## Question

###### The following specification applies to a position control: $K_{v}=10 .$ On hand is an amplifier with a variable gain, $K_{2}$, with which to drive a motor. Two one-turn pots to convert shaft position into voltage are also available, where $\pm 3 \pi$ volts are placed across the pots. A motor is available whose transfer function is $$\frac{\theta_{m}(s)}{E_{a}(s)}=\frac{K}{s(s+\alpha)}$$ where $\theta_{m}(s)$ is the motor armature position and $E_{c}(s)$ is the armature voltage. The components ar

The following specification applies to a position control: $K_{v}=10 .$ On hand is an amplifier with a variable gain, $K_{2}$, with which to drive a motor. Two one-turn pots to convert shaft position into voltage are also available, where $\pm 3 \pi$ volts are placed across the pots. A motor is available whose transfer function is $$\frac{\theta_{m}(s)}{E_{a}(s)}=\frac{K}{s(s+\alpha)}$$ where $\theta_{m}(s)$ is the motor armature position and $E_{c}(s)$ is the armature voltage. The components are interconnected as shown in Figure P7.24. The transfer function of the motor is found experimentally as follows. The motor and load are driven separately by applying a large, short square wave (a unit impulse) to the armature. An oscillograph of the response shows that the motor reached $63 \%$ of its final output value 0.5 second after application of the impulse, Furthermore, with 10 volts dc applied to the armature. the constant output speed was 100 rad/s. Draw the completed block diagram of the system, specifying the transfer function of each component of the block diagram.