Coordination control of multiple axes mechanical systems: Theory and applications to machining and computer disk file systems

One fundamental problem in motion control is that the motion of multiple axes or motors must be coordinated to achieve specific performance objectives. This dissertation introduces a geometric framework to analyze and design coordinated motion controllers such that the coordination objective can be explicitly taken into consideration. Three design approaches to coordinated motion control are proposed and supported by experimental studies on contouring accuracy of machining applications and spindle phase angle synchronization in computer disk array systems.; A desired motion for an m axes mechanical system is interpreted as a differentiable curve in the m-dimensional Euclidean space. The coordination objective of the desired motion is to maintain the outputs of the system on the specific curve. By identifying the tangential direction of the curve, a task (local) coordinate frame can be formed. The tracking error, defined by the difference between the desired output and the actual output, can be transformed to the task coordinate frame where the tangential and normal errors are defined. A linear quadratic (LQ) approach is proposed to weight the tangential and normal errors differently in the LQ cost function. The resulting state feedback gain which is time-varying for general coordination objectives, is selectively increased in the normal direction of the desired motion. A linear time-varying controller is derived to achieve the desired error dynamics in the task coordinate frame. By making the normal dynamics stiffer than the tangential dynamics, improved coordination performance can be observed. A Lyapunov synthesis approach to the problem is introduced. The resulting control law projects the control action onto a direction that is the compromise between the tracking and coordination requirements.; Experiments performed on a machine tool feed drive system and an array of disk drive spindles showed improvements in coordination performance for all three designs. In machining applications, the contouring errors remain within {dollar}pm{dollar} 3 {dollar}mu{dollar}m for circular contours with 3 m/min. feed rate and {dollar}pm{dollar} 6 {dollar}mu{dollar}m for 6 m/min. feed rate. In spindle phase angle synchronization, improvements were observed both in transient and steady state responses.