## Integrator

Fig. 18-11. HEAO-I Position Plus Rate Controller Block Diagram (0=^, or and 8*=oiy or uj.

Either position only, rate only, or position plus rate control may be achieved by the control law shown in Fig. 18-11, where 0 and 8 are the angular position and rate errors about a body axis and / is the computed thrust duration. Note that, in the figure, environmental disturbance torques, Ne, are integrated and added to the commanded control torques. To avoid excessive thruster activity, commands are issued only if the required thrust duration, /, exceeds a minimum time, A/. For large t, the thrust interval is set equal to the sampling rate and the thruster fires continuously.

The action of the position plus rate controller is illustrated in the state space diagram in Fig. 18-12 where the ordinate is the rate error and the abscissa is the position error. If the attitude state lies within the shaded region or deadband, thruster commands are inhibited. However, if the attitude enters the region above or below the deadband, corrective thrusts are commanded. Above and to the right of the deadband, the angular velocity is decreased by the control law; below and to the left, it is increased. After large errors are removed, each thrust yields a minimum rate change of M= Nbt/I, where N is the thruster torque. A/ is the minimum thrust duration, and J is the moment of inertia about the controlled axis. Initially, thrust commands will be issued by the controller, causing approximately a vertical trajectory* on Fig. 18-12, until the deadband boundary is reached. The

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