Performance Enhancement of Spacecraft Attitude Control Using Modified Robust Design Optimization in Presence of Sensor Noise

In this study, a robust design optimization (RDO) algorithm is customized to reduce the effect of sensor noise on the accuracy of a nonlinear spacecraft attitude control. The spacecraft attitude is controlled using an anti-windup modified proportional–integral–derivative (PID) algorithm, modulated with the pulse-width pulse-frequency (PWPF) technique, and actuated by on–off thrusters. The modulator output frequency is limited to 50 Hz. The thruster actuator is modeled with a pure delay of 0.02 s followed by a second-order binomial transfer function with an equivalent time constant of 0.01 s. A set of quasi-normalized equations is utilized in order that the obtained results are applicable in wide range values of spacecraft moment of inertia and maximum thruster torque. The time-average of the absolute pointing error is selected as a performance index for the RDO algorithm in quasi-normalized form. A weighted combination of standard deviation and expected value of the performance index is chosen as the statistical objective function. The controller gains are set with RDO and DDO (deterministic design optimization) methods by means of the genetic algorithm (GA). Using the Monte Carlo simulation, the optimization procedure is iterated for each noise sample function that generates by the Latin hypercube sampling (LHS) method. The compared results between the RDO and the deterministic approach show that the customized RDO algorithm is able to reduce the noise effects on the performance index. Finally, an approximate formula for the standard deviation-expected value of the time-average absolute pointing error is proposed in order to select an appropriate value of the objective function weight coefficient.