**1. Introduction**

The demand for switching converters has been steadily increasing. The desired converters should be small and have high power density, high efficiency, good responsiveness, and good robustness. High responsiveness and high robustness are required for the control systems of switching converters. Voltage mode control (VMC) is the most basic control system of switching converters [1, 2]. Since the voltage mode control uses only one voltage sensor, it can be constructed at very low cost. However, since the stability of the control system is low, current mode control (CMC) is used for a general switching converter [3, 4]. Some studies suggest that responsiveness and robustness can be significantly improved using the current mode control (CMC) approach [1–4]. However, it is difficult to improve the performance of boost-type DC-DC converters significantly using only this technology. Although buck-type DC-DC converters can be regarded as approximately linear circuits (regardless of the time-varying circuit), this is not so for boost-type DC-DC converters. This is because in boost-type DC-DC converters, the ON and OFF circuit states are different. As a result, the transfer function of any boost-type DC-DC converter includes an unstable zero (right half plane zero (*RHP-zero*)). Therefore, control systems based on boost-type DC-DC converters cannot set the

gain-crossover frequency (which determines the high-frequency response) due to the presence of this unstable zero.

*dx t*ð Þ

8 < :

*Power Balance Mode Control for Boost-Type DC-DC Converter*

*b*, input matrix; *c*, output matrix; *d*, direct matrix.

*d dt*

8 >>>>><

>>>>>:

*i*Lð Þ*t v*Cð Þ*t*

*v*oðÞ¼ *t* ½ � *c*<sup>11</sup> *c*<sup>12</sup>

*2.1.2 Circuit state averaging using duty ratio*

*dx*ð Þ*t*

8 >>><

>>>:

**Figure 2.**

**251**

*D*<sup>0</sup> ¼ 1 � *D*

" #

*DOI: http://dx.doi.org/10.5772/intechopen.82787*

equation are expressed using the following equations:

<sup>¼</sup> *<sup>a</sup>*<sup>11</sup> *<sup>a</sup>*<sup>12</sup>

*i*Lð Þ*t v*Cð Þ*t*

shows the equivalent circuit for the ON and OFF states of the switch Q1.

ratio, the state equation and the output equation are given as follows:

*Equivalent circuits for the ON and OFF states. (a) Switch Q1: ON; (b) switch Q1: OFF.*

" #

*<sup>a</sup>*<sup>21</sup> *<sup>a</sup>*<sup>22</sup> " # *<sup>i</sup>*Lð Þ*<sup>t</sup>*

*dt* <sup>¼</sup> *Ax*ðÞþ*<sup>t</sup> bu*ð Þ*<sup>t</sup> y t*ðÞ¼ *cx*ðÞþ*t du*ð Þ*t*

where *u***(***t***)**, input vector; *x***(***t***)**, state vector; *y*(*t*), output vector; *A*, state matrix;

With respect to the circuit shown in **Figure 2**, the state equation and the output

*v*Cð Þ*t*

þ ½ � *d*<sup>11</sup> *d*<sup>12</sup>

In Eq. (2), the inductor current and capacitor voltage comprise the state vector, while the input voltage and the output current comprise the input vector. **Figure 2**

When the state of a circuit is averaged over one switching period using the duty

*dt* <sup>¼</sup> *<sup>D</sup>A*on <sup>þ</sup> *<sup>D</sup>*<sup>0</sup> <sup>ð</sup> *<sup>A</sup>*offÞ � *<sup>x</sup>*ð Þþ*<sup>t</sup> <sup>D</sup>b*on <sup>þ</sup> *<sup>D</sup>*<sup>0</sup> <sup>ð</sup> *<sup>b</sup>*offÞ � *<sup>u</sup>*ð Þ*<sup>t</sup> v*oðÞ¼ *t Dc*on þ *D*<sup>0</sup> ð *c*offÞ � *x*ð Þþ*t Dd*on þ *D*<sup>0</sup> ð *d*offÞ � *u*ð Þ*t*

Here *D* and *D*<sup>0</sup> represent the time ratio of the ON and OFF periods in one switching cycle, respectively. The switching converter averages the circuit state by the duty ratio, and it can be regarded as a linear time-invariant system for frequencies lower than the switching frequency. Additional characterization includes static characteristic analysis, steady-state dynamic analysis, and Laplace transforms. Although the transfer function of the switching converter can be derived using the above, in this study the following derivation is omitted. The transfer function of the

þ

*b*<sup>11</sup> *b*<sup>12</sup> *<sup>b</sup>*<sup>21</sup> *<sup>b</sup>*<sup>22</sup> " # *<sup>V</sup>*ið Þ*<sup>t</sup>*

*V*ið Þ*t I*oð Þ*t*

" #

*I*oð Þ*t*

" #

" #

(1)

(2)

(3)

On the other hand, control of switching converter using sliding mode control (SMC) has been studied [5–9]. Sliding mode control has high robustness and is resistant to influences by plant fluctuations. However, the control system has a problem that it is very complicated compared with VMC and CMC.

In this research, we developed power balance mode control (PBMC), which is a new control method that incorporates SMC concept into CMC [10]. In the PBMC approach, the input voltage and the output current are incorporated into the control system as in the conventional control method, and new control items are added by calculation. As a result, the performance of the control system can be greatly improved, when compared with the conventional control method. Furthermore, since the added control items are constituted by four arithmetic operations, implementation is also very easy.
