Theory and Applications of the Robust Cross-Coupled Control Design

Abstract

The cross-coupled control (CCC) has been recognized as an efficient motion controller that reduces contouring errors, but theoretical analysis of it is lacking, and there is no systematic design approach for obtaining a CCC system with guaranteed control performance. Consequently, the compensators C in CCC are commonly implemented in a PID structure and their contouring accuracy is usually degraded in real applications under different operating conditions. In an attempt to overcome the CCC design limitations described above, this paper introduces a robust CCC design based on a novel formulation: the contouring error transfer function (CETF), leading to an equivalent formulation as in the feedback control design problem. Then, methods in robust control design can be readily employed to achieve robust CCC with specified stability margins and guaranteed contouring performance. Furthermore, the proposed design has been verified as being internally stable. All provided experimental results indicate that the proposed robust CCC design consistently renders satisfactory contouring accuracy under different operating conditions.

Position command shaping control in a retrofitted milling machine

“…The similar functional relationship 1=ð1C C c P f Þ between the coupled and uncoupled systems is defined as the contour error transfer function (CETF) in Yeh and Hsu's research [10]. In order to design C c , understanding 'what is P f ?'…”

“…A typical cross-coupling controller essentially consists of an algorithm for calculating the contour error and a control law for eliminating the contour error. Many control laws such as traditional PID control [5], optimal control [7], adaptive control [8], fuzzy logic control [9], and robust control (QFT design algorithm) [10] have been proposed to implement the CCC. Chiu and Tomizuka view the contouring performance as a regulation problem in a moving task coordinate frame to attach the desired contour [11].…”

Contouring Controller for Precise Motion Control Systems

“…One of the earliest works towards the increasing of contouring performance, namely cross coupled controller (CCC), has been published in [4]. Many consecutive works explored the advantages of CCC with additional robust [5], self-tuning [6], [7], and fuzzy-logic [8] control methods. Besides CCC, some other control architectures were developed involving coordinate transformation.…”

A novel cross-coupling control design for Bi-axis motion

“…The similar functional relationship 1 1 ϩ C c P between the coupled and uncoupled systems is defined as the contour error transfer function (CETF) in Yeh and Hsu's research [8]. In order for us to design C c , understanding 'what is P?'…”

“…Many control laws such as traditional PID control [3], optimal control [5], adaptive control [6], fuzzy logic control [7], and robust control (QFT design algorithm) [8] have been proposed to implement the CCC.…”