using genetic algorithms

Abstract

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