Consider the helicopter altitude control problem shown in the following diagram,

where Helicopter Altitude Control Problem J = helicopter inertia, Br(t) =reference helicopter attitude, B(t) =actual helicopter attitude, Ks = sensor gain, Kr =reference scaling gain, w(t) = disturbance torque.

(a) Use proportional control D(s) = Kp. Does this controller provide additional damping>?

(b) Use PD control, D(s) = Kp + Kns. Determine the tracking and disturbance-rejection pmperties (i.e., find and e;::s) for step inputs on Br(t) and w(t).
J(

(c) Use PI control, D( s) = f( p + - 1 . Discuss the effect of this controller s on the stability of the system.
K {d) Use PID control, D(s) = Kp + __!_ + KDs. Discuss the effect of this controller on the stability and steady st'~te errors of the system.

(e) What are the two system types (one with n~spect to the reference and the other with respect to the disturbance) when the PID controller is employed?
Problem