A Study on the L-infinity/L-2 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 L-2 to L-infinity (which is also denoted by the L-infinity/L-2-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-infinity/L-2 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-infinity/L-2-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.