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Model-free sliding mode enhanced proportional, integral, and derivative (SMPID) control

Zhu, Quanmin

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Quan Zhu
Professor in Control Systems


This study proposes a type of Sliding Mode-based Proportional, Integral, and Derivative (SMPID) controllers to establish a model-free (treat dynamic plants as a whole uncertainty) sliding model control (MFSMC) platform for Bounded-Input and Bounded-Output (BIBO) dynamic systems. The SMPID design (1) proposes a sliding mode error (rather than error) as the PID input, (2) directly links to Lyapunov asymptotic stability to provide total robust nonlinear dynamic inversion (NDI), and (3) reduces the chattering effects in terms of Lyapunov definite positive stability. Further, the study proposes a general SMC framework to accommodate asymptotic time stabilisation and finite-time stabilisation for both model-based and model-free designs. A U-control framework is presented to integrate the SMPID control (for NDI) and an invariant control (IC) (for specifying the whole control system’s dynamic and static responses), which significantly relaxes the PID tunings and generates the specified performance. To provide assurance and guidance for applications and expansions, this study presents the relevant fundamental analyses and transparent simulated bench tests. It should be noted that the new SMPID in forms of (Formula presented.) is different from that studied (Formula presented.) in expression and functionality.

Journal Article Type Article
Acceptance Date Jul 19, 2023
Online Publication Date Jul 25, 2023
Publication Date Jul 25, 2023
Deposit Date Aug 27, 2023
Publicly Available Date Aug 29, 2023
Journal Axioms
Electronic ISSN 2075-1680
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 12
Issue 8
Article Number 721
Keywords Geometry and Topology, Logic, Mathematical Physics, Algebra and Number Theory, Analysis
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