PID with dead zone for high frequency switching power supply

In digital control systems, due to the inherent numerical quantization error, the deviation between the sampled value of the feedback quantity and the digital given quantity (i.e., the control error) e(n) is generally not zero. When the control error e(m) falls within the allowable error band △, that is,

It can be determined that e(t) is already zero and the control amount u(n) will not be changed. In other words, △ is the control error dead zone. The control algorithm is shown in the figure.

PID algorithm with dead zone

If no control dead zone is added, then when the error e(n) has fallen within the error band but is always greater than or less than zero, according to formula (9-18), the value of the error integral term will continue to accumulate and increase over time, which can easily cause oscillation of the control system.