Input-output stability analysis of relay servo systems

The presented approach deals with the problem of input-output stability of relay servo systems, which is related to the stability of the limit cycle and this is demonstrated in the paper. The presented case study is based upon the use of the locus of a perturbed relay system (LPRS) method that allows for small time delays and relay hysteresis causing chattering in a sliding mode control to be taken account of exactly. It is shown that neglect of these small parameters may lead to a wrong conclusion about input-output stability of the system. The example of the system thought of as input-output stable being analyzed with small parameters neglected, but actually exhibiting complex motion called in the paper "stable limit cycle with unstable center" is given and studied. A state space description based form of LPRS is proposed. Conditions of input-output stability are presented. An algorithm of input-output analysis is substantiated