Mixed H₂/H_∞ attitude control of a LEO microsatellite in the presence of inertia matrix uncertainty

Owing to a great decrease in size and weight, the pointing of microsatellite is vulnerable to disturbances and the uncertainty of moment-of-inertia variation. Mixed H₂/H_∞ control, giving consideration to both stability robustness and root-mean-square (rms) performance, is an effective approach for attitude controller design of microsatellites in face of exogenous disturbances and plant uncertainties. This paper applies mixed H₂/H_∞ controller to address a critical condition that during the translation thrusting the attitude of microsatellite is affected by the unbalanced torque of coupled thrusters and the resulting variation of moment-of-inertia from operation mode switch. By using linear matrix inequality method, the numerical solution of mixed H₂/H_∞ state-feedback controller can be efficiently solved. The results of an integrated test including reaction wheel dynamics prove that mixed H₂/H_∞ controller has satisfactory rms performance of pointing control and remarkable robustness to inertia matrix uncertainty by making a compromise between H₂ and H_∞ costs.