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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