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Hierarchical-type Model Predictive Control and Experimental Evaluation for a Water-Hydraulic Artificial Muscle with Direct Data-Driven Adaptive Model Matching

Satoshi Tsuruhara, Kazuhisa Ito

TL;DR

The work tackles the challenge of achieving high-precision displacement control for water-hydraulic artificial muscles, whose hysteresis complicates modeling. It introduces a hierarchical controller that marries DF-based adaptive FRIT (A-FRIT) inner-loop model matching with a model-predictive outer loop (FMPC), using a pseudo-linear PL model to enable input-constrained MPC while reducing dependence on prior data. Key contributions include integrating A-FRIT with FMPC to form A-FMPC, optimizing the PL time constant within E-FRIT, and demonstrating robustness across 36 experimental scenarios with varying pre-experiment data and design parameters. The findings indicate improved control performance, reduced sensitivity to initial conditions and prior data, and practical guidance for designing constraint-aware, data-driven predictive controllers for hysteretic actuators.

Abstract

High-precision displacement control for water-hydraulic artificial muscles is a challenging issue due to its strong hysteresis characteristics that is hard to be modelled precisely, and many control methods have been proposed. Recently, data-driven control methods have attracted much attention because they do not explicitly use mathematical models, making design much easier. In our previous work, we proposed fictitious reference iterative tuning (FRIT)-based model predictive control (FMPC), which combines data-driven and model-based methods for the muscle and showed its effectiveness because it can consider input constraints as well. However, the problem in which control performance strongly depends on prior input-output data remains still unsolved. Adaptive FRIT based on directional forgetting has also been proposed; however, it is difficult to achieve the desired transient performance because it cannot consider input constraints and there are no design parameters that directly determine the control performance, such as MPC. In this study, we propose a novel data-driven adaptive model matching-based controller that combines these methods. Experimental results show that the proposed method could significantly improve the control performance and achieve high robustness against inappropriate initial experimental data , while considering the input constraints in the design phase.

Hierarchical-type Model Predictive Control and Experimental Evaluation for a Water-Hydraulic Artificial Muscle with Direct Data-Driven Adaptive Model Matching

TL;DR

The work tackles the challenge of achieving high-precision displacement control for water-hydraulic artificial muscles, whose hysteresis complicates modeling. It introduces a hierarchical controller that marries DF-based adaptive FRIT (A-FRIT) inner-loop model matching with a model-predictive outer loop (FMPC), using a pseudo-linear PL model to enable input-constrained MPC while reducing dependence on prior data. Key contributions include integrating A-FRIT with FMPC to form A-FMPC, optimizing the PL time constant within E-FRIT, and demonstrating robustness across 36 experimental scenarios with varying pre-experiment data and design parameters. The findings indicate improved control performance, reduced sensitivity to initial conditions and prior data, and practical guidance for designing constraint-aware, data-driven predictive controllers for hysteretic actuators.

Abstract

High-precision displacement control for water-hydraulic artificial muscles is a challenging issue due to its strong hysteresis characteristics that is hard to be modelled precisely, and many control methods have been proposed. Recently, data-driven control methods have attracted much attention because they do not explicitly use mathematical models, making design much easier. In our previous work, we proposed fictitious reference iterative tuning (FRIT)-based model predictive control (FMPC), which combines data-driven and model-based methods for the muscle and showed its effectiveness because it can consider input constraints as well. However, the problem in which control performance strongly depends on prior input-output data remains still unsolved. Adaptive FRIT based on directional forgetting has also been proposed; however, it is difficult to achieve the desired transient performance because it cannot consider input constraints and there are no design parameters that directly determine the control performance, such as MPC. In this study, we propose a novel data-driven adaptive model matching-based controller that combines these methods. Experimental results show that the proposed method could significantly improve the control performance and achieve high robustness against inappropriate initial experimental data , while considering the input constraints in the design phase.
Paper Structure (13 sections, 1 theorem, 17 equations, 18 figures, 4 tables, 3 algorithms)

This paper contains 13 sections, 1 theorem, 17 equations, 18 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Overview of A-FRIT algorithm
  3. FRIT
  4. E-FRIT
  5. A-FRIT
  6. Proposed method
  7. PL model utilizing A-FRIT
  8. Adaptive model predictive controller design
  9. Experimental results and discussion
  10. Experimental setup
  11. Experimental conditions
  12. Experimental results
  13. Conclusion

Key Result

Lemma 1

Assume that there exists a controller parameter $\theta$ such that Then, by replacing the initial I/O data, $u_0(k)$ and $y_0(k)$ with I/O data, $u(k)$ and $y(k)$ for each time step, we obtain the convex evaluation function as follows: where regressor vector $\phi(k)\triangleq \beta(z)\{1-G_m(z)\}y(k)$ and the reference input $d(k)\triangleq G_m(z)u(k)$ are I/O data.

Figures (18)

  • Figure 1: Block diagram of the adaptive FRIT method
  • Figure 2: Conceptual diagram of direct data-driven adaptive model matching
  • Figure 3: Conceptual diagram of MPC design using PL model
  • Figure 4: Block diagram of control method; FRIT-based MPC (FMPC) and adaptive FRIT-based MPC (A-FMPC)
  • Figure 5: experimental circuit
  • ...and 13 more figures

Theorems & Definitions (9)

  • Lemma 1
  • Proof 1
  • Remark 1
  • Remark 2
  • Definition 1
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6