DEAR BENO

HOPE THIS INFO COULD HELP

For good observer design, observer poles should be 2 - 5 times faster than controller poles, so that the observer estimates the states quickly compared to the dynamics of controller.  

Dear Zlatan 

That is what I really try to do.. could you help me to do so ?

I tried to create switch to feedback the measured signal fir certain time afterwards I switched to estimated value but does not work ..

Thank you for all of your answers

Hi,

I have read a few papers on Observer-based controllers and typically, the controllers do not operate in the initial phase of convergence. There is some metric threshold based on output function and estimated output function which aids this. Once this threshold is reached, then you only have to make sure your observer poles provide 2-5 times faster response as mentioned above.

Also, it is impractical to use controller without convergence because often one might have slow dynamics in the system which might take longer for settling. You are fortunate to have convergence in the end.

Also if you want to lessen tracking error in initial phase, you have to slow down observer poles and then as the error reduces, increase the magnitudes.

I think the initial conditions are not very important. The observer gains are more important. set the initial conditions of the observer to zero. At initial times, set the observer gain to small values to prevent from high control effort. Then, slowly and smoothly increase it to higher values to improve the tracking error.

Dear Abdul,

the behavior you are experiencing is called peaking phenomenon. Take a look on Prof. Khalil's book on nonlinear systems or search for peaking phenomenon in high-gain observers.

In 2013, I proposed on IJRNC a dwell-time strategy to avoid peaking in output-feedback control based on high-gain observers: http://dx.doi.org/10.1002/rnc.1837

Please check it!

Best regards,

Tiago

--

Prof. Tiago Roux Oliveira

Dept. of Electronics and Telecommunication Engineering - DETEL

State University of Rio de Janeiro - UERJ

Rua São Francisco Xavier 524 - sala 5018E - Bloco E

Rio de Janeiro, RJ 20550-900

Brazil

Phone: 55-21-2334-0026 and 55-21-99692-1023 (mobile)

E-mail address: [email protected], [email protected], [email protected]

http://lattes.cnpq.br/2236381891580848

Hi Abdul and all.  

The topic has always fascinated me, so I would like to add few words.

Dear Abdul, you are  definitely facing  the peaking phenomena.  The large observer output occurs for some initial conditions (not far all). but  it is impossible to avoid it playing with initial conditions.

In fact, the peaking phenomena  is in some sense a very natural behavior.

Let say, you control some  system and would like  to guarantee that its state that  is initially in the unit ball  reaches the    small neighborhood of zero  ( epsilon–size)after a short  time T.

You  must have the velocity  of the order ( 1-epsiolon)/T. So shorter is T – higher is the maximal velocity at some point t< T.   If your system is of the order higher than 1 ( and the control enters   only in the last equation) than your acceleration  at some point must be of the order  1/T^2 and so on. E.g  T=0.1, thn V_max~10, a_max ~100 etc… (!)

   Due to  duality – the same is happening  in the observers, when the fast dynamics is synthesized using high gains. There is a large body of literature   mainly related to the name of professor Khalil and his colleagues,  as mentioned in the post of professor Oliveira.

  Roughly :  if and observer is fast ( and  therefore  - high gains are  used) ) - before the settling of the observer the information it provides may contains  large error.

  Two views are possible on the problem:  either (1) not use  the information provided by the observer (  or use it carefully !)   until we may guarantee it is OK – this is essentially the  technique proposed  for using high gain observers. Or (2) we may try to develop an observer that does not have such a drawback – this is sometimes possible.  For the latter approach I may refer to my work    

Journal of Dynamic Systems, Measurement and Control 2005, Vol. 127(2), pp. 267-274.(Observer and Controller Design using Time-Varying Gains : Duality and Distinctions.)

 Also the sliding mode observers may be used for  achieving  similar properties.

 Last  comment  is about the professor Movva post. Although choosing observer poles 2-5 time faster than controller poles  is often  suggested,  and it is a good engineering practic – it does not eliminate peaking ( at least, according to my experince)  -  it simply makes their value somehow ``acceptable`.  In fact, in my  older work`:

Journal of Dynamic Systems, Measurement and Control  2000, Vol. 122, pp. 348-351.(The Response of the System Incorporating an Observer in the Control Loop)

 It was shown (although it sounds a bit strange) that switching the poles from  observer to controller, or even shuffling them arbitrarily  - results in the same  transient process in observer-based controller.

 Best regards.

 Vladimir Polotski

Pay attention to zero in denominator of your observer equations. This can be also the source of Problem. In this case some Initial conditioning may help, if not try to choose your initial parameters close to reality of your physical model.

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

Article From PID to Nonlinear State Error Feedback Controller

Article Improved Sliding Mode Nonlinear Extended State Observer base...

Article On the Improved Nonlinear Tracking Differentiator based Nonl...