A study on the L∞/L2 performance of a computed torque controller

Abstract

This paper introduces a new performance analysis method for a computed torque controller against disturbances with the framework of the induced norm from L2 to (which is also denoted by the L∞/L2-induced norm). To this end, we first derive a linear time-invariant (LTI) representation of the system obtained by connecting a robot manipulator and a computed torque controller. We then formulate the problem definition associated with the L∞/L2 performance of the computed torque controller in which the maximum magnitude of the output for disturbances of finite energy is adopted as the performance measure. We next show that the L∞/L2-induced norm of the derived LTI system can be explicitly computed by solving the continuous-time Lyapunov equation. Finally, some experiment results are provided to demonstrate the effectiveness of the introduced performance analysis method. ？ 2018 IEEE.