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.