An IPMC (ionic polymer-metal composite) is a Nafion sheet

Chapter 4, Problem 67

(choose chapter or problem)

A dc-dc converter is a device that takes as an input an unregulated dc voltage and provides a regulated dc voltage as its output. The output voltage may be lower (buck converter), higher (boost converter), or the same as the input voltage. Switching dc-dc converters have a semiconductor active switch (BJT or FET) that is closed periodically with a duty cycle d in a pulse width modulated (PWM) manner. For a boost converter, averaging techniques can be used to arrive at the following state equations (Van Dijk, 1995):

\(\begin{aligned} & L \frac{d i_L}{d t}=-(1-d) u_c+E_s \\ & C \frac{d u_C}{d t}=(1-d) i_L-\frac{u_C}{R} \end{aligned}\)

where L and C are, respectively, the values of internal inductance and capacitance; \(i_L\) is the current through the internal inductor; R is the resistive load connected to the converter; \(E_s\) is the dc input voltage; and the capacitor voltage, \(u_C\), is the converter's output.

(a) Write the converter's equations in the form

\(\begin{aligned} \dot{\mathbf{x}} & =\mathbf{A x}+\mathbf{B u} \\ \mathbf{y} & =\mathbf{C x} \end{aligned}\)

assuming d is a constant.

(b) Using the A, B, and C matrices of Part a, obtain the converter's transfer function \(\frac{U_C(s)}{E_s(s)}\).