Towards The High Performance Contouring Control Systems

Contouring control system is one of the fundamental motion control systems inmodern manufacturing industries. This research is motivated by demands of high per-formance motion control in contour-following applications. Since there are many factorsthat will in?uence the performance of the contouring control system, this dissertationstarts from the aspect of control.In the contouring control system, the contour error, which is the shortest distancefrom the current actual position to the reference contour, gives a better assessment of thecontouring performance than the tracking error, which is is the distance from the currentactual position to the current reference position. As a result, reducing the contour error isof importance in the task of contour following and control law aims to reduce the contourerror directly is desirable.Once the contour error is treated as the control objective, information of the real-time contour error has to be obtained before performing the control. A typical way isto approximate the reference contour by its tangent line locally and estimate the con-tour error by the distance from the actual position to the tangent line at the referenceposition. However, this approach suffers from a significant error due to line approxima-tion, especially when the curvature of the reference contour is nonzero. Based on thegeometric interpretation of the contour error and the reference contour, the approach ofapproximating by the osculating circle at the current reference position is proposed. Inthis approach, the estimated contour error can be calculated by the difference betweenthe radius of curvature at the current reference position and the current radius. Further-more, when an artificial coordinate frame, which is obtained by the transformation ofthe contour-dependent frame at the reference position, is established, the real-time esti-mated contour error becomes the coordinate of the actual position with respect to suchan artificial frame.After the real-time contour error is estimated, it is incorporated in a position loop-based cross-coupled control (PLCCC) strategy. The PLCCC system ejects the cross com-pensated control effort into the position inputs, instead of the velocity inputs which is adopted in the typical CCC system. In terms of the symmetric structure of the PLCCCsystem, the cross-coupling gains are then determined by the entries of the transformationmatrix which is employed in contour error estimation and coupled control effort distri-bution. An equivalent robust control system, established from the contour error transferfunction (CETF), is developed to analyze the stability of the closed-loop PLCCC system.Moreover, a contour error switching control scheme is proposed to improve the contour-ing accuracy when the tangent-line approximation is adopted in the PLCCC system.With the fact that the contouring performance can be improved by only modify-ing the reference position inputs from the PLCCC system, a direct contour error com-pensation scheme, with respect to the global fixed coordinate frame, is developed. Interms of a projection map, generated from the unit normal vector of a new coordinateframe, the real-time contour error can then be estimated from the decomposition of thetracking error in the global fixed coordinate frame. As the consequence, compensationof the contour error is performed directly to the position inputs of the individual axialloops. Moreover, condition for the stability of the closed-loop compensation system isdiscussed.Experiments performed on a biaxial motion stage show that the accuracy of contourerrors estimation from circular approximation are improved at least 75%, relative to thatestimated from the tangent-line approach. Estimation accuracy of the direct tracking er-ror decomposition is as precise as the circular approach. In the contour-following exper-iments, contouring performance is improved more than 50% when the PLCCC strategywith circular approximation is adopted, relative to the case without any cross-coupledcontrol. Improvements from the contour error switching scheme are still evident. Whenthe direct contour error compensation scheme is applied, contouring accuracy is also im-proved. More than 20% is achieved, compared to the case without any compensation tothe contour error.