I need help solving this problem, with a explanation of steps so I can get a better understanding.

The DC motor speed control shown in the figure below is described by: y(1) + 60y(t) = 600v.(t) - 1500w(t). where y () is the motor speed, Va() is the armature voltage, and w(f) is the load torque. OW 1500 RO D -O 3+ 60 Assume that the armature voltage is computed by using the PI control law Va(t ) = kpe(t ) thi | e(T) di, where e(t) = r(t) - y(1). a) Compute the transfer function from W (s) to Y ($) as a function of k, and ky- b) Compute the transfer function from R(s) to Y(s) as a function of kp and ky . c) Compute values for p and ky so that the characteristic equation of the closed-loop system will have roots at -60 60j. d) For the values of p and ky you found in part (c), compute steady-state errors: i. For a unit-step reference input ii. For a unit-ramp reference input iii. For a unit-step disturbance input iv. For a unit-ramp disturbance input v. Verify your answers to parts (i) through (iv) using MATLAB. Note that a ramp response can be generated as the step response of a system modified by an added integrator at the specified input