A high-performance helicopter has a model. The goal is to control the pitch angle 0 of the helicopter by adjusting the rotor thrust angle 8.
The equations of motion of the helicopter are

where x is the translation in the horizontal direction. For a military high-performance helicopter, we find that

all in appropriate SI units.
Find (a) a state variable representation of this system and (b) the transfer function representation for 9(s)/S(s). (c) Use state variable feedback to achieve adequate performances for the controlled system.
Desired specifications include (1) a steady-state for an input step command for dd(s), the desired pitch angle, less than 20% of the input step magnitude; (2) an overshoot for a step input command less than 20%; and (3) a settling (with a 2% criterion) time for a step command of less than 1.5 seconds.

0 dr 0.4 15 2-1.43 2 0.0198 .6.27 ,-0.0111 g 9.8