Relative Dead Zone Research Articles

Application of augmented UD identification with selective forgetting in an adaptive control loop

Robustness of parameter estimator plays a vital role in adaptive controllers. A modified identification algorithm is proposed based on the augmented UD identification (AUDI) primary version. Augmented UD identification with selective forgetting (AUDSF) method is derived as a robust derivation of AUDI to be integrated with input-output data filtering, relative dead zone, and data normalisation features. AUDSF is incorporated by generalised predictive controller (GPC) strategy to produce an applicable adaptive control method. The comparative performances of the developed approach have been explored on two-mass spring challenging benchmark problem, which demonstrates its excellent behaviour under conducted parameter and disturbance uncertainty scenarios.

Robust Self-Tuning Regulator of Time-Varying Linear Systems with Bounded External Disturbances

robust self-tuning regulator of a class of linear systems, which can be described by the input-output Auto-Regressive Moving Average with exogenous (ARMAX) mathematical model with unknown and time-varying parameters, at bounded external disturbances is developed. A scheme of polynomial approximation has been applied to approximate the unknown and time-varying parameters of systems. The modified recursive extended least squares RELS estimation algorithm with a relative dead zone is proposed and applied to estimate the unknown and time-varying parameters intervening in the ARMAX mathematical model. The formulation of the explicit schemes of self-tuning regulation problem is resolved by using the minimum variance output or the generalized minimum variance output. The obtained control law, which is an optimal solution of minimizing a correspondent criterion, permit to reduce the effect of noise upon the output of system. An example of numerical simulation illustrates the effectiveness of the explicit schemes of self-tuning regulator and presents the performances by using the modified recursive extended least squares estimation algorithm with a relative dead zone in a step of the parametric estimation of a linear time-varying systems.

Robust adaptive control of linear time-delay systems with point time-varying delays via multiestimation

This paper presents an adaptive pole-placement based controller for continuous-time linear systems with unknown and eventually time-varying point delays under uncertainties consisting of unmodeled dynamics and eventual bounded disturbances. A multiestimation scheme is designed for improving the identification error performance and then to deal with possibly errors between the true basic delay compared to that used in regressor vector of measurements of the adaptive scheme and also to prevent the closed-loop system against potential instability. Each estimation scheme in the parallel disposal possesses a relative dead-zone which freezes the adaptation process for small sizes of the adaptation error compared to the estimated size of the absolute value of the contribution of the uncertainties to the filtered output versus time. All the estimation schemes run in parallel but only that which is currently in operation parameterizes the adaptive controller to generate the plant input at each time. A supervisor chooses the appropriate estimator in real time which respects a prescribed minimum residence time at each estimation algorithm in operation. That strategy is the main tool used to ensure the closed-loop stability under estimates switching. The relative dead-zone in the adaptation mechanism prevents the closed-loop system against potential instability caused by uncertainties.

Adaptive control of time‐invariant systems with discrete delays subject to multiestimation

This paper deals with a robustly stable adaptive pole‐placement‐based controller for time‐delay linear systems with unknown point delays within known intervals of sufficiently small lengths under unmodeled dynamics and bounded disturbances. A multiestimation scheme is used to improve the identification error and then to deal with possible errors between the true basic delays compared to that used in the regressor of the adaptive scheme. Each estimation scheme possess a relative dead zone for each estimation scheme which freezes the adaptation for small sizes of the adaptation error compared with the estimated size of the contribution of the uncertainties to the filtered output. All the estimation schemes run in parallel but only that, which is currently in operation, parameterizes the adaptive controller to generate the plant input at each time. A supervisory scheme chooses in real time the appropriate estimator subject to a minimum residence time which is the tool to ensure closed‐loop stability under switching between the estimators in the estimation scheme. The dead zone adaptation mechanism prevents the closed‐loop system against potential instability caused by uncertainties.

Robust stable pole-placement adaptive control of linear systems with multiestimation

This paper is concerned with a robust pole placement-based adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics with the use of multiple estimation schemes working in parallel. The multiestimation scheme consists of the above set of various single estimation schemes while being a tool used to minimize the plant identification error by building an estimate which is a convex combination of the estimates at all time. The weighting functions of the individual estimates are provided at each time by a suboptimization scheme for a quadratic loss function The robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise.

Robustly stable pole-placement based adaptive control of continuous linear systems with multiestimation

This paper deals with the pole-placement type robust adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics with the use of multiple estimation schemes working in parallel. The multiestimation scheme consisting of the above set of various single estimation schemes is a tool used to minimize the plant identification error by building an estimate which is a convex combination of the estimates at all time. The weighting functions of the individual estimates are provided at each time by a suboptimization scheme for a quadratic loss function of a possibly filtered tracking error and/or control input. The robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise. The basic results are derived for two different estimation strategies which have either a shared regressor with the plant or individual regressors for the input contribution and its relevant time-derivatives. In this second case, the plant input is obtained through a similar convex combination rule as the one used for the estimators in the first approach. An extension of the basic strategies is also pointed out including a combined use of the suboptimization scheme with a supervisor of past measures for the on-line calculation of the estimator weights in the convex combination.

ROBUST ADAPTIVE CONTROL WITH MULTIPLE ESTIMATION MODELS FOR STABILIZATION OF A CLASS OF NON‐INVERSELY STABLE TIME‐VARYING PLANTS

ABSTRACTThis paper presents an indirect adaptive control scheme for nominally stabilizable non‐necessarily inversely stable continuous‐time systems with unmodelled dynamics. The control objective is the adaptive stabilization of the closed‐loop system with the achievement of a bounded tracking‐error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor which selects the appropriate estimator at every certain time and keeping it operating for at least a minimum period of residence time. This selection is based on a performance criterion related to a measure of the estimation errors obtained with each estimator. In this way, the performance of the output signal is improved with regard to the performance achieved with a unique estimation algorithm. All the estimators are either of the least‐squares type or gradient type. However, any well‐posed estimation algorithm is potentially valid for application. These estimators include relative dead‐zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant, which is crucial for proving the stabilizability of the plant via adaptive pole‐placement designs.

Robust stable pole-placement-based adaptive control of continuous linear systems with two parametrical estimation schemes

This paper deals with the pole-placement-type robust adaptive control of continuous linear systems in the presence of bounded noise and a common class of unmodeled dynamics provided that two estimation schemes are used in parallel. Both estimation schemes are introduced in order to minimize the plant identification error by selecting, as plant parameter estimates, a convex combination of both parameter estimates which leads to the selection of one of the estimation schemes, via a switching rule, on time intervals of at least a minimum prefixed residence duration. The weights of the individual parameter vector estimates are provided at each time by an optimization or suboptimization scheme for a quadratic loss function of the possibly filtered tracking error and/or control input. The robust stability of the overall adaptive scheme is ensured by an adaptation relative dead zone which takes into account the contribution of the unmodeled dynamics and bounded noise. The basic results are derived for two different estimation strategies which have either a shared regressor with the plant or individual regressors for the input contribution and its contributed derivatives. In this second case, the plant input is obtained from a similar convex combination rule as the one used for the estimators in the first approach. An extension of the basic strategies is also pointed out including a combined use of the (sub) optimization scheme with a supervisor of past measures for the on-line calculation of the estimator weights in the convex combination. Finally, the extension of the scheme for the use of any number of parametrical estimators is focused on.

Robust Stable Adaptive Control of Uncertain Bilinear Plants and Its Application for Distillation Column

A robust adaptive control design is considered for a class of bilinear plants with unmodeled high-order dynamics and bounded disturbances. A basic optimal control law is first introduced by the generalized minimum variance control strategy, followed by a modification of introducing the modeling error estimate to the control law. Modified least-squares scheme with a relative dead zone is developed to form a novel robust adaptive controller. The resulting closed loop system is proven theoretically to have a zero average tracking error and robust stability. Furthermore, the simulation and an application in controlling of sensitive plate temperature of distillation column demonstrate the effectiveness of the algorithm.

Robust adaptive stabilizer of a class of time-varying plants using multiple controllers

This paper presents an indirect adaptive control scheme for nominally stabilizable, non-necessarily inversely stable, first-order continuous-time systems with unmodeled dynamics. The control objective is the adaptive stabilization of the closed-loop system with a bounded tracking error between the system output and a reference signal given by a stable filter. The adaptive control scheme includes several estimation algorithms and a supervisor to select the appropriate estimator at certain time instants while keeping it in operation during at least a minimum residence or dwell time. Such selection is based on a criterion relative to the estimation errors obtained with each estimator. All estimators are of either least square or gradient type. The estimators include relative dead-zones for robustness purposes and parameter ‘a posteriori’ modifications to ensure the controllability of the estimated models of the plant. This is crucial to prove the stabilizability of the plant via adaptive pole-placement designs. The multi-estimation scheme renders the overall system highly nonlinear.

Robust adaptive control of dynamic hybrid systems

Deals with the problem of synthesizing a robust adaptive controller for a class of single-input single-output time-invariant hybrid plant which can operate under bounded disturbances and/or unmodelled dynamics. The hybrid plant dealt with is composed of two subsystems one being of continuous-time type while the other is digital. The system is simultaneously driven by the standard continuous-time input plus an extra signal. A relative adaptation dead zone is used in the parameter estimation scheme whose role is the robust adaptive stabilization in the presence of uncertainties.

Adaptive stabilization of first-order systems using estimates modification based on a Sylvester determinant test

This note presents an adaptive control scheme for first-order continuous-time systems subject to bounded noise and unmodelled dynamics. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The estimation scheme involves the use of a relative dead zone which freezes the estimation process when the size of the prediction error is small compared to the contribution of the unmodelled dynamics. The singularities are avoided through the use of a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That property is achieved by ensuring that the absolute value of its determinant does not lie below a prefixed positive threshold. In addition, the use of a hysteresis switching function is not used for a modification of the estimates while the absence of chattering is guaranteed in the eventual case when the Sylvester determinant tends to zero. The global stability of the closed-loop system is also guaranteed.

A new robust adaptive control algorithm for linear time-varying plants

Robustness is an important property of a control system. Robust adaptive control has been an active research area for more than a decade. Since it was shown that un-modelled dynamics or even a small bounded disturbance can cause most adaptive control algorithms to go unstable, various modifications of the adaptive control algorithms have been developed to counteract instability and improve robustness with respect to unmodelled dynamics and bounded disturbances. However, we know that most of the modified approaches to achieve robustness require knowledge of either the parameter of bounding function on the unmodelled dynamics, or the upper bound on the disturbances, or the bound on the norm of unknown matching controller/plant parameters, and such knowledge can hardly be obtained in practice. A new indirect adaptive control algorithm for linear time-varying plants is proposed to achieve robustness to a class of unmodelled dynamics, bounded disturbances and plant parameter time variations. A modified relative dead zone technique is used, so that knowledge of the parameters of the upper bounding function on the unmodelled dynamics and the disturbances is not required. The stability analysis and the robust performance of adoptively controlled time-varying systems are provided for the new scheme. A simulation example is given to show the effectiveness of the proposed algorithm.

Experimental and numerical validation of the dead-zone model for longitudinal dispersion in rivers

Experimental results of longitudinal dispersion in rivers are discussed in the light of new findings with respect to the “dead-zone” theory. Both the experiments made by authors as well as some literature results are taken into consideration. The dead-zone model parameters, namely the relative dead-zone volume, penetration time of the tracer into dead-zones, constant mean flow velocity and dispersion coefficient, are obtained with the use of the nonlinear least square technique applied to the image functions of concentration time-distributions. The statistical moments of the concentration time distributions as functions of distance are also analyzed. Expressions for statistical moments, recently obtained by authors, are found to agree well with both experimental and computational results.

Robust Adaptive Tracking with Pole Placement of First-Order Potentially Inversely Unstable Continuous-Time Systems

This note presents an indirect adaptive control scheme applicable to nominally con- trollable non-necessarily inversely stable first-order continuous linear time-invariant systems with unmodelled dynamics. The control objective is to achieve a bounded tracking-error between the system output and a reference signal . A least-squares algorithm with normalization is used to es- timate the plant parameters by using two additional design tools, namely: 1) a modification of the parameter estimates and2) a relative adaptation dead-zone . The modification is based on the properties of the inverse of the least-squares covariance matrix and it uses an hysteresis switching function. In this way, the non-singularity of the controllability matrix of the estimated model of the plant is ensured. The relative dead-zone is used to turn off the adaptation process when an absolute augmented error is smaller than the value of an available overbounding function of the unmodelled dynamics contribution plus, eventually, bounded noise.

Decentralized adaptive linear control of complex systems using relative deadzones

This paper aims to analyse the system stability when decentralized adaptive controllers are applied to multi-input/multi-output non-linear interconnected systems. The local adaptive controllers are designed based on linear models by employing relative deadzones. Using a small-gain-type argument, we can derive an M-matrix test condition for local stability. If the system to be controlled can be described by global Lipschitz functions, a global stable closed-loop svstem is obtained.

On the robust stability of a Clarke-Gawthrop type of self-tuning controller

In this paper the Clarke-Gawthrop type of self-tuning controller is modified and shown to be robust stable with respect to unmodelled plant uncertainties and bounded disturbances. A self-tuning controller is proposed here consisting of two steps: the first, an optimal control law, is derived by means of minimizing a quadratic cost function of the Clarke-Gawthrop type; the second, the optimal control law, is modified by introducing an estimate of the modelling error as a feedback. For the parameter estimation, a modified least-squares scheme with a relative dead zone is employed. The robustness results are derived by neither requiring too much a priori knowledge of the plant parameters, nor using any assumptions about the adaptive signals.

Improved recursive estimator with a relative deadzone

An improved recursive estimation algorithm is presented for robust adaptive control. The estimator has the tightest dead zone which ensures ‘convergence of the estimates whilst maintaining maximum alertness’.

Robust direct adaptive control with least prior knowledge

A new, robust, discrete time, singularity-free, direct adaptive-control scheme is proposed with respect to a class of modeling uncertainties in this paper. Two key features of this scheme are that a relative dead zone is used, but no knowledge of the parameters of the upper bounding function on the class of modeling uncertainties is required, and no knowledge of the lower bound on the leading coefficient of the parameter vector is required to ensure the control law singularity free. Global stability and convergence results of the scheme are provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust adaptive rejection of unknown deterministic disturbances

This paper discusses robust adaptive control for unknown linear discrete time plants with rejection to unknown deterministic disturbances. A new algorithm is proposed. Adaptive implementation of the internal model principle is used for asymptotical cancellation of the disturbances, and the adaptation for the dead zone bound is employed for implementation of the relative dead zone algorithm which ensures global stability of the closed loop system. No knowledge of the dead zone bound is required and thus this algorithm greatly improves its applicability in practice. Simulation results are provided for support of the analysis.