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This article presents a model-based motion planning and control system for autonomous vehicles and its experimental validation. The system consists of four modules: 1) global routing; 2) behavior planner; 3) local trajectory generation; and 4) trajectory tracking. The algorithm and software of each module are detailed, including a behavior planner with unified models to handle typical scenarios in both highway and urban driving, a deterministic sampling algorithm for robust responsive trajectory generation, and a dynamics-and-delay-aware preview algorithm to achieve accurate trajectory tracking. The developed system is implemented and tested at the Mcity test facility with a full-size automated car and a dozen of challenging traffic scenarios.