Example of State Space Observer

Example of a state space observer in simulink

This example simulates a simple 2-dimensional state space system. For this system, we construct an observer that starts from different initial values for the states, but manages after a short period to observe the statees of the system (i.e. the error between real and simulated state goes to zero).

The user may try different initial values for the plant and the observer or different inputs (step, ramp, sinusoid). The observer always manages to minimize the error!

Additionally, the user may try a different output feedback matrix L. For example, if we choose the poles of the observer to be near the imaginary axis, then the observation will take longer time to "reach" the actual states of the plant (i.e. ti will take longer time for the error to be eliminated).

This is included in [1].

Course on Automatic Control:

https://www.youtube.com/playlist?list=PL9y6bivP9mhENl_frOQbJrPkH159kxbPh

References:

[1] An introduction to Control Theory Applications Using Matlab, https://www.researchgate.net/publication/281374146_An_Introduction_to_Control_Theory_Applications_with_Matlab

https://www.youtube.com/watch?v=fSV24QsPWIE

https://www.youtube.com/watch?v=H_qH2ZmGsls

See also the video discussing this topic for descriptor systems, which are a more general family:

https://www.youtube.com/watch?v=gYrmrLSS_fQ

References:

[2] K. Ogata. Modern Control Engineering 5th ed. 2009. Prentice Hall.