I guess you could use a BJT or a JFET?? Why do you want to avoid MOSFETs and IGBTs?

You can't avoid PWM, however--you definitely can't do MPPT with a linear regulator.

@Hearth I am studying the use of extremum search systems in MPPT controllers, as an continious analogue to perturbation and observation. There are many works on this topic, but the general scheme of such control remains unchanged. It is not very difficult, but it shows poor performance with a discrete device under PWM control and under conditions of limited duty cycle $d=0...1$.

@Hearth If we make the simplifying assumption that the MOS or IGBT is just a variable resistance, and by selecting it, the optimal state is achieved, then the system works much better. It was here that I had a thought - are there such continuous devices in reality? Therefore, I asked the question here.

Using the active device as a variable resistance is what a linear regulator does. Linear regulators are incredibly inefficient and wholly unsuited for MPPT.

@Hearth is it due to heat and loss? or something else?

That's what "inefficient" means in this context, yes.

@Hearth let's say PWM has advantages over similar devices and it is preferable to use it. PWM, in fact, converts a continuous signal into a sequence of pulses with a variable duty cycle ... Here's what became interesting to me, PWM pulses are an alternating signal with a frequency that depends on the duty cycle and on the frequency of the sawtooth modulating signal.

@Hearth But what if there are devices that convert this very duty cycle into smooth analogs of a PWM signal, which can then be filtered out. I'm not sure if I'm asking the question correctly, I'm still worried about the poor pairing of algorithms with pvm ... what do you advise to do?

I think you might be combining the concept of pwm with your control loop. The frequency of the pwm is much higher than your control loop so consider them separate. For the purposes of simulation you may be able to consider pwm as a linear black box.

@Kartman thanks for the advice! this is exactly what I came to while working on the circuit on my own

@Hearth see my edit

@Kartman see my edit

I sense an XY problem. Why avoid the cheap and proven MOSFETs and IGBTs?

@winny Hey! ) I used them in a new circuit as part of an h-bridge. A conventional boost converter with one MOS or one IGBT does not fit well with the extremum search system with a sinusomal search signal (negatively affects the quality of the load voltage). In my circuit, the signal is smoother, and the system is better at searching for the extremum.

Please explain how the choice of semiconductor has any impact on your MPPT algorithm.

I think you are confusing yourself by mixing up the power stage from the regulation. Start with designing your power stage to give you sufficiently low input and output ripple, efficiency and voltage margin at a fixed operational point (I would choose the maximum power the system is supposed to handle) as an open loop with fixed duty cycle. Then design your control scheme for the aforementioned converter.

@winny I understand what you are talking about. I will gladly accept your recommendations, but at the moment I do not have enough time to master this. I work mainly in the field of control theory, but I do not know how to design converters. Therefore, I need to take from the ready-made. I ask you to clarify why my scheme with h-bridge is bad?

I would suggest you change your DC/DC converter using real elements to just an ideal transfer function which takes voltage and duty cycle input and gives out voltage output accordingly and you spend your time on the control part. I need a real schematic with component values to give you any guidance for your H-bridge.

Sorry, your graph only serves to confuse. The axis have no units. What are we observing? femtovolts/parsecs?

@Kartman see new edit with scheme parameters and more descriptive graphs

@winny see my edit, I displayed the parameters of circuit elements, converters, diodes, etc. I did not change anything in the parameters of diodes and converters. These are the usual Matlab settings.

@Kartman

@winny