##### 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*when the transistor is OFF; hence, we get

_{out}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*is the current through the inductor with inductance

_{L}*L*. We have for the voltage drop

*V*across a capacitor, where

_{C}*I*is the current through the capacitor with capacitance

_{C}*C*. By Ohm's law, the voltage drop

*V*across a resistor is given by

_{R}*V*=

_{R}*RI*, where

_{R}*I*is the current through the resistor with resistance

_{R}*R*. By KirchhofF's current law we get

*I*=

_{L}u*I*+

_{C}*I*. Denote

_{R}*x*

_{1}=

*I*,

_{L}*x*

_{2}=

*V*. By taking into account that

_{C}*V*=

_{R}*V*=

_{C}*V*, we obtain the bilinear switched...

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