Approaches Towards A Systematic Tuning of Interval Observers via Norm-Bounded Error Dynamics and LMIs

Abstract

Interval observers typically rely on performance criteria that specify the estimation accuracy. Inappropriately parameterized performance criteria can lead to linear matrix inequalities (LMIs) that do not yield feasible solutions. Retuning the output specification of the error dynamics allows for exploiting structural feasibility. The overall goal of this paper is to design a TNL interval observer for systems for which the LMIs do not yield a feasible solution with the standard specification of the performance criteria. As an example, the proposed tuning methods are applied to the state estimation of a lithium-ion battery cell. The LMIs introduced together with this observer structure initially do not have a feasible solution for the investigated battery model. To obtain feasible solutions, we propose extended design conditions for the TNL interval observer based on a virtual output equation for the error dynamics that is utilized to reduce the influence of uncertainties on the estimation results. Additionally, we present two techniques to enforce interpretable structures in the observer gains to enhance the estimation accuracy. The first technique enforces a desired ratio between the elements of selected observer gains, the second technique influences the estimation accuracy by specifying the eigenvalues of the scaled observer system matrix. To demonstrate the fundamental application of the tuning methods, the proposed techniques are initially applied to the state estimation of a mass-spring-damper system. Subsequently, the effectiveness of the proposed techniques is shown for the state estimation of the lithium-ion battery cell. With both techniques, the estimation accuracy can be significantly enhanced. Furthermore, they provide a framework for systematically designing TNL interval observers.