I have designed a different topology of boost converter. I calculated the transfer function of the converter. Their is a zero at the right half plane.
1. What will be the effect of that zero on the stability of the circuit?
2. Can any one explain to me how i can analyze the Bode plot of this transfer function. In the attachment is the bode plot.
3. Does PI controller will be suitable for the compensation in close loop system?
It introduces unstability causing your phase to fall quickly, but your phase crossover should be more than gain crossover. Left half zero is preferred to make system stable.
1.Due to RHP zero phase margin will decrease resulting stability also decrease.
2.You can either shift the RHP zero to left half or infinite.
3.Using PI controller you can remove your zero...thats good,but sometime it may decrease the stability .
The attached diagram does not look like it has RHP zero. It looks more like two complex poles. I say that for following reasons:
1. There is a peaking in magnitude plot with -180 degrees sudden phase shift.
2. Magnitude roll off is nearly -40db/decade
A RHP zero does give a negative (-90 degrees) phase shift but it does not give magnitude roll off. Peaking is also not generally associated with single RHZ.
Best way to stabilize it is to eliminate complex poles and make it two real widely separated poles. You may try to introduce a LHP zero near UGB but that would increase your UGB further and that can make higher frequency poles significant.
To answer your initial question: a RHP zero can be the worst thing (of course except RHP poles) that can occur for your stability. It gives a negative phase shift (bad for stability) with positive magnitude roll off (bad again). For good stability make sure it is well beyond your UGB.
Saurabh.
In my opinion, the Evans Root Locus method is the best to understand the role of RHP zeros. Overall, RHP zeros "attract" closed loop poles when the controller gain increases (you can write the PI as a function of one gain K). Then, the system becomes unstable when the closed loop poles are RHP.
RHP zeros are a good method to model the system delay in power electronics converters and analyze its influence in the closed loop stability.
Dear Aamir,
The right half plane zero has gain similar to that of left half plane zero but its phase nature is like a pole i.e., it adds negative phase to the system. Instead phase increasing from 0 to 90 degrees, its phase increases from 0 to -90 degrees. This causes delay in your system response which can lead to instability if not taken care.
The intuitive way of understanding right half plane zero can be as follows. Imagine you have a boost converter 24V to 48V i.e., duty of 0.5. Due to some reason, the input voltage has decreased to 20 and the output voltage falls to 40V if operated at 0.5. In order to restore output voltage to 48V, we have to increases the duty to 0.5833. Assume that, you have increased the duty from 0.5 to 0.5833. If you observe the output voltage closely, the voltage decreases below 40V instead of increasing to 48V and after some time the voltage starts increasing towards 48V.
The reason is that, we have increased the duty from 0.5 to 0.5833 i.e., we have increased the ON time of the switch from 50% to 58.33%. If you see the circuit during on time, the inductor is connected to the input source and the output is supplied by capacitor alone. So when we increase the ON time of switch, that much amount of time the capacitor discharges to the load which would decrease output voltage further compared to the previous switching cycle. If your controller is very fast, it assumes that the voltage is decreasing instead of increasing and it increases the duty further which eventually makes the system unstable. Ideally, your controller should wait for the output voltage to fall and then increase towards the desired value and then do corrective action if required. This is done just by making the system slow i.e., by selecting lower bandwidth (gain crossover frequency). In general, if you take gain crossover frequency as one tenth of the right half plane zero frequency, your system will be stable.
This phenomena of instant fall in voltage and then raising towards the reference value becomes a right half plane zero in the transfer function. The instant fall in voltage in spite of increasing command (opposite action to that of the desired action) is the negative phase of right half plane zero. I hope this is helpful.
Regards
Srikanth
Hi Srikanth Kotra,
THANK YOU! THANK YOU! I have been trying to understand this for a long long time in a way that makes sense. It was one the most spot on explanation I have ever heard about any topic.
Regards.
Ahmed.
I think that the presence of a right half plane (RHP) zero results in a "Non-Minimum Phase Characteristics leading to difficulty high-bandwidth control design.
In NMP you have unstable zeros that add phase lag. The response of a non minimum phase system to a step input has an "undershoot". This means, if the output was initially zero tending towards a steady state positive value, the output first becomes negative before changing direction and converging to its positive steady state value . Try Mag and Freq plot of this G(s) = [s-1][s+2]
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