Schematic diagram of current tracking waveform of high-frequency switching power supply

FIG1 is a schematic diagram of the current tracking waveform, wherein the solid triangle wave represents the iL waveform when ui is not disturbed, and the dotted triangle wave represents the iL waveform when ui is disturbed.

Figure 1 Current tracking waveform diagram

The jth switching cycle after the disturbance is defined as:

That is, the system is asymptotically stable.

On the contrary, when k>1, that is, d>0.5, equation (9-7) does not hold. However, due to periodic control, the quantities in equations (9-4) to (9-7) are always less than the switching period Ts and will not be infinite. The actual phenomenon is that the switching frequency is reduced and the current and voltage ripples are significantly increased.

After adding the ramp function compensation, define

Mc is the slope of the compensation sawtooth wave.

Similarly, it can be proved that

Therefore, as long as k'<1, that is,

Equation (9-7) still holds. That is to say, under the condition of appropriate ramp function compensation, the system can be asymptotically stable even if Du>0.5.