Research On PID Control And NURBS Curve Interpolation Of Polishing Machine Tool

The main research content of this project is the control system of the four-axispolishing machine tool. PID module and interpolation module are two core parts ofthe control system, so this paper mainly focuses on the PID control and the NURBScurve interpolation.In this paper, it is found that the parameters of PID have a great influence oncontrol performance. The position and velocity errors of the four-axis polishingmachine are very big when using the parameters gave by the system, so theparameters of the PID controller need to adjust. The optimization of PID parametersincludes the following contents：(1) The servo loop of the A3200controller is analyzed and the whole loop isdevided into velocity loop and position loop, then the mathematical models of transferfunction of the two loops are established.(2) The4:1decline curve method is used to adjust the proportional gain Kp，theintegral gain Kiof the velocity loop, the proportional gain Kposof the position loop andthe parameters inside the position loop.(3) When tuning the position loop, it is hard to ajdust the parameters because ofthe complex loop construction. In order to solve this problem, a equivalent controlmethod is proposed in this paper. The position loop is simplified so that it can beequivalent to a traditional PID controller. Thus, the tuning of position loop can betransformed into the tuning of the traditional PID controller. In this way, the tuningprocess is simplified.(4) The control performance under different parameters which can be reflectedby response curves is analyzed though simulation. Simulation results show that usingthe parameters after tuning can get better control performance.(5) An experiment is done on z axis of the four-axis polishing machine tool.Experiment results show that after the parameter tuning the position and velocityerrors decrease a lot, the control performance and precision of movement areimproved. NURBS curve interpolation consists of pre-processing, parameter densification,feedrate-adaptive control and acceleration/deceleration(Acc/Dec) control fourprocesses. Aiming at the key problems of these processes, rearch on NURBS curveinterpolation mainly includes the following aspects in this paper:(1) The feedrate-adaptive control algorithm with the constraints of chord errorand normal acceleration is adopted so that the interpolation feedrate can adjustaccording to the change of the curvature of the curve.(2) The S-shape Acc/Dec algorithm is introduced. The deceleration point can bepredicted through the combination of inverse interpolation and monitoring theinterpolation distance. In this paper, a new algorithm is proposed to eliminate theinteraction between two adjacent feedrate-sensetive points.(3) Simulation of NURBS curve interpolation is done. Simulation results showthat the interpolation algorithm prorosed in this paper can obtain smooth velocity andacceleration curve, the jerk and the chord error can be limited within the allowablerange; The comparison simulation indicates that he interpolation algorithm prorosedin this paper can get higher interpolation accuracy and efficiency.(4) An interpolation experiment is done on the four-axis polishing machine tool.The position, velocity and acceleration curves of each axis are analyzed in detail.Experiment results show that the proposed algorithm is effective.