Tuning an adaptive controller using a robust control approach (original) (raw)

Adaptive control scheme using real time tuning of the parameter estimator

IEE Proceedings - Control Theory and Applications, 1997

The paper presents an adaptive controller for discrete-time systems, with parameters modelled as a Gauss-Markov process with an unknown noise covariance matrix. The cost function adopted in the optimisation of the control performance is the sum of the output variances up to A4 steps ahead in time. Optimal predictors are used to estimate the future outputs y(k + i), i = 1, 2, ..., M , that are needed in the solution of the optimisation problem that yields the value of the control signal at a given time k. The estimates for the system parameters are obtained using a Kalman filter, together with an algorithm to tune the covariance matrix in real time. The adaptation mechanism reduces the risk of divergence of the Kalman filter, as shown by simulation results that illustrate the actual performance of the new controller under uncertainty in the noise covariance matrix.

A new linear adaptive controller: design, analysis and performance

IEEE Transactions on Automatic Control, 2000

The certainty equivalence and polynomial approach, widely used for designing adaptive controllers, leads to "simple" adaptive control designs that guarantee stability, asymptotic error convergence, and robustness, but not necessarily good transient performance. Backstepping and tuning functions techniques, on the other hand, are used to design adaptive controllers that guarantee stability and good transient performance at the expense of a highly nonlinear controller. In this paper, we use elements from both design approaches to develop a new certainty equivalence based adaptive controller by combining backstepping based control law with a normalized adaptive law. The new adaptive controller guarantees stability and performance, as well as parametric robustness for the nonadaptive controller, that are comparable with the tuning functions scheme, without the use of higher order nonlinearities.

Concepts, methods and techniques in adaptive control

American Control Conference, 2002

This tutorial paper looks back at almost 50 years of adaptive control trying to establish how much more we need to be able to offer the industrial community an adaptive controller which will be used and referred to with the same ease as existing PID controllers. Since the first commercial adaptive controller, significant progress in the design and analysis of these controllers has been achieved. Various forms of adaptive controllers are now readily available targeting a significant range of industries from process to aerospace. A general overview of adaptive control will allow the reader to place on the map several industrial architectures for such controllers, all with the aim of bridging the gap between academic and industrial views of the topic. Such a presentation of design and analysis tools currently opens a more philosophical question "Has the critical mass in adaptive control been reached?".

Introduction to Adaptive Control 1.1 Adaptive Control—Why

Adaptive Control covers a set of techniques which provide a systematic approach for automatic adjustment of controllers in real time, in order to achieve or to maintain a desired level of control system performance when the parameters of the plant dynamic model are unknown and/or change in time. Consider first the case when the parameters of the dynamic model of the plant to be controlled are unknown but constant (at least in a certain region of operation). In such cases, although the structure of the controller will not depend in general upon the particular values of the plant model parameters, the correct tuning of the controller parameters cannot be done without knowledge of their values. Adaptive control techniques can provide an automatic tuning procedure in closed loop for the controller parameters. In such cases, the effect of the adaptation vanishes as time increases. Changes in the operation conditions may require a restart of the adaptation procedure. Now consider the case when the parameters of the dynamic model of the plant change unpredictably in time. These situations occur either because the environmental conditions change (ex: the dynamical characteristics of a robot arm or of a mechanical transmission depend upon the load; in a DC-DC converter the dynamic characteristics depend upon the load) or because we have considered simplified linear models for nonlinear systems (a change in operation condition will lead to a different linearized model). These situations may also occur simply because the parameters of the system are slowly time-varying (in a wiring machine the inertia of the spool is time-varying). In order to achieve and to maintain an acceptable level of control system performance when large and unknown changes in model parameters occur, an adaptive control approach has to be considered. In such cases, the adaptation will operate most of the time and the term non-vanishing adaptation fully characterizes this type of operation (also called continuous adaptation). Further insight into the operation of an adaptive control system can be gained if one considers the design and tuning procedure of the " good " controller illustrated in Fig. 1.1. In order to design and tune a good controller, one needs to:

Issues, progress and new results in robust adaptive control

International Journal of Adaptive Control and Signal Processing, 2006

We overview recent progress in the field of robust adaptive control with special emphasis on methodologies that use multiple-model architectures. We argue that the selection of the number of models, estimators and compensators in such architectures must be based on a precise definition of the robust performance requirements. We illustrate some of the concepts and outstanding issues by presenting a new methodology that blends robust nonadaptive mixed µ-synthesis designs and stochastic hypothesis-testing concepts leading to the so-called Robust Multiple Model Adaptive Control (RMMAC) architecture. A numerical example is used to illustrate the RMMAC design methodology, as well as its strengths and potential shortcomings. The later motivated us to develop a variant architecture, denoted as RMMAC/XI, that can be effectively used in highly uncertain exogenous plant disturbance environments. 00:0-0 Prepared using acsauth.cls 4 S. FEKRI, M. ATHANS, AND A. PASCOAL domain. Therefore, the adaptive design must explicitly reflect these frequency-domain bounds on the unmodeled dynamics. The presence of unmodeled dynamics immediately brings into sharp focus the fact that we must use the state-of-the-art in nonadaptive robust control synthesis, i.e. mixed-µ synthesis ; and associated Matlab software .

Performance Study of an Adaptive Controller in the Presence of Uncertainty

IEEE Transactions on Control Systems Technology, 2000

This letter addresses the performance study of an adaptive controller in the presence of gain and delay uncertainties. The nonlinearities in the controller presented here do not allow an analytical study of the effect of uncertainties on performance. A numerical study is done instead using the sampling, learning, prediction, and optimization capabilities of the software Global Optimization, Sensitivity and Uncertainty in Models (GoSUM).

Design of linear quadratic adaptive control: Theory and algorithms for practice

A linear quadratic gaussian adaptive digital controller based on recursively identified (multivariate) regression model is presented. Writing the paper the authors had in mind the basic question of a potential user: "How to use your controller in my specific problem?" That is why more attention than usually is devoted to the thorough problem fprmulation including motivations for the chosen methodology and description of head-stone algorithms for identification and control synthesis. To provide a feeling for the applicability range, brief information about related software as well as available practical experience is added.

Performance improvement in adaptive control of nonlinear systems

2009 American Control Conference, 2009

This paper demonstrates how the finite-time identification procedure [1] can be used to improve the overall performance of adaptive control systems. First, we develop an adaptive compensator which guarantees exponential convergence of the estimation error provided the integral of a filtered regressor matrix is positive definite. The approach does not involve online checking of matrix invertibility and computation of matrix inverse nor switching between parameter estimation methods. The convergence rate of the parameter estimator is directly proportional to the adaptation gain and a measure of the system's excitation. The adaptive compensator is then combined with existing adaptive controllers to guarantee exponential stability of the closed-loop system. The effectiveness of the proposed method is illustrated with simulation examples.