Right Half-Plane Zero Physical Manifestations and Solution Limits

Boost Converter Right Half-Plane Zero Physical Manifestations and Solution Limits

Hello I just learned about the inherent Right Half-Plane Zero (RHPZ) problem that is found in some power supply topologies such as the boost converter and the flyback converter. As I've seen in the website, **broken link removed** , Christopher Basso says that the effect of the Right Half-Plane Zero can be seen for instance in a boost converter when you apply a large step increase in load current, the output voltage dips down before going back up again into steady-state. The solution stated in the site is that we reduce the rate of change of the duty ratio through proper compensation. I have some questions regarding this.

1.) Are there other physical manifestations resulting from this?
2.) When compensated properly, is it possible that the RHPZ could be eliminated completely, as in no onset of the dip during the occurrence of the step load could be seen? Or is it only possible to reduce this 'dip' but not completely remove it.
3.) As far as I understand, the RHPZ increases gain but reduces phase, which greatly reduces the phase margin. This is what causes the instability effects. So the RHPZ could also cause physical manifestations such as oscillations that occur forever? maybe small amplitude ripple that goes on and on causes by imbalance of charging the output capacitor and charging the inductor current.
4.) Would you know of a good source which says how to compensate for the RHPZ in a boost converter in current-mode control? The link I provided discusses it for Voltage mode control but for current-mode control the equations seem very complicated hence I rely on my simulator to tweak the gain and phase margins. In the first place, I do not even know the limitation of solving this problem as seen in the time domain hence my question number 2. Or would you know how?

Thanks!

Dear kanmaedexandzelbladex,
Your post and the wording of your questions is very clear. This is more than can be said for the article you cite at **broken link removed**. Sometimes some very simple ideas can be completely buried in a layer of something or other that seems designed to obscure. The term right half plane zero belongs in frequency domain talk, but is here related to a problem that is by far most clearly stated by considering the circuit in the time domain. If you have a boost regulator with continuous inductor current, and there is a step increase in inductor current demand, then in the short term the controller will have to devote some time to charging the inductor up to the new, higher, demanded current. This is, of course, time with the switch closed - time when current is not flowing in the output diode. If we restrict our focus on the power circuit (as opposed to the control loop), we can say that the short term response to an increase in output current demand will be a reduction in output current. What can we do about that before we even turn to control loop comensation?
First, if we really do need continuous inductor current, we need to size the output capacitor to keep the output voltage within spec. during an increase in current demand. Second, you are not restricted to a particular topology. Whereas Mr Christpohe Basso restricts himself to integrated circuits offered by his employer, you needn't. In a discontinuous inductor current design, the time domain effect which translates to RHPZ does not arise. Have you considered a discontinuous current design? Such a design makes the switch on event much less stressful for the switch.
So, I reckon the answer to your question 2 lies in correct control scheme, and not in achieving "compensated correctly" condition. I believe that your questions 3 and 4 disapear if you focus on the power circuit scheme design to meet the circuit requirements first, and the placement of the poles and zeros in your control loop second.
Richard Schurmann

It's not possible to eliminate the RHP zero, without either changing the topology or not using continuous conduction. So you're usually stuck with it. And it's impossible to compensate for it using normal feedback schemes. If you look at published literature there are lots of proposed novel methods for compensating it out, but as far as I know none of them have been adopted broadly.

The short story is that when you have a CCM boost/buckboost converter, you simply have to accept a control bandwidth that is less than the RHP zero frequency. Also keep in mind that more sophisticated topologies have even more RHP zeros: the Cuk converter has two, and SEPIC has three.

man oh man! the Cuk and SEPIC converters..i wish I understood them to a practical level.

Yeah, the RHP zero is tricky SOB. You have two ways: Switch the topology or go discontinous and a mutual intersection of the options presented to you, is: a dcm mode FLyback.

Easy to compensation, can provide isolation and fun to work with. Know this: This topology, while widespread, is not treated with the respect and caution it deserves. In DCM, the switch will undergo significant stress and you need fair amount of filtering on the output. You can settle for CCM in FLyback but you will need slope comp. (assuming your converter is CM control)


Post back if you require further direction/clearification

Dear Sir,
I would like to continue the discussion regarding elimination of rhp zero using topological methods, what best and likely possible topological modification methods are possible for elimination of RHP zero without using control schemes, and can you please give your suggestions and view regarding this sir.
Secondly, if i want to use converters like SEPIC, CUK, or combinations with boost, for multi-input DC-DC converters without using control schemes, how far it is feasible to eliminate RHP zero.
Please do comment.
Thank you.

The easier solution is really to reduce and reduce the inductance. Or for assurance of complete removal of the RHPZ, work under DCM. This holds for the boost converter, not sure about the multiple RHPZ's of the Cuk and SEPIC. This has tradeoffs however such as increase in current ripple. Ultimately, the most optimal methods would be to change the mode of control, or to have a better compensation scheme. The trick is to limit the bandwidth of the feedback loop to about 1/3 or less of the worst-case RHPZ location.

First of all thanks for the reply,
There are four general methods for rhp zero elimination being:
1) Using damping - resulting in lower efficiency
2) Using Coupled inductor - resulting in higher switch stress
3) PWM techniques (Leading or Trailing) - resulting in programming difficulties
4) Using topological modification - resulting in infeasible conversion
So apart from it if the modification can be done in topology itself, the requirement of other schemes gets reduced, so if any one can help regarding the topological modifications, i will be happy. Wherein the design and cost levied on other things gets reduced.
Thanks

RHP zero can only be avoided with a farily low bandwidth and an educated "high" freq. pole placed at the minimum load the converter is going to power.

Why? The zero moves and assuming you have learnt that a DCM converter will help you (provided you size the switch and the filter accordingly), the compensation scheme will be modest. The pole i menitoned above is to counter act that the smallest load RHP zero manifestation.

I think OP needs to start some simulations and using Basso's techniques, view the the RHP zero and its load dependencies. A word of advice: Read up on DCM mode Flyback/boost/buckboost topologies.

Dont worry about the fine details (such conduction/switching losses, leakage inductances, reflected capacitances, tanks etc). They will distract from the basics.

vargil said:

Dear Sir,
I would like to continue the discussion regarding elimination of rhp zero using topological methods, what best and likely possible topological modification methods are possible for elimination of RHP zero without using control schemes, and can you please give your suggestions and view regarding this sir.
Secondly, if i want to use converters like SEPIC, CUK, or combinations with boost, for multi-input DC-DC converters without using control schemes, how far it is feasible to eliminate RHP zero.
Please do comment.
Thank you.

Click to expand...

I fear some danger here that this discussion might degenerate into an interaction that has the appearance of substance, but no actual substance. The concept of a right half plane zero is a concept that applies to a mathematical function. Usually this would be a transfer function. Such a thing would not exist at all if we were "without using control schemes". You can run your supply from a clock generator that is free running, and has no feedback at all. (e.g. a boost converter with a 50% duty cycle clock. Think of a petrol engine Kettering ignition system.) Where would the right half plane zero be? The question needs to be more carefully thought out and re-expressed.

Richard Schurmann said:

I fear some danger here that this discussion might degenerate into an interaction that has the appearance of substance, but no actual substance. The concept of a right half plane zero is a concept that applies to a mathematical function. Usually this would be a transfer function. Such a thing would not exist at all if we were "without using control schemes". You can run your supply from a clock generator that is free running, and has no feedback at all. (e.g. a boost converter with a 50% duty cycle clock. Think of a petrol engine Kettering ignition system.) Where would the right half plane zero be? The question needs to be more carefully thought out and re-expressed.

Click to expand...

I thank you for your comments, first of all i want to make it clear that, the RHP-zero is not only a problem of control systems, it is a problem of even circuits, for example if a capacitor is taken at the load side of a boost converter, the behavior of capacitor is different for low and high frequencies, i mean at low frequencies capacitor is essentially open circuited, and the response is in phase with the excitation, and at high frequencies the capacitor is short circuited, so response is out of phase by 180 degrees, with excitation. So there are two frequency dependent paths from excitation to response, the gain of high frequency path may obtain which results in a negative sign of the RHP zero accounts for the fact that low and high frequency gains are opposite in polarity.
I would like to listen to your comments, in this and may not always the RHPZ is not the concept of control systems alone, it is even the concept of circuits also, so different elimination methods may be sought out using circuit theory approaches, by applying what control is doing the same parallel guidelines of addition of pole zero i.e., designing inductor and capacitor (topological modifications) can be done in literature various methods are available there which you might not be aware. \
Thank you.

vargil said:

I thank you for your comments, first of all i want to make it clear that, the RHP-zero is not only a problem of control systems, it is a problem of even circuits, for example if a capacitor is taken at the load side of a boost converter, the behavior of capacitor is different for low and high frequencies, i mean at low frequencies capacitor is essentially open circuited, and the response is in phase with the excitation, and at high frequencies the capacitor is short circuited, so response is out of phase by 180 degrees, with excitation. So there are two frequency dependent paths from excitation to response, the gain of high frequency path may obtain which results in a negative sign of the RHP zero accounts for the fact that low and high frequency gains are opposite in polarity.
I would like to listen to your comments, in this and may not always the RHPZ is not the concept of control systems alone, it is even the concept of circuits also, so different elimination methods may be sought out using circuit theory approaches, by applying what control is doing the same parallel guidelines of addition of pole zero i.e., designing inductor and capacitor (topological modifications) can be done in literature various methods are available there which you might not be aware. \
Thank you.

Click to expand...

I am sure that this is not deliberate on your part, Vargil, but your choice of words makes it impossible to discern exact meaning. Do you mean that you connect the capacitor across the output of the boost converter? Now you write of "low frequencies" and "high frequencies". This is commonly done, but there has to be an implication that the writer and the reader shares that they know what is happening at either a low or high frequency. What do you mean? (a) Capacitor current, (b) capacitor voltage, (c) perturbation of input voltage, or(d) variation in load current??? I cannot make sense of your post with any of these assumptions. What I DO know is, that you do not mean frequency of perturbation of a control voltage of the converter, as you insist that you are not writing of a "control system".
Please make your meaning clear.
Richard.