Abstract: It is difficult for classical methods to implement a positioning follow-up system with no overshoot,little static errors and much shorter transition time.In this paper a technique of linear quadratic index of state feedback(LQSF) is proposed which improves the dynamic and static performences of follow-up systems.Those unmeasurable states have been reconstructed by state observers.Experiment and simulation results show that this technique is encouraging and satisfactory,bringing about the acceleration of system response speed and the realization of static error minimization.