Synthesis of Proportional-Integraldiferential Control System for Longitudinal Feed of CNC Lathe

Abstract

Relevance As part of the study, the MATLAB software package has developed a longitudinalintegral- differential control system for driving the longitudinal supply of a CNC lathe. Experimental studies have shown the effectiveness of the control system, which is expressed in the economical use of the synchronous motor life. Resource efficiency is achieved due to the ability to optimize and adjust the speed of rotation of the electric motor at any stage in the implementation of the part processing process. Aim of research The main aims of the research develop a parametric PID system for controlling the electric drive of a CNC lathe. Study the developed management system for stability according to several criteria. Research methods To achieve computer-automated modeling, control system development methods were used. In particular, the MATLAB SIMULINK software package was used. Results Parametric proportional-integral-trimming control system for longitudinal supply of CNC lathe has been developed. It is worth noting that the control is based on the empirical dependence of the roughness of the treated surface of the part on the radius at the tip of the cutter and feed. The self-control process begins in the PID function block. It is based on the mateamtic dependencies of the applied coefficients (P – longitudinal; I – integral; D – differential). It is found that dynamic control of fuzzy values of electric motor parameters is provided due to transfer function of ball-screw pair. The functions of the converter, the torque motor, are performed by the gearbox. It is worth noting that the control system is customizable, the user has the ability to independently set the time after which the PID unit responds and performs the control function. In this study, the response time is 20 s, taking into account the operation of the transport delay unit. Stability studies of the developed electric motor control system were performed as part of confirmation of the obtained simulation results. The stability index was analyzed on the basis of three main criteria: Hurwitz; Mikhailov; Vyshnegradsky. The results of calculations according to the Hurwitz criterion showed that the electric drive control system is stable (stable), since positive values were obtained as a result of the calculations. In the Mikhailov study, the corresponding gradograph was obtained, which shows that the control system is stable, since the curve starting with the real positive semi-axis (gradograph) bends counterclockwise around the origin and passes through three quadrants in turn. The results of calculations according to the Vyshnegradsky criterion showed that the control system corresponds to inequality, а1а2 ≥ а2а3, therefore, it can be concluded that the control system is stable. Keywords: parametric proportional-integral-differential control system, resistance studies, Hurwitz criterion