## Quiz on Feedforward and Cascade Control

**1.** About how much faster should an inner loop be than an outer loop in cascade control?

**A.**2 times as fast

- Incorrect. If the inner (secondary) loop is too slow then the primary loop and secondary loop can create an instability. 2x is generally too slow but may work in some cases.

**B.**30 seconds faster

- Incorrect. The speed of the inner (secondary) loop is relative to the outer loop (primary)

**C.**At least 3 times as fast

- Correct. If the inner (secondary) loop is too slow then the primary loop and secondary loop can create an instability

**D.**10 times as fast

- Incorrect. It is desirable to have the inner loop faster but 10x is not required

**2.** For a complicated multilayer cascade control system that is performing poorly, what are some solutions for better performance? Select two possible solutions.

**A.**Replace all the cascade control with feedforward control

- Incorrect. A cascade controller inner loop rejects a disturbance before it can affect the outer loop process variable. It is often preferable to control the disturbance versus compensate with feedforward trim.

**B.**Add more layers

- Incorrect. More complexity can make the interacting system even worse

**C.**Decouple interacting controllers with better pairing of actuator and process variable.

- Correct. An RGA (Relative Gain Array) can assist in this analysis.

**D.**Place the primary controller in manual and retune the secondary (inner loop) controller

- Correct. This is often effective to reject a disturbance before it affects the primary controller process variable

**3.** Which of the following is a difference between feedforward and cascade control?

**A.**Cascade control uses two controllers

- Incorrect. The correct answer is D

**B.**Feedforward uses a disturbance model to determine the feedforward gain

- Incorrect. The correct answer is D

**C.**Cascade has an inner control loop to directly reject disturbances

- Incorrect. The correct answer is D

**D.**All of the above

- Correct.

**4.** Under what circumstances does feedforward control not reject disturbances?

**A.**Dynamics are known for the actuator and the process

- Incorrect. Transfer functions for the process and actuator are typical. Transfer functions can be combined by multiplying the transfer functions in series.

**B.**Process time delay is less than the disturbance time delay `\theta_p < \theta_d`

- Incorrect. Feedforward control works well if the process dead time is less than the disturbance dead time

**C.**Process and disturbance time constants are significantly different `\tau_p` and `\tau_d`

- Incorrect. This is more challenging, but requires a lead-lag controller `G_{ff}` instead of a feedforward controller gain `K_{ff}`

**D.**Dead time on the process is too great to act in anticipation of the disturbance

- Correct. Feedforward control is not effective when `\theta_p` is greater than `\theta_d`

**5.** Given the following two transfer functions for a process and disturbance, find the feedforward control gain `K_{ff}`.

$$G_p(s) = \frac{7.0e^{-4s}}{5s + 1}$$

$$G_d(s) = \frac{4.0e^{-5s}}{4s + 1}$$

**A.**7

- Incorrect. This is the process gain

$$K_p = \lim_{s \to 0} G_p(s) = \lim_{s \to 0} \frac{7.0e^{-4s}}{5s + 1} = 7$$

**B.**-`{4}/{7}`

- Correct.

$$K_p = \lim_{s \to 0} G_p(s) = \lim_{s \to 0} \frac{7.0e^{-4s}}{5s + 1} = 7$$

$$K_d = \lim_{s \to 0} G_d(s) = \lim_{s \to 0} \frac{4.0e^{-5s}}{4s + 1} = 4$$

$$G_{ff} = -\frac{K_d}{K_p} = -\frac{4}{7}$$

**C.**`{5}/{4}`

- Incorrect. Review the Final Value Theorem (FVT) to find the gain of the process and disturbance

**D.**`{4}/{7}`

- Incorrect. It is missing the negative sign