Nonlinear and adaptive control

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies

Adaptive control: Myths and realities

It was found that all currently existing globally stable adaptive algorithms have three basic properties in common: positive realness of the error equation, square-integrability of the parameter adjustment law and, need for sufficient excitation for asymptotic parameter convergence. Of the three, the first property is of primary importance since it satisfies a sufficient condition for stabillity of the overall system, which is a baseline design objective. The second property has been instrumental in the proof of asymptotic error convergence to zero, while the third addresses the issue of parameter convergence. Positive-real error dynamics can be generated only if the relative degree (excess of poles over zeroes) of the process to be controlled is known exactly; this, in turn, implies perfect modeling. This and other assumptions, such as absence of nonminimum phase plant zeros on which the mathematical arguments are based, do not necessarily reflect properties of real systems. As a result, it is natural to inquire what happens to the designs under less than ideal assumptions. The issues arising from violation of the exact modeling assumption which is extremely restrictive in practice and impacts the most important system property, stability, are discussed

Indirect adaptive control for systems with an unknown dead zone

Dead-zone inverse methods have been used in adaptive control schemes to compensate for systems with an unknown dead zone. The problem with these techniques is that steady state error may still exist. It is shown in this paper that controller with integrating action can be used to remove steady state error arising from the unknown dead zone. By treating the effect of an unknown dead zone as a bounded disturbance being injected into the system, a plant parametrization that is linear in a set of unknown parameters is developed and the estimation algorithm is proposed. A novel feature of the adaptive controller proposed here is the integrating action in the controller. Stability analysis shows that the adaptive scheme ensures boundedness of all closed-loop signals and eliminates tracking errors. As illustrated in a simulation example, the proposed adaptive controller is simple to implement and accurate tracking can be achieved.published_or_final_versio

Final report on robust stochastic adaptive control

Includes bibliographical references.Supported by the Office of Naval Research under contract N00014-82-K-0582 NR606-003 MIT OSP no.92775prepared by Lena Valavani, Michael Athans ; submitted to Office of Naval Research, Mathematical Sciences Division

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

Adaptive neural network cascade control system with entropy-based design

A neural network (NN) based cascade control system is developed, in which the primary PID controller is constructed by NN. A new entropy-based measure, named the centred error entropy (CEE) index, which is a weighted combination of the error cross correntropy (ECC) criterion and the error entropy criterion (EEC), is proposed to tune the NN-PID controller. The purpose of introducing CEE in controller design is to ensure that the uncertainty in the tracking error is minimised and also the peak value of the error probability density function (PDF) being controlled towards zero. The NN-controller design based on this new performance function is developed and the convergent conditions are. During the control process, the CEE index is estimated by a Gaussian kernel function. Adaptive rules are developed to update the kernel size in order to achieve more accurate estimation of the CEE index. This NN cascade control approach is applied to superheated steam temperature control of a simulated power plant system, from which the effectiveness and strength of the proposed strategy are discussed by comparison with NN-PID controllers tuned with EEC and ECC criterions

Jednostavna neizrazita identifikacija implementirana u naprednom regulatoru

The paper focuses on identification issues of the advanced controller ASPECT* that is implemented on a simple PLC platform with an extra mathematical coprocessor and is intended for the advanced control of complex plants. The model of the controlled plant is obtained by means of experimental modelling using an online learning procedure that combines model identification with pre- and post-identification steps that provide reliable operation. It is shown that acceptable performance of the system is obtained despite difficult conditions that may arise during operation.Ovaj se rad usredotočuje na problematiku identifikacije na osnovi naprednog regulatora ASPECT* implementiranog na jednostavnoj PLC platformi s dodatnim matematičkim koprocesorom, koji se želi koristiti za naprednu regulaciju složenih postrojenja. Model reguliranog postrojenja dobiva se eksperimentalnim modeliranjem, pri čemu se koristi on-line procedura učenja s pred- i post-identifikacijskim koracima koji osiguravaju pouzdan rad. Pokazano je da se prihvatljive performance sustava dobivaju unatoč teškim uvjetima koji se mogu pojaviti tijekom rada