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Quantifying Maximum Actuator Degradation for a Given $H_2/H_{\infty}$ Performance with Full-State Feedback Control

Hrishav Das, Eliot Nychka, Raktim Bhattacharya

Abstract

In this paper, we address the issue of quantifying maximum actuator degradation in linear time-invariant dynamical systems. We present a new unified framework for computing the state-feedback controller gain that meets a user-defined closed-loop performance criterion while also maximizing actuator degradation. This degradation is modeled as a first-order filter with additive noise. Our approach involves two novel convex optimization formulations that concurrently determine the controller gain, maximize actuator degradation, and maintain the desired closed-loop performance in both the $H_2$ and $H_{\infty}$ system norms. The results are limited to open-loop stable systems. We demonstrate the application of our results through the design of a full-state feedback controller for a model representing the longitudinal motion of the F-16 aircraft.

Quantifying Maximum Actuator Degradation for a Given $H_2/H_{\infty}$ Performance with Full-State Feedback Control

Abstract

In this paper, we address the issue of quantifying maximum actuator degradation in linear time-invariant dynamical systems. We present a new unified framework for computing the state-feedback controller gain that meets a user-defined closed-loop performance criterion while also maximizing actuator degradation. This degradation is modeled as a first-order filter with additive noise. Our approach involves two novel convex optimization formulations that concurrently determine the controller gain, maximize actuator degradation, and maintain the desired closed-loop performance in both the and system norms. The results are limited to open-loop stable systems. We demonstrate the application of our results through the design of a full-state feedback controller for a model representing the longitudinal motion of the F-16 aircraft.
Paper Structure (9 sections, 2 theorems, 22 equations, 6 figures, 1 table)

This paper contains 9 sections, 2 theorems, 22 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Survey
  3. Key Contributions
  4. Preliminaries
  5. Technical Results
  6. Examples
  7. F-16 Flight Control Application
  8. Simulation Results
  9. Summary & Conclusions

Key Result

Theorem 1

For the system in (eqn:system_dynamics), the state-feedback gain that guarantees $\left\| \to\boldsymbol{z}\right\|_\infty \leq \gamma$ for the system in (eqn:system_dynamics), with maximum actuator noise, and minimum control magnitude and rate, is given by the following convex optimization problem, with where $\lambda_a$, $\lambda_{\boldsymbol{\omega}_c}$, and $\lambda_{\boldsymbol{x}_F}$ are us

Figures (6)

  • Figure 1: Modeling of a faulty actuator.
  • Figure 2: Closed-loop system with full-state feedback controller and faulty actuator.
  • Figure 3: Minimum actuator cutoff frequencies (rad/s).
  • Figure 4: Minimum actuator dcgain.
  • Figure 5: Maximum actuator noise scaling.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 3