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Article

Total Model-Free Robust Control of Non-Affine Nonlinear Systems with Discontinuous Inputs

by
Quanmin Zhu
1,*,
Jing Na
2,
Weicun Zhang
3 and
Qiang Chen
4
1
School of Engineering, University of the West of England, Frenchy Campus, Coldharbour Lane, Bristol BS16 1QY, UK
2
Faculty of Mechanical & Electrical Engineering, Kunming University of Science & Technology, Kunming 650500, China
3
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
4
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
*
Author to whom correspondence should be addressed.
Processes 2025, 13(5), 1315; https://doi.org/10.3390/pr13051315
Submission received: 7 April 2025 / Revised: 23 April 2025 / Accepted: 24 April 2025 / Published: 25 April 2025
(This article belongs to the Special Issue Design and Analysis of Adaptive Identification and Control)

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.
Keywords: nonlinear systems; agnostic systems; model-free robust control; dead zone; viscous friction; backlash nonlinear systems; agnostic systems; model-free robust control; dead zone; viscous friction; backlash

Share and Cite

MDPI and ACS Style

Zhu, Q.; Na, J.; Zhang, W.; Chen, Q. Total Model-Free Robust Control of Non-Affine Nonlinear Systems with Discontinuous Inputs. Processes 2025, 13, 1315. https://doi.org/10.3390/pr13051315

AMA Style

Zhu Q, Na J, Zhang W, Chen Q. Total Model-Free Robust Control of Non-Affine Nonlinear Systems with Discontinuous Inputs. Processes. 2025; 13(5):1315. https://doi.org/10.3390/pr13051315

Chicago/Turabian Style

Zhu, Quanmin, Jing Na, Weicun Zhang, and Qiang Chen. 2025. "Total Model-Free Robust Control of Non-Affine Nonlinear Systems with Discontinuous Inputs" Processes 13, no. 5: 1315. https://doi.org/10.3390/pr13051315

APA Style

Zhu, Q., Na, J., Zhang, W., & Chen, Q. (2025). Total Model-Free Robust Control of Non-Affine Nonlinear Systems with Discontinuous Inputs. Processes, 13(5), 1315. https://doi.org/10.3390/pr13051315

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