The Hysteresis-modulation technique can limit the operating frequency of switching power converters by tuning the hysteresis parameter. The frequency is only limited, it is still variable. This technique does not need an estimator. The downside is that the operating frequency is limited which increases the switching losses and filter complexity.
The equation for the sliding surface uses output voltage regulation error, integral term of voltage error, and output current
$$s=K_p(V_{ref}-V_o)+i_o-\int\frac{uV_i-V_o}{L}dt$$
which can also be represented as
$$s=\frac{1}{R_LC}(V_{ref}-V_0)+\frac{d}{dt}(V_{ref}-V_0)=\frac{1}{R_LC}(V_{ref}-V_0)-\frac{i_c}{C}$$
Where \(K_p\) is a positive constant and \(i_o\) is the output current. The control law is
$$u=\begin{cases}
1, \text{ if }s>K \\
0, \text{ if }s<-K \\
\text{unchanged}, \text{ otherwise}
\end{cases}$$
Which takes the hysteresis band into account. The control system has a 2nd-order response.
- wuSlidingModeControl2022