Total model-free robust control of non-affine nonlinear systems with discontinuous inputs

Zhu, Quanmin; Na, Jing; Zhang, Weicun; Chen, Qiang

Abstract

Taking the plant as a total uncertainty in a black box with measurable inputs and attainable outputs, this paper presents a constructive control design of agnostic nonlinear dynamic systems with discontinuous input (such as hard nonlinearities in the forms of dead zones, friction, and backlashes). This study expands the model-free sliding mode control (MFSMC), based on the Lyapunov differential inequality, to a total model-free robust control (TMFRC) for this class of piecewise systems, which does not use extra adaptive online data fitting modelling to deal with plant uncertainties and input discontinuities. The associated properties are analysed to justify the constraints and provide assurance for system stability analysis. Numerical examples in control of a non-affine nonlinear plant with three hard nonlinear inputs—a dead zone, Coulomb and viscous friction, and backlash—are used to test the feasibility of the TMFRC. Furthermore, real experimental tests on a permanent magnet synchronous motor (PMSM) are also given to showcase the control’s applicability and offer guidance for implementation.

• Journal Article Type: Article
• Acceptance Date: Apr 24, 2025
• Online Publication Date: Apr 25, 2025
• Publication Date: Apr 25, 2025
• Deposit Date: May 20, 2025
• Publicly Available Date: May 20, 2025
• Journal: Processes
• Electronic ISSN: 2227-9717
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 5
• Article Number: 1315
• DOI: https://doi.org/10.3390/pr13051315
• Keywords: backlash, nonlinear systems, model-free robust control, dead zone, agnostic systems, viscous friction
• Public URL: https://uwe-repository.worktribe.com/output/14414475