Hi everybody,
How can I design a back stepping controller for this system? h1 and h2 are states of the system and q is the input.
Because, in Khalil's book, design is said for specific type of systems.
Hi,
If you want to stablize the above system, you can select the term sqrt(k1-k2) in the second equation as a virtual control and after finding a simple role for stablizing the second eq, try to find the control q in the first equation. in closing, you should select sqrt(k1-k2) as the virtual control. however, i guess there are some other alternatives.
Hello. i implementation the all of the slotin nonlinear book using matlab software.
in the attached file. the matlab simulation files is added. download that and see how that designed. you can design your problem with this simulation.(similar way)
three problem is simulated.
The backstopping control algorithm need that the system must be in para-metrical form. your system don't meet this request.
I have a question: what is the controlled output for your system?
Thank you Yazdan,
Thank you Javad,
Thank you Nadir. What is the para-metrical form ? h2 is output of the system.
Your system is not smooth enough for backstepping design if you want to stabilize the system to the origin. But, due to the structure of the system may exist if one considers only 0 \leq h_2 \leq h_1 region in the state space. (The system is only well defined in that region.) Now, change the coordinates to (x_1,x_2) = (h_2,h_1 - h_2) and use x_1 as the output, q as the input, and x_2 as the virtual control input. Remember that x_1 and x_2 are both nonnegative and you don't have full control authority in the stabilization of x_1 dynamics. But, x_1 will go to zero if x_2 is zero. So, set the virtual control law x_2 = 0 and continue to the second step of backstepping, where you have full control authority with input q. Try this to see the result.
I think that for your system, it will be easy to use the input output feedback linearization control.
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