Design of Gain-Scheduled Strictly Positive Real Controllers Using Numerical Optimization for Flexible Robotic Systems

摘要

The design of gain-scheduled strictly positive real (SPR) controllersnusing numerical optimization is considered. Our motivation isnrobust, yet accurate motion control of flexible robotic systems vianthe passivity theorem. It is proven that a family of very strictlynpassive compensators scheduled via time- or state-dependentnscheduling signals is also very strictly passive. Two optimizationnproblems are posed; we first present a simple method to optimizenthe linear SPR controllers, which compose the gain-scheduledncontroller. Second, we formulate the optimization problem associatednwith the gain-scheduled controller itself. Restricting our investigationnto time-dependent scheduling signals, the signals arenparameterized, and the optimization objective function seeks tonfind the form of the scheduling signals, which minimizes a combinationnof the manipulator tip tracking error and the control effort.nA numerical example employing a two-link flexible manipulator isnused to demonstrate the effectiveness of the optimal gainschedulingnalgorithm. The closed-loop system performance is improved,nand it is shown that the optimal scheduling signals are notnnecessarily linear.