Rejection of Disturbances with Uncertain Spectra: Theory and Applications

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

P.I: Pierre T. Kabamba, Department of Aerospace Engineering Co P.I: Semyon M. Meerkov, Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, MI Proposal Number: 0073302 Title: Rejection of Disturbances with Uncertain Spectra: Theory and Applications Project Abstract The objectives of this project are to develop novel, specialized analytical tools for analysis and design of control systems that are robust with respect to disturbance model uncertainty, and to demonstrate their applicability in industrial situations. Disturbance rejection is a pervasive problem in control systems engineering, and our previous work has highlighted the importance of uncertainty in disturbance models. Among others, the following problems will be addressed: 1. Rejection of disturbances with uncertain spectra in systems with saturated actuators. 2. Investigation of performance measures other than variance (e.g., l-infinity norm) and disturbance models other than colored noise (e.g., a train of delta-functions with uncertain inter-arrival time). 3. Application of the results obtained to analysis and design of controllers in the aerospace (in co-operation with Boeing) and automotive (in co-operation with Ford) industries. The approach of the research is based on (a) a functional equation, that could be viewed as converse of the standard spectral factorization Lemma and (b) the method of stochastic linearization, that allows analysis and design of nonlinear systems driven by random inputs. The work is planned as follows: Problem 1 will be addressed the first year, problem 2 during the second and third year, and problem 3 will be underlying our work throughout. The impact of the research is in providing the control engineer with an analytical methodology for analysis and design of controllers that are robust with respect to uncertainties in the disturbance model. While such analysis is typically carried out today by simulations, the availability of the analytical tools to be developed will provide a useful alternative.