Parameter Adaptation Algorithm Research Articles

Stability and Robustness Analysis of a Class of Adaptive Controllers for Robotic Manipulators

The stability and robustness properties of the adaptive control scheme proposed by Sadegh and Horowitz (1987) are stud ied. The properties include the global exponential stability and Lp input/output stability of the nonadaptive (i.e., fixed- parameter) control system and the global asymptotic stability of the adaptive control scheme. Sufficient conditions for the convergence of the estimated parameters to their true values are also given. A computationally efficient adaptation scheme that is a modified version of the original scheme is proposed. The modified scheme utilizes the desired trajectory outputs, which can be calculated a priori, instead of the actual joint outputs in the parameter adaptation algorithm and the non linearity compensation controller. Sufficient conditions for guaranteeing all the stability properties of the original scheme in the modified scheme are also explicitly derived. A com puter simulation study of the performance of both schemes in the presence of noise disturbances is conducted.

Nonlinear adaptive control of robotic manipulators - hyperstability approach

A nonlinear model reference adaptive controller based on hyperstability approach, is presented for the control of robot manipulators. Use of hyperstability approach simplifies the stability proof of the adaptive system. The unknown parameters of the system, as well as its variable payload, are estimated on line and are adaptive to their actual values; tending to reduce the system error. In addition, any sudden change in the system parameters or payload is detected by the proposed intelligent controller. Robot path tracking, with unknown parameter values and variable payload, is simulated to show the effectiveness of the proposed adaptive control algorithm. Both system output error and parameter estimation error vanish under the proposed parameter adaptation algorithm.

Adaptive Pulse Width Control for Precise Positioning Under the Influence of Stiction and Coulomb Friction

Conventional linear digital control fails to provide precise positioning of a control object under the influence of static friction, Coulomb friction, and backlash. This paper presents an adaptive pulse width control (PWC) scheme for a precise point-to-point positioning system. This scheme is developed based on the relationship between the displacement of a control object due to a single pulse input and the pulse width. The coefficient appearing in this relationship is estimated by a parameter adaptation algorithm. Sufficient conditions for asymptotic stability of this adaptive scheme are developed using Popov hyperstability theorem. This adaptive PWC is tested on a laboratory positioning table and is shown to be effective.

Simultaneous generation of sensitivity functions—Transfer function matrix approach

Sensitivity functions are used in many model parameter identification methods and adaptive control algorithms. Since one sensitivity model has to be used for each parameter, the computation requirement is large when many parameters have to be identified or adjusted. This paper proposes a method to reduce the computation requirement by using one sensitivity model suitable for the generation of sensitivity functions for all parameters. Instead of using modal transformations and eigenvector sensitivities as previously proposed, this paper uses an input-output transfer function matrix approach. Several sufficient conditions in terms of controllability are given for the implementation of the method. An estimate of computation savings is provided.

Adaptive Prediction of Anode-effects in Aluminium Reduction Cells

The paper describes two parameter adaptive prediction algorithms applied to an aluminium reduction cell. The goal is to predict the cell resistance ahead of time. Detecting its rate of increase the anode-effect can be avoided by feeding alumina into the cell. Without feeding the time of anode-effect can also be predicted. Based on real-time measurements many computer simulations have been made to characterize predictor behaviour. The influence of operational events on the estimation, such as anode movement (AM) and alumina feeding (F) have also been investigated, as well as restarting the estimation after an anode-effect.

Simultaneous Generation of Sensitivity Functions using only One Sensitivity Model

Sensitivity functions are used in many model parameter identification methods and adaptive control algorithms. Since one sensitivity model has to be used for each parameter, the computation requirement is large when many parameters have to be identified or adapted. This paper proposes a method to reduce the computation requirement by using one sensitivity model suitable for the generation of sensitivity functions for all parameters. Instead of using modal transformations and eigenvector sensitivities as previously proposed, this paper uses an input-output transfer function approach. Several sufficient conditions in terms of controllability are given for the implementation of the method.

An Adaptively Controlled Electrohydraulic Servo-Mechanism: Part 1: Adaptive Controller Design

A systematic model reference adaptive control design scheme is presented. The control scheme is developed and analysed within the framework of a sampled data system with a parameter adaptive algorithm designed on the basis of hyper stability theory. A number of supervisory functions are used to supplement the basic adaptive control system in order to enhance robust controller action.

Experimental Study on Discrete Time Adaptive Control of an Industrial Robot Arm

This paper deals with an implementation of a discrete time adaptive controller for two axes of an industrial manipulator. The friction terms are shown to be detrimental to the parameter adaptation algorithm and to the stability of overall system unless they are properly included in the model. In this paper, the effect of friction is minimized by a cancellation technique based on off-line estimation of friction terms. The primary purpose of the adaptive controller is to compensate for inertia variations due to payload changes and other disturbances.

In-Process Detection of Tool Breakage in Milling

An adaptive signal processing scheme for the cutting force signal was used to detect the fracture and chipping of a cutting tool during milling operation. The cutting force signal was modeled by a discrete autoregressive model where parameters were estimated recursively at each sampling instant using a parameter adaptation algorithm based on a model reference adaptive system approach. The sensitivity of the prediction error and the estimated parameters to the frature and chipping of a cutting tool are presented. The influence of the adaptation algorithm parameters on the estimation results is discussed. The effect of the change in cutting conditions on the estimation results is also investigated.

Robustness of discrete-time direct adaptive controllers

The problem of preserving stability of discrete-time adaptive controllers in spite of reduced-order modeling and output disturbances is addressed in this paper. Conditions for global stability (convergence of the tracking error with bounded signals) are derived for a discrete-time pole-zero placement adaptive controller where the parameter estimator is modified in terms of normalized signals. Following an input-output perpective, the overall system is decomposed into two subsystems reflecting the parameter estimation and modeling errors, respectively, and its stability is studied using the sector stability and passivity theorems. First the analysis is carried for the class of disturbances and reference inputs that are either decaying or can be exactly hulled by a linear controller of the chosen structure. In this L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -framework, it is shown that the only substantive assumption to assure stability is the existence of a linear controller such that the closed-loop transfer function verifies certain conicity conditions. The convergence speed and alertness properties of various parameter adaptation algorithms regarding this condition are discussed. The results are further extended to a broader class of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_{\infty}</tex> disturbances and reference inputs.

Control of an Industrial Drum Filter by Using Adaptive Models

Vacuum filters are often used to dry and wash lime mud before calcining it in the lime kiln of a sulphate pulp mill. The control of the kiln itself is quite problematic because of long time delays and complicated burning reactions. To avoid many kiln's control problems and to achieve energy savings in the kiln, the mud filter should operate steadily and produce dry mud. Here, based on a systematic study of the process, a self-tuning type two-variable control scheme is proposed for the filter. First, adaptive process models are specified based on mill experiments. The self-tuning control scheme is then developed for the drum filter. The proposed control method consists of a twovariable parameter adaptive control algorithm which includes compensation for filter efficiency and some other disturbances. Optimization of the blowing and scraping intervals is also possible. The controller is directly applicable to mud filters provided that they are controllable and the process model is identified. Energy savings of about 10 % can be achieved using this method. The method provides a general approach for drum filter control. In the end the general applicability of the methods and the results are also discussed.

A Comparison of Several Multivariable Parameter Adaptive Controllers

In recent years, many contributions to multivariable parameter adaptive control algorithms have been proposed, particularly in the areas of generalised minimum variance, pole assignment and state feedback methodologies. This paper examines the performances of some of these strategies in the control of a non-linear model of a pilot plant process. The study is restricted to considering two-input and two-output cases.

New structure for an adaptive servomechanism controller

A new stable adaptive controller structure for ensuring asymptotic tracking with disturbance rejection is proposed. The controller structure is identical to the robust servomechanism controller structure when the adaptation is over. The process is assumed to be a linear minimal-phase process. The exogenous signals may be unbounded, but satisfy a known linear difference equation. The parameter adaptation algorithm ensures global convergence of the tracking error.

On the Model-Process Mismatch Tolerance of Various Parameter Adaptation Algorithms in Direct Control Schemes : A Sectoricity Approach

Designing adaptive controllers under model-process mismatched situations is considered. A suitable representation for the uncertainty is explicitly incorporated, what renders the stability analysis problem suitable for a sector condition formulation (Safonov, 1980). The performance from the robustness point of view, of various currently used parameter adaptation algorithms is compared. This is done by determining regions on the complex plane where an uncertainty dependent Nyquist locus must be contained to insure boundedness of the tracking error. It is shown that uniform boundedness of all signals may only be proven for a weighted least squares scheme under suitable weighting coefficients selection knowledge of the process steady-state gain is required to insure convergence to zero of the tracking error. The proposed framework is shown to be amenable for the study of non-stably invertible or mismatched delay systems.

An On-line Method for Improvement of the Adaptation Transients in Adaptive Control

A method is proposed to improve the adaptation transients in adaptive systems whose philosophy consists basically of the implementation of a “a posteriori” correcting action of a local nature in at least one of the parameters associated with the used adaptation algorithm. To develop this technique, one takes advantage of the freedom in the choice of such parameters while maintaining the stability properties, in many of the commonly used parameter-adaptive algorithms. As an intermediate step, an equivalent timevarying and near-linear system, which is an approximate model for the whole adaptive scheme is derived in order to apply a bang-bang (or, eventually, linear) mode suboptimal input.

A discrete time model reference adaptive control scheme with reduced on-line computations

A parameter adaptation algorithm, suitable for direct-parameter discrete time model reference adaptive control systems, is proposed. This algorithm has a simpler structure than the algorithms suggested earlier. Consequently, the implementation of the algorithm requires less complex hardware with reduced on-line computations. The asymptotic stability of the proposed adaptive scheme in its error space is established.

A stability theorem with applications to adaptive control

A theorem for the global asymptotic stability of a class of feedback systems is established. It is shown that the equivalent feedback representation of the equation associated with the generalized error of the model reference adaptive system (MRAS) belongs to this class. A general form of the parameter adaptation algorithm which contains as particular forms various known adaptation algorithma is introduced. Explicit stability conditions are obtained for the case of this general type algorithm. The usefulness of the results is illustrated by their application to the straightforward generalization of some recent MRAS designs.

Development, Comparison and Application of Various Parameter-Adaptive Digital Control Algorithms

Various recursive parameter estimation algorithms and controller design procedures can be combined to build up parameter adaptive control algorithms. Three parameter estimators and seven control algorithms have been selected taking into account good convergence properties and small computational expense and regarding the conditions for closed loop identification. The resulting 21 adaptive control algorithms are compared and tested with a process computer in on-line operation with analog simulated stable and unstable processes for stochastic and deterministic disturbances without and with external perturbation signals. The results are very promising. In many cases a good control performance is achieved. As a priori knowledge only the sampling time, the process model order and time delay and in some cases a weighting factor for the process input signal are required.The best adaptive control algorithms are applied for digital adaptive control of a nonlinear pipeline pilot plant and an air heater. Conclusions are given for the selection of parameter adaptive control algorithms, depending on the type of process and its disturbances.The adaptive control algorithms can be applied for adaptive control of constant and time variant, linear and nonlinear, stable and unstable processes with process computers or micro computers or for self-tuning of control algorithms or tuning of conventional analog PID controllers.

Self-Organizing Control and Applications to Trainable Manipulators and Learning Prostheses

Self-Organizing Control (S.O.C.) has been defined as the descriptive which treats dynamic systems with uncertainties operating in deterministic or stochastic environments. Self-organization is performed by the controller to on-line reduce the uncertainties pertaining to the behavior of the systems and to drive its output to attain the desired goal. Parameter Adaptive S. O. Controls explicitly identify the uncertainties of the system dynamics, which are characterized by a parameter vector, while Performance Adaptive S. O. Controls improve the uncertainties that pertain only to the improvement of its performance, and therefore, identify the systems implicitly. A collection of successful methods for both Parameter Adaptive and Performance Adaptive Algorithms are discussed and compared in this paper to demonstrate the desirability and applicability of explicit or implicit parameter identification in a SOC system. The implementations of these algorithms requires the use of digital computers of various sizes depending on their specific application at hand. An interesting application of S. O. Control to trainable industrial manipulators and learning prosthetic devises, using minimcomputers is currently investigated by the author. Parameter Adaptive schemes, using explicit parameter identification of the system dynamics for an “attitude control” type of hierarchical arm-joint coordination seems more appropriate for training industrial manipulators to perform mechanical tasks. On the other hand, Performance Adaptive techniques are more suitable for human prosthetic devices with learning capabilities, controlled from the nervous or muscular system of the computer with visual feedback, to perform purely anthropomorphic functions. Current results of this investigation will be discussed.