Time-frequency analysis of a motion system with learning control

Rotariu, I.; Ellenbroek, Rogier; Steinbuch, M Maarten

doi:10.1109/acc.2003.1244131

Cited by 20 publications

(15 citation statements)

References 6 publications

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“…This paper proposes a solution for reducing the dependency of the learned feedforward signal on the reference setpoint. In [8] and [9], we show that the proposed method does not lead to noise amplification. The final problem, position-dependent behavior, is addressed in [10] and [11].…”

Section: Introductionmentioning

confidence: 84%

Adaptive Iterative Learning Control for High Precision Motion Systems

Rotariu

Steinbuch

Ellenbroek

2008

IEEE Trans. Contr. Syst. Technol.

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Abstract-Iterative learning control (ILC) is a very effectivetechnique to reduce systematic errors that occur in systems that repetitively perform the same motion or operation. However, several characteristics have prevented standard ILC from being widely used for high precision motion systems. Most importantly, the learned feedforward signal depends on the motion profile (setpoint trajectory) and if this is altered, the learning process has to be repeated. Secondly, ILC amplifies non-repetitive disturbances and noise. Finally, its performance may be limited due to position-dependent dynamics. This paper presents the design and implementation of a time-frequency adaptive ILC that is applicable for motion systems which executes the same motion or operation. It employs the same control system block diagram as standard ILC, but instead of a fixed robustness filter it uses a time-varying filter. By using the results of the time-frequency adaptive ILC, i.e., the shape of the learned feedforward signal, a "piecewise ILC" is proposed that leads to the design of a single learned feedforward signal suitable for different setpoints. The results are experimentally shown to work for a high precision motion system.

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Section: Introductionmentioning

confidence: 84%

Adaptive Iterative Learning Control for High Precision Motion Systems

Rotariu

Steinbuch

Ellenbroek

2008

IEEE Trans. Contr. Syst. Technol.

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“…Zhang et al proposed a cutoff-frequency phase-in method [15]. Adaptive schemes of cutoff frequency are also proposed in frequency domain [11], [16]- [18] to improve performance. In [16], an iteration varying filter method is presented but the performance of this scheme heavily depends on system model.…”

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confidence: 99%

“…In [16], an iteration varying filter method is presented but the performance of this scheme heavily depends on system model. In [11], [17], [18], continuous Wigner transform is used to analyze the signal. Chen et al [11] is a pioneering work in introducing time-frequency domain analysis into ILC.…”

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confidence: 99%

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Wavelet Transform-Based Frequency Tuning ILC

Zhang

Wang

2005

IEEE Trans. Syst., Man, Cybern. B

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Abstract-In this paper, a discrete wavelet transform-based cutoff frequency tuning method is proposed and experimental investigation is reported. In the method, discrete wavelet packet algorithm, as a time-frequency analysis tool, is employed to decompose the tracking error into different frequency regions so that the maximal error component can be identified at any time step. At each time step, the passband of the filter is from zero to the upper limit of frequency region where the maximal error component resides. Hence, the filter is a function of time as well as index of cycle. The experimental results show that this method can suppress higher frequency error components at proper time steps. While at the time steps where the major tracking error falls into lower frequency range, the cutoff frequency of the filter is set lower to reduce the influence of noises and uncertainties. This way, learning transient and long-term stability can be improved.Index Terms-Cutoff frequency tuning, discrete wavelet packet algorithm, distribution index, iterative learning control (ILC).

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“…These shortcomings can be improved using time-frequency analysis of the feedforward signal [28,41]. The high energy of the error signal is concentrated very locally in time, the learning process outside these intervals leads to an amplification of the present noise.…”

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confidence: 99%

Iterative learning control with wavelet filtering

Merry

Molengraft

Steinbuch

2007

Intl J Robust & Nonlinear

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SummaryIterative learning control (ILC) has proven to be a powerful method to derive a high performance feedforward signal for systems that perform repetitive tasks. The feedforward signal is derived through several iterations, based on the tracking error of a feedback controlled system. In practical applications, the tracking error consists of a repetitive part and a non-repetitive part. ILC only compensates for the repetitive part of the error. The non-repetitive part also enters the learning scheme and affects the tracking performance. The problem definition of this thesis is defined as:Determine how non-repetitive errors affect the tracking error and the learned feedforward signal of ILC and design a method to eliminate the effect of non-repetitive errors.An expression for the tracking error of an arbitrary iteration is derived as a function of the reference, load disturbances and measurement disturbances. With this expression, the influence of disturbances on ILC can be analyzed. The expression also shows the influence of model uncertainties on the tracking error. The disturbances of the last two iterations appear to have the greatest influence on the tracking error, earlier disturbances only have a limited affect on the tracking error.In order to reduce the effect of disturbances, three filtering methods are developed. The filtering methods are based on the discrete wavelet transform (DWT). The DWT decomposes a signal into wavelet coefficients in various frequency bands. From these wavelet coefficients, the original signal can be reconstructed again. The DWT performs a local time-frequency decomposition. The nonrepetitive part of the disturbances can be removed by changing the wavelet coefficients, i.e. the frequency content of the signal at specific time instants. The designed wavelet filtering methods calculate a measure for the similarity between two sets of wavelet coefficients at an equal iteration of ILC. The repetitive part of the error results in equal wavelet coefficients, the non-repetitive part in different wavelet coefficients. The repetitive part is identified by adjusting the wavelet coefficients based on thresholding of the similarity measure. The adjusted wavelet coefficients are used to reconstruct a disturbance free error signal, which is the input for ILC.The wavelet filtering methods differ in the amount of simulations/experiments (runs) required each iteration of ILC and the way the error signals are obtained. The first method uses two runs each iteration. The two error signals are decomposed into two sets of wavelet coefficients which are used to calculated the similarity measure. The second method is recursive and performs only one run each iteration. The second error signal is constructed using the error of the previous iteration and the feedforward update signal of the present iteration, which is linear filtered with a model of the process sensitivity. For the third method, four runs are performed each iteration, which makes it possible to calculate two similarity criteria and to b...

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Time-frequency analysis of a motion system with learning control

Cited by 20 publications

References 6 publications

Adaptive Iterative Learning Control for High Precision Motion Systems

Adaptive Iterative Learning Control for High Precision Motion Systems

Wavelet Transform-Based Frequency Tuning ILC

Iterative learning control with wavelet filtering

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