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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 VB s motor voltage speed • We increase the voltage and the speed increases (crudely) 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 VM 1 VB 2 Controllers • We want to know what effective VM to apply to get the speed we want VM sT controller Target speed s motor Voltage • This is what our controller will choose Actual speed 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 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 kVM VM sT k s VM Disturbances • Open loop is very simple but affected by disturbances Disturbance sT Controller VT VM (program) Target speed Target voltage VT sT k (1) VM s k (2) Actual voltage • Typical disturbance: battery isn’t fully charged 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 V Disturbance OUT VIN sT Controller VT VM (program) Target speed Target voltage Actual voltage sT VT k VIN VOUT Feedback Control • Observe the process output, not the disturbance Disturbance sT VT Controller s VM Motor • Modify the controller action to minimise the error 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 Disturbances sT s VT Controller Robot VT k1 (sT s)