Dear colleagues .we have one mechanical system and proved that vibration of this system was chaotic then i gonna use nonlinear control method to control this system. is it possible or no??
Can you introduce some sources for help me.. .......
thanks
You can use the nonlinear controllers but it should incorporated with some intelligent techniques like fuzzy.For your system I can suggest Fuzzy Sliding mode controller.
In other sense you can try with some adaptive control technique
Maybe tensor product (TP) transformation based control worth a try. See http://www.tp-control.hu
First of all, what is the aim of your controller? I guess, the compound system of your mechanical system and the controller should not be chaotic, maybe no movement at all, or maybe a oscillation with a fixed base frequency. Chaotic behaviour is characterized by the occurrence of frequencies in a wide range, including very large and very small ones, the frequencies on both ends cannot be neglected. The controller must suppress them all (except the targeted frequency) if I guessed correctly. In terms of PID controllers, the D part may be present but should be small because of the high frequencies in the given system, similarly for the I part. Adaptive control techniques mentioned in a previous answer are a way to treat the very low frequencies.
Anyway, controlling a nonlinear chaotic system does not necessarily require a nonlinear controller: the compound system remains nonlinear even in case of a linear controller. And investigating the behaviour of the compound system still needs techniques from nonlinear system theory (e.g. the guidelines to design a PID controller are rules of thumb at best).
Sorry, I am not able, to give a more specific answer.
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