Multivariable Analysis and Controller Design for Coordinated Multi-Axial Motion Control

An effective and formal design procedure for the design of coupled controllers for coordinated multi-axial motion control applications is described here. The design procedure relies upon representation of the system dynamics using task-based coordinates along and orthogonal to the desired contour in motion space. The multivariable system dynamics, when represented thus, are diagonally dominant or can be made so by the addition of dynamic precompensation. Moreover, performance measures of interest such as contouring error and tracking error are strongly and directly related to diagonal elements of the precompensated system transfer function matrix. The multivariable controller design problem thus reduces to a number of single loop controller design problems, each of which is strongly linked to one of the performance measures of interest mentioned above. The controller design for these single loop problems is performed here using frequency domain methods. The resulting controllers, when implemented in the actuator-based coordinate system, are time-varying coupled dynamic compensators. The time variation of the controllers is directly related to the time-variation of the desired motion coordination. The design procedure is applied in the paper to improve the performance of a simulated bi-axial motion control system for high speed motion, by controller design.