Neuron Optimization Based PID Approach for Cutting Force Control

To improve the cutting efficiency, one of key approaches is to control with constant force in the full depth working condition. And the controller design is vital to realize the real-time feasibility and robustness of the system. A neuron optimization based PID approach is proposed in this paper and adopted in the NC cutting process. This approach optimizes the parameters of PID controller real-timely with the neural network control principle. It not only overcomes the mismatch of the open-loop system model which occurred in constant PID control, but also solves the contradiction between the calculation speed and precision in the neural network which caused by the node choosing of the hidden layer. At last, the simulation has been carried out on a NC milling machine to prove the validity and effectiveness of the proposed approach. Introduction The method to improve NC cutting efficiency is to increase the metal wipe rate in the permission range of machine-tool-workpiece system [1]. In the machining process, the constant force control method by adjusting the feed rate real-timely is one of the main approaches to reach the goals above. In the traditional NC programming, the velocity is preset according to the experiential knowledge or cutting database. However, when the value of the feeding rate is too high, it will cause the vibration of the machine, reduce the life of cutter and result in the high price and low cutting efficiency. It will decrease the dimension precision and the surface quality of the workpiece. So adjusting the feed rate online and making the actual force track the reference value, namely achieving the constant force control in the cutting process is very important to the practical engineering [2,3]. As the NC cutting process itself is a nonlinear procedure, the PID control methods controlled the nonlinear cutting process by an approximately linear model; there is a mismatch of the open-loop system model in the control. Meanwhile, the tuning method for constant PID controller, such as Z-N method, Cohen-Coon method, are usually applied by that it tuned the parameters with the empirical equation according to the critical oscillation principle by matching the control member into single order inertial segment, so it is another problem to be solved about how to acquire the accurate parameters of the controller. And for the neural network control in the working process, the choosing of the hidden layer is of the most importance. In particular, there is no certain mode on node choosing. In addition, the Model Reference Adaptive Control, Fixed-gain Integration Control, Direct Adaptive Control and Adaptive Pole-Zero Cancellation, all have the problem of model mismatch, especially the bad robustness caused by the finite segmentation of feeding velocity in the current NC system. In this paper, a neuron optimization based PID approach for cutting force control is proposed. The method adjusts the parameters of PID controller real-timely with the neural network principle. The proposed approach is adopted in the NC cutting process to prove the validity and effectiveness. Adaptive PID Control in the Cutting Process The closed loop of neuron optimization based PID control system for a NC cutting process is shown in Fig.1, F is cutting force, r F is the reference cutting force, u is the feeding command and f is the feeding rate. Key Engineering Materials Vols. 315-316 (2006) pp 85-89 online at http://www.scientific.net © (2006) Trans Tech Publications, Switzerland Online available since 2006/Jul/15 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.33-14/04/08,12:01:32) Fig.1 Closed loop of neuron optimization base PID control for cutting process Milling Process. The servo system can be simplified into a first order continuous system, the transfer function is ). 1 /( ) ( / ) ( ) ( + = = s T K s U s s G M M a Ω Ω (1) where, a U is armature voltage of the servo motor, Ω is the output angular velocity of the servo motor, Ω G is the transfer function of the motor, M K , M T is transfer coefficient and the time constant. Adopt the spiral bar milling cutter as cutting tool, and consider the distortion condition in the principal direction, the milling force can be simplified to the endpoint of the cutter tool. . / ) ( ) ( t K t F t = δ (2) where, t K is stiffness of the cutter; δ is distortion of the end of cutter tool. Take linearization to the cutting force according to the reference [1]. ). ( ) ( t h K t F m s = (3) ). 1 ( ) ( ) 1 ( ) ( − + − − = t t t f t h z m δ δ (4) . ) ( ) ( z n t f t f z ′ = (5) where, m h is maximum cutting depth; s K is coefficient depend on material, geometric parameters of the cutter and maximum cutting depth; z f is feeding value of each tooth; n is rotate speed of the spindle; z′ is tooth number of the cutter. In order to simplify the calculation, the cutting force can be simplified into a first order continuous system. So the whole non-vibration cutting process can be depicted by a second order model [5]. ). 1 )( 1 /( ) ( s T s T K s G C M n + + = (6) where, C T is milling time constant; n K is gain coefficient. In the Eq.6, n K is a time varying parameter depended on the cutting condition. So the transfer function of the cutting process is a second order model with time varying parameter. Design of Neuron Optimization based PID controller. The classical PID controller can be expressed as       + + = ∫ dt t de T dt t e T t e K t u D t I p ) ( ) ( 1 ) ( ) ( 0 . (7) The corresponding discrete expression is )] 1 ( ) ( [ ) ( ) ( ) ( 0 − − + + = ∑ = k e k e K j e K k e K k u D k