Question: The differential equation model for the motor torque m(t) required for a certain speed control system is where the desired speed is !d(t) and K

The differential equation model for the motor torque m(t) required for a certain speed control system is

 4m + 4Km + K²m = K?i,


where the desired speed is !d(t) and K is a constant called the control gain.

a. Use the Laplace transform method to find the unit-step response [that is, υd(t) is a unit-step function]. Use zero initial conditions.

b. Use symbolic manipulation in MuPAD to nd the value of the peak torque in terms of the gain K.

4m + 4Km + Km = K?i,

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