Inverse Problem Of Task Coordinate Frame Approach Of Contouring Control

The inverse problem of the task coordinate frame of contouring control approachis discussed in this paper. The task coordinate frame approach shows that contouringperformance can be viewed as a regulation problem in a moving task coordinate frame thatis attached to the desired contour. By transforming the machine tool feed drive dynamicsto this task coordinate frame, a control law is designed to assign different dynamics tothe tangential and normal directions. The transformation also illustrated the effect ofcontour curvature and feed rate in the control action as well as the system dynamics inthe task coordinate frame. The resulting control law consists of a linear time-varyingproportional-plus-derivative(PD) position error feedback control law and a linear timeinvariant trajectory feedforward control law. The key point of the inverse problem is togive the desired dynamics of the system in the task coordinate frame. three problems willbe met: the contour error estimation, the decoupling of the error, and parameters designfor single axis. By three main steps a method of how to give the dynamics matrix thatcan guarantee the contour error is proposed. At last experiment results were verified themethod.System identification is a very important part of work in the control system design,in this paper,we chose the pseudo-random signal to be the input signal, since this signalhas plenty of frequency components. The drive is set under the torque model. Then thepseudo-random signal is send to the motion control board by the PC, the A/D converter onthe motion control board transforms the signal to analog signal and send it to the driver,then get the position feedback signal of the motor by the coder of the driver. Afterwardswe identify the system by sending the pseudo-random signal and the feedback positionsignal to the Matlab system identification box. At last we can get the model of the feeddrive system.Then we used the model from the system identification to design the control law ofthe machine feed drive system, and did lots of experiments on the X-Y table. By analyzingthe experiments results, we verified that the method proposed is correct. Then we gave therelationship between some key parameters and the system performance. At last, due tothe limitations of the method, some ideas of improvements of the method were proposed.