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What is the effect of pole zero cancellation?
Unfortunately, this method is always unreliable. The problem is that when the added zero does not exactly cancel the pole (which is always the case in real life), a part of the root locus will be trapped in the right-half plane. This causes the closed-loop response to be unstable.
What is pole zero cancellation?
When an open-loop system has right-half-plane poles (in which case the system is unstable), one idea to alleviate the problem is to add zeros at the same locations as the unstable poles, to in effect cancel the unstable poles.
What is the effect of a zero on the controller response?
Adding a LHP zero to the transfer function makes the step response faster (decreases the rise time and the peak time) and increases the overshoot. Adding a RHP zero to the transfer function makes the step response slower, and can make the response undershoot.
Is it possible to cancel a zero in a pole?
Even if a perfect pole-zero cancellation were possible, the system would not be practically implementable because of internal stability issues. For example, if you designed a controller with an unstable pole that cancelled a zero in the plant, the output of the controller could grow unbounded to the point…
What happens when a zero is added to a pole?
Unfortunately, this method is unreliable. The problem is that when an added zero does not exactly cancel the corresponding unstable pole (which is always the case in real life), a part of the root locus will be trapped in the right-half plane. This causes the closed-loop response to be unstable.
Which is more stable 2 or 1 pole zero?
The system with relative degree (number of poles minus number of zeros) 2 is more stable than the one with relative degree 1. If you think about the Bode diagram and the Nyquist plot, it has infinite gain margin. Not so with the 1st system, which can be made unstable with a high enough feedback gain.
How to cancel the unstable pole in MATLAB?
Inspecting the root locus above, we see that the unstable pole is in the vicinity of s = 0.3. Delete the rlocus command, and add the following lines into your m-file to add a zero at 0.3. From the new root locus you can see that the unstable pole has almost been canceled. Now let’s see what the closed-loop response looks like.