A Nonlinear Fuel Optimal Reaction Jet Control Law

We derive a nonlinear fuel optimal attitude control system (ACS) that drives the final state to the desired state according to a cost function that weights the final state angular error relative to the angular rate error. Control is achieved by allowing the pulse-width-modulated (PWM) commands to begin and end anywhere within a control cycle, achieving a pulse width pulse time (PWPT) control. We show through a MATLAB{reg_sign} Simulink model that this steady-state condition may be accomplished, in the absence of sensor noise or model uncertainties, with the theoretical minimum number of actuator cycles. The ability to analytically achieve near-zero drift rates is particularly important in applications such as station-keeping and sensor imaging. Consideration is also given to the fact that, for relatively small sensor and model errors, the controller requires significantly fewer actuator cycles to reach the final state error than a traditional proportional-integral-derivative (PID) controller. The optimal PWPT attitude controller may be applicable for a high performance kinetic energy kill vehicle