current control PWM switch model?
In these expressions, \$V_c\$ and \$V_{err}\$ refer to the same variable, the control voltage delivered by the error amplifier. Small-signal variables like \$v_{ac}\$ for instance have to be replaced by the right value depending on the PWM switch wiring diagram. For instance, in a buck CM, terminal c would be the node going to the inductor while terminal a would go to \$V_{in}\$. As \$v_{ap} = v_{in}\$ and \$v_{in}\$ is 0 V in this ac analysis, then the controlled source featuring \$v_{ap}\$ is also 0 in ac, simplifying the circuit by open-circuiting it. You have the example of a derivation in my APEC 2014 seminar using the PWM switch in a buck converter as shown below:



Now, this structure remains a 3rd-order linear network with controlled sources. I would recommend to use the FACTs to determine the control-to-output transfer function and express it in a low-entropy form.