A Structured Linear Quadratic Gaussian Based Control Design Algorithm for Machine Tool Controllers Including Both Feed Drive and Process Dynamics

A new extension of the stochastic linear quadratic Gaussian (LQG) regulator problem is developed and used for the design of new suboptimal cross-coupling controllers for machine tool drives. This new extension allowed us to combine both the drive and the cutting dynamics into a unified model driven by the static and the dynamic portions of the cutting force. The dynamic portion of the cutting force is considered as a stochastic random process in end milling contouring processes. The outputs of the axes are corrected by the cutting tool deflections which result from the cutting force-workpiece resistance interactive dynamics. Most importantly, the LQG extension developed here is directly applicable to the design and optimization of centralized, decentralized, and hierarchical machine tool controllers that have previously appeared in the literature. This is possible because our extension allows the assignment of a different control structure for each control input even if more than one control input are contributing to the same axis. Furthermore, the method admits each controller to function in any chosen subset of the available measurements. Thus, it provides us with a powerful means for designing any of the above-mentioned controllers using the same approach. The results of our suboptimal cross-coupling controllers were magnificent when compared to the commercially available positioning controllers.