Mark Edward John Butcher

On the Consistency of Certain Identification Methods for Linear Parameter Varying Systems

The consistency of certain identification methods for Linear Parameter Varying systems is considered. More precisely, methods for the identification of SISO input-output models are analysed. In order to perform a consistency analysis the application of ergodicity is required, which is not obviously applicable with these types of time-varying systems. It is therefore shown that, when the scheduling parameter satisfies certain conditions, ergodicity type results can be applied to the methods considered. An analysis is then carried out for two cases: that of noise-free measurements of the scheduling parameter, and then the more realistic case of noisy scheduling parameter measurements. The latter is shown to be an errors-in-variables type problem. In both cases the least squares technique is shown to typically give biased estimates and the instrumental variables method is proposed as a way of resolving this. The analysis carried out is reinforced by results in simulation.

Linear Parameter-Varying Iterative Learning Control With Application to a Linear Motor System

In this paper, an iterative-learning-control (ILC) algorithm is proposed for a certain class of linear parameter-varying (LPV) systems whose dynamics change between iterations. Consistency of the algorithm in the presence of stochastic disturbances is shown. The proposed algorithm is tested in simulation and the obtained tracking performance is compared with that obtained using a standard linear time-invariant ILC algorithm. Better results are obtained using the proposed method. The method is also applied to a linear, permanent-magnet synchronous motor system, which is shown to be an LPV system for a specific class of movements. Greatly improved tracking is achieved.

A statistical analysis of certain iterative learning control algorithms

Iterative learning control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, first by a statistical analysis and then by simulation results and their application to a linear motor. New expressions for the expected value and variance of the controlled error are developed for each algorithm. The different algorithms are then tested in simulation and finally applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectra are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate.

Iterative Learning Control based on Stochastic Approximation

In this paper stochastic approximation theory is used to produce Iterative Learning Control (ILC) algorithms which are less sensitive to stochastic disturbances, a typical problem for the learning process of standard ILC algorithms. Two algorithms are developed, one to obtain zero mean controlled error and one to minimise the mean 2-norm of the controlled error. The former requires a certain knowledge of the system but in the presence of noise can give reasonably rapid convergence. The latter can either use a model or be model free by employing a second experiment.

Model-Free Precompensator Tuning Based on the Correlation Approach

High-performance output tracking can be achieved by precompensator or feedforward controllers based on the inverse of either the closed-loop system or the plant model, respectively. However, it has been shown that these inverse controllers can adversely affect the tracking performance in the presence of model uncertainty. In this paper, a model-free approach based on only one set of acquired data from a simple closed-loop experiment is used to tune the controller parameters. The approach is based on the decorrelation of the tracking error and the desired output and is asymptotically not sensitive to noise and disturbances. From a system identification point of view, the stable inverse of the closed-loop system is identified by an extended instrumental variable algorithm in the framework of errors-in-variables identification methods. By a frequency-domain analysis of the criterion, it is shown that the weighted two-norm of the difference between the controller and the inverse of the closed-loop transfer function can be minimized. The method is successfully applied to a high-precision position control system.

Model-Free Precompensator and Feedforward Tuning Based on the Correlation Approach

High performance output tracking can be achieved by precompensator or feedforward controllers based on the inverse of the closed-loop system or the plant model. However, it has been shown that these inverse controllers can affect adversely the tracking performance in the presence of model uncertainty. In this paper, a model-free approach based on only one set of acquired data from a simple closed-loop experiment is used to tune the controller parameters. The approach is based on the decorrelation of the tracking error and the desired output and is not asymptotically sensitive to noise and disturbances. By a frequency-domain analysis of the criterion, it is shown that the weighted two-norm of the difference between the controller and the inverse of the plant model (or the closed-loop transfer function) can be minimized. The method is successfully applied to a high precision position control system.

Data-driven precompensator tuning for linear parameter varying systems

Methods for direct data-driven tuning of the parameters of precompensators for LPV systems are developed. Since the commutativity property is not always satisfied for LPV systems, previously proposed methods for LTI systems that use this property cannot be directly adapted. When the ideal precompensator giving perfect mean tracking exists in the proposed parameterisation of the precompensator, the LPV transfer operators do commute and an algorithm using only two experiments on the real system is proposed. It is shown that this algorithm gives consistent estimates of the ideal parameters despite the presence of stochastic disturbances. For the more general case, when the ideal precompensator does not belong to the set of parameterised precompensators, another technique is developed. This technique requires a number of experiments equal to twice the number of precompensator parameters and it is shown that the calculated parameters minimise the mean squared tracking error.

A Comparison of Iterative Learning Control Algorithms with Application to a Linear Motor System

Iterative learning control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, firstly by a statistical analysis and then by their application to a linear motor. Expressions for the expected value and variance of the error are developed for each algorithm. The different algorithms are then applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectrums are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate

Linear Parameter Varying Iterative Learning Control

In this paper an Iterative Learning Control (ILC) algorithm is proposed for a certain class of Linear Parameter Varying (LPV) systems whose dynamics change between iterations. Consistency of the algorithm in the presence of stochastic disturbances is shown. The proposed algorithm is tested in simulation and the obtained tracking performance is compared with that obtained using a standard Linear Time Invariant ILC algorithm. Better results are obtained using the proposed method.

Iterative Learning Control Using Stochastic Approximation Theory with Application to a Mechatronic System

In this paper it is shown how Stochastic Approximation theory can be used to derive and analyse well-known Iterative Learning Control algorithms for linear systems. The Stochastic Approximation theory gives conditions that, when satisfied, ensure almost sure convergence of the algorithms to the optimal input in the presence of stochastic disturbances. The practical issues of monotonic convergence and robustness to model uncertainty are considered. Specific choices of the learning matrix are studied, as well as a model-free choice. Moreover, the model-free method is applied to a linear motor system, leading to greatly improved tracking.