# Consider the dc motor of Problem 16.2.3 to be operating at rated voltage in steady state with a…

Consider the dc motor of Problem 16.2.3 to be operating at rated voltage in steady state with a field current of 1 A, and with the starting resistance in series with the armature reduced to zero.

(a) Obtain the equivalent capacitive circuit neglecting the armature self-inductance and calculate the steady armature current.

(b) If the field current is suddenly reduced to 0.8 A while the armature applied voltage is constant at 220 V, compute the initial armature current ia(0) on the basis that the kinetic energy stored in the rotating parts cannot change instantaneously.

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(c) Determine the final armature current ia(∞) for the condition of part (b).

(d) Obtain the time constant τ ‘am of the armature current for the condition of part (b), and express the armature current as a function of time on the basis that ia = ia(∞) + [ia(0) − ia(∞)] e−t/τ‘am .

Problem 16.2.3

A 5-hp, 220-V, separately excited dc motor has the following parameters: Ra = 0.5 Ω, k = 2 H, Rf = 220 Ω, and Lf = 110 H. The armature winding inductance is negligible. The torque required by the load is proportional to the speed, and the combined constants of the motor armature and the load are J = 3 kg·m2 and B = 0.3 kg·m2 /s. Consider the armature-controlled dc motor, whose speed is made to respond to variations in the applied motor armature voltage vt. Let the field current be maintained constant at 1A.

(a) Develop a block diagram relating the motor speed and the motor applied voltage, and find the corresponding transfer function.

(b) Compute the steady-state speed corresponding to a step-applied armature voltage of 220 V.

(c) How long does the motor take to reach 0.95 of the steady-state speed of part (b)?

(d) Determine the value of the total effective viscous damping coefficient of the motor-load configuration.

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