I am unclear regarding the overarching purpose of the Extended State Observer for SISO and potentially MIMO systems.
In the ADRC control paradigm, presented by J. Han in 2008 (published 2009), and expanded on by M. Fliess also in 2009, and updated in 2011 and 2013, the Extended State Observer (ESO) is used to construct the required conditioning and cancelling input signal, allowing an unknown Minimal Phase SISO system to be reduced to a single integrator.
Within the context of the ADRC control structure, the ESO takes the current system output, determines its derivative, adds the previous system input, and uses that result to modify the present system input.
In the case of a SISO system, the ESO simply finds the time derivatives of whatever system input you send it, which we can accomplish with similar precision by using a transfer function.
In the case of a MIMO system, the ESO (properly tuned and with the proper amount of states) is still only able to compute time derivatives of the output that we send it. It does not seems capable of providing any information regarding other states which are not themselves a time derivative of the ESO input.
So is there a way to enable the ESO to provide information regarding internal system states (which are not pure derivatives of the system/plant output) in either a SISO or MIMO system?
And if not, then what does the ESO provide for us that a [dx/dt] block or a [1 0]/[1e-6 1] TF block does not?
Aactive disturbance rejection control (ADRC) is considered to be superior to PID control and has gained significant traction in recent years.
The following References may be of some help in your Pursuit.
1. From PID to Active Disturbance Rejection Control
Jingqing Han
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 3, MARCH 2009
Active disturbance rejection control (ADRC) can be summarized as follows: it inherits from proportional–integral– derivative (PID) the quality that makes it such a success: the error driven, rather than model-based, control law; it takes from
modern control theory its best offering: the state observer; it embraces the power of nonlinear feedback and puts it to full use; it is a useful digital control technology developed out of an experimental platform rooted in computer simulations. ADRC
is made possible only when control is taken as an experimental science, instead of a mathematical one. It is motivated by the ever increasing demands from industry that requires the control technology to move beyond PID, which has dominated the practice for over 80 years. Specifically, there are four areas of weakness in PID that we strive to address: 1) the error computation; 2) noise degradation in the derivative control; 3) oversimplification and the loss of performance in the control law in the form of a linear weighted sum; and 4) complications brought by the integral control. Correspondingly, we propose four distinct measures:
1) a simple differential equation as a transient trajectory generator; 2) a noise-tolerant tracking differentiator; 3) the nonlinear control laws; and 4) the concept and method of total disturbance estimation and rejection. Together, they form a new set of tools and a new way of control design. Times and again in experiments and
on factory floors, ADRC proves to be a capable replacement of PID with unmistakable advantage in performance and practicality,providing solutions to pressing engineering problems of today
2. Electronics 2013, 2, 246-279; doi:10.3390/electronics2030246
A Simulative Study on Active Disturbance Rejection Control (ADRC) as a Control Tool for Practitioners
Gernot Herbst
Siemens AG, Clemens-Winkler-Straße 3, Chemnitz 09116, Germany;
E-Mail: [email protected]; Tel.: +49-371-475-2883.
As an alternative to both classical PID-type and modern model-based approaches
to solving control problems, active disturbance rejection control (ADRC) has gained significant traction in recent years. With its simple tuning method and robustness against process parameter variations, it puts itself forward as a valuable addition to the toolbox of control engineering practitioners. This article aims at providing a single-source introduction and reference to linear ADRC with this audience in mind. A simulative study is carried out using generic first- and second-order plants to enable a quick visual assessment of the
abilities of ADRC. Finally, a modified form of the discrete-time case is introduced to speed up real-time implementations as necessary in applications with high dynamic requirements.
Keywords: active disturbance rejection control (ADRC); extended state observer (ESO)
P.S.
It's just viewing the disturbance as the output of an exosystem. Then, the original system together with the exosystem becomes the system for observer design. The control part is a bit more involved since the combined system is not controllable. So LQG control does not work. One can use backstepping design method to arrive at a controller. The scheme works since the original system is minimum phase and the exosystem is stable in the sense of Lyapunov.
The problem has already been solved in adaptive control context. See our papers.
Article Adaptive controller design and disturbance attenuation for S...
Conference Paper Adaptive controller design and disturbance attenuation for S...
Can anybody help me ...what are limitations or drawbacks of extended state observer?
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...
Please refer to this article:
https://www.researchgate.net/publication/318726178_An_Improved_Active_Disturbance_Rejection_Control_for_a_Differential_Drive_Mobile_Robot_with_Mismatched_Disturbances_and_Uncertainties
Conference Paper An Improved Active Disturbance Rejection Control for a Diffe...
Please refer to this article:
https://www.researchgate.net/publication/318726178_An_Improved_Active_Disturbance_Rejection_Control_for_a_Differential_Drive_Mobile_Robot_with_Mismatched_Disturbances_and_Uncertainties
Conference Paper An Improved Active Disturbance Rejection Control for a Diffe...
Please refer to this article:
https://www.researchgate.net/publication/318726178_An_Improved_Active_Disturbance_Rejection_Control_for_a_Differential_Drive_Mobile_Robot_with_Mismatched_Disturbances_and_Uncertainties
Conference Paper An Improved Active Disturbance Rejection Control for a Diffe...
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