This model is written in Octave.
Some preliminary documentation of the approach can be found here.
Modeling and design of the DC/DC power stage in e.g. Libre Solar charge controllers for improved control in nanogrid and/or MPPT applications.
The script models the plant and divider circuitry using the state space method. From analysis of the zeros and poles, a second order approximation of the system is used (since the dominant response is second order). The second and third order responses are compared to show this is a valid approximation.
Ziegler Nichols tuning techniques are applied using the rules here
However, the output of this does not provide an improved step response.
Next steps
Calculate the PID parameters based on: The ultimate gain method OR the pole placement method.
NOTE: There is a legacy issue (from the Matlab implementation) surrounding the use of the stepinfo function. A GNU Octave alternative has been proposed here, however this is not tested and verified. So the use of this for calculating the bandwidth of the system is omitted.