I think the solution to the inverted pendulum problem that I posted earlier boils down to the controller for non-minimum phase system. Can anybody suggest type of feedback system for the non-minimum phase system?
Regards,
Shashikant
Hi Shashi
I find the Nyquist approach extremely useful for all kinds of unstable systems, including non-minimum phase.
The maths is not challenging if you have a grasp of complex numbers, and the insight it provides will amaze you. Once you use a suitable criterion to determine whether you have an unstable closed loop system or not, you go one step further and use your plot to directly find pole-zero content for a compensator which has a chance of stabilising your system - then you shape the frequency content using a Bode or Nichols method.
For the inverted pendulum problem, for example, the approach allows you to decide that it is not possible to stabilise the inner loop system (i.e. get the desired number of circulations about -1+0j in the open-loop plane) without changing the sign of the gain of the compensator, and this matches practise - since you have to move a stabilised pendulum cart backwards a little to get it to go forward to stabilise at a new position...
Here's another hint, so that you approach a solution that will make everyone happy: model the actuation with input saturation and the measurement with noise!
(Its an interesting problem, and perhaps a little less interesting if you don't solve it yourself - so I'll stop now.)
cheers,
John
Shashikant N Sarada wrote:
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