TPS549B22: How can I understand the control Mode of D-CAP3?

Luck,

The simple answer is below:

Voltage mode control compares the the fed back output voltage after it has been compensated by the error amplifier to a fixed frequency PWM signal to set the duty cycle and regulate the output.

DCAP mode does not have an internal oscillator.  It uses adaptive on time and hysteretic off time to control the duty cycle.  Te analog on time circuit is designed in such a way that the switching frequency is "quasi-fixed".  The hysteretic off time controller requires a significant ripple content on the feed back signal.  Typically DCAP control will use electrolytic output capacitors with moderate to large ESR.  The inductor ripple current times the ESR generates the required ripple voltage that is in phase with the switching waveform.  If low ESR capacitors such as ceramic types are used, then an external ripple injection circuit is required.

DCAP2 is like DCAP, except that the ripple injection is internal to the controller.  It can support ceramic output capacitors directly.

DCAP3 removes one half of the internal ripple amplitude to increase set point accuracy (DCAP and DCAP2 regulate to the valley voltage and the output voltage is the average) and improve transient response.

Let me know if this is sufficient.  I have more detailed information, but it would need to be edited to supply outside TI.

Luck,
DCAP, DCAP2 and DCAP3 are proprietary TI control schemes. Like Voltage Mode Control, Current Mode Control is a widely used control scheme. There is a lot of information available about it. Basically, instead of a PWM ramp generator as used in VMC, CMC uses the switch current as the 'ramp' signal. Here is a link to a paper on Control mode:
www.ti.com.cn/.../snva555.pdf
I'm sure there are many, many other on line resources.