- Author:
- Ross, Johnathan Paul
- Area of Honors:
- Electrical Engineering
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Jeffrey Scott Mayer, Thesis Supervisor
Jeffrey Scott Mayer, Thesis Supervisor
John Douglas Mitchell, Thesis Honors Advisor
- Keywords:
- Poincare Map
Non-linear state space modeling
Transfer Functions
Bilinear Transform
State Space Averaging
- Abstract:
- Modern power converter analysis and design uses transfer functions based upon weighted state space representations of the circuit. The steady state value of the duty cycle must be known in order to determine the weighted steady state representation. Under complex control modes the duty cycle is dependent upon on a state variable and a reference signal, leading to particular solutions for each control mode. In this thesis a general approach to solving for the power converter transfer function is found using a Poincaré Map of the periodic, piecewise-linear-time-invariant state space model of the converter system. The Jacobians of the Poincaré Map are used to determine a discrete-time transfer function of the converter system including the control mode. The power converter transfer function is then found after applying the Bilinear Transform and deconstructing the closed loop transfer function model. The results of this method show that it accurately describes the response of the power converter to perturbations in the input for frequencies up to one order of magnitude below the switching frequency.
