Simple Control Theory Jeremy Wyatt School of Computer Science University of Birmingham

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

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

A simple example A DC motor can be thought of as process We increase the voltage and the speed increases (crudely) motor voltagespeed VBVB s

Pulse width modulation (PWM) The Handyboard has constant V B Q: So how do we vary the voltage? A: We switch it on and off quickly VB0VB0 VB0VB0

Controllers We want to know what effective V M to apply to get the speed we want This is what our controller will choose motor VoltageActual speed VMVM s controller Target speed sTsT

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

Open Loop Control IDEA –build a model of how V M affects s –then invert it –plug in s T (target speed) –hope it works Suppose so VMVM s

Disturbances Open loop is very simple but affected by disturbances Typical disturbance: battery isn’t fully charged Target voltage VMVM Controller (program) Target speed sTsT VTVT Disturbance Actual voltage (1) (2)

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

Feedforward Control Target voltage VMVM Controller (program) Target speed sTsT VTVT Disturbance Actual voltage

Feedback Control Observe the process output, not the disturbance Modify the controller action to minimise the error Controller sTsT VTVT VMVM Disturbance Motor s

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

Proportional Error Control (PE) Add a proportion of the error to the control signal Controller sTsT VTVT Disturbances Robot s