Direction-cosine-matrix-based attitude control subject to actuator saturation

Set-point attitude control of a rigid body explicitly preventing actuator saturation is considered. The attitude control approach developed does not employ any sort of direction-cosine-matrix (DCM) parameterisation, such as Euler angles or quaternions. Rather, the DCM is used directly within the feedback control algorithm. Together a proportional control term and an angular velocity control term make up the attitude controller. The angular velocity control is composed of a strictly positive real system subject to a special input non-linearity. The specific form of the proportional control and angular velocity control ensure control torques are below the saturation level of the on-board actuators. Two controller synthesis methods are considered. The first uses the linearised system, the solution to the linear quadratic regulator problem, and the Kalman-Yakubovich-Popov lemma to design the controller. The second employs a simple low-pass filter that is guaranteed to stabilise the closed-loop system; tuning the low-pass filter is also considered. Numerical simulation results demonstrate effective closed-loop control in the presence of plant disturbances and sensor noise.