*4.2.2 Mode 2:* i*L\* <* i*<sup>L</sup>*

In this mode, the calculated inductor current *i*L\* is lower than the detected inductor current *i*L. An example would be the case in which a shift to a light load occurs. Because the output current suddenly extracts electric charge from the output capacitor, the calculated output *P*o\* power decreases. On the other hand, as the input voltage corresponds to a DC voltage source such as a battery, the voltage does not fluctuate significantly even when the load fluctuates. Therefore, the calculated inductor current *i*L\* decreases according to the load. In contrast, the inductor current for detection increases. Therefore, until the input power becomes equal to the output power, the relationship of Eq. (12) holds.

$$
\dot{\mu}\_{\rm L}^\* < \dot{\mu}\_{\rm L} \tag{12}
$$

single-phase boost-type DC-DC converter, which is the analysis circuit. The control

**Description Symbol Value** Inductor current (100 W design) *I*<sup>L</sup> 8.33 A Output voltage *V*<sup>o</sup> 48 V Output power *P*<sup>o</sup> 100/200 W Switching frequency *f*<sup>s</sup> 100 kHz Inductance (100 W design) *L* 36 μH Output capacitance (100 W design) *C*<sup>o</sup> 500 μH Equivalent series resistance (ESR) of *C*<sup>o</sup> *r*<sup>C</sup> 58.5 mΩ DC resistance of *L* (DCR) *r*<sup>L</sup> 20 mΩ Resistance of drain to source (ON) of Q1 *r*<sup>Q</sup> 58 mΩ Forward resistance of Q1 (diode: D) *r*<sup>D</sup> 130 mΩ

To provide a reference for the responses of these control systems, the gain crossover frequencies of the loop transfer functions for the different control methods were designed to be equal. In addition, the voltage compensator for the PBMC used the

systems were constructed using these circuit parameters.

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

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

this 3-pole-2-zero compensator is given in Eq. (15).

*<sup>G</sup>*cðÞ¼ *<sup>s</sup> <sup>ω</sup>*<sup>i</sup>

*s* �

*<sup>G</sup>*cðÞ¼ *<sup>s</sup> <sup>ω</sup>*<sup>i</sup>

<sup>1</sup> <sup>þ</sup> *<sup>s</sup> <sup>ω</sup>*z1 <sup>1</sup> <sup>þ</sup> *<sup>s</sup>*

<sup>1</sup> <sup>þ</sup> *<sup>s</sup> <sup>ω</sup>*p1 <sup>1</sup> <sup>þ</sup> *<sup>s</sup>*

A secondary delay system was included in both *G*vd(*s*) and Gvd(*s*) in the loop transfer function of the CMC. However, the current control loop is in the inner loop, and the second-order lag system is approximately canceled out. Therefore, the phase delay became smoother, when compared with VMC, and the resonance peak did not appear. Therefore, the CMC used a 2-pole-1-zero (type-2) compensator. The transfer function of the 2-pole-1-zero compensator is given in Eq. (16).

*s* �

where *ω*i, integral frequency; *ω*z, zero point frequency (*ω*<sup>z</sup> and *ω*z1: first point, *ω*z2: second point); *ω*p, pole frequency (*ω*<sup>p</sup> and *ω*p1: first point, *ω*p2: second point).

<sup>1</sup> <sup>þ</sup> *<sup>s</sup> ω*z 

> <sup>1</sup> <sup>þ</sup> *<sup>s</sup> ω*p

*<sup>ω</sup>*z2

*<sup>ω</sup>*p2 (15)

(16)

*5.1.1 Voltage mode control (VMC)*

*Circuit parameters and specifications.*

**Table 1.**

**259**

*5.1.2 Current mode control (CMC)*

same 2-pole-1-zero (type-2) compensator as the current mode control.

The transfer function of the VMC includes second-order lag systems, as expressed by Eq. (4). In addition, the phase lags by 180° or more, owing to the RHP-zero. To improve the phase delay and to stabilize the operation of the control system, a 3-pole-2-zero (type-3) compensator was used. The transfer function of

As a result, the signal to be added to the output signal of the voltage compensator becomes negative and the duty ratio decreases.
