Solutions For Control Systems Engineering, International Student Version Chapter 9 Problem 37P

From Figure 1

Speed at no-load is given by

And

Gear ratio is given by

Motor transfer function, when load is transmitted to input side is given by

Therefore the transfer function of given motor is

(b)

Given that a power amplifier has a gain equals to 1 and preamplifier of gain 5000.

Gear ratio: 0.1.

A tachometer compensator block diagram is shown in Figure 2.

Figure 2

Block diagram shown in Figure 2 can be represent in unity feedback close loop system as shown in Figure 3

Figure 3

Where, motor and load having transfer function

And

...... (1)

Since system shown in Figure 3, is a Type-1 system, comparing this transfer function with second order unity feedback Type-1 transfer function

…… (2)

By comparing equations (1) and (2), for a desired damping ratio, we get

And

(c)

Uncompensated system:

Uncompensated system has equals to zero so forward path transfer function becomes

Natural frequency is given by

And

Settling time is given by

Percentage overshoot is given by

Compensated system:

Forward path transfer function is given by

Natural frequency is given by

And

Settling time is given by

Percentage overshoot is given by