Based on generalized the variation method, by introducing Hamilton function and Lagrange multiplier, this paper proposed a linear quadratic optimal control strategy for an incomplete controllable system with fixed terminal state and time. Applying the proposed optimal control to the simple two-input dual-stage actuator magnetic head positioning system with three degrees-of-freedom, the simulation results show that the system has no residual vibration at the terminal position and time, which can reduce the total access time during head positioning process. To verify the validation of the optimal control strategy of three degrees-of-freedom spring-mass models in actual magnetic head positioning of hard disk drives, a finite element model of an actual magnetic head positioning system is presented. Substituting the optimal control force from simple three degrees-of-freedom spring-mass models into the finite element model, the simulation results show that the magnetic head also has no residual vibration at the end of track-to-track travel. That is to say, the linear quadratic optimal control technique based on simple two-input dual- stage actuator system with three degrees-of-freedom proposed in this paper is of high reliability for the industrial application of an actual magnetic head positioning system.
