Answers

3.3 Tuning the gain

Control · Robot club · about 20 min

What this lesson is about

Sluggish, good, oscillating. Loop speed and driving speed.

• Too little
• Too much
• Why the loop speed matters
• Measure the sweep
• Speed and gain together

Questions 7 marks in all

1. [1 mark]With a gain of 1 on the curving robot, what happens?

   1. AThe correction is too weak: the error grows and the robot ends well off the line
   2. BThe robot snakes from side to side
   3. CThe robot holds the heading perfectly
   4. DThe robot spins on the spot
   Answer: A. A controller that is too weak is called sluggish. It never even crosses the target.

2. [1 mark]With a gain of 40, the robot snakes. What is that called?

   1. AOscillation
   2. BCoasting
   3. CDrift
   4. DThe dead band
   Answer: A. A tiny error becomes a huge rotation, which overshoots, which becomes a huge rotation the other way.

3. [1 mark]Rotation is capped at 100. With a gain of 40, above what heading error is the controller just bang-bang again? Give the number of degrees.

   Answer: 2.5. 40 times 2.5 is 100. Any error bigger than that asks for more than 100, so it gets the full 100 every time.

4. [1 mark]What does this program print?

   errors = [5, 2, -1, -3, 1, 4, -2]
   worst, flips, last = 0, 0, 0
   for error in errors:
       worst = max(worst, abs(error))
       if error * last < 0:
           flips += 1
       last = error
   print("worst", worst, "and", flips, "sign changes")

   Answer:

   worst 5 and 3 sign changes

   A sign change is when this error and the last one have opposite signs, so they multiply to a negative. That happens at -1, 1 and -2. The biggest size is 5.

5. [1 mark]Why is a high gain with a slow loop the worst combination?

   1. AA big correction keeps running for too long before the next look
   2. BA slow loop makes the gain smaller
   3. CThe robot cannot drive while waiting
   4. DThe sensor stops working
   Answer: A. Between looks the robot keeps doing what you last said. A big push for 0.3 seconds is a big overshoot.

6. [1 mark]In a sweep of gains, where is the good gain?

   1. AJust before the sign changes start climbing
   2. BThe highest gain you can type
   3. CThe lowest gain, 1
   4. DWherever the worst error is biggest
   Answer: A. Raising the gain shrinks the worst error, until the robot starts crossing the target back and forth.

7. [1 mark]A gain works well at speed 50. What might happen at speed 100?

   1. AIt may be sluggish, because the fault acts faster
   2. BIt will oscillate more, because speed makes the gain bigger
   3. CNothing, the gain does not care about speed
   4. DThe robot will drive backwards
   Answer: A. This robot turns about twice as hard at 100. The same gain has twice as much fault to fight.

The task: hold the heading, fast

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

def wrapped(h):
    return (h + 180) % 360 - 180

while position()[1] < 72:
    error = wrapped(0 - heading())
    # forward, sideways, rotation: -100 to 100 each, until the next command
    drive(60, 0, error * 40)
    # pause 0.05 s (the robot keeps doing what it was told)
    wait(0.05)
# all motors off
stop()

from bugbot import *
connect()
def wrapped(h):
    return (h + 180) % 360 - 180
while position()[1] < 72:
    error = wrapped(heading())
    drive(100, 0, -error * 4)
    wait(0.05)
stop()