DOI: 10.3390/axioms12080721 ISSN: 2075-1680

Model-Free Sliding Mode Enhanced Proportional, Integral, and Derivative (SMPID) Control

Quanmin Zhu
  • Geometry and Topology
  • Logic
  • Mathematical Physics
  • Algebra and Number Theory
  • Analysis

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 u=SMPID(σ(e))=PID(sliding-mode) is different from that studied u=sliding-mode(PID(e)) in expression and functionality.

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