Worksheet

U5.6 Saturation and windup

Feedback control · University · about 25 min

What this lesson is about

What a controller should do when the actuator has nothing left to give.

• Where this robot saturates
• The symptom
• The fix
• Where else this bites

Questions 6 marks in all

1. [1 mark]A PI controller with conditional integration, run on four errors. What does it print?

   KP, KI, DT = 1.5, 0.7, 0.1
   integral = 0.0
   for error in (30, 40, 30, 10):
       want = KP * error + KI * integral
       cmd = max(-55, min(55, want))
       if abs(want - cmd) < 0.01:
           integral += error * DT
       print(round(cmd, 2), round(integral, 2))

2. [1 mark]drive() is asked for 250 and then for 6. What does the robot get each time?

   1. A100, then nothing
   2. B250, then 6
   3. C100, then 6
   4. D100, then 15

3. [1 mark]What is the name of the anti-windup method that stops accumulating the integral while the actuator is saturated?

4. [1 mark]With back-calculation, integral -= (want - cmd) / Kt. If want = 62.1, cmd = 55 and Kt = 2, by how much is the integral reduced? Give two decimal places.

5. [1 mark]A robot switches from manual driving to a PI controller and jumps. What is the fix?

   1. AInitialise the integral so the controller's first output matches what was already being sent
   2. BReset the integral to zero at the switch
   3. CRaise Kp during the switch
   4. DClamp the command to 15 percent

6. [1 mark]A diagonal drive command saturates the lateral axis but not the forward one. What happens?

   1. AThe robot travels in the wrong direction, because one component is clipped and the other is not
   2. BThe robot slows down but keeps its direction
   3. CNothing, because each axis is controlled separately
   4. DThe robot stops

The task: anti-windup

The same blocker, the same 12 cm. Run a PI controller with anti-windup, keep KI at 0.7, plot error and i term, and be settled 12 cm from the blocker, within 3 cm, from 21 seconds onwards. Without protection the integral winds up on the way in and the robot is not settled until about 25 seconds; with it, about 15.

from bugbot import *
connect()

KP, KI = 1.5, 0.7
TARGET = 12.0
DT = 0.1
integral = 0.0

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/u5-6-saturation/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Run it with and without the anti-windup and put the two i term charts side by side.
2. Implement back-calculation instead and compare the recovery.
3. Add a lower limit: refuse to send a command below the dead band, and send zero instead. Does the loop behave better or worse?