This study designed an optimal control algorithm based on linear quadratic regulator （LQR） and proposed the integration of output residual integral control to improve the performance of the optimal controller. A controllable and observable model of the servo system was built under friction-neglected conditions. Based on the LQR optimal control theory， the optimal control law for the system was derived. The influence of friction on the controller's performance was studied， and integral control was incorporated into the optimal control loop to improve steady-stage performance. Experimental results show that， compared with the PID lead-lag compensator， the proposed optimal controller exhibits zero overshoot during the presetting stage， reduces settling time by 47%， decreases steady-stage response delay by more than 55% while lowering the decoupling rate by over 50%. With the addition of output residual integral control， the issues of overshoot and tailing caused by friction in the steady stage are effectively eliminated， resulting in a decoupling rate below 4% and a further delay reduction exceeding 40%. Vibration tests indicate that the designed optimal controller possesses both stability and robustness， thereby laying a foundation for the future engineering application of the optimal control method in product models.