$\mathscr{L}_{1}$ Adaptive Control Design Using CMPC: Applied to Single-Link Flexible Joint Manipulator

Abstract

Controlling flexible robots is a challenging issue for a variety of reasons, including: highly nonlinear dynamics, strong coupling, time-varying specifications, vibration and deviation. In addition, the existence of dependent uncertainties on their dynamics and kinematics is inevitable, so that accurate models for controller design are not available in such systems. In this paper, one “ <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathscr{L}_{1}$</tex> adaptive controller <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$({\mathscr{L}_{1}}\_{\text{AC}})$</tex> ” using “continuous-time model predictive control (CMPC)” is proposed on position tracking and removing vibration and deviation in “single-link flexible joint manipulator (SLFJM)” with existence of the unknown nonlinear dynamics and uncertainties. Eventually, in order to evaluate the efficiency of the proposed method, this method is simulated on SLFJM and the results are compared with conventional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\mathscr{L}_{1}}\_{\text{AC}}$</tex> and “Model Reference Adaptive Control (MRAC)” methods.