Multiestimation Scheme Research Articles

Multiestimation Scheme for Identification and Adaptive Control of Nonlinear Laboratory Model DTS200

This paper is focused on usability of multiestimation scheme approach in the area of identification and control of nonlinear systems. A multiestimation scheme is introduced and subsequently used for the adaptive control of real-time nonlinear system. The multiestimation scheme integrates on-line identification of suitable models of a controlled system and a controller synthesis on base of the identified model. The real-time testing has been carried out by the control of nonlinear laboratory model of interconnected tanks (DTS200 by Amira company).

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.

MULTIMODEL DISCRETE CONTROL WITH ONLINE UPDATING OF THE FRACTIONAL ORDER HOLD GAINS

A multiestimation scheme for adaptive discrete-time control is presented. The different models of the scheme to be estimated are obtained from a set of different discretizations of a continuous-time unknown transfer function under a fractional order hold of correcting gain (β-FROH) which leads to distinct associate discrete-time models for the given continuous-time plant. The objective is to design a scheme being able to find the most appropriate value for the gain β to enhance the identification and tracking performances. The scheme chooses online the value of β with the best reference tracking performance by implementing eventually switches through time among a prefixed set of values characterizing the discrete models of the plant in a parallel multiestimation scheme. The switching rule is subjected to a minimum residence time in order to guarantee the closed loop stability. Simulations for two different practical cases, a controlled DC motor and a resonant circuit, are presented.

MULTIESTIMATION SCHEME FOR ADAPTIVE CONTROL OF THREE TANK SYSTEM

This paper deals with a one possibility of improvement of a self-tuning controller reliability and performance. A simple estimation scheme is replaced by so-called a multiestimation scheme and the self-tuning controller is then synthesized from this scheme. A higher level switching structure between various estimation schemes is used to supervise the reparametrization of the self-tuning controller in real time. The basic usefulness of the proposed scheme is to improve the accuracy of estimated parameters of the controlled system and then better transient response is obtained.

Robustly Stable Adaptive Control of a Tandem of Master–Slave Robotic Manipulators With Force Reflection by Using a Multiestimation Scheme

The problem of controlling a tandem of robotic manipulators composing a teleoperation system with force reflection is addressed in this paper. The final objective of this paper is twofold: 1) to design a robust control law capable of ensuring closed-loop stability for robots with uncertainties and 2) to use the so-obtained control law to improve the tracking of each robot to its corresponding reference model in comparison with previously existing controllers when the slave is interacting with the obstacle. In this way, a multiestimation-based adaptive controller is proposed. Thus, the master robot is able to follow more accurately the constrained motion defined by the slave when interacting with an obstacle than when a single-estimation-based controller is used, improving the transparency property of the teleoperation scheme. The closed-loop stability is guaranteed if a minimum residence time, which might be updated online when unknown, between different controller parameterizations is respected. Furthermore, the analysis of the teleoperation and stability capabilities of the overall scheme is carried out. Finally, some simulation examples showing the working of the multiestimation scheme complete this paper.

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.

A multiestimation-based scheme for modelling single-input–single-output discrete adaptive control systems

A pole-placement multiestimation-based adaptive controller is synthesised for linear single-input–single-output time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient behaviour while guaranteeing closed loop stability. The scheme becomes specifically useful when extended to linear plants whose parameters are piecewise constants while changing abruptly to new constant parameterisations or in the case when the parameters are slowly time-varying rather than constant. Thus, the scheme becomes attractive from a modelling point of view since the plant, while being potentially time-varying, or in particular, possessing several operation points, is modelled in a conceptually simple way as a set of time-invariant plant unknown parameterisations each one possessing its corresponding estimation scheme. A description of the controller architecture with multiple parameterisations, together with its associated multiestimation scheme is given. Moreover, graph theory is used to describe in a formal and concise way the switching mechanism between the various plant parameterisations of the switched system. Thus, the switching rule is formally represented by a graph (or finite automaton). Also, the proofs of boundedness of all the relevant signals are given.

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 multiestimation scheme for adaptive control andidentification with model reduction issues

A discrete pole‐placement‐based and multiestimation‐based adaptive control scheme involving a relative adaptation dead zone is presented for a plant with known poles and unknown zeros. The basic usefulness of the proposed multiestimation scheme is related to the use of a set of models of reduced order associated with the multiestimation scheme instead of a high‐order one. Depending on the frequency spectrum characteristics of the input and on the estimates evolution, the multiestimation scheme selects on‐line the most appropriate model and its related estimation scheme in order to improve the identification and control performances. Robust closed‐loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes as it has been confirmed by simulation results. The scheme chooses in real time the estimator/controller associated with a particular reduced model possessing the best performance according to an identification performance index by implementing a switching rule between estimators. The switching rule is subject to a minimum residence time at each identifier/adaptive controller parameterization for closed‐loop stabilization purposes. A conceptually simple higher‐level supervisor, based on heuristic updating rules which estimate on‐line the weights of the switching rule between estimation schemes, is discussed.

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.

Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.

Stable multi-estimation model for single-input single-output discrete adaptive control systems

A pole-placement-based adaptive controller synthesized from a multi-estimation scheme is designed for linear single-input single-output time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterization of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient behaviour while guaranteeing closed loop stability. The scheme becomes specifically useful when extended to linear plants whose parameters are piecewise constants while changing abruptly to new constant parameterizations or in the case when the parameters are slowly time varying rather than constant. Thus, the scheme becomes attractive from a modelling point of view since the plant, while being potentially time varying, or in particular, possessing several operation points, is modelled as a set of time-invariant plant unknown parameterizations each possessing its own estimation scheme. In that way, the model description becomes conceptually simple and easy to implement concerned with both estimation and control issues. A description of the controller architecture with multiple parameterizations, together with its associated multi-estimation scheme is given. In addition, the proofs of boundedness of all the relevant signals are given so that the closed-loop system is proved to be stable.

A supervised discrete adaptive control scheme with multiestimation

A discrete pole placement-based adaptive controller with multiestimation is synthesized for linear time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the re-parameterization of the adaptive controller in real time. The basic usefulness of the proposed multiestimation scheme relies into the improvement of the adaptation transient behavior while robust closed-loop stability is proved even in the presence of unmodeled dynamics of sufficiently small sizes. The scheme becomes specifically attractive when the various estimators are adaptive identifiers for the plant which is being modeled as possessing different possible amounts of unmodeled dynamics including different nominal orders and parametrical uncertainties. The influence of free design parameters is discussed through exhaustively worked simulations.

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.