I'm sorry I didn't get this. When I load the material into the output plates the resonant capacitor would change and so would the frequency. The would change the switching of the mosfets out of their zero voltage / zero voltage switching. I want to achieve zvs / zcs even though the capacitor and frequency changes.
It should be pretty easy to get it to behave. Mind that you will need the two phase signals of interest: presumably, output voltage and resonant current. You can't use the oscillator output directly due to phase shift through the driver and output chain.
Yeah, you might not like what lock condition it's in, but it's never not in a lock condition. In Diff Eq, this is a non-homogeneous system. When the system is linear (as an RLC network is), the steady-state solutions are always at the driven frequency (assuming the "driver" is a periodic signal, of course).
In simpler terms: no matter what frequency you're driving at, the network is always doing whatever it's doing, at that same frequency. There is no locking to be done*, because it's always locked on frequency.
*In the sense that the phase might go outside of (-pi, pi] (in terms of total phase, not modulo phase).
This makes PLLing a resonant network much easier than the general case (typically, a PLL locking to a completely arbitrary and separate signal, like for radio). So that helps!
PLLing a class E stage (with no output network) is even easier still, because it's not resonant at all, as such. It's quasi-resonant. There's a half-sine* hump, then the voltage goes back to its initial state, and current goes back to ramping up. The ramp duration is variable. To a certain extent, you can drive over a wide frequency range, and get output power proportional to frequency (though this is probably prohibitive because of peak current and voltage demands on the switch).
*It's still not actually a sine part, but a segment of a decaying sinusoid. And if we include real components, not even that, because MOSFET Coss is nonlinear, so the zero crossings are rather slower (more Coss at lower Vds) than expected.
Be very careful talking about precise things like waveforms! If you say "sine wave", I fully expect something very tightly defined in the frequency domain: one spectral line, no distortion, no sidebands (maybe a DC offset, but strictly speaking, no). As soon as you have "sine wave BUT", the spectrum goes out the window, and it simply doesn't have the properties of a sine wave, and should not be called that.
Tim