*5.1.1 Voltage mode control (VMC)*

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

$$G\_{\mathbf{c}}(\mathbf{s}) = \frac{a\mathbf{o}\_{\mathbf{i}}}{\mathfrak{s}} \cdot \frac{\left(\mathbf{1} + \frac{s}{a\mathbf{o}\_{\mathbf{i}1}}\right)\left(\mathbf{1} + \frac{s}{a\mathbf{o}\_{\mathbf{i}2}}\right)}{\left(\mathbf{1} + \frac{s}{a\mathbf{o}\_{\mathbf{i}1}}\right)\left(\mathbf{1} + \frac{s}{a\mathbf{o}\_{\mathbf{i}2}}\right)}\tag{15}$$

#### *5.1.2 Current mode control (CMC)*

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).

$$G\_{\mathbf{c}}(\mathbf{s}) = \frac{\alpha\_{\mathbf{i}}}{\mathfrak{s}} \cdot \frac{\left(\mathbf{1} + \frac{s}{\alpha\_{\mathbf{i}}}\right)}{\left(\mathbf{1} + \frac{s}{\alpha\_{\mathbf{p}}}\right)}\tag{16}$$

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).

#### *5.1.3 Power balance mode control (PBMC)*

In the PBMC, the difference between the calculated inductor current *iL*\* and the detected inductor current *iL* is added to the output signal of the voltage compensator. The responsiveness of the output voltage is determined by the crossover frequency in the open loop transfer function. Therefore, the change in the inductor current's reference value (calculated inductor current *i*L\*) is much slower than the change in the detected inductor current *i*L. Therefore, if the reference value of the inductor current is regarded approximately as the DC value in the steady state, it is almost equivalent to the configuration of the CMC.

Therefore, the voltage compensator used a 2-pole-1-zero compensator similar to the CMC. In our simulations, for simplicity, the values of the correction coefficients *a*, *b*, *c*, and *d* were set to 1. However, for the CMC, *e* was set to the CMC's current sensor gain (*e* = *K*<sup>i</sup> = 0.08). In addition, by setting the various sensor gains according to Eq. (17), calculation of the power balance control loop can be easily dealt with.

$$\begin{cases} K\_{\text{vo}} = \mathbf{1}/V\_{\text{o}} \\ K\_{\text{io}} = \mathbf{1}/I\_{\text{o}} \\ K\_{\text{vi}} = \mathbf{1}/V\_{\text{i}} \\ K\_{\text{ii}} = \mathbf{1}/I\_{\text{i}} \end{cases} \tag{17}$$

Therefore, the sampling frequency was reduced and a low-pass filter (LPF) was used. In addition, the settling time of the output voltage in the step response was set to the time required for reaching 0.2 V (approximately 1%) from the steady

**Figure 9** shows the output voltage during load transient in each control method. Compared with CMC, over/undershoot of output voltage is small and settling time is short in PBMC. In particular, the settling time of the output voltage of the PBMC is very short compared with other control methods. Therefore, the PBMC can

*Output voltage responses for load transients. (a) Step-up load transient and (b) step-down load transient.*

value of 48 V.

**Figure 9.**

**261**

*5.2.1 Output voltage response for load transients*

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

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

instantaneously respond to load fluctuations.

Various parameters represented by capital letters on the right side of Eq. (17) are design values. As a result, the input/output voltage/current/power parameters were all 1 by design.

#### **5.2 Comparative verification using circuit simulation**

In this section, a comparative verification of each control system using circuit simulation is described. For the simulation, a circuit simulator PSIM manufactured by Powersim Corporation is used. Configure the configuration of the power stage and control stage using PSIM. The circuit constants of the power stage are shown in **Table 1**, and the parameters of the voltage compensator of the control stage are shown in **Table 2** described later. In addition, each sensor gain and correction constants are as in Section 5.1.3.

**Table 2** shows the compensators' parameters for the different control methods. In addition, the gain crossover frequency of the loop transfer function was *ω*<sup>c</sup> = 6283.19 rad/s (*f*<sup>c</sup> = 1.0 kHz). The extent of the fluctuation and the settling time of the output voltage and the inductor current during the transient state of the load and the input voltage were compared. The load transients were a step-up load transient that fluctuated from 100 to 200 W and a step-down load transient that fluctuated from 200 to 100 W. In addition, the input voltage transients were a stepup input voltage transient that fluctuated from 12 to 24 V and a step-down input voltage transient that fluctuated from 24 V to 12 V. In the simulations, the ripple component was large and it was difficult to identify the different components.


#### **Table 2.**

*Compensator* G*c(*s*) parameters for different control methods.*

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

Therefore, the sampling frequency was reduced and a low-pass filter (LPF) was used. In addition, the settling time of the output voltage in the step response was set to the time required for reaching 0.2 V (approximately 1%) from the steady value of 48 V.
