## Quiz on PID Control

**1.** If the set point is constant `(\frac{dSP(t)}{dt}=0)` which of the following is equivalent to `\frac{de(t)}{dt}`?

**A.**`-\frac{dPV}{dt}`

- Correct. `\frac{de(t)}{dt} = \frac{dSP(t)}{dt} - \frac{dPV(t)}{dt} = - \frac{dPV(t)}{dt}`

**B.**`\frac{dPV}{dt}`

- Incorrect. `\frac{de(t)}{dt} = \frac{dSP(t)}{dt} - \frac{dPV(t)}{dt} = - \frac{dPV(t)}{dt}`

**C.**`\frac{dSP}{dt}`

- Incorrect. `\frac{de(t)}{dt} = \frac{dSP(t)}{dt} - \frac{dPV(t)}{dt} = - \frac{dPV(t)}{dt}`

**D.**0

- Incorrect. `\frac{de(t)}{dt} = \frac{dSP(t)}{dt} - \frac{dPV(t)}{dt} = - \frac{dPV(t)}{dt}`

**2.** What is the advantage of using the replacement for `\frac{de(t)}{dt}` from question 1?

**A.**It is a simple reformulation with no particular advantage

- Incorrect. It removes derivative kicks, removing unnecessary stress on valves

**B.**Removing derivative kicks has the effect of significantly improving the overall operation of the system

- Incorrect. The change to remove derivative kicks usually has little impact on the overall performance of the system, but can harm a valve or similar part that the actuator acts on

**C.**It will reduce potential wear/stress on valves by removing derivative kicks

- Correct. A derivative kick typically sends the actuator to an upper or lower limit for one controller cycle. It typically has little effect on the process but can wear out a valve or other equipment.

**D.**It simplifies the equation.

- Incorrect. It removes derivative kicks when there are set point changes, removing unnecessary stress on valves or other actuators.

**3.** What are the simple tuning correlations (IMC with `\theta_p=0`)? Try to recall this without referencing the page. Choose from the options below.

**A.**`K_c = K_p`, `tau_I = \tau_p`, `\tau_D = 0`

- Incorrect. Correct answer is b

**B.**`K_c = \frac{1}{K_p}`, `\tau_I = \tau_p`, `tau_D = 0`

- Correct. Correct

**C.**`K_c = \frac{1}{K_p}`, `\tau_I = 0`, `\tau_D = \tau_p`

- Incorrect. Correct answer is b

**D.**`K_c = K_p`, `\tau_I = 0`, `\tau_D = \tau_p`

- Incorrect. Correct answer is b

**4.** What is the value of the derivative filter constant `\alpha` with moderate tuning and negligible dead time `\theta_p`?

**A.**0

- Incorrect. The value approaches `\frac{\tau_p^2}{\tau_p^2}` which is 1.

**B.**-1

- Incorrect. The value approaches `\frac{\tau_p^2}{\tau_p^2}` which is 1.

**C.**`\tau_p`

- Incorrect. The value approaches `\frac{\tau_p^2}{\tau_p^2}` which is 1.

**D.**1

- Correct. The value approaches `\frac{\tau_p^2}{\tau_p^2}`