The dynamics of a rotor-pendulum plant are de- scribed by the following transfer function from the voltage input u(t) to the angle output y(t): G(S) = Y(s) U(s) 0.07895 $+0.731s+31.58 -0.15s This plant should be controlled by means of a digital controller with a sampling period of T = 0.15 s. The desired closed-loop specifications are: optimal damping, a 2% settling time of 2 s, and a zero steady-state tracking error to a step input. (a) Show that the digital equivalent transfer function of the plant G(s) is given by: GhoG(z) = 8.075 x 10-4(z+0.9632) z(z1.262z+0.8961)