Robust Stability eEaluation of Multi-loop Control Systems Based on Experimental Data of Frequency Response

In this paper, we describe the composition of frequency response bands based on experimental data of plants (controlled systems) with uncertainty and nonlinearity, and the robust stability evaluation of feedback control systems. Analysis and design of control systems using the upper and lower bounds of such experimental data would be effective as a practicable method which is not heavily dependent upon mathematical models such as the transfer function. First, we present a method to composite gain characteristic bands of frequency response of cascade connected plants with uncertainty and a recurrent inequality for the composition. Next, evaluation methods of the robust stability of multi-loop control systems obtained through feedback from the output terminals and multi-loop control systems obtained through feedback into the input terminals are described. In actual control systems, experimental data of frequency responses often depends on the amplitude of input. Therefore, we present the evaluation method of the nominal value and the width of the frequency response band in such a case, and finally give numerical examples based on virtual experimental data.