A receding time horizon linear quadratic optimal control approach is formulated for multi-axis contour tracking. The approach employs a performance index with a fixed weighting on quadratic contouring error, tracking error, and control input over a future finite horizon. The problem is then cast into a standard receding horizon LQ problem with time varying weighting matrices, which are functions of the future contour trajectory within the receding horizon. The formulation thus leads to an optimal solution of time varying state feedback and finite preview gains. The choice of relative weighting of tracking errors and contour errors makes it possible to increase contour tracking accuracy while sacrificing tracking accuracy. Other related strategies such as finite time horizon LQ and finite preview LQ tracking control are discussed and compared with the proposed approach. Simulation results on a X-Y motion control problem demonstrate the effectiveness of the control scheme.
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