An automatic depth-control system for a robot submarine is shown in Figure P3.7. The depth is measured by a pressure transducer. The gain of the stern plane actuator is K = 1 when the vertical velocity is 25 m/s.

The submarine has the transfer function

(s+ 2) G(s) = $2+2 and the feedback transducer is H(s)=s+3. Determine a state variable representation for the system.