Stability Analysis and Optimization of a Parasitic Buck Converter Using Leverrier's Algorithm and PI Controller

This paper presents the modelling of a second-order DC-DC converter using the State Space Averaging (SSA) technique in the presence of non-idealities of active and passive components, especially source resistance, which researchers ignore. The resolvent matrix of the linearised state-space model needs to be calculated to acquire the small signal transfer function of a DC-DC buck converter. Therefore, this paper introduces a simple systematic approach to obtain the resolvent matrix. This approach is derived from Leverrier's Algorithm. The conventional matrix inversion formula for acquiring a resolvent matrix is cumbersome, whereas this method is quite efficient. To demonstrate the implementation of this algorithm, duty cycle-to-output voltage and input voltage-to-output voltage transfer functions of second-order buck converter are acquired. A PI controller is also implemented in the DC-DC converter to synchronize its output voltage with input voltage and load disturbances. The tuning of the PI controller parameter is done using the Ziegler-Nichols method. At last, these studies are verified through MATLAB Simulation.