Stability Analysis of GPC for Multi-axis Coordinated Motion Systems

For better synchronization performance we have previously proposed a cross-coupling gengeralized predictive controller for motion systems [1]. In this paper the problem formulation is extended to a general case. Also, as the fact that the proposed algorithm is derived in the the framework of input-ouput transfer function does not lead itself easily to an analysis of the closed loop stability, one way to deal with the dilemma by embedding GPC into the more powerful strategy of Linear Quadratic Gaussian (LQG) optimal control has been developed. Based on solving the Riccati Difference Equation (RDE) the stability of GPC can be easily analyzed, and some stability properties are given. An example of an electro-hydraulic process with two motion axes reveals that the stability of GPC can be guaranteed by selecting suitable control parameters.