State Feedback Controllers with Operational Constraints

TL;DR

This paper develops a control design for MIMO linear systems that enforces operational constraints using a combination of Nagumo Theorem, comparison lemma, and min-norm controllers, with applications demonstrated in aerial flight systems.

Contribution

It introduces a novel control approach that integrates constraints directly into state feedback controllers, including anti-windup logic, based on invariance principles and optimal control.

Findings

Effective constraint enforcement in simulation for aerial systems

Integration of anti-windup protection in constrained control design

Demonstrated benefits over traditional control methods

Abstract

In this paper, a state feedback control design with min/max operational limiting constraints is developed for multi-input-multi-output linear time invariant systems. Specifically, servo-tracking control problems with input and output constraints are considered. For static servo-controllers, the output design limits are imposed component-wise on the system selected output, which is of the same dimension as the control input. For dynamic servo-controllers, operational constraints are applied to the system inputs and outputs. The proposed control solution also includes an anti-windup protection logic for dynamic servo-controllers with integral action. The developed method is based on the Nagumo Theorem for forward invariance, the Comparison Lemma for inclusion of input/output inequality constraints, and on the min-norm optimal controllers for synthesis. The derived design is similar and directly related to the method of Control Barrier Functions. Simulation trade studies are presented to illustrate benefits of the proposed control methodology for aerial flight critical systems.