The goal of vertical take-off and landing (VTOL) aircraft is to achieve operation from relatively small airports and yet operate as normal aircraft in level flight. An aircraft taking off in a form similar to a missile (on end) is inherently unstable. A control system using adjustable jets can control the vehicle as shown in Figure 3. R(s) Desired vertical path Controller Aircraft dynamics Gc(s) Y(s) s(S-1) Actual vertical path Figure 3 a) Is the system stable when the controller Gr(s) = K ? Why? b) Determine the range of gain for which the system is stable when the controller is G(s) = K(s+2) (s+10)* c) Determine the gain K for which the system is marginally stable and the roots of the characteristic equation for this value of K. d) Using Matlab program, plot the response of the system to a unit step input for K = 50 and record the maximum overshoot of the system. e) Discuss the effects of varying the value of gain K on the system performance.