Simple Control Theory

1
Simple Control Theory

• Jeremy Wyatt
• School of Computer Science
• University of Birmingham

2
Aims

• Understand what control theory is
• See why its useful
• A little of the maths
• How to apply it to simple mobile robots

3
What is Control Theory?

• In designing an intelligent robot we are
  designing an interaction between agent and
  environment
• Both are composed of many low level, continuous
  processes
• Control theory is about describing these
  processes and manipulating them so they do what
  we want

4
A simple example

• A DC motor can be thought of as process
• We increase the voltage and the speed increases
  (crudely)

VB
s
motor
voltage
speed
5
Pulse width modulation (PWM)

• The Handyboard has constant VB
• Q So how do we vary the voltage?
• A We switch it on and off quickly

VB 0
VB 0
6
Controllers

• We want to know what effective VM to apply to get
  the speed we want
• This is what our controller will choose

VM
s
sT
motor
controller
Voltage
Actual speed
Target speed
7
Controllers

• How should we decide on VM?
• There are three popular classes of methods
• Open loop control
• Feedforward control
• Feedback control
• We will look at each in turn

8
Open Loop Control

• IDEA
• build a model of how VM affects s
• then invert it
• plug in sT (target speed)
• hope it works
• Suppose
• so

s
VM
9
Disturbances

• Open loop is very simple but affected by
  disturbances
• Typical disturbance battery isnt fully charged

Disturbance
(1)
sT
VM
VT
Controller (program)
(2)
Target voltage
Target speed
Actual voltage
10
Feedforward control

• IDEA
• Watch the disturbances
• Add them to a better model
• Invert the model
• Hope
• Good if disturbances have known effect
• But
• Model can become very complicated
• Hard to measure disturbances

11
Feedforward Control
Disturbance
sT
VM
VT
Controller (program)
Target voltage
Target speed
Actual voltage
12
Feedback Control

• Observe the process output, not the disturbance
• Modify the controller action to minimise the error

Disturbance
s
sT
VM
VT
Controller
Motor
13
Feedback Control

• Good
• Very general, because it works whatever the
  disturbances are
• Model stays (relatively) simple
• Bad
• Problems arise if the rate of process change is
  much higher than the speed of sensing and control

14
Proportional Error Control (PE)

• Add a proportion of the error to the control
  signal

Disturbances
s
sT
VT
Controller
Robot