From Design Of Nonlinear Control Systems With The Highest Derivative In Feedback, Volume 16

7.6 Switching Regulator for Boost DC-to-DC Converter

7.6.1 Boost DC-to-DC Converter Circuit Model

Let us consider the application of the above design methodology to the problem of switching controller design for a boost DC-to-DC converter circuit as shown in Fig. 7.3.

Figure 7.3: Boost DC-to-DC converter circuit.

By Kirchhoff's voltage law we have E = V L when the transistor is ON and E = V L + V out when the transistor is OFF; hence, we get

where the state of the ideal switches (transistor and diode) is represented by the control variable u and u ? {0,1}.

The voltage drop V L across an inductor is given by , where I L is the current through the inductor with inductance L. We have for the voltage drop V C across a capacitor, where I C is the current through the capacitor with capacitance C. By Ohm's law, the voltage drop V R across a resistor is given by V R = RI R, where I R is the current through the resistor with resistance R. By KirchhofF's current law we get I Lu = I C + I R. Denote x 1 = I L, x 2 = V C. By taking into account that V R = V C = V out, we obtain the bilinear switched...

Copyright World Scientific Publishing Co. Pte. Ltd. 2004 under license agreement with Books24x7

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