Robust series cascade controller design for non-minimum phase system via novel data-driven VRFT approach

Non-minimum phase (NMP) systems control is more challenging than minimum phase systems in real-time applications. This work proposes a data-driven cascade controller design using Virtual Reference Feedback Tuning (VRFT) to enhance performance and robustness for discrete NMP systems. The VRFT method defines closed-loop control specifications through a reference model (M(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{M}(\text{z})$$\end{document}), making model selection crucial. Unlike standard VRFT, the proposed design uses maximum sensitivity (Ms\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{M}}_{\text{s}}$$\end{document}) as a criterion for selecting M(z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{M}(\text{z})$$\end{document}, leading to a more robust controller. The approach includes four structures: Standard Series Cascade Structure with one reference model (SSC-1), two reference models (SSC-2), Modified Series Cascade Structure with one reference model (MSC-1), and two reference models (MSC-2). VRFT filters are tailored to these structures for controller parameter design. The robustness against perturbed plants and fragility with perturbed controllers is also addressed. Simulation results show that the proposed approach outperforms traditional methods in both performance and robustness.