Robust Time-Varying Tracking Control of Sandwich Nonlinear Systems with Sandwiched Saturation Nonlinearity
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Robust Time-Varying Tracking Control of Sandwich Nonlinear Systems with Sandwiched Saturation Nonlinearity Meysam Azhdari1 · Tahereh Binazadeh1 Received: 6 January 2019 / Revised: 10 April 2020 / Accepted: 13 April 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper addresses the output-tracking control problem for a class of nonlinear sandwich systems with external disturbances and model uncertainties. Sandwich systems are a special class of nonlinear systems in the cascade structure, which are made up of several distinct subsystems while the non-smooth nonlinear functions are sandwiched among their separate subsystems. This paper concentrates on the sandwich systems consisting of two arbitrary-order nonlinear cascaded subsystems, while the saturation nonlinearity is sandwiched between them. The robust control law is designed such that the output of the sandwich system tracks the desired time-varying reference signal despite the saturation occurrence. Due to the characteristics of the saturation function and also the existence of the external disturbances and model uncertainties, the considered problem is facing some serious challenges. To deal with these difficulties, the design procedure is divided into two phases. In the first phase, the second subsystem and the sandwiched saturation nonlinearity are considered. In this phase, by utilizing the backstepping approach, the desired input signal of the saturation function is designed. In the second phase, the control input of the first subsystem is designed based on the sliding mode technique in a way that the output of the first subsystem tracks the desired signal which is obtained in the first phase. Finally, to verify the effectiveness of the proposed method, it is applied to a practical sandwich system. Keywords Sandwich systems · Sandwiched saturation function · Output tracking · Robust performance · Lyapunov analysis · Nussbaum function
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Meysam Azhdari [email protected] Tahereh Binazadeh [email protected] Department of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, P.O. Box 71555-313, Shiraz, Iran
Circuits, Systems, and Signal Processing
1 Introduction A wide class of practical systems has a cascade structure or in another mean, they can be described as the interconnections of several separate subsystems. A special class of these systems is related to systems that are made up of several linear or nonlinear distinct subsystems such that the non-smooth nonlinearities are located between their distinct subsystems. Such structures are called sandwich systems because the nonsmooth nonlinearities are sandwiched between their separate subsystems. The common types of static nonlinearities are saturation and dead-zone, and dynamic ones are backlash and hysteresis. These non-smooth nonlinearities can occur due to the physical imperfection of system components or the inherent characteristics of the dynamics of the system. They typically exist in many practical syste
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