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
G(s) = (s + 1)2 / s2 + 1.
and the feedback transducer is H(s) = 2s + 1. Determine a state variable representation for the system.

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Actuator Depth Rs) Desired depth Prossure measurement H) FIGURE P3.7 Submarine depth control,