Finite-horizon integration for continuous-time identification: bias analysis and application to variable stiffness actuators

ABSTRACT

Direct identification of continuous-time dynamical models from sampled data is now a mature discipline, which is known to have many advantages with respect to indirect approaches based on the identification of discretised models. This paper faces the problem of continuous-time identification of linear time-invariant systems through finite-horizon numerical integration and least-square estimation. The bias in the least-squares estimator due to the noise corrupting the signal observations is quantified, and the benefits of numerical integration in the attenuation of this bias are discussed. An extension of the approach which combines numerical integration, least-squares estimation and particle swarm optimisation is proposed for the identification of nonlinear systems and nonlinear-in-the-parameter models, and then applied to the estimation of the torque-displacement characteristic of a commercial variable stiffness actuator driving a one-degree-of-freedom pendulum.

Keywords:

• Continuous-time identification
• least-squares methods
• parameter estimation
• variable stiffness actuators

Acknowledgments

The author is grateful to qb-robotics s.r.l. for providing the laboratory equipments used in the experimental case study.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 An improper choice of the instruments might lead to high-variance estimates of the model parameters (Söderström & Stoica, 1983).

2 The signals $u\left(t\right)$ and $x\left(t\right)$ are assumed to be sampled at a regular interval just to keep the notation simple. Nevertheless, the identification algorithm discussed in the paper can be also applied to the case of non-uniformly sampled data.