Computer Vision Group Prof. Daniel Cremers

Autonomous Navigation for Flying Robots Lecture 4.2 : Feedback Control

Jürgen Sturm

Technische Universität München

Motivation: Position Control

Move the quadrotor to a desired location

How can we generate a suitable control signal ?

Current location (observed through sensors)

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Controller (you!)

Sensor (you!)

Feedback Control – Generic Idea

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Desired value

35°

Turn hotter (not colder)

System

25°

35°

45°

25°

35°

45°

Measured temperature

error

Feedback Control – Block Diagram

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Controller

System

Sensor

Reference Measured error + -

Control State

Measured state

Proportional Control

P-Control:

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Effect of Noise

What effect has noise in the process/measurements?

Poor performance for K=1

How can we fix this?

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Proper Control with Noise

Lower the gain… (K=0.15)

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What do High Gains do?

High gains are always problematic (K=2.15)

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What happens if sign is messed up?

Check K=-0.5

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Saturation

In practice, often the set of admissible controls u is bounded

This is called (control) saturation

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Delays

In practice most systems have delays

Can lead to overshoots/oscillations/de-stabilization

One solution: lower gains (why is this bad?)

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Delays

What is the total dead time of this system?

Can we distinguish delays in the measurement from delays in actuation?

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Measurement

Controller –

System

1000ms delay in water pipe

200ms delay in sensing

Smith Predictor

Allows for higher gains

Requires (accurate) system model

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Controller –

System with delay

Delay-free system model

Delay model –

–

Sensor

Smith Predictor

Assumption: System model is available, 5 seconds delay

Smith predictor results in perfect compensation

Why is this unrealistic in practice?

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Smith Predictor

Time delay (and system model) is often not known accurately (or changes over time)

What happens if time delay is overestimated?

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Smith Predictor

Time delay (and plant model) is often not known accurately (or changes over time)

What happens if time delay is underestimated?

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Lessons Learned

Control problem

Feedback control

Proportional control

Delay compensation

Next video:

PID control

Position control for quadrotors

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