Robustness guarantees for linear control designs with an estimated nonlinear model error model

Abstract

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. Abstract. 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. Keywords

ZD Method Based Nonlinear and Robust Control of Agitator Tank

“…A novel nonlinear feedback control law for continuous stirred tank reactors, obtained by exact input/output linearization and Sontag's input-to-state stability feedback control redesign methods, was studied [19]. In addition, the robustness [21][22][23] of nonlinear systems needs to be further investigated. Notably, almost all of the aforementioned methods investigated the control of the agitator tank.…”

“…To the best of the authors' knowledge, unified controllers that can simultaneously perform liquid level and concentration tracking control have not been presented. In addition, the robustness of nonlinear systems needs to be further investigated.…”

Controllers for Amplitude Limited Model Error Models

“…In (Glad et al, 2004) the following situation was considered. A nominal model S of the system is constructed, e.g.…”

“…In (Glad et al, 2004) linear models were used to represent S. Here we introduce more general nonlinear models of the forṁ…”

“…It is then natural to replace the term α √ T in (4) with a general function α(T ). As was argued in (Glad et al, 2004), it is often natural to assume that the model error model is valid only in a certain amplitude range for the input u. In particular we have this situation when the model is identified from data, and the validation has only been performed for certain classes of inputs.…”