When simulating, you use constant values for the capacitor and inductance. In a real system, capacitance and inductance are voltage / current / temperature dependent. The time constant can vary up to 100-600 times depending on the types of capacitors and magnetic materials. This may be the reason for the observed difference.

This may be the case if you are comparing simulation results with the characteristics of a real system.

Dear James:

The main difference is that the lag compensator adds negative phase to the system over the specified frequency range, while a lead compensator adds positive phase over the specified frequency.

The side effect of the lag compensator is the negative phase that is added to the system between the two corner frequencies

It is difficult to answer, because I cannot see how the real buck converter is modelled. But several possible explanations are:

a) If the converter is non-synchronous (i.e. with a diode), than one problem could be that there could be a change in operation modes form DCM to CCM and vice versa during start up. The modelled transfer just describes CCM mode.

b) Another effect would be, that the transfer function modells are linearized small signal representations and therefore depend on the operating point. Therefore in the modelled transfer function the gain may be changing (as this depends on the steady state duty cycle).

c) If the circuit model has limiters (e.g. maximum duty cycle reached or a current limit is implemented) than the real model response will deviate from the ideal transfer function characteristic. E.g. if your duty cycle signal command signal d increases to valus d>1, than in the real buck converter the value will be limited to d=1 and this will show a delayed startup (as your pictures indicate). In contrast the "ideal" transfer function model without limits will not see any problem with unrealistic d>1 (or even d

Hi Viktor Todorenko it is a simulated buck converter in circuit form, as such I am not sure if this is the case. Thank you for the assistance nevertheless.

Yes. I saw it. But after the simulation, there is usually a very painful process of confirming the results with traditionally large discrepancies. I believe you will succeed.

hi Burkhard Ulrich I have attached the buck converter circuit used as an image on here.

a) the converter seems to be non-synchronous as far as I'm aware so this could be a talking point of which I could use, hopefully it isn't significant enough to cause the substantial error seen.

b) I am not sure what you mean by this comment.

c) The duty cycle shown to be very high when not limited and also went negative. Limiting it to 0 and 1 did not show any change in results. Limiting the max value to 0.4 did show improvements.

The things mentioned to check.

a) The duty cycle was not within these limits.

b) I do not know what you mean by this.

I am still uncertain as to why both controllers present such an increase in overshoot and settling time in respect to there transfer function counterparts. I appreciate the help you have provided so far.

side note: the duty cycle in open loop for 5v is 1/3. I have also uploaded the PID controller with saturation limits advised, it becomes over damped although the response is fine.

Thank you for your response.

Viktor Todorenko I am having enough trouble on a simulated circuit representation haha. Thank you for the heads up, I appreciate it

Hi James Keen

as I can now see, the power stage is asynchronous therefore, there could be a change from DCM to CCM, in DCM your transfer function will be approximately a first-order type, and in CCM a second-order type. If this happens you will have a deviation in the transient response, which cannot be modeled using a linear model as then your plant transfer function will change.

Additionally, I try to explain what I meant in b) (although I think this is not an issue here, as for a buck converter the transfer function should be operating point independent at constant input voltage Vin). The problem could be that the transfer function you use is just valid for small-signal variations about some operating point. Usually, you have to linearize transfer functions of power converters and this is done about some operating point. If the operating point changes, then your transfer function is changing. E.g. looking at Eq. (1) in AN149 Modeling and Loop Compensation Design of Switching Mode Power Supplies (analog.com) , you can see that the contro-to-output transfer function of a buck converter depends on the input voltage Vin, therefore if Vin is changing then your plant transfer function will also change. In your case the input voltage is constant, therefore this buck converter plant should have an unchanged transfer function. I hope this explanation helps.

Hi Burkhard Ulrich

It has helped thank you and I appreciate the assistance you have given.

I feel there may be something else going on with just how much of a difference the results are showing unless you feel the resultant responses are acceptable under the reasoning's provided?

On a side note would I be better off choosing a buck converter which does not go into the discontinuous state if I wish to model in a similar manner as I have currently? I Imagine there are more issues at play if the overshoot and rise time are at such values.