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One of the concerns in vehicle steering controls regards how to manipulate a vehicle to follow a designated path accurately. Generally, this issue is usually solved by linear or nonlinear control techniques based exclusively on vehicle kinematics or on a solution that partially combines dynamics. In this paper, an integral robust multi-tiered model-based vehicle steering control strategy is proposed in order to consider both kinematics and dynamics simultaneously. In this strategy, the kinematic controller provides yaw rate commands to converge the vehicle to a designated path by tuning an embedded sliding surface based on vehicle capability. To minimize steady-state errors caused by path curvature discontinuity, integral control is also applied. A robust dynamic controller is designed to reject modeling errors and disturbances caused by side slip angle from robust observer estimations. Steering rate is implemented to consider steering actuator capabilities and to smooth steering commands. Simulations and experiments validate control performance with a full-size passenger vehicle.