Hybrid passivity and finite-gain properties of reset systems
An application to stability analysis in the frequency domain
M.B. Kaczmarek (TU Delft - Mechanical Engineering)
Erik Steur – Mentor (TU Delft - Team Bart De Schutter)
S. Hassan Hassan HosseinNia – Mentor (TU Delft - Mechatronic Systems Design)
Niranjan Saikumar – Mentor (TU Delft - Mechatronic Systems Design)
B. De Schutter – Graduation committee member (TU Delft - Delft Center for Systems and Control)
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Abstract
Reset control is a "simple" nonlinear control strategy that has the potential of being widely adopted and improving the performance of systems traditionally controlled with PIDs. Lack of suitable methods for proving stability, that are in line with the current industrial practice, hampers the wider acceptance of reset control. In this thesis, novel sufficient conditions for stability of reset control systems, that can be evaluated using measured frequency response function of a system to be controlled, are derived using the hybrid passivity and finite-gain framework. A method for analysing the hybrid passivity and finite-gain parameters of reset systems, that can be extended to other classes of nonlinear systems, is developed. Additionally, a variant of the “Constant in Gain Lead in Phase” reset element, that facilitates the use of the proposed method for the stability analysis, is introduced. Stability of several precision positioning systems with reset controllers, designed for different objectives, is studied to demonstrate the applicability of the proposed hybrid passivity and finite-gain approach for the stability analysis of reset control systems. Guidelines for design of reset systems such that their stability can be concluded using the hybrid passivity and finite gain method are shown. This thesis presents a new view on the stability of reset systems and addresses the need for frequency-domain tools for stability analysis of nonlinear control systems in precision mechatronics applications.