Summary of Lesson 15

1 Open-Loop

An open-loop system with disturbance has this diagram:

The formula for the output is

$$P_L(s) = G(s) V_{in}(s) K_C + G(s) P_D(s)$$

For a first-order system, the output equation becomes

$$P_L(s) = \frac{K_C}{\tau s + 1} V_{in}(s) + \frac{1}{\tau s + 1} P_D(s)$$

2 Closed-Loop

A closed-loop system with disturbance has this diagram:

The formula for the output is

$$P_L(s) = \frac{G(s) K_C}{1 + G(s) K_C K_F} V_{in}(s) + \frac{G(s)}{1 + G(s) K_C K_F} P_D(s)$$

For a first-order system, the output equation becomes

$$P_L(s) = \frac{\frac{K_C}{1+K_C K_F}}{\frac{\tau}{1+K_C K_F} s + 1} V_{in}(s) + \frac{\frac{1}{1+K_C K_F}}{\frac{\tau}{1+K_C K_F} s + 1} P_D(s)$$