Infinity norm measurement of sensitivity function based on limit cycles in a closed-loop experiment

This paper proposes a new method for the measurement of the infinity norm of the sensitivity functions of linear systems. A nonlinear feedback structure is derived from existing relay experiments. The proposed scheme may produce a limit cycle at a frequency where the sensitivity function of a given system achieves a selected magnitude. Necessary and sufficient conditions for the occurrence of the limit cycles are discussed using the describing function method. If the magnitude is chosen larger than the sensitivity infinity norm, the strictly passivity of the scheme can be demonstrated. Based on these analyses, a simple procedure is then proposed to identify the infinity norm of the sensitivity function for a large class of processes. Simulation results show the effectiveness and simplicity of the proposed method.