Fundamental limitations of monotonic tracking systems

TL;DR

This paper investigates the fundamental limitations of monotonic tracking control in continuous-time SISO systems, detailing conditions for solvability and bounds on controller design based on plant zeros.

Contribution

It provides necessary and sufficient conditions for monotonic tracking control and reveals fundamental bounds related to plant zeros, controller order, and decay rate.

Findings

Identifies exact feasible plant zero locations for monotonic tracking.

Determines the minimum controller order needed.

Establishes the maximum achievable decay rate for closed-loop systems.

Abstract

We consider the monotonic tracking control problem for continuous-time single-input single-output linear systems using output-feedback linear controllers in this paper. We provide the necessary and sufficient conditions for this problem to be solvable and expose its fundamental limitations: the exact feasible locations of the plant zeros, the minimum controller order possible, and the fastest decay rate achievable for the closed-loop system. The relationship between these bounds is explained by a simple geometric shape for plants with a pair of complex-conjugate zeros.