Application of the locus of a perturbed relay system to sliding mode relay control design

This paper proposes a further development of the locus of a perturbed relay system (LPRS) method and its application to design of sliding mode relay control systems. A relation between the locus configuration and possibility of the sliding mode to occur is derived. A notion of the quasi-sliding mode is used to indicate the chattering mode occurred due to non-zero hysteresis of the relay in a real system designed as a sliding mode relay system. It is shown that the difference between the two modes in respect to the linearized system dynamics lies in finite and infinite values of the equivalent gain of the relay, which can be calculated with use of the locus method. The presented approach involves the quasi-sliding mode design with sliding mode being considered a limiting case of the quasi-sliding mode. An example of the design of DC motor servo system is given to demonstrate the proposed approach.