Nonlinear backstepping method and Lyapunov theory

In summary, Charles is looking for resources on designing a controller for a nonlinear vibration control system using the backstepping principle. He is currently reading "nonlinear systems" by Khalil but is having difficulty understanding the complex mathematics. He is also in need of resources for modeling a magnetic bearing for his thesis on nonlinear vibration control. Other forum members have offered to provide links for further assistance.
  • #1
quadrotor
1
0
Hi Everybody,

I have just finished the control systems components of the engineering degree and found it very enjoyable. I'm now undertaking a holiday project to create a quad rotor aircraft. There is a surprising amount of information on these aircraft on the internet and while most of it is over my head I am very interested in learning from it and understanding the material.

To this end I would like to konw if anyone has any sources that can explain the backstepping method for nonlinear control design?? Lyapunov theory explanations are also required and they seem to be part of the backstepping method.

Any links or explanations you could provide would be extremely useful. I need to understand the method behind creating a controller for a non-linear system based on the backstepping method and by using Lyapunov theory.

Thanks for your help
Mike Berg
 
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  • #2
quadrotor said:
Hi Everybody,
I have just finished the control systems components of the engineering degree and found it very enjoyable. I'm now undertaking a holiday project to create a quad rotor aircraft. There is a surprising amount of information on these aircraft on the internet and while most of it is over my head I am very interested in learning from it and understanding the material.
To this end I would like to konw if anyone has any sources that can explain the backstepping method for nonlinear control design?? Lyapunov theory explanations are also required and they seem to be part of the backstepping method.
Any links or explanations you could provide would be extremely useful. I need to understand the method behind creating a controller for a non-linear system based on the backstepping method and by using Lyapunov theory.
Thanks for your help
Mike Berg
I'm vaguely familiar with Lyapunov methods, which can be used to make statements about the stability of nonlinear systems. Never head of backstepping though. Probably because I'm not a controls person.
 
  • #3
Need help with Backstepping as well!

Hi all,

I'm doing a thesis on nonlinear vibration control via a magnetic thrust bearing actuator. I also need to know how to design a controller via the backstepping principle. I'm reading "nonlinear systems" by Khalil but the maths is quite full on and finding it hard to understand. Does anybody know other resources on this topic that are somewhat easier to understand?

I also need to find information to model my magnetic bearing. Anyone know some good resources?

Cheers

Charles
 
  • #4
If you still need some help on backstepping I can suggest you some links.

bg
alex
 

Related to Nonlinear backstepping method and Lyapunov theory

1. What is the nonlinear backstepping method?

The nonlinear backstepping method is a control design approach used to stabilize and control nonlinear systems. It involves breaking down a complex nonlinear system into a series of simpler subsystems and designing controllers for each subsystem, which are then combined to form a controller for the overall system.

2. How does the nonlinear backstepping method differ from other control design methods?

The nonlinear backstepping method differs from other control design methods in that it can handle highly nonlinear and uncertain systems, as well as systems with multiple inputs and outputs. It also has the advantage of being able to design controllers that can guarantee stability and performance in the presence of disturbances and uncertainties.

3. What is Lyapunov theory?

Lyapunov theory is a mathematical tool used to analyze the stability of dynamical systems. It involves the use of Lyapunov functions, which are scalar functions that measure the energy or “distance” of a system from its equilibrium point. By analyzing the properties of these functions, it is possible to determine the stability of a system and design controllers to stabilize unstable systems.

4. How is Lyapunov theory used in conjunction with the nonlinear backstepping method?

The Lyapunov theory is used in conjunction with the nonlinear backstepping method to design controllers for each subsystem in the backstepping procedure. The Lyapunov functions are used to analyze the stability of the subsystems, and the controllers are designed to ensure that the Lyapunov functions decrease along the trajectories of the subsystems, thus guaranteeing stability of the overall system.

5. What are the benefits of using the nonlinear backstepping method and Lyapunov theory?

The nonlinear backstepping method and Lyapunov theory have several benefits, including the ability to handle highly nonlinear and uncertain systems, the ability to design controllers that guarantee stability and performance, and the ability to handle systems with multiple inputs and outputs. They also offer a systematic and structured approach to control design, making it easier to analyze and understand the behavior of complex systems.

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