State-space models and order reduction for DC-DC switching converters in discontinuous modes

The state-space modeling and related order reduction problems of switching DC-DC converters operating in discontinuous (D) mode are treated in this paper. A unified discrete-time full-order model is proposed assuming the discontinuous current and voltage mode (DCVM) as a general operation mode from which the discontinuous current mode (DCM), the discontinuous voltage mode (DVM), and continuous made (CM) derive as special cases. Such a model permits a straightforward study of the control-to-output response, in each operation mode. The order reduction of the transfer function is carried out by means of the principal component analysis considering the joint controllability and observability properties of the circuit. It is shown that a proper order reduction can be gained not only in DC mode, as expected, but also in DV and DCV modes. A substantial difference between DC and DV modes is also evidenced in terms of controllability. The frequency analysis and state-space model order reduction for a Cuk converter are proposed to show that the method is free of the limitations affecting other methods of analysis and that its predictions fit experimental measurements