Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Passive iFIR Filters for Data-Driven Control

Zixing Wang, Yongkang Huo, Fulvio Forni

TL;DR

This work tackles designing passive iFIR controllers that integrate an integrator with a passive FIR to achieve flexible, data-driven control without full plant models or large datasets. It extends virtual reference feedback tuning (VRFT) by enforcing passivity through three convex formulations: a KYP-based LMI, a Finite Toeplitz relaxation, and a positive-realness constraint on the FIR's frequency response, enabling scalable, guaranteed-stability design. The key contributions are the (i) integration of VRFT with passivity constraints, (ii) development of computationally efficient Toeplitz and PR-based methods, and (iii) demonstration on both linear and nonlinear plants showing accurate reference matching and stability where PID may underperform. The practical impact lies in providing a robust, data-efficient approach for passive control in robotics and electro-mechanical systems, with potential extensions to MIMO and nonlinear controllers.

Abstract

We consider the design of a new class of passive iFIR controllers given by the parallel action of an integrator and a finite impulse response filter. iFIRs are more expressive than PID controllers but retain their features and simplicity. The paper provides a model-free data-driven design for passive iFIR controllers based on virtual reference feedback tuning. Passivity is enforced through constrained optimization (three different formulations are discussed). The proposed design does not rely on large datasets or accurate plant models.

Passive iFIR Filters for Data-Driven Control

TL;DR

This work tackles designing passive iFIR controllers that integrate an integrator with a passive FIR to achieve flexible, data-driven control without full plant models or large datasets. It extends virtual reference feedback tuning (VRFT) by enforcing passivity through three convex formulations: a KYP-based LMI, a Finite Toeplitz relaxation, and a positive-realness constraint on the FIR's frequency response, enabling scalable, guaranteed-stability design. The key contributions are the (i) integration of VRFT with passivity constraints, (ii) development of computationally efficient Toeplitz and PR-based methods, and (iii) demonstration on both linear and nonlinear plants showing accurate reference matching and stability where PID may underperform. The practical impact lies in providing a robust, data-efficient approach for passive control in robotics and electro-mechanical systems, with potential extensions to MIMO and nonlinear controllers.

Abstract

We consider the design of a new class of passive iFIR controllers given by the parallel action of an integrator and a finite impulse response filter. iFIRs are more expressive than PID controllers but retain their features and simplicity. The paper provides a model-free data-driven design for passive iFIR controllers based on virtual reference feedback tuning. Passivity is enforced through constrained optimization (three different formulations are discussed). The proposed design does not rely on large datasets or accurate plant models.
Paper Structure (7 sections, 4 theorems, 23 equations, 7 figures, 1 table)

This paper contains 7 sections, 4 theorems, 23 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data-driven design of iFIR controllers
  3. Passive iFIR controllers
  4. Examples
  5. Fitting of passive FIR filters
  6. Velocity control of a compliant mechanical system
  7. Conclusions

Key Result

Theorem III.1

Given the iFIR eq:sec2-9-d of order $m$, consider the state-space realization of the FIR part where $w(t),z(t)$ are the input and output of the FIR part.$A_{c}\in \mathbb{R}^{m-1 \times m-1},B_{c} \in \mathbb{R}^{m-1} ,C_{c} \in \mathbb{R}^{m-1},D_{c} \in \mathbb{R}$ are given by The optimal iFIR controller given by eq:vrft_obj constrained to the following LMIs in the unknown $X\in \mathbb{R}^{

Figures (7)

  • Figure 1: Block diagram of the closed-loop system.
  • Figure 2: Nyquist diagrams of Example \ref{['sec:example1']}. Blue - target filter; black - identified passive FIR filter. Top: $C_1$ (left), $C_1$ and excess of passivity (right). Bottom: $C_2$ (left), $C_3$ (right).
  • Figure 3: A compliant two-cart system.
  • Figure 4: Nyquist plots of the FIR part of the iFIR controller. Blue - unconstrained \ref{['eq:vrft_obj']}; black - constrained \ref{['eq:vrft_obj']}, \ref{['eq:toeplitz_constr']}. Left: $M_{r1}$; Right: $M_{r2}$.
  • Figure 5: Step responses. Red: target response. Black: closed-loop response with passive iFIR controller \ref{['eq:vrft_obj']}, \ref{['eq:toeplitz_constr']}. Blue-continuous: closed-loop response with PID. Blue-dashed: open loop. Left: $M_{r1}$; Right: $M_{r2}$.
  • ...and 2 more figures

Theorems & Definitions (10)

  • Theorem III.1: KYP approach
  • proof
  • Theorem III.2: Infinite Toeplitz approach
  • proof
  • Theorem III.3: Finite Toeplitz approach
  • proof
  • Theorem III.4: Positive realness approach
  • proof
  • Remark III.5
  • Remark III.6