Inversion-Based Output Tracking and Unknown Input Reconstruction of Square Discrete-Time Linear Systems

TL;DR

This paper introduces an inversion-based control framework for discrete-time linear systems, enabling accurate output tracking and unknown input reconstruction for systems with various zero configurations, including non-minimum phase and transmission zeros on the unit circle.

Contribution

It presents a novel inversion scheme that reconstructs system states and inputs for complex systems, extending output tracking capabilities to non-minimum phase and transmission zero cases.

Findings

Reconstruction error decreases exponentially with increased delay.

Almost perfect reconstruction achievable with sufficient delay.

Method successfully applied to systems with transmission zeros on the unit circle.

Abstract

In this paper, we propose a framework for output tracking control of both minimum phase (MP) and non-minimum phase (NMP) systems {as well as systems with transmission zeros on the unit circle}. Towards this end, we first address the problem of unknown state and input reconstruction of non-minimum phase systems. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter for a delayed non-minimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the output-tracking control problem. {We have also proposed a methodology to handle the output tracking problem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros.} Simulation case studies are also presented that demonstrate the merits and capabilities of our proposed methodologies.