Integral state-feedback control of linear time-varying systems: A performance preserving approach

TL;DR

This paper introduces an integral extension to linear time-varying state-feedback controllers that maintains nominal performance and rejects certain disturbances, with stability guarantees and practical tuning guidelines demonstrated through simulation.

Contribution

It presents a novel integral control method for linear time-varying systems that preserves performance and enhances disturbance rejection, including windup prevention and stability analysis.

Findings

Effective disturbance rejection for constant-effect disturbances

Maintains performance in unperturbed conditions

Demonstrated success in simulation on a two-tank system

Abstract

An integral extension of state-feedback controllers for linear time-varying plants is proposed, which preserves performance of the nominal controller in the unperturbed case. Similar to time-invariant state feedback with integral action, the controller achieves complete rejection of disturbances whose effective action on the plant is constant with respect to the control input. Moreover, bounded-input bounded-state stability with respect to arbitrary disturbances is shown. A modification for preventing controller windup as well as tuning guidelines are discussed. The efficacy of the proposed technique is demonstrated in simulation for a two-tank system that is linearized along a time-varying reference trajectory.