An Introduction to System Modeling and Control

8System Responses

8.1 First‐Order System Response

Recall the block diagram of a DC motor shown in Figure 8.1.

Figure 8.1 Block diagram of a DC motor.

Setting and, along with a block diagram reduction, this simplifies to the block diagram of Figure 8.2.

Figure 8.2 Simplified block diagram of a DC motor.

Our interest now is the response of the motor's angular speed to a step input voltage. Removing the integrator for and defining

we obtain a first‐order system whose block diagram is given in Figure 8.3.

Figure 8.3 Time constant form for a first‐order transfer function.