H. Unbehauen

Structure identification of nonlinear dynamic systems—a survey on input/output approaches

Abstract In the past several methods have been elaborated for the identification of nonlinear dynamic systems. Most of the methods assume that the structure of the system is given a priori. Therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation. However in nonlinear system theory several methods are known to determine the structure of a system. In this paper structure identification of block-oriented (especially cascade) models, of semi-linear dynamic models with signal-dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered. Different structure selection methods are summarized based on step and impulse tests, frequency response measurements, correlation analysis, repeated reproducible tests and normal operating data.

Continuous-time approaches to system indentification—a survey

Abstract At the outset this paper discusses the relevance and importance of continuous-time approaches in systems and control in general and in problems of identification in particular. The various continuous-time approaches to system identification are outlined by drawing attention to some earlier surveys, books and monographs and by highlighting certain recent approaches. Some indirect approaches via non-parametric models and via discrete time techniques are discussed along with some direct approaches. A class of system reference adaptive model (SRAM) methods influenced by and arising out of stable adaptive control techniques which are based on output error (OE) minimization is also outlined. Certain unifying features among some seemingly different methods are exposed. Some of the techniques outlined are then illustrated with the aid of examples and a comparison is made among them. Extensions to MIMO models, and to special problems of identification involving unknown time-varying elements, time delays and non-linear elements within the broad framework of some of the techniques are then outlined. The paper concludes by discussing possibilities of inclusion of some of the techniques in standard computer program packages for general and real-time applications.

Technical Communique: Robust reliable control for a class of uncertain nonlinear state-delayed systems

This paper deals with the problem of robust reliable control design for a class of nonlinear uncertain state-delayed systems. The system under consideration involves state time delay, parameter uncertainties and unknown nonlinear disturbances. The nonlinearities are assumed to satisfy the boundedness condition, and the parameter uncertainties are allowed to be time-varying unstructured. The purpose of this problem is to design the state feedback controller such that, for all admissible uncertainties as well as actuator failures occuring among a prespecified subset of actuators, the plant remains globally exponentially stable, independently of the time delay. An effective, modified algebraic Riccati equation approach is developed to solve the problem addressed. It is shown that designed nonlinear time-delay control systems provide guaranteed robust reliable stability despite possible actuator failures. We present an illustrative example to demonstrate the applicability of the proposed design approach.

A review of identification in continuous-time systems

This paper aims at taking the reader on a guided tour of the field of identification of continuous-time systems. It presents a birds eye view of the continuous-time related aspects of the greater field of system identification. Continuous-time based contributions to system identification began in the nineteen-fifties but were overshadowed by a ‘go completely digital’ spirit which was spurred by parallel developments in digital computers during the following two decades. The nineteen seventies have witnessed a resurgence of continuous-time spirit and the field of continuous-time system identification has now matured to merit a review as is intended here. This paper is divided into three parts. An overview of the basic techniques of identification of continuous-time systems in a unified framework is presented in Part A. Parts B and C outline some recent developments in the identification of linear systems and nonlinear systems, respectively.

An adaptive fuzzy sliding-mode controller

This paper deals with a new adaptive fuzzy sliding-mode controller and its application to a robot manipulator arm. The theory for this approach and for the heuristics-based linguistic adaptation is presented, and a mathematical description is derived. Furthermore, an application of this adaptive controller for a two-link robot arm is shown. The obtained results show the high efficiency of the new controller type.

A new algorithm for discrete-time sliding-mode control using fast output sampling feedback

This paper presents a new approach for sliding-mode control (SMC) of discrete-time systems using the reaching law approach together with the fast output sampling (FOS) feedback technique. This method does not need the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement. A numerical example demonstrates the design technique. Simulation results show that the proposed FOS SMC technique produces the same results as obtained by state feedback SMC technique.

Tests for determining model order in parameter estimation

The accuracy of the models estimated with the direct least-squares- and maximum-likelihood-methods is investigated critically. In order to determine also the most accurate order of the model, seven structure testing methods are thoroughly investigated. Using the determinant ratio test first, the possible model orders can essentially be limited. The investigated control system was simulated on an analogue computer under diverse working conditions. With the results obtained, rules for the application of these structure testing methods are formulated. Because of the large number of cases investigated, the probability of the general validity of these rules is high.

Robust H∞ observer design of linear time-delay systems with parametric uncertainty

Abstract This paper deals with the problem of H∞ observer design for a class of uncertain linear systems with delayed state and parameter uncertainties. This problem aims at designing the linear state observers such that, for all admissible parameter uncertainties, the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified H∞ norm upper bound constraint, independently of the time delay. The time delay is assumed to be unknown, and the parameter uncertainties are allowed to be norm-bounded and appear in all the matrices of the state-space model. An effective matrix inequality methodology is developed to solve the proposed problem. We derive the conditions for the existence of the desired robust H∞ observers, and then characterize the analytical expression of these observers in terms of some free parameters. A numerical example demonstrates the validity and applicability of the present approach.

Robust H/sub 2//H/sub /spl infin//-state estimation for systems with error variance constraints: the continuous-time case

The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H/sub /spl infin// norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H/sub /spl infin// norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approach.

Study of predictive controller tuning methods

Several tuning guidelines for model predictive control proposed in literature have been converted into suitable tuning rules and investigated with the help of simulations of two typical transfer functions and a nonlinear unstable chemical reactor as well as a real-time laboratory turbogenerator control application. A modified version of a supervisory performance tuning procedure has also been applied to explore the possibility of application of auto-tuning in model predictive control. A new tuning procedure is finally presented on the basis of the results obtained using several previously existing tuning guidelines.