For autonomous navigation systems, when the agricultural machinery changes speed, it usually leads to the worsening of control precision and stability. As the Beidou satellite navigation technology and the MEMS inertial sensor technology become increasingly mature, the research and development of autonomous navigation system of agricultural machinery have been greatly promoted. The Dongfeng agricultural tractor DF1004-2 was modified to be an experimental platform, and the crucial devices such as intelligent controller, wheel angle sensor, RTK base station were designed and developed for the tractor’s intelligent modification. Moreover, the state space model, including yaw rate state was established to achieve a stable feedback controller that adapted to large speed changes. Traditionally, the path tracking control of intelligent tractors assumed speed to be constant and designed controllers with a kinematic model or used pursuit strategy without a model. For these controllers, the convergence speed can be slow due to lack of yaw rate information, moreover, when speed switched, the steering magnitude of front wheel grew, which decreased the control accuracy and stability. The state-space model with yaw dynamics was established via system identification, and then a flexible LQR control strategy was designed based on the state-space model, which provided a solution to the challenge. Experimental results from agricultural fields showed that the control precision was 3cm without speed switch, and 5cm with speed switch, which met the production requirements of agricultural machinery.