Evaluation of reduced-order and robust reduced-order controllers on a two-link manipulator

This paper examines the synthesis of various robust controllers for command tracking of trajectories that excite many of the arm dynamics. The model used for all the designs is a 20-degree-of-freedom lumped-spring-mass-damper model of 40th order that is reduced to 18th order by balanced truncation. First, a standard linear-quadratic-Gaussian (LQG) controller is designed and tested, and robustness at the control loop is recovered with a loop transfer recovery (LQG/LTR) controller design. Next, loop transfer recovery based on the special coordinate basis analysis of the plant is covered. In order to make the LQG/LTR and LTR controllers more practical, controller reduction is applied using modal residualization and balanced truncation. Next, a fourth-order SANDY direct optimization design is covered and experimentally evaluated. In addition, a robust SANDY design is explained and experimentally evaluated. In both the reduced-order and robust reduced-order cases, the objective is to avoid excitation of the flexible modes and to concentrate on the rigid body characteristics of the arm. The results show that reduced-order controllers can provide performance comparable to that of full-order controllers.