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Cooperative Control of Parallel Actuators for Linear Robust Output Regulation of Uncertain Linear Minimum-phase Plants

Liang Xu, Tao Liu, Zhiyun Lin

Abstract

This paper investigates the robust output regulation problem for an uncertain linear minimum-phase plant with cooperative parallel operation of multiple actuators. Building on the internal model approach, we first propose a dynamic output feedback control law to solve the robust output regulation problem with a single actuator. Then, we construct a distributed dynamic output feedback control law that is nearly independent of the number of actuators and incorporates coupling terms to address the linear robust output regulation problem with cooperative parallel operation of multiple actuators over undirected communication networks. We reveal the connection in the design of parameters between the dynamic output feedback control law under single actuator operation and the distributed dynamic output feedback control law under cooperative parallel operation with multiple actuators. Moreover, we remove the existing assumption that the actuator dynamics must be Hurwitz stable, thereby enabling the incorporation of unstable actuators in our framework. Finally, two numerical examples are provided to validate the effectiveness of the proposed control laws.

Cooperative Control of Parallel Actuators for Linear Robust Output Regulation of Uncertain Linear Minimum-phase Plants

Abstract

This paper investigates the robust output regulation problem for an uncertain linear minimum-phase plant with cooperative parallel operation of multiple actuators. Building on the internal model approach, we first propose a dynamic output feedback control law to solve the robust output regulation problem with a single actuator. Then, we construct a distributed dynamic output feedback control law that is nearly independent of the number of actuators and incorporates coupling terms to address the linear robust output regulation problem with cooperative parallel operation of multiple actuators over undirected communication networks. We reveal the connection in the design of parameters between the dynamic output feedback control law under single actuator operation and the distributed dynamic output feedback control law under cooperative parallel operation with multiple actuators. Moreover, we remove the existing assumption that the actuator dynamics must be Hurwitz stable, thereby enabling the incorporation of unstable actuators in our framework. Finally, two numerical examples are provided to validate the effectiveness of the proposed control laws.

Paper Structure

This paper contains 17 sections, 7 theorems, 119 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Robust Output Regulation with A Single Actuator
  4. Internal Model
  5. Augmented System
  6. Solvability of Problem \ref{['Problem-Robust_output_regulation']}
  7. Robust output regulation with cooperative control of parallel actuators
  8. Robust Output Regulation
  9. Input Sharing Property
  10. Solvability of Problem \ref{['Problem-Robust_output_regulation_multiple_actuators']}
  11. Numerical Examples
  12. Linear robust output regulation with strictly stable actuators
  13. Linear robust output regulation with unstable actuators
  14. Conclusion
  15. A Technical Lemma
  16. ...and 2 more sections

Key Result

Lemma 1

Under Assumption Ass-nonnegative, there exist a positive constant $k^{*}_1$ and a positive function $\phi_1(k_1)$ such that, for any $k_2>\phi_1(k_1)$ with $k_1>k^{*}_1$, the robust stabilization problem of the augmented system eq-augmented_system_transformed is solved by the following static state where $\gamma_s, s=0,1,\dots,r-2$, are positive constants such that the polynomial $f(\lambda)$ def

Figures (13)

  • Figure 1: The motor-driven system of one electric motor driving an uncertain shaft.
  • Figure 2: Plant output and reference signal under single motor operation.
  • Figure 3: The motor-driven system of five electric motors collectively driving a common uncertain shaft.
  • Figure 4: Communication network of five actuators.
  • Figure 5: Plant output and reference signal with cooperative parallel operation of five electric motors.
  • ...and 8 more figures

Theorems & Definitions (15)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Remark 4
  • Remark 5
  • Lemma 3
  • Remark 6
  • ...and 5 more