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In this paper, we present a systematic approach for high-performance and efficient trajectory tracking control of autonomous wheel loaders. With the nonlinear dynamic model of a wheel loader, nonlinear model predictive control (MPC) is used in offline trajectory planning to obtain a high-performance state-control trajectory while satisfying the state and control constraints. In tracking control, the nonlinear model is embedded into a Linear Parameter Varying (LPV) model and the LPV-MPC strategy is used to achieve fast online computation and good tracking performance. To demonstrate the effectiveness and the advantages of the LPV-MPC, we test and compare three model predictive control strategies in the high-fidelity simulation environment. With the planned trajectory, three tracking control strategies LPV-MPC, nonlinear MPC, and LTI-MPC are simulated and compared in the perspectives of computational burden and tracking performance. The LPV-MPC can achieve better performance than conventional LTI-MPC because more accurate nominal system dynamics are captured in the LPV model. In addition, LPV-MPC achieves slightly worse tracking performance but tremendously improved computational efficiency than nonlinear MPC. A video with loading cycles completed by our autonomous wheel loader in the simulation environment can be found here: https://youtu.be/QbNfS_wZKKA.