Answers

U5.2 Proportional control

Feedback control · University · about 30 min

What this lesson is about

One gain, the whole trade-off, and the steady state error it cannot remove.

• What the gain means
• Turning it up
• Where the overshoot is
• The steady state error
• Choosing Kp by hand

Questions 6 marks in all

1. [1 mark]A proportional controller has Kp = 1.5 percent per cm. What command, in percent, does an error of 12 cm produce?

   Answer: 18. command = Kp x error = 1.5 x 12 = 18 percent.

2. [1 mark]The error is in centimetres and the command in percent. What are the units of Kp?

   Answer: percent per centimetre. Kp converts centimetres of error into percent of command, so it is percent per centimetre. That is why a gain does not carry over to a different robot.

3. [1 mark]This drive does not move below 15 percent. With Kp = 2, what is the largest error in cm that proportional control alone leaves uncorrected?

   Answer: 7.5 (accept within 0.01). The command reaches 15 percent at 15 / 2 = 7.5 cm. Any smaller error asks for a push the motors cannot deliver, so it stays.

4. [1 mark]In the lesson's turning cell at Kp = 4, the error trace falls fast, crosses zero, comes back and crosses again before settling. What does that say?

   1. AThe gain is too high: fast but underdamped
   2. BThe gain is too low
   3. CThere is steady state error
   4. DThe sensor is biased
   Answer: A. Overshoot and ringing are the signature of too much proportional gain for how fast the robot turns and how often the loop looks. At Kp = 1 the same turn arrives without swinging.

5. [1 mark]Why does a low-gain proportional controller stop short of the target and stay there?

   1. AIt needs an error to produce a command, and the command for a small error is below the drive's dead band
   2. BThe integral has wound up
   3. CThe sensor filter delays the last few centimetres
   4. DThe sign of the error is wrong
   Answer: A. Proportional control only pushes in proportion to the error. When that push falls below 15 percent nothing moves, so the error never shrinks further.

6. [1 mark]Put the lesson's hand-tuning recipe for Kp in order.

   Number the lines 1 to 3 to put them in the right order.

   1. Halve that value
   2. Start low, around 1
   3. Double it until the robot overshoots or wobbles
   Answer:

   Start low, around 1
   Double it until the robot overshoots or wobbles
   Halve that value

   Find the gain where trouble starts, then back off by half.

The task: find a gain that works

from bugbot import *
connect()

KP = 1.0
TARGET = 30.0

from bugbot import *
connect()

KP = 2.5
TARGET = 30.0
for tick in range(350):
    error = distance() - TARGET
    plot("error", error)
    drive(max(-60.0, min(60.0, KP * error)), 0, 0)
    wait(0.1)
stop()
print("kp:", KP)