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

• *K*io: output current sensor gain

*Control Theory in Engineering*

• *K*vi: input voltage sensor gain

ered as the values for the power stage.

multiplier, the output is expressed by Eq. (9).

are given in Eq. (8).

expressed by Eq. (10).

**Figure 7.**

**256**

*Power balance mode control.*

• *K*ii: input current (inductor current) sensor gain

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

> *a* ¼ 1*=K*vo *b* ¼ 1*=K*io *c* ¼ 1*=K*vi *d* ¼ 1*=K*ii

As a result, all output signals of the correction coefficients' block can be consid-

First, when the detected output voltage and output current are fed into the

*v*<sup>o</sup> � *K*vo � *a* � *i*<sup>o</sup> � *K*io � *b*≈ *v*<sup>o</sup> � *i*<sup>o</sup> ¼ *P*<sup>o</sup>

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

(8)

<sup>∗</sup> (9)

8 >>>>>><

>>>>>>:

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

**Figure 8.** *The flowchart of the control methods.*

inductor current *i*L\* increases 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. (11) holds.

$$
\dot{\mathfrak{u}}\_{\mathcal{L}}{}^\* > \dot{\mathfrak{u}}\_{\mathcal{L}} \tag{11}
$$

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