A geometric approach to the feedback control of switch mode DC-to-DC power supplies

Using the theory of variable structure systems (VSSs), a geometric approach is presented for the analysis and design of control schemes in bilinear DC-to-DC switch-mode power supplies. A time scale separation property, which naturally describes desirable transient behavior of the power converter, is used to identify the slow manifold of the average system in which a stable sliding mode trajectory can be locally sustained. It is shown that the geometry associated with the sliding mode control is easy to understand and could be particularly exploited in circuits which are designed to exhibit a time scale separation property. It can be generally shown that sliding modes are locally exhibited on integral manifolds of average models of pulse-width-modulation schemes. Thus, VSS theory provides the designer with an alternative, systematic method of geometric nature for the specification of regulation loops in DC-to-DC power converters, which is equivalent to the traditional pulsewidth modulation design technique in terms of average behavior