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Hybrid Control Technique for Switched LPV Systems and Its Application to Active Magnetic Bearing System

Fen Wu

TL;DR

The paper tackles stability and performance challenges in switched LPV systems experiencing large parameter variations, with a focus on active magnetic bearing (AMB) applications. It introduces a hybrid LPV control framework that combines hysteresis switching with a controller-state reset, formulating the synthesis as convex LMIs to jointly design region-specific gains and reset matrices. Lyapunov-based conditions guarantee stability under switching, while boundary conditions are convexified via an Elimination Lemma, reducing conservatism. Applied to AMBs, the approach partitions the speed range into overlapping regions, enabling tailored gains that improve high-speed disturbance rejection and reduce chattering, as demonstrated by simulations. The work offers a scalable method for robust gain-scheduling in fast-rotating machinery and sets the stage for extensions to flexible-mode AMB models and robust/hybrid design integrations.

Abstract

This paper proposes a novel hybrid control framework for switched linear parameter-varying (LPV) systems under hysteresis switching logic. By introducing a controller state-reset mechanism, the hybrid LPV synthesis problem is reformulated as a convex optimization problem expressed in terms of linear matrix inequalities (LMIs), enabling efficient computation of both switching LPV controller gains and reset matrices. The proposed approach is then applied to active magnetic bearing (AMB) systems, whose rotor dynamics exhibit strong dependence on rotational speed. Conventional LPV designs are often conservative due to large speed variations. The proposed hybrid gain-scheduled controller explicitly accounts for bounds on parameter variation rates, employs multiple LPV controllers over distinct operating regions, and uses hysteresis switching to reduce chattering and ensure stability. The effectiveness of the approach is demonstrated through a detailed AMB control design example.

Hybrid Control Technique for Switched LPV Systems and Its Application to Active Magnetic Bearing System

TL;DR

The paper tackles stability and performance challenges in switched LPV systems experiencing large parameter variations, with a focus on active magnetic bearing (AMB) applications. It introduces a hybrid LPV control framework that combines hysteresis switching with a controller-state reset, formulating the synthesis as convex LMIs to jointly design region-specific gains and reset matrices. Lyapunov-based conditions guarantee stability under switching, while boundary conditions are convexified via an Elimination Lemma, reducing conservatism. Applied to AMBs, the approach partitions the speed range into overlapping regions, enabling tailored gains that improve high-speed disturbance rejection and reduce chattering, as demonstrated by simulations. The work offers a scalable method for robust gain-scheduling in fast-rotating machinery and sets the stage for extensions to flexible-mode AMB models and robust/hybrid design integrations.

Abstract

This paper proposes a novel hybrid control framework for switched linear parameter-varying (LPV) systems under hysteresis switching logic. By introducing a controller state-reset mechanism, the hybrid LPV synthesis problem is reformulated as a convex optimization problem expressed in terms of linear matrix inequalities (LMIs), enabling efficient computation of both switching LPV controller gains and reset matrices. The proposed approach is then applied to active magnetic bearing (AMB) systems, whose rotor dynamics exhibit strong dependence on rotational speed. Conventional LPV designs are often conservative due to large speed variations. The proposed hybrid gain-scheduled controller explicitly accounts for bounds on parameter variation rates, employs multiple LPV controllers over distinct operating regions, and uses hysteresis switching to reduce chattering and ensure stability. The effectiveness of the approach is demonstrated through a detailed AMB control design example.
Paper Structure (6 sections, 1 theorem, 33 equations, 5 figures, 3 tables)

This paper contains 6 sections, 1 theorem, 33 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Hybrid LPV Control Approach
  3. AMB Control Case Study
  4. Rotor Dynamics Modeling
  5. Hybrid LPV Controller Design and Simulation
  6. Concluding Remarks

Key Result

Theorem 1

Consider the open-loop switched LPV system (eqn:lpvolp), the parameter set ${\cal P}$ and an overlapped covering $\left\{{\cal P}_i \right\}_{i \in Z_{N_p}}$. Suppose there exist continuously differentiable, positive definite matrix functions $R_i(\cdot), S_i(\cdot): \mathbf{R}^s \rightarrow \mathbf holds with performance level $\gamma_i > 0$ and for $\rho \in \mathcal{S}_{ij}$, there exist matric

Figures (5)

  • Figure 1: Hysteresis switching regions.
  • Figure 2: The proposed hybrid control scheme.
  • Figure 3: Weighted open-loop interconnection for the magnetic bearing system.
  • Figure 4: The performance of hybrid LPV controller for a time-varying rotor speed profile.
  • Figure 5: LPV controller activition sequence.

Theorems & Definitions (1)

  • Theorem 1