Research and optimal sliding mode control switching element covered feedback

This paper considers the organization of optimal and sliding modes in control system for non-stationary second order object with parameters that change on some interval. The main object of the control system is the three-position relay controller with feedback and defined area of the hysteresis. The article proves the optimal control problem for stationary objects on stage of achieving slip trajectory when there is a pair of control signals (-1, 0) or (0, 1). The proposed functional transformation of the object parameters into the controller parameters allows setting up closed system using the experimental transients. The method provides time-optimal control without calculating the switching curve in the phase space for an object with known and stationary parameters. The method has robust properties when object parameters vary within certain limits and does not require estimates of the derivative of the measured signal. In case of transport delay in the system, the relay controller generates a quasi-optimal control with sliding mode. The necessary condition for the existence of a sliding mode indicates indirect dependence of sliding trajectory parameters from the object parameters and robust properties of the system in terms of asymptotic stability. Time-optimal control is confirmed by modeling and experiments on the existing heating system of industrial type. The presence of delay and object transfer coefficient triple modification lead to the sliding mode with a pair of signals (-1, 0) or (0, 1).

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