The engagement quality of a helicopter dry clutch has a significant impact on the service life and overall flight performance of the helicopter. The engagement oil pressure is an important factor affecting the clutch engagement quality. Firstly, a nonlinear input–output dynamic model for the dry clutch is developed to investigate the optimization and control of dry clutch engagement pressure in this paper. Secondly, to efficiently obtain the optimal pressure curve, an optimal method combining the developed dynamic model with the state feedback gain of a linear quadratic optimization regulator (LQR) solver is proposed. Thirdly, considering that hydraulic actuators may struggle with tracking certain pressure curves, a hydraulic actuator for accurately tracking pressure curves based on fuzzy PID is proposed. The simulation results indicate that the developed hydraulic actuator exhibits an excellent tracking performance. Moreover, compared with linear and segmented pressure curves, the optimal pressure curve derived from the proposed method significantly reduces jerk, friction work, and engagement duration, resulting in improved helicopter dry clutch engagement quality.