Transfer function of full bridge inverter using mosfet and LLC circuit
Unfortunately, there is no simple approach to determine the transfer function of a LLC circuit. I have seen papers applying extended describing functions (EDF) to the structure but the resulting expression is intractable and difficult to use. The best approach in my opinion is simulating the circuit with a piece wise linear (PWL) simulator such as SIMPLIS or PSIM.

SPICE is a linear solver and must linearize point by point any nonlinear behavior. A PWL simulator, on the other hand, manipulates elements that are always linear. This is because a diode is not described by its Shockley equation but by a succession of linear segments: the current is flat for an anode-cathode voltage below \$V_f\$ and linearly increases with a \$\frac{1}{r_d}\$ slope afterwards. Two segments are therefore enough to describe the simplest diode. You can add more segments to obtain a better precision but it affects simulation time.

The below circuit works on the SIMPLIS demo version Elements. It describes a simple voltage-controlled oscillator-based modulator. The output voltage is fixed in this simple open-loop configuration:



Once the simulation is run (a few seconds), you can plot the control-to-output transfer function and apply your compensation strategy: