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Identification of Additive Continuous-time Systems in Open and Closed loop

Rodrigo A. González, Koen Classens, Cristian R. Rojas, James S. Welsh, Tom Oomen

Abstract

When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system. Traditional linear system identification may not consider the most parsimonious model when relying solely on unfactored transfer functions, which typically result from standard direct approaches. This paper presents a novel identification method that delivers additive models for both open and closed-loop setups. The estimators that are derived are shown to be generically consistent, and can admit the identification of marginally stable additive systems. Numerical simulations show the efficacy of the proposed approach, and its performance in identifying a modal representation of a flexible beam is verified using experimental data.

Identification of Additive Continuous-time Systems in Open and Closed loop

Abstract

When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system. Traditional linear system identification may not consider the most parsimonious model when relying solely on unfactored transfer functions, which typically result from standard direct approaches. This paper presents a novel identification method that delivers additive models for both open and closed-loop setups. The estimators that are derived are shown to be generically consistent, and can admit the identification of marginally stable additive systems. Numerical simulations show the efficacy of the proposed approach, and its performance in identifying a modal representation of a flexible beam is verified using experimental data.
Paper Structure (14 sections, 6 theorems, 71 equations, 6 figures)

This paper contains 14 sections, 6 theorems, 71 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System and Model Setup
  3. Stationary Points for Additive Continuous-time System Identification
  4. Open-loop setting
  5. Closed-loop setting
  6. Additive System Identification: An Instrumental Variable Solution
  7. Derivation of the instrumental variable solution
  8. Consistency Analysis
  9. Simulations
  10. Open-loop Experiment
  11. Closed-loop Experiment
  12. Experimental Validation
  13. Conclusions
  14. Technical Lemma

Key Result

Lemma 1

Assume that the instrument vector $\bm{\zeta}(t_k)$ is uncorrelated with the output noise $v(t_k)$, and that $r(t_k)$ and $v(t_l)$ are quasi-stationary and mutually independent for all integers $k$ and $l$. Then, the estimator betacl is generically consistent if $\overline{\mathbb{E}}\left\{\bm{\zet

Figures (6)

  • Figure 1: Block diagrams for the open (a) and closed-loop (b) settings studied in this paper.
  • Figure 2: Bode plot of the open-loop continuous-time system under study.
  • Figure 3: Mean square error of the DC gain estimates with respect to the sample size $N$, open-loop identification. The proposed method delivers parameter estimates with less MSE for $b_{2,0}$ and $b_{3,0}$, while having similar performance to the SRIVC estimator in the other parameters.
  • Figure 4: Mean square error of the system parameter estimates with respect to the sample size $N$, closed-loop identification. All estimators give consistent estimates, and the proposed method gives the least mean-square error for every parameter.
  • Figure 5: Prototype experimental flexible beam setup. The moving part is indicated by ⓐ and is suspended by wire flexures ⓑ. The deflection is measured with five contactless fiber optic sensors, of which middle sensor is used ⓒ and the setup is actuated with three current-driven voice coils of which the middle actuator used ⓓ.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Lemma 2
  • Theorem 2
  • Lemma 3: Generic Nonsingularity