*5.2.1 Output voltage response for load transients*

*5.1.3 Power balance mode control (PBMC)*

*Control Theory in Engineering*

all 1 by design.

PBMC

**Table 2.**

**260**

constants are as in Section 5.1.3.

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

almost equivalent to the configuration of the CMC.

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

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.

> *K*vo ¼ 1*=V*<sup>o</sup> *K*io ¼ 1*=I*<sup>o</sup> *K*vi ¼ 1*=V*<sup>i</sup> *K*ii ¼ 1*=I*<sup>i</sup>

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

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

**Table 2** shows the compensators' parameters for the different control methods.

*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.

*G***c(***s***)** *ω***<sup>i</sup> (rad/s)** *ω***z1 (***ω***z) (rad/s)** *ω***z2 (rad/s)** *ω***p1 (***ω***p) (rad/s)** *ω***p2 (rad/s)** VMC 35.3 1.86 � 103 1.86 � 103 4.00 � <sup>10</sup><sup>4</sup> 3.42 � 104 CMC 105.0 86.8 – 3.42 � 104 –

In addition, the gain crossover frequency of the loop transfer function was

(17)

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**5.2 Comparative verification using circuit simulation**

**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 instantaneously respond to load fluctuations.
