Optimal Control Approach to Design a Three-Loop Autopilot for a Tactical Missile

Conventionally, the Three-Loop Autopilot is dominated by three main parameters namely the damping factor, time constant and the open-loop crossover frequency, to achieve the desired performance. In developing the autopilot gains, the same gains as the conventional approach can also be obtained using the general optimality theory. The basic idea of setting the design parameters and the feedback gains using methods of optimal control revolves around the proper selection of the performance index for which the control is optimized. In this paper, an explicit formula for autopilot gains is driven by taking into account the relations between the desired performance and the open-loop frequency, phase margin and time constant without the need to adjust the LQR weights. Since each set of design parameters selection doesn’t guarantee the existence of the optimal control law, the optimization criteria for the three-loop autopilot are derived to know the set of design parameters for which the control is optimized. Finally, an optimal criterion to select the design parameters and therefore the autopilot gains is developed, where the time constant is set to the designer objective while the open-loop crossover frequency and the phase margin as design constraints.