Selecting uncertainty structures in identification for robust control with an automotive application

The selection of uncertainty structures is an important aspect in system identification for robust control. The aim of this paper is to investigate the consequences for multivariable systems. Hereto, first a theoretical analysis is performed that establishes the connection between the associated model set and the robust control criterion. Second, an experimental case study for an automotive application confirms these connections. In addition, the experimental results provide new insights in the shape of associated model sets by using a novel validation procedure. Finally, the improved connections are confirmed through a robust controller synthesis. Both the theoretical and experimental results confirm that a recently developed robust-control-relevant uncertainty structure outperforms general dual-Youla-Kucera uncertainty, which in turn outperforms traditional uncertainty structures, including additive uncertainty

Control design in Hankel Iterative Learning Control

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Hankel Iterative Learning Control for residual vibration suppression with MIMO flexible structure experiments

In this paper, we consider residual vibration suppression in flexible structures performing a point-to-point motion, based on Hankel ILC. Initially, design freedom in Hankel ILC is discussed, including different choices for the actuation time window and the observation time window. Subsequently, a three input three output flexible beam is presented as an experimental setup for Hankel ILC. The different practical and theoretical issues related to implementation of Hankel ILC on the setup are discussed extensively. Thereby, versatility in the choice for the time windows is shown to be essential for a successful implementation. Experimental results illustrate the capability of Hankel ILC to suppress the residual vibrations in the flexible beam

Non-parametric identification of higher order sinusoidal output describing functions

In this paper the concept of the Higher Order Sinusoidal Output Describing Functions (HOSODF) is presented. HOSODF can be defined for the class of causal, stable, time invariant non-linear systems which give a sinusoidal response to a specific harmonic excitation. The HOSODF relate the magnitude and phase of the individual harmonics, which together compose that specific input signal, to the sinusoidal output signal of such a system. HOSODF are the dual of the Higher Order Sinusoidal Input Describing Functions (Nuij 2006). Like the HOSIDF, the HOSODF are the results of an extension of linear techniques towards non-linear systems analysis. Using the HOSODF, the non-linear systems under investigation can be modeled as a cascade of the HOSODF and a Virtual Harmonics Compressor (VHC). The VHC is defined as a non-linear component which transforms a harmonic input signal ¿(t) into a sinusoidal output signal y(t) with frequency ¿, amplitude â and phase f. This input signal ¿(t) consists of an infinite amount of harmonics of the output signal y(t) with frequency n¿, amplitude â and phase nf with n=0,1,…8. Special attention is paid to the non-parametric identification of the HOSODF. The identification requires control of the frequency and amplitude of the sinusoidal output of the system within its domain of possible sinusoidal output signals. This specific state of these non-linear systems can be reached by incorporating the system under test in a feedback loop. In this loop the desired sinusoidal output is defined as the control objective of a dedicated repetitive controller consisting of a memory loop with positive feedback. The design of the learning filter required for stability is also addressed. As a spinoff of the identification technique, the authors see opportunities for advanced non-linear control of shaker systems aimed at sinusoidal excitation of non-linear systems

Non-parametric identification of higher order sinusoidal output describing functions

In this paper the concept of the Higher Order Sinusoidal Output Describing Functions (HOSODF) is presented. HOSODF can be defined for the class of causal, stable, time invariant non-linear systems which give a sinusoidal response to a specific harmonic excitation. The HOSODF relate the magnitude and phase of the individual harmonics, which together compose that specific input signal, to the sinusoidal output signal of such a system. HOSODF are the dual of the Higher Order Sinusoidal Input Describing Functions (Nuij 2006). Like the HOSIDF, the HOSODF are the results of an extension of linear techniques towards non-linear systems analysis. Using the HOSODF, the non-linear systems under investigation can be modeled as a cascade of the HOSODF and a Virtual Harmonics Compressor (VHC). The VHC is defined as a non-linear component which transforms a harmonic input signal ¿(t) into a sinusoidal output signal y(t) with frequency ¿, amplitude â and phase f. This input signal ¿(t) consists of an infinite amount of harmonics of the output signal y(t) with frequency n¿, amplitude â and phase nf with n=0,1,…8. Special attention is paid to the non-parametric identification of the HOSODF. The identification requires control of the frequency and amplitude of the sinusoidal output of the system within its domain of possible sinusoidal output signals. This specific state of these non-linear systems can be reached by incorporating the system under test in a feedback loop. In this loop the desired sinusoidal output is defined as the control objective of a dedicated repetitive controller consisting of a memory loop with positive feedback. The design of the learning filter required for stability is also addressed. As a spinoff of the identification technique, the authors see opportunities for advanced non-linear control of shaker systems aimed at sinusoidal excitation of non-linear systems

A robust-control-relevant perspective on model order selection

Abstract onl

Aliasing of Resonance Phenomena in Sampled-Data Feedback Control Design: Hazards, Modeling, and a Solution

High-performance control design for electromechanical sampled-data systems with aliased plant dynamics is investigated. Though from a theoretical viewpoint the aliasing phenomenon is automatically handled by direct sampled-data control, such an approach cannot be used in conjunction with models derived through system identification. From a practical viewpoint, aliasing is often considered as an undesirable phenomenon and a typical remedy is the increase of the sampling frequency. However, the sampling frequency is upper bounded due to physical and economical constraints and aliasing may be inevitable. Control design for plants with aliased dynamics has not received explicit attention in the literature and it is not clear how to handle this situation. In this paper, it is shown that aliased resonance phenomena can effectively be suppressed in sampled-data feedback control design without the need for increasing the sampling frequency. Furthermore, it is shown experimentally on an industrial wafer stage that ignoring aliasing during control design can have a disastrous effect on closed-loop performance. Additionally, a novel, practically feasible procedure for identification of (possibly aliased) resonance phenomena based on multirate system theory is proposed

Approximate realization with time delay

This paper describes the application of an approximate realization algorithm to dynamical systems with a time delay. First, a well-known algorithm is presented to obtain an approximate realization from an impulse response sequence. Then the limitation that a time delay imposes on the accuracy of this algorithm is discussed, and it is pointed out that time delays should be explicitly taken into account. Therefore, a time delay estimation method is proposed that utilizes the presented approximate realization algorithm. Simulation results show that the method is likely to provide an accurate estimate for the time delay in a dynamical syste