ANALYSIS OF MATHEMATICAL MODELS USED IN METALWORKING ADAPTIVE CONTROL SYSTEMS

Abstract

Control algorithms are based on the use of a mathematical model of the control object. The control system, using one of the search algorithms, determines the best control action first on the mathematical model, and then applies the found optimal (in this situation) values of control actions directly on the control objectTo build a mathematical model of the machining process, it is necessary to analytically set a system of technical restrictions for the search area for optimal cutting conditions and express the dependence of the optimality criterion on the elements of cutting conditions. The measured parameters characterizing the cutting process, as a rule, are cutting force, vibration, temperature in the cutting zone, torque Mcr on the spindle,drive power of the main engine, etc.Such a customizable model can be used not only for control purposes, but also, for example, in diagnostic tasks, acting as a sensor of parametric disturbances and informing about the parameters going beyond safe limits. At the same time, the use of a customizable model in the control loop also leads directly to an increase in the reliability of the system in relation to less flexible controllers with fixed parameters.Thus, the solution of problems of building control systems is closely related to the development of algorithms for adapting the model in real time, the use and study of the speed and noise immunity of such algorithms.