Is it possible to apply simple backstapping and SMC technique on nonlinear model of inverted pendulum? because coupling occur in it model. If possible then then send me reference of book or paper. Advance thanks for your kind cooperation.
Regard
SAFEER ULLAH
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Yes, it is possible. The inverted pendulum is a chain of integrators with two systems, so you can divide the study into two systems. With one control you can control the pendulum and with the other control the car. Therefore, you will have two surfaces, the first is the integral of the state with the control 1 and the second the integral of the state of the control 2. With Lyapunov you can obtain the equivalent control without problems.
On the other hand. The motivation of the inverted pendulum is holding the pendulum in a very small angle, therefore, I recommend you to use the linear model
Dear Jesus...
Thanks. I know it but when we apply smc or backstepping then we get two different control inputs and we need only one control input to control both pendulum and cart. That's why I confused.
If you want one law of control, it is possible to transform the system to its regular form. In the Utkin´s book illustrates the regular form, or you can consult works of Dr. Loukianov to obtain the regular form.
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