Control and identification of parameters of a joint of a manipulator based on PID, PID 2-DOF, and least squares

Proportional-integral-derivative (PID) is one of the most used forms of control in the industry, and there are several variations of its architecture. PID 2-DOF controller aims to improve plant disturbances through faster control actions. This paper presents the identification through the non-recursive least squares (LS) mathematical method of a rotational joint of a cylindrical manipulator and the application of PID and PID 2-DOF controllers. The identification of the 1st-order model of the manipulator’s joint is performed to apply the tuning methods Ziegler/Nichols (ZN), Chien–Hrones–Reswick (CHR), internal model control (IMC), and Skogestad IMC method (SIMC) in the proposed controllers. To compare the results of controllers, the following performance criteria are used: rise time (tr\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 (ts\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}), overshoot, integral of absolute error (IAE), and integral of squared error (ISE). In the end, it is concluded that the CHR and IMC tuning methods obtained better results for both the PID and the PID 2-DOF.