Consider the feedback control system shown in Figure 10.35, in which the plant is the DC motor-driven cart given in Example 10.2. The input to the plant is the voltage applied to the DC motor, and the output is the position of the cart. Design a proportional-derivative (PD) controller such that the maximum overshoot in the response to a unit-step reference input is less than \(10 \%\), and the rise time is less than \(0.15 \mathrm{~s}\).

Data From Example 10.2:

The transfer functions of the plant (combining the cart and the DC motor), the controller, and the sensor are \[G(s)=\frac{3.778}{s^{2}+16.883 s}, \quad C(s)=85, \quad H(s)=1\]

Transcribed Image Text:

E(s) R(s) kp + kps U(s) C(s) FIGURE 10.35 Block diagram of a feedback control system. 3.778 $2+16.883s G(s) Y(s)