Optimum control of an unstable booster with actuator position and rate limits

The general problem of designing an autopilot to achieve optimum response of a rigid aerodynamically unstable booster is considered. The vehicle is represented by a second-order linear model, and the actuator is represented by a first-order model having rate and position limits. The maximum principle of Pon try agin and its extension to bounded state variables are employed to obtain general conditions that the optimum control law must satisfy, and it is shown that operation at either maximum rate or maximum deflection is optimum when the performance measure is explicitly independent of the control. The switching surface for time-optimum control is calculated, and expressions are obtained for the maximum stability region. A readily implemented suboptimum control law was devised, and its performance was investigated by analog simulation. The results achieved showed that this suboptimum control law yields excellent transient response and realizes the maximum stability region.