## Quiz on Proportional Control

**1.** What is the issue with using an excessively large `K_c` value?

**A.**It causes excessive offset

- Incorrect. A low `K_c` value can give persistent offset between the SP and PV for non-integrating systems.

**B.**It increases controller bias

- Incorrect. Not related. The controller bias is set when the controller is switched from manual to automatic.

**C.**It increases response time

- Incorrect. A larger `K_c` value reduced response time and the controller reacts faster to a deviation between the SP and PV.

**D.**It can cause excessive oscillatory behavior

- Correct. Most real systems have dead-time, discrete sensor sampling rate, controller output limits, and higher-order dynamics than simple first-order. These lead to oscillating behavior with a high controller gain.

**2.** Use the servo control tuning correlation to find the controller gain `K_c` for an FOPDT model with parameters: `K_p` = 3.0, `\theta_p` = 2.5, and `\tau_p` = 2.3.

**A.**0.1523

- Incorrect. Use set point tracking correlation not disturbance rejection.

**B.**0.0602

- Correct. Nice work!

$$K_c = \frac{0.20}{K_p}\left(\frac{\tau_p}{\theta_p}\right)^{1.22}=0.0602$$

**C.**0.1658

- Incorrect. Use the set point tracking (servo) correlation. This is the solution for the disturbance rejection correlation.

$$K_c = \frac{0.50}{K_p}\left(\frac{\tau_p}{\theta_p}\right)^{1.08}=0.1658$$

**D.**0.1423

- Incorrect. Use the set point tracking (servo) correlation.

**3.** Which of the following combinations of conditions will **not** lead to good control?

**A.**Reverse acting controller with a negative `K_p`

- Correct. Reverse acting implies positive `K_p` and `K_c` values. The controller may be unstable if the sign is incorrect.

**B.**Positive `K_c` values with positive `K_p` values

- Incorrect. `K_c` values match the sign of the `K_p` values

**C.**Extremely large `\tau_p` value with a large amount of dead time `\theta_p`

- Incorrect. Large dead times `\theta_p` are can still lead to good control performance as long as `\tau_p` is much larger.

**D.**All of the above lead to acceptable control performance.

- Incorrect. Option A does not lead to acceptable control performance.