Geometrical error compensation of precision motion systems using radial basis function

Geometrical error compensation and control of an XY table using neural networks

“…It is a key objective to attain improved compensation performance with less or comparable memory, using this approach. The individual geometrical error component will be decomposed into forward and reverse ones, when they are significantly different, instead of simply taking the mean as in the conventional approach and Tan et al (2000). Real machine measurements, to be provided in this paper, will strongly reinforce this necessity.…”

“…In this paper, the results in Tan et al (2000) are extended to a general case using multilayer NNs. It is a key objective to attain improved compensation performance with less or comparable memory, using this approach.…”

“…In Tan, Huang, Lim, Leow, and Liaw (2005), an overview of the application of NN to specific configurations of motion system is presented. In this paper, full experimental results are shown for an XY table, and the stability issue, which is not considered in Tan et al (2000Tan et al ( , 2005, is also addressed. Finally, the overall geometrical error is computed from these NNs based on a kinetic equation for the machine in point.…”

“…Among the limitations (highlighted in detail in Tan, Huang, & Seet (2000)), a look-up table incurs an extensive memory space, is incapable of nonlinear interpolation, and it possesses a rigid structure which is not amenable to consider other factors which may cause the geometrical error model to change. Dispensing with the look-up table, a radial basis function (RBF) error model can be built based on the calibrated points (Tan et al, 2000) to serve as the basis for error compensation. The overall error can then be directly computed from the output of these RBFs based on a geometrical overall model for the machine in point.…”

Nonovershooting multivariable tracking control for time-varying references

“…Precision control of an XY-table is an important problem in manufacturing, and transfer functions for the linear relation between the x and y components of the motion and the corresponding motor input currents for the table used in [8] were given in [14]. Representing these in state space form and combining them as two decoupled SISO systems yields a MIMO system Σ 1 in the form (1) Thus the problem is for the pencil to draw a circle, commencing from the origin in xy-coordinates.…”