Dear Robert,

This is an interesting question. I would like to add some points to this discussion. 

High-gain observers have some advantages that can be summarized as follows:

1-High-gain observers are relatively simple to design as you do not need to solve complex differential equations nor use complicated formulae. Determining a suitable value for the gain is typically done through experimentation.

2- For large class of nonlinear systems, they can provide global or semi-global stability results for large class of systems. This means that their use can provide stability guarantees for any arbitrarily chosen initial conditions.

3-They can be relatively fast.

4-They can be robust to modeling uncertainty and external disturbances.

5- For (nonlinear) systems represented in the normal form, it was shown that when high-gain observers are used in output feedback control they can recover the performance of the state feedback controller. In other words, assuming that all the states are measured, you can design a controller that satisfies some performance specifications such us some a desired overshoot and settling time. Then, when the states are provided by the high-gain observer, the output feedback controller can provide a very similar performance to the state feedback case.     

The disadvantages of the high-gain observers can be summarized as follows:

1- They are sensitive to measurement noise. Although there have been some results in the literature that tackled this problem, solving this problem still deserves more research. 

2- They suffer from the 'peaking' phenomenon, where, due to the high-gain, there is an initial sharp spike in the response of the state estimates. This phenomenon can cause instability for some types of systems. One practical solution to this problem is to use saturation outside the operating range of the system states. 

A recent survey regarding high-gain observers in feedback control can be found in the following paper:

Khalil, Hassan K., and Laurent Praly. "High‐gain observers in nonlinear feedback control." International Journal of Robust and Nonlinear Control 24.6 (2014): 993-1015.

Article High-gain observers in nonlinear feedback control

So long as you don't have very much of noise in your measurements (e.g., small noise power) or process disturbances (meaning you have very good models as in vehicle dynamics), high gain observers do much better, as the state estimate converges to the actual state rapidly. This can be beneficial in cases where the dynamics change frequently (as in robots or cranes lifting loads), and the observer has to be adjusted. This is also beneficial where you are trying to observe and attenuate disturbances when the frequency content of the disturbance is known (e.g., any rotor dynamics such as disk drives or helicopter rotor/BVI noise).

Dear Robert,

Enclosed, one of our paper using high-gain observer may be you can be convinced by its advantages!!

Regards,

Mohamed

@Kartik, Hi professor, would you elaborate more on "This is also beneficial where you are trying to observe and attenuate disturbances when the frequency content of the disturbance is known "

Your question could be restated as how to identify the gain of an observer. Actually, there is no mathematical method to 'estimate' gains. How large or how small is dependent on each project. The gain may be considered as large in one case but actually small in other cases. You may want to do a lot of experiments to identify the proper values of the gain for your project. The rule of thumb is that the gain tends to be larger when there is less noise in measurements, and smaller when more noise in measurements compared to input disturbances. Anyway, gains mean heuristics.

Dear Robert,

This is an interesting question. I would like to add some points to this discussion. 

High-gain observers have some advantages that can be summarized as follows:

1-High-gain observers are relatively simple to design as you do not need to solve complex differential equations nor use complicated formulae. Determining a suitable value for the gain is typically done through experimentation.

2- For large class of nonlinear systems, they can provide global or semi-global stability results for large class of systems. This means that their use can provide stability guarantees for any arbitrarily chosen initial conditions.

3-They can be relatively fast.

4-They can be robust to modeling uncertainty and external disturbances.

5- For (nonlinear) systems represented in the normal form, it was shown that when high-gain observers are used in output feedback control they can recover the performance of the state feedback controller. In other words, assuming that all the states are measured, you can design a controller that satisfies some performance specifications such us some a desired overshoot and settling time. Then, when the states are provided by the high-gain observer, the output feedback controller can provide a very similar performance to the state feedback case.     

The disadvantages of the high-gain observers can be summarized as follows:

1- They are sensitive to measurement noise. Although there have been some results in the literature that tackled this problem, solving this problem still deserves more research. 

2- They suffer from the 'peaking' phenomenon, where, due to the high-gain, there is an initial sharp spike in the response of the state estimates. This phenomenon can cause instability for some types of systems. One practical solution to this problem is to use saturation outside the operating range of the system states. 

A recent survey regarding high-gain observers in feedback control can be found in the following paper:

Khalil, Hassan K., and Laurent Praly. "High‐gain observers in nonlinear feedback control." International Journal of Robust and Nonlinear Control 24.6 (2014): 993-1015.

Article High-gain observers in nonlinear feedback control

Dear all,

Please let me add a comment regarding the problem of sensitivity to measurement noise mentioned by Almuatazbellah. This drawback has been treated by replacing the constant high-gain parameter by a robust adaption scheme in several publications. A quite simple adation scheme is proposed in our attached paper that you might find interesting. An advantage of our proposed observer is also that you do not need to determine suitable values for the gain by experiments, but the observer adapts itself to the actual needed value.

Best regards,

Thomas