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
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.)
Shashikant N Sarada wrote:
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