**4. Power balance mode control (PBMC)**

In this section, the sliding mode control (SMC) of the buck-type DC-DC converter and the power balance mode control (PBMC) applied to the boost-type DC-DC converter are explained.

#### **4.1 Sliding mode control (VMC) of the buck-type DC-DC converter**

The SMC in the buck-type DC-DC converter, which is the foundation of the PBMC, is described here. **Figure 6** shows the block diagram of the SMC. One of the SMCs in the buck-type DC-DC converter is the feedforward input of the charge/ discharge current of the output capacitor to the output signal of the voltage compensator. For this reason, the voltage compensator adjusts the duty ratio and finely adjusts it with the charge/discharge current of the output capacitor.

In the steady state, the amounts of charge and discharge are equivalent, and the feedforward input can be neglected. In the transient state, the amounts of charge and discharge are different, and the feedforward input directly adjusts the duty ratio.

*Power Balance Mode Control for Boost-Type DC-DC Converter DOI: http://dx.doi.org/10.5772/intechopen.82787*

**Figure 6.** *Buck-type DC-DC converter using sliding mode control.*

current is remarkable, and when the overcurrent protection (OCP) operates, the DC-DC converter halts. For these reasons, VMC is typically not used in DC-DC

**Figure 5** shows the block diagram of the CMC. In the CMC, a control loop is added to the voltage control loop. The loop transfer function *G*loop(*s*) of the CMC is

> *F*<sup>m</sup> 1 þ *F*<sup>m</sup> � *G*idðÞ� *s K*<sup>i</sup>

From Eq. (7), the second-order lag system 1/*P*(*s*) in the transfer function of the

plant is approximately canceled out. In addition, the peak of the gain near the resonance frequency disappears. As a result, no overshoots or undershoots of the inductor current occur following sudden changes such as load changes, and stable operation is ensured without reaching the OCP threshold. Therefore, stability and responsiveness of the control system are much better, compared with the VMC. Additional modes, not discussed in this chapter, include the peak current mode control (PCMC), which is based on the CMC, and the average current mode control

In this section, the sliding mode control (SMC) of the buck-type DC-DC converter and the power balance mode control (PBMC) applied to the boost-type

The SMC in the buck-type DC-DC converter, which is the foundation of the PBMC, is described here. **Figure 6** shows the block diagram of the SMC. One of the SMCs in the buck-type DC-DC converter is the feedforward input of the charge/ discharge current of the output capacitor to the output signal of the voltage compensator. For this reason, the voltage compensator adjusts the duty ratio and finely

In the steady state, the amounts of charge and discharge are equivalent, and the feedforward input can be neglected. In the transient state, the amounts of charge and discharge are different, and the feedforward input directly adjusts the duty ratio.

**4.1 Sliding mode control (VMC) of the buck-type DC-DC converter**

adjusts it with the charge/discharge current of the output capacitor.

(ACMC), which is used in power factor correction (PFC) converters.

� *G*vdðÞ� *s K*<sup>v</sup> (7)

converters.

**Figure 5.**

*Current mode control.*

*Control Theory in Engineering*

given in Eq. (7):

**3.2 Current mode control (CMC)**

*G*loopðÞ¼ *s G*cvðÞ� *s*

**4. Power balance mode control (PBMC)**

DC-DC converter are explained.

**254**

Because the CMC also feeds back the inductor current, the duty ratio is finely adjusted. However, in the transient state, the inductor suppresses sudden changes in the current, and the system's responsiveness worsens.

On the other hand, when the charge/discharge current of the output capacitor is used as the feedforward input, the charge/discharge current in the transient state rapidly changes depending on the capacitor. As a result, the duty ratio can be changed faster than for the CMC. Furthermore, when shifting from the transient state to the steady state, the average charge/discharge current becomes zero, and the influence of the feedforward input automatically decreases. Therefore, the feedforward input gain automatically becomes minimal during the transient and in the steady state.

In addition, by appropriately designing the various sensor gains and compensators of this control system, it is possible to set an operation state called the sliding mode. It is known that the control system operating in this sliding mode is not affected by disturbances or plant fluctuations. Therefore, responsiveness and robustness can be improved by operating in sliding mode.

Although this output capacitor current can be detected directly, equivalent series resistance (ESR) and equivalent series inductance (ESL) increase owing to the addition of a shunt resistance and a current transformer, which affects the control system and output voltage. In addition, in digital control systems, analog-to-digital conversion cannot be performed precisely owing to an increase in the noise associated with charging/discharging. On the other hand, it is possible to derive the charge/discharge current of the output capacitor without directly detecting it, by appropriately detecting the output current and the inductor current and performing the calculation. However, as the inductor current of the boost-type DC-DC converter flows only to the output side during the OFF period, the output current differs from the inductor current.

Therefore, it is necessary to consider the control system corresponding to the step-up-type DC-DC converter considering output capacitor current detection and digital control. In the next section, we describe the PBMC with improved responsiveness and robustness for boost-type DC-DC converters.

## **4.2 Power balance mode control**

**Figure 7** shows the block diagram of the PBMC. First, various blocks are described.


In addition, *a*, *b*, *c*, *d*, and *e* denote the correction coefficients. Further, the mathematical symbols � and ÷ are the multiplier and the divider, respectively. As shown in **Figure 7**, these correction coefficients are applied to all output signals from various sensor gains. For simplicity, the correction coefficients *a*, *b*, *c*, and *d* are the inverses of the sensor gain. Accordingly, the various correction coefficients are given in Eq. (8).

$$\begin{cases} a = \mathbf{1}/K\_{\text{vo}} \\\\ b = \mathbf{1}/K\_{\text{io}} \\\\ c = \mathbf{1}/K\_{\text{vi}} \\\\ d = \mathbf{1}/K\_{\text{ii}} \end{cases} \tag{8}$$

*v*<sup>o</sup> � *K*vo � *a* � *i*<sup>o</sup> � *K*io � *b*

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

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

the control methods.

*4.2.1 Mode 1:* i*L\* >* i*<sup>L</sup>*

**Figure 8.**

**257**

*The flowchart of the control methods.*

*<sup>v</sup>*<sup>i</sup> � *<sup>K</sup>*vi � *<sup>c</sup>* <sup>≈</sup> *<sup>v</sup>*<sup>o</sup> � *<sup>i</sup>*<sup>o</sup>

Thus, the input current can be calculated. Because the input current of the boost-type DC-DC converter is equivalent to the inductor current, it is denoted by *i*L\*. Finally, the calculated inductor current is compared with the detected inductor current, and the final duty ratio is determined by adding the result of this comparison and the output of the voltage compensator. From the relationship between the calculated inductor current *i*L\* and the detected inductor current *i*L, the operation can be divided into the following three patterns. **Figure 8** shows the flowchart of

In this mode, the calculated inductor current *i*L\* is higher than the detected inductor current *i*L. As an example, consider the case in which a shift to a heavy load occurs. Because the output current suddenly extracts electric charge from the output capacitor, the calculated output *P*o\* power increases. 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

*v*i

¼ *i*<sup>i</sup>

<sup>∗</sup> <sup>¼</sup> *<sup>i</sup>*<sup>L</sup>

<sup>∗</sup> (10)

As a result, all output signals of the correction coefficients' block can be considered as the values for the power stage.

First, when the detected output voltage and output current are fed into the multiplier, the output is expressed by Eq. (9).

$$
v\_{\rm o} \cdot K\_{\rm vo} \cdot a \cdot i\_{\rm o} \cdot K\_{\rm io} \cdot b \approx v\_{\rm o} \cdot i\_{\rm o} = P\_{\rm o} \,\,\,\tag{9}$$

Thus, the output power can be calculated. Next, when the calculated output power and the detected input voltage are provided to the divider, the output is expressed by Eq. (10).

**Figure 7.** *Power balance mode control.*

*Power Balance Mode Control for Boost-Type DC-DC Converter DOI: http://dx.doi.org/10.5772/intechopen.82787*

$$\frac{v\_{\rm o} \cdot K\_{\rm vo} \cdot a \cdot i\_{\rm o} \cdot K\_{\rm io} \cdot b}{v\_{\rm i} \cdot K\_{\rm vi} \cdot c} \approx \frac{v\_{\rm o} \cdot i\_{\rm o}}{v\_{\rm i}} = i\_{\rm i}^\* = i\_{\rm L} \,\tag{10}$$

Thus, the input current can be calculated. Because the input current of the boost-type DC-DC converter is equivalent to the inductor current, it is denoted by *i*L\*. Finally, the calculated inductor current is compared with the detected inductor current, and the final duty ratio is determined by adding the result of this comparison and the output of the voltage compensator. From the relationship between the calculated inductor current *i*L\* and the detected inductor current *i*L, the operation can be divided into the following three patterns. **Figure 8** shows the flowchart of the control methods.
