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Energy-Based Control Approaches for Weakly Coupled Electromechanical Systems

N. Javanmardi, P. Borja, M. J. Yazdanpanah, J. M. A. Scherpen

TL;DR

This work addresses regulation and trajectory tracking for weakly coupled electromechanical systems by casting the dynamics in a port-Hamiltonian framework and applying Lyapunov and contraction theory to derive static, PDE-free energy-shaping controllers. A key novelty is the introduction of coupled damping, which injects energy dissipation between mechanical and electrical subsystems to improve transient performance without requiring coordinate transformations. The paper develops two regulation schemes and two tracking schemes for different damping regimes, all under a contractive-system perspective, and demonstrates their effectiveness on MEMS/MagLev-inspired simulations. The results offer a practically relevant, physically interpretable approach to stabilizing and guiding EM devices while avoiding PDE solvers and dynamic extensions. These contributions have potential impact on MEMS actuators, magnetic levitation systems, and other weakly coupled EM technologies where robust, simple controller design is critical.

Abstract

This paper addresses the regulation and trajectory-tracking problems for two classes of weakly coupled electromechanical systems. To this end, we formulate an energy-based model for these systems within the port-Hamiltonian framework. Then, we employ Lyapunov theory and the notion of contractive systems to develop control approaches in the port-Hamiltonian framework. Remarkably, these control methods eliminate the need for solving partial differential equations or implementing any change of coordinates and are endowed with a physical interpretation. We also investigate the effect of coupled damping on the transient performance and convergence rate of the closed-loop system. Finally, the applicability of the proposed approaches is illustrated in two applications of electromechanical systems via simulations.

Energy-Based Control Approaches for Weakly Coupled Electromechanical Systems

TL;DR

This work addresses regulation and trajectory tracking for weakly coupled electromechanical systems by casting the dynamics in a port-Hamiltonian framework and applying Lyapunov and contraction theory to derive static, PDE-free energy-shaping controllers. A key novelty is the introduction of coupled damping, which injects energy dissipation between mechanical and electrical subsystems to improve transient performance without requiring coordinate transformations. The paper develops two regulation schemes and two tracking schemes for different damping regimes, all under a contractive-system perspective, and demonstrates their effectiveness on MEMS/MagLev-inspired simulations. The results offer a practically relevant, physically interpretable approach to stabilizing and guiding EM devices while avoiding PDE solvers and dynamic extensions. These contributions have potential impact on MEMS actuators, magnetic levitation systems, and other weakly coupled EM technologies where robust, simple controller design is critical.

Abstract

This paper addresses the regulation and trajectory-tracking problems for two classes of weakly coupled electromechanical systems. To this end, we formulate an energy-based model for these systems within the port-Hamiltonian framework. Then, we employ Lyapunov theory and the notion of contractive systems to develop control approaches in the port-Hamiltonian framework. Remarkably, these control methods eliminate the need for solving partial differential equations or implementing any change of coordinates and are endowed with a physical interpretation. We also investigate the effect of coupled damping on the transient performance and convergence rate of the closed-loop system. Finally, the applicability of the proposed approaches is illustrated in two applications of electromechanical systems via simulations.
Paper Structure (18 sections, 5 theorems, 75 equations, 4 figures)

This paper contains 18 sections, 5 theorems, 75 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Contractive pH systems
  4. Modeling and Problem Formulation
  5. Closed-loop system with coupled damping
  6. Set-point Regulation Control Design
  7. Regulation for EM systems with only partial mechanical damping
  8. Regulation for EM systems with only partial or no mechanical damping
  9. Tracking control design
  10. Tracking for EM systems with only partial mechanical damping
  11. Tracking for EM systems with only partial or no mechanical damping
  12. Coupled damping and performance assessment
  13. Simulation
  14. Micro electro-mechanical optical switch
  15. Regulation
  16. ...and 3 more sections

Key Result

Theorem 1

Consider the following system with $\mathcal{F}_{\tt d}\triangleq \mathcal{J}_{\tt d}-\mathcal{R}_{\tt d}$, where $\mathcal{J}_{\tt d}=-\mathcal{J}^\top_{\tt d}$ and $\mathcal{R}_{\tt d}=\mathcal{R}^\top_{\tt d}\succeq 0$ are the desired constant interconnection and damping matrices, respectively. The system closed sys is contra

Figures (4)

  • Figure 1: $q(t)$ converges to the desired position $q_{\tt d}$ for the initial condition $[15\times 10^{-6},\ 0,\ 0 ]^\top$ via control \ref{['eq:c1']} without and with the coupled damping, respectively.
  • Figure 2: $q(t)$ exponentially tracks the signal $q^\star(t)$ for the initial condition $[15\times 10^{-6},\ 0,\ 0 ]^\top$ via tracking control \ref{['eq:u1-track']} without and with the coupled damping, respectively .
  • Figure 3: $q(t)$ exponentially tracks the signal $q^\star(t)$ via tracking controller \ref{['eq:controlmaglv']} without and with the coupled damping, and different electrical damping ($\bar{R}_{\tt e1}<\bar{R}_{\tt e2}$).
  • Figure 4: $\mathcal{L}_2$-norms of the error for four different cases (upper plot). The control signal plot (bottom left) corresponds to Case 3. The error signals are depicted in the plot at the bottom right.

Theorems & Definitions (13)

  • Definition 1
  • Theorem 1: yaghmaei2017trajectory
  • Remark 1
  • Proposition 1
  • Proposition 2
  • Remark 2
  • Remark 3
  • Theorem 2
  • Remark 4
  • Theorem 3
  • ...and 3 more