Performance comparison of structured <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi mathvariant="script">H</mi> <mi>∞</mi> </msub> </math> based looptune and LQR for a 4-DOF robotic manipulator.

Abstract

We explore looptune, a MATLAB-based structured <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi mathvariant="script">H</mi> <mi>∞</mi> </msub> </math> synthesis technique in the context of robotics. Position control of a 4 Degree of Freedom (DOF) serial robotic manipulator developed using Simulink is the problem under consideration. Three full state feedback control systems were developed, analyzed and compared for both steady-state and transient performance using the Linear Quadratic Regulator (LQR) and looptune. Initially, a single gain feedback controller was synthesized using LQR. This system was then modified by augmenting the state feedback controller with Proportional Integral (PI) and Integral regulators, thereby creating a second and third control system respectively. In both the second and third control systems, the LQR synthesized gain and additional gains were further tuned using looptune to achieve improvement in performance. The second and third systems were also compared in terms of tracking a time-dependent trajectory. Finally, the LQR and looptune synthesized controllers were tested for robustness by simultaneously increasing the mass of each manipulator link. In comparison to LQR, the second system consisting of Single Input Single Output (SISO) PI controllers and the state feedback matrix succeeded in meeting the control objectives in terms of performance, optimality, trajectory tracking, and robustness. The third system did not improve performance in contrast to LQR, but still showed robustness under mass variation. In conclusion, our results have shown looptune to have a comparatively better performance over LQR thereby highlighting its promising potential for future emerging control system applications.