Lightly-damped System Research Articles

FRF estimation using multiple kernel-based regularisation

Nonparametric kernel-based modelling of dynamical systems offers important advantages over other nonparametric techniques; the estimate is a continuous function, the model complexity is continuously tuneable, and stability, causality and smoothness are imposed on the impulse response estimate. However, for lightly damped systems, most of the existing kernel-based approaches for estimating the impulse- or frequency response function fail because classical kernels are not appropriate for describing lowly damped resonances. Smoothness is imposed on the entire frequency axis with the diagonal correlated or stable spline kernel, with as a result that resonances cannot be captured well. By introducing the superposition of different kernels, carrying prior knowledge about the resonant poles of the system, we make the kernel-based modelling of lightly-damped systems possible with high-accuracy. We use a frequency domain local rational modelling technique as preprocessing step to determine the most dominant poles, and include these as prior knowledge in the kernels. The performance of the new kernel is demonstrated on a highly resonating simulated system and compared to the state of the art nonparametric frequency domain approaches.

Improved frequency response function estimation by Gaussian process regression with prior knowledge

Abstract Kernel-based modelling of dynamical systems offers important advantages such as imposing stability, causality and smoothness on the estimate of the model. Here, we improve the existing frequency domain kernel-based approach for estimating the transfer function of a linear time-invariant system from noisy data. This is done by introducing prior knowledge in the kernel. We use a local rational modelling technique to determine the most significant poles, and include these poles as prior knowledge in the kernel. This results in accurate models for the identification of lightly-damped systems.

Enhanced Positioning Bandwidth in Nanopositioners via Strategic Pole Placement of the Tracking Controller

Tracking triangular or staircase trajectories is a challenge for a piezo-driven nanopositioner due to vibration problems. The piezo-driven nanopositioner is a lightly-damped system because of its mechanical construction. These reference trajectories are high-frequency components that tend to excite the mechanical resonance of the nanopositioner, causing vibration and thus affecting the accuracy. The Integral Resonant Controller (IRC) is employed to damp the resonance and thereby furnish a larger gain margin for a high-gain tracking controller to be implemented. The IRC, however, introduces a low-frequency pole. Due to other control issues, such as hysteresis nonlinearity, Integral (I) or Proportional Integral (PI) tracking control is used as a tracking loop to address uncertainties (hysteresis). The traditional method using a PI controller has a limited positioning bandwidth. This paper presents the strategic zero placement of the PI controller to enhance the positioning bandwidth, thereby overcoming the limitations of tracking error. Using experimental validations to confirm the feasibility of the proposed method, it is shown that significant improvement regarding bandwidth and disturbance rejection are reported.

Frequency Domain Subspace Identification of Multivariable Dynamical Systems for Robust Control Design

Black-box system identification is subjected to the modelling uncertainties that are propagated from the non-parametric model of the system in time/frequency-domain. Unlike classical H1/H2 spectral analysis, in the recent robust Local Polynomial Method (LPM), the modelling variances are separated to noise contribution and nonlinear contribution while suppressing the transient noise. On the other hand, without an appropriate weighting on the objective function in the system identification methods, the acquired model is subjected to bias. Consequently, in this paper the weighted regression problem in subspace frequency-domain system identification is revisited in order to have an unbiased estimate of the frequency response matrix of a flexible manipulator as a multi-input multi-output lightly-damped system. Although the unbiased parametric model representing the best linear approximation (BLA) of the system in this combination is a reliable framework for the control design, it is limited for a specific signal-to-noise (SNR) ratio and standard deviation (STD) of the involved input excitations. As a result, in this paper, an additional step is carried out to investigate the sensitivity of the identified model w.r.t. SNR/STD in order to provide an uncertainty interval for robust control design.

A local rational model approach for [formula omitted] norm estimation: With application to an active vibration isolation system

Robust control design hinges on the availability of an accurate uncertainty model. The aim of this paper is to develop an approach for accurate uncertainty modeling. The proposed method is based on H∞-norm estimation, or peak amplitude. A new approach is developed that explicitly takes into account inter-grid frequency behavior while only requiring a reduced experiment time, modeling effort, and limited user intervention. In particular, the proposed method relies on local rational models. Experimental results on an active vibration isolation system confirm that the approach is able to handle lightly-damped systems with significantly less data compared to spectral estimation and local polynomial estimation techniques.

Internal Model Control of Lightly Damped Systems Subject to Periodic Exogenous Signals

This paper presents an internal model control (IMC) design for lightly-damped systems subject to periodic exogenous signals. For such systems, the conventional design of the so-called IMC filter in the IMC structure can result in oscillatory behavior even when the closed-loop transfer function is designed to be well damped. To circumvent this problem, several band-pass filters are incorporated into the IMC filter based on knowledge of the frequencies of the plant's resonance modes and exogenous signals. The track-following system of an optical disk drive is employed to illustrate the design of the proposed IMC filter. Experimental results confirm the effectiveness of the proposed design.