The design of a lunar excursion module (LEM) is an interesting control problem. The attitude control system for the lunar vehicle is shown in Figure PI 0.1. The vehicle damping is negligible, and the attitude is controlled by gas jets. The torque, as a first approximation, will be considered to be proportional to the signal V(s) so that T(s) = K2V(s). The loop gain may be selected by the designer in order to provide a suitable damping. A damping ratio of £ = 0.6 with a settling time (with a 2% criterion) of less than 2.5 seconds is required. Using a lead network compensation, select the necessary compensator Gc(s) by using (a) frequency response techniques and (b) root locus methods.