Interest in unmanned underwater vehicles has been increasing recently, with a large number of possible applications being considered. These include intelligence gathering, mine detection, and surveillance applications. Regardless of the intended mission, a strong need exists for reliable and robust control of the vehicle. The proposed vehicle is shown below. You want to control the vehicle through a range of operating conditions. The vehicle is 30 feet long with a vertical sail near the front. The control inputs are stern plane, rudder, and shaft speed commands. In this case, we wish to control the vehicle roll by using the stern planes. The control system is shown as well, where R(s) = 0, the desired roll angle, and T_d(s) = 1/s. Suppose that the controller is G_c(s) = K(s + 2). (a) Design the controller gain K such that the maximum roll angle error due the unit step disturbance is less than 0.05. (b) Compute the steady-state roll angle error to the disturbance input and explain the result