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Multi-Objective Complementary Control

Jiapeng Xu, Xiang Chen, Ying Tan, Kemin Zhou

Abstract

This paper proposes a novel multi-objective control framework for linear time-invariant systems in which performance and robustness can be achieved in a complementary way instead of a trade-off. In particular, a state-space solution is first established for a new stabilizing control structure consisting of two independently designed controllers coordinated with a Youla-type operator ${\bm Q}$. It is then shown by performance analysis that these two independently designed controllers operate in a naturally complementary way for a tracking control system, due to the coordination function of ${\bm Q}$ driven by the residual signal of a Luenberger observer. Moreover, it is pointed out that ${\bm Q}$ could be further optimized with an additional gain factor to achieve improved performance, through a data-driven methodology for a measured cost function.

Multi-Objective Complementary Control

Abstract

This paper proposes a novel multi-objective control framework for linear time-invariant systems in which performance and robustness can be achieved in a complementary way instead of a trade-off. In particular, a state-space solution is first established for a new stabilizing control structure consisting of two independently designed controllers coordinated with a Youla-type operator . It is then shown by performance analysis that these two independently designed controllers operate in a naturally complementary way for a tracking control system, due to the coordination function of driven by the residual signal of a Luenberger observer. Moreover, it is pointed out that could be further optimized with an additional gain factor to achieve improved performance, through a data-driven methodology for a measured cost function.
Paper Structure (11 sections, 6 theorems, 91 equations, 17 figures, 1 table)

This paper contains 11 sections, 6 theorems, 91 equations, 17 figures, 1 table.

Table of Contents

  1. Introduction
  2. Motivation
  3. Two-Controller Structure
  4. Two-controller structure with shared observer
  5. Two-controller structure with static controllers
  6. Multi-Objective Complementary Control (MOCC)
  7. Performance analysis
  8. A specific MOCC design: LQ tracking (LQT) $+\mathcal{H}_{\infty}$
  9. Data-driven Optimization of Performance
  10. Example
  11. Conclusion

Key Result

Proposition 1

Given two arbitrarily designed stabilizing controllers $\bm{C}$ in (xc) and $\bm{K}$ in (xk) and letting $L$ and $L_c$ be any matrices such that both $A+LC_2$ and $A_c+L_cC_c$ are stable, then a stable ${\bm Q}$ in (xq) can be realized with such that $\bm {K_{CQ}}$ in (KCQ) is stabilizing and $\bm{K_{CQ}}(s)=\bm{K}(s)$.

Figures (17)

  • Figure 1: Tracking control system.
  • Figure 2: Generalized internal model control (GIMC) structure.
  • Figure 3: A GIMC implementation of 2DOF controller.
  • Figure 4: Two-controller structure.
  • Figure 5: Two-controller structure with shared observer.
  • ...and 12 more figures

Theorems & Definitions (17)

  • Remark 1
  • Proposition 1
  • Remark 2
  • Remark 3
  • Proposition 2: Shared Observer
  • Remark 4
  • Proposition 3: Static Controller
  • Remark 5
  • Definition 1: zhou1994mixed
  • Lemma 1
  • ...and 7 more