IntermediateTopic 62 of 101Signals, Control & Comms
Observers
Estimate unmeasured states from inputs and outputs.
In depth
An observer (Luenberger) x̂'=Ax̂+Bu+L(y-Cx̂) reconstructs unmeasured states; L is chosen so A-LC is stable, usually faster than the controller. Separation principle allows independent design of controller and observer for LTI systems. Kalman filter is the optimal stochastic observer.
Key points
- Estimation error dynamics
- Observer bandwidth vs noise
- Reduced-order observers
ExampleA drone estimates velocity from position measurements with an observer.
What is Observers?
Estimate unmeasured states from inputs and outputs.
Why is it important to understand observers?
Observers estimate hidden states from measurements, so state feedback works even when some states cannot be measured.
What is a Luenberger observer?
An observer that runs a model of the system and corrects its estimate using the difference between measured and predicted output.
How fast should an observer be?
Faster than the controller, but not so fast that it amplifies noise, which is a common design trade-off.
How is Observers used in practice?
Typical applications include estimating the speed of a motor from its current and position encoder, estimating the internal temperature of a battery from surface readings and running a Luenberger observer for a level control in a tank.
What should I learn before Observers?
Study "State feedback and pole placement" first (topic 61 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Observers?
Estimation error dynamics. Observer bandwidth vs noise. Reduced-order observers.
Can you give an example of Observers?
A drone estimates velocity from position measurements with an observer.
What comes after Observers?
The next topic is "LQR", which builds directly on this one.
How difficult is Observers?
It is classed as Intermediate in Signals, Control & Comms (topic 62 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.