AQ: Constant on-time control
There are three different more or less widely used types of constant on-time control. The first one is where the off-time is varied with an error signal. A loop with this type of control has a control-to-output voltage frequency response (or Bode plot if you prefer) similar to that of the constant-frequency voltage-mode control. The second one is where the off-time is terminated with a comparator that monitors the inductor current, and when that current goes below a level set by the error signal, the switch is turned on. This control (also called constant on-time valley-current control) has a control-to-output voltage frequency response similar to the constant-frequency valley-current control. The main difference is that its inner current-control loop does not suffer from the subharmonic instability of the constant-frequency version, so it does not require a stabilizing ramp and the control-to-output voltage response does not show the half-frequency peaking. The third version is where the off-time is terminated when the output voltage (or a fraction of it) goes below the reference voltage. This control belongs to the family of ripple-based controls and it cannot be characterized with the usual averaging-based control-to-output frequency response, for the reason that the gain is affected by the output ripple voltage itself.
As for the hysteretic control, the current-mode version is a close relative of the constant on-time valley-current-control. The version that uses the output ripple voltage instead of the inductor current ripple for turning on and off the switch (also called “hysteretic regulator”) is a close relative of the constant on-time ripple-based control.
Although the ripple-based control loops cannot be characterized with the usual Bode plots, the converters can still be unstable, but not in the meaning of the traditional control-loop instability that power-supply engineers are used to. Furthermore the hysteretic regulator is essentially unconditionally stable. The instabilities with ripple-based control are called “fast-scale” because the frequency of the instability is closely related to the switching frequency (either subharmonic, similar to the inner-loop instability of some of the current-mode controller, or chaotic in nature).
The paper I wrote a couple of years ago (“Ripple-Based Control of Switching Regulators—An Overview”) is a good introduction to ripple-based control and discusses some of the stability issues. There are also quite a few papers with detailed analyses on the stability of converters with feedback loops where the ripple content of the feedback signal is significant.
