Robustness and modeling error characterization (original) (raw)
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Model validation for robust control and controller validation in a prediction error framework
2000
This paper presents a coherent framework for model validation for control and for controller validation (for stability and for performance) in the context where the validated model uncertainty sets are obtained by prediction error identification methods. Thus, these uncertainty sets are parametrized transfer function sets, with parameters lying in ellipsoidal regions in parameter space. Our results cover two distinct aspects: (1) Control-oriented model validation results, where we show that a measure of size of the validated model set is connected to the size of the modelbased controller set that robustly stabilizes the model set, leading to validation design guidelines.
New measures for robustness in linear multivariable feedback systems
The Canadian Journal of Chemical Engineering, 1990
New measures for robustness are proposed for linear multivariable control systems. A new theorem is presented to account for the controllability of systems that contain an integrating element, in the presence of additive uncertainties. The theorem leads to the definition of a sufficient condition for robust integral controllability: robustness margin (RM). The ratio of robustness margins for competing control or processs structures can be used to discriminate between these structures. These measures are useful, especially in design stages, since their calculation depends only on steady state information. Applications to several published distillation systems show the merits of these robustness measures. On propose de nouvelles mesures de robustesse pour des systemes de contrdle multivariables linkaires. Un nouveau thioreme est present6 tenant compte de la capacite de contrele des systemes contenant un tlCment d'intkgration, en prCsence d'incertitudes additives. Le theorbme mbne h la definition d'une condition suffisante pour la capacitC robuste de contrdle integral: la marge de robustesse (RM). Le rapport des marges de robustesse pour le contrdle cornpetitif ou les structures de procedes peut &re utilise pour dkpartager ces structures. Ces mesures sont utiles, particulikrement a I'Ctape de la conception, car leur calcul ne depend que des donnees B I'Ctat permanent. Des applications B plusieurs systtmes de distillation publiCes montrent les merites de ces mesures de robustesse.
Robustness of systems with uncertainties in the input
Journal of Mathematical Analysis and Applications, 1981
Proceedings of the 7th IFAC World Congress, Helsinki. 1978") a new notion of "robustness" was defined for a class of dynamical systems having uncertainty in the input+utput relationship. This paper generalizes the results in the abovementioned references in two fundamental ways: (i) We make significantly less restrictive hypotheses about the manner in which the uncertain parameters enter the system model. Unlike the multiplicative structure assumed in previous work, we study a far more general class of nonlinear integral flows, (ii) We remove the restriction that the admissible input set be compact. The appropriate notion to investigate in this framework is seen to be that of approximate robustness. Roughly speaking, an approximately robust system is one for which the output can be guaranteed to lie "E-close" to a prespecified set at some future time T> 0. This guarantee must hold for all admissible (possibly time-varying) variations in the values of the uncertain parameters. The principal result of this paper is a necessary and sufficient condition for approximate robustness. To "test" this condition, one must solve a finite-dimensional optimization problem over a compact domain, the unit simplex. Such a result is tantamount to a major reduction in the complexity of the problem; i.e., the original robustness problem which is infinite-dimensional admits a finite-dimensional parameterization. It is also shown how this theory specializes to the existing theory of Barmish and Barmish and Lin under the imposition of additional assumptions. A number of illustrative examples and special cases are presented. A detailed computer implementation of the theory is also discussed.
Robustness guarantees for linear control designs with an estimated nonlinear model error model
International Journal of Robust and Nonlinear Control, 2004
Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a non-linear system. We describe how a non-linear model error model can be developed, that allows a complete linear design process that results in a closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) against the nonlinear error. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of "practical stability" for robust control design, with possible nonlinear model errors. We use affine norms for that purpose.
Automatica, 2003
We propose a model validation procedure that consists of a prediction error identification experiment with a full order model. It delivers a parametric uncertainty ellipsoid and a corresponding set of parametrized transfer functions, which we call PE (for Prediction Error) uncertainty set. Such uncertainty set differs from the classical uncertainty descriptions used in robust control analysis and design. We develop a robust control analysis theory for such uncertainty sets, which covers two distinct aspects. (1) Controller validation. We present necessary and sufficient conditions for a specific controller to stabilize -or to achieve a given level of performance with -all systems in such PE uncertainty set. (2) Model validation for robust control. We present a measure for the size of such PE uncertainty set that is directly connected to the size of a set controllers that stabilize all systems in the model uncertainty set. This allows us to establish that one uncertainty set is better tuned for robust control design than another, leading to control-oriented validation objectives.
Model validation: A connection between robust control and identification
1992
Modern robust control synthesis techniques aim at providing robustness with respect to uncertainty in the form of both additive noise and plant perturbations. On the other hand, most popular system identification methods assume that all uncertainty is in the form of additive noise. This has hampered the application of robust control methods to practical problems. This paper begins to address the gap between the models used in control synthesis and those obtained from identification experiments by considering the connection between uncertain models and data. The model validation problem addressed here is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard H ∞ /µ framework models. A necessary condition for such a model to describe an experimental datum is obtained. Furthermore, for a large class of models, in the robust control framework, this condition is computable as the solution of a quadratic optimization problem.
Behavioral approach to robustness analysis
1994
This paper introduces a general and powerful framework for modeling and analysis of uncertain systems. One immediate concrete result of this work is a practical method for computing robust performance in the presence of norm-bounded perturbations and both norm-bounded and white-noise disturbances.
A robustness enhancer for model-based controllers
Proceedings of IECON '93 - 19th Annual Conference of IEEE Industrial Electronics, 1993
AbstTact-For the purpose of enhancing the robustness of model-based controllers against modelling uncertainties and external disturbances, a simple robustness enhancer is proposed in this paper. By using the given robustness enhancer, compact analytical results of uncertainty reduction and robustness enhancement can be obtained. It is shown that with such a scheme, both modelling uncertainties and disturbances can be reduced, and hence the robustness of the control system can be enhanced by a given factor through the proper design of relevant components of the robustness enhancer.