This chapter discusses the design of fractional order (FO) modified IMC (m-IMC) for integrating time delay processes. The m-IMC constitutes an additional controller in the basic IMC control loop, which broadens the applicability of IMC and can be used to enhance the performance and robustness of the close loop system. In this work, the additional controller is used to enhance the bandwidth of the close loop system. The IMC controller constitutes the minimum phase part of the plant model and a filter. In the proposed controller, a FO filter is chosen with two tuning parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}, which are used to achieve desired gain margin (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_m$$\end{document}) and phase margin (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi _m$$\end{document}) of the close loop system. The additional controller is chosen as PI with only one tuning parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi $$\end{document} and used to enhance the close loop bandwidth. Two types of integrating process models are considered, first, integrating plus time delay (IPTD), and second, second-order integrating plus time delay (SOIPTD) process. Simulation studies are carried out for nominal and uncertain plant models with 30% uncertainty for set-point tracking and disturbance rejection. The performance of the controller for set-point tracking is measured in terms of rise time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(T_r)$$\end{document}, settling time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(T_s)$$\end{document}, integral absolute error (IAE), and integral of time-weighted absolute error (ITAE). Whereas the disturbance rejection performance is measured in terms of IAE and ITAE and the control effort is measured in terms of time variance (TV).
Fractional Order Modified IMC for Integrating Processes for Given Stability Margins and Increased Closed Loop Bandwidth
stud. in Infrastructure & Control
2022-09-11
18 pages
Article/Chapter (Book)
Electronic Resource
English
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