350 Solved Electrical Engineering Problems: For the FE/PE Exams in Electrical Engineering

Chapter 3.0: Control

3.1 Open-loop control

The open-loop controller shown in Figure 3.1 consists of an integrated circuit differential amplifier. Determine the open-loop gain.


Figure 3.1: Open-loop control

Solution:

Let V out = V a + V b

V a / V 1 = R f / R in

V b / V 2 = [R f / (R f + R in)] [(R f + R in) / R in] = R f / R in

V out / V 1 / (R f / R in) + V 2 / (R f / R in)

V out = (R f / R in) (V 2 V 1) = 100 Asin( ?t + ? ??t) = 100 Asin ?

3.2 Closed-loop control

The closed-loop controller shown in Figure 3.2 consists of an integrated circuit differential amplifier, and two cascaded inverting op amps. Determine the closed-loop gain.


Figure 3.2: Closed-loop control

Solution:

A v = R 2 / R 1 = 100

A f = (-R 1 / R 2)(-R 1 / R 1) = R 1/ R 2 = 0.01

V out = (V in V f) A v

V f = V out A f

V out = (V

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