Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator

Abstract

This paper proposes the design of a hybrid iterative learning controller for a four-degree-of-freedom (DOF) robotic machining manipulator (RMM). It combines a nonlinear saturated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>proportional + integral + derivative (PID) control with desired gravity compensation (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="bold">d</mml:mi><mml:mi mathvariant="bold">g</mml:mi><mml:mi mathvariant="bold">c</mml:mi></mml:math>) and proportional + derivative- (PD-) based iterative learning control (ILC). The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="bold-italic">P</mml:mi><mml:mi mathvariant="bold-italic">I</mml:mi><mml:mi mathvariant="bold-italic">D</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>control is the primary component that maintains the local stability of the entire RMM system and the PDILC component provides robustness to parameter variations and uncertainties in the robot dynamics. Global asymptotic stability of the proposed control algorithm is conducted using Lyapunov direct method and LaSalles invariance principle. Simulation results show the effectiveness and robustness of the proposed hybrid iterative learning controller. It is also shown that the proposed controller achieved better tracking performances compared to conventional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi mathvariant="bold-italic">s</mml:mi><mml:mi mathvariant="bold-italic">a</mml:mi><mml:mi mathvariant="bold-italic">t</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="bold-italic">P</mml:mi><mml:mi mathvariant="bold-italic">D</mml:mi><mml:mi mathvariant="bold-italic">d</mml:mi><mml:mi mathvariant="bold-italic">g</mml:mi><mml:mi mathvariant="bold-italic">c</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>feedback controller.