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Many biaxial contouring systems involve competing control objectives of maximizing accuracy while minimizing traversal time. A model predictive controller for contouring systems is proposed where the control inputs are determined by minimizing a cost function which reflects the tradeoff between these competing objectives, subject to state and actuator constraints. The path speed is automatically adjusted to maintain accuracy along the path, and the cost function can be tuned towards higher contouring accuracy and lower path speed, or vice versa. To facilitate real-time implementation, a linear time-varying approach is proposed. The controller is successfully implemented in real time on an X-Y table, and experimental results demonstrate that the new contouring control scheme achieves an improvement in performance compared to both industry standard and advanced tracking controllers.