Multi-objective LQR with Optimum Weight Selection to Design FOPID Controllers for Delayed Fractional Order Processes

TL;DR

This paper presents a multi-objective LQR-based method for designing FOPID controllers for delayed fractional order systems, optimizing performance and control effort trade-offs with analytical delay handling techniques.

Contribution

It introduces a novel multi-objective optimization framework for FOPID controller tuning in delayed FO systems, comparing two delay handling approaches within an LQR design.

Findings

Pareto optimal solutions balance tracking and control effort.

Two delay handling methods are compared for effectiveness.

Load disturbance suppression is demonstrated with the proposed controllers.

Abstract

An optimal trade-off design for fractional order (FO)-PID controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain control objectives. The deviation of the state trajectories and control signal are automatically enforced by the LQR. A class of delayed FO systems with single non-integer order element has been controlled here which exhibit both sluggish and oscillatory open loop responses. The FO time delay processes are controlled within a multi-objective optimization (MOO) formulation of LQR based FOPID design. The time delays in the FO models are handled by two analytical formulations of designing optimal quadratic regulator for delayed systems. A comparison is made between the two approaches of LQR design for the stabilization of time-delay systems in the context of FOPID controller tuning. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance for unit set-point change and total variation (TV) of the control signal. Numerical simulations are provided to compare the merits of the two delay handling techniques in the multi-objective LQR-FOPID design, while also showing the capability of load disturbance suppression using these optimal controllers. Tuning rules are then formed for the optimal LQR-FOPID controller knobs, using the median of the non-dominated Pareto solution to handle delays FO processes.