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In the current missile weapon system, the majority of control systems rely on classical PID control. However, as control performance requirements continue to advance, PID controllers are struggling to achieve both rapid response and stable tracking processes simultaneously. To address these challenges in engineering, an optimal controller is designed, with the optimal control law derived in the form of a linear quadratic regulator(LQR). Simulation results demonstrate that the optimal controller exhibits no static difference in tracking step signals, an adjustment time of 0.034 seconds, and a stable rising process without overshoot. When tracking slope and sinusoidal signals, the tracking error is less than , with a lag time of only a few milliseconds. This optimal controller system exhibits rapid and accurate tracking performance for step, slope, and sinusoidal signals. Compared to the classical PID controller, this approach offers higher control precision, improved control performance and stability, effectively resolving the issue of PID controllers struggling to achieve both rapidity and stationarity in engineering applications.