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 1.4.3 Where does the steering servomechanism damping come from:

The servomechanism block diagram shows that we are dealing with a follower servomechanism where the INPUT or 2-Wheeler lean angle to the vertical, follows the OUTPUT or torso lean angle to the vertical.

This block diagram also shows that as soon as an error between INPUT and OUTPUT exists, a signal is generated to correct the OUTPUT. The problem is that if the corrective signal is very strong, the OUTPUT will be corrected but may overshoot the INPUT. Another corrective signal will then be generated in the opposite direction… So the OUTPUT will oscillate without stabilization. The servomechanism will then be said to be 'pumping'. This simply explains why all servomechanisms must have a certain amount of damping. But in the case of our steering servomechanism, there is no hydraulic damper slowing down the right-left leaning motions of the 2-Wheeler chassis. It is thus surprising that this steering servomechanism is so stable (Excluding the 'wobble' effect of the front fork, which is something different).

Thus, there must exist some other sort of 'dynamic' damping stabilizing the steering servomechanism. Fortunately, it's possible to get an idea of where it comes from:

An error between INPUT and OUTPUT generates a front wheel orientation that generates a centrifugal force that corrects the OUTPUT. At first look, this correcting force seems directly and solely proportional to this error between INPUT and OUTPUT, but it is not: For example, consider as a starting condition the rider and 2-Wheeler being at certain steady state angles to the vertical in a constant curve. The rider may lean further, so the 2-Wheeler will follow the lean angle after a short time and turn in a shorter radius on the road. Thus, if the speed is kept constant, the 2-Wheeler will be turning faster around its vertical axis. (A motorcycle at 15Km/h turns faster around its vertical axis while turning in a parking lot than while turning in a long slow curve on a highway at the same speed.) Its rotational kinetic energy around this axis will have increased, compared to the starting condition.

It is precisely this increase in rotational kinetic energy that will have slowed down and 'dampened' the leaning motions of the 2-Wheeler. This dampening is 'dynamic' and it’s not an energy loss through heating as for a conventional hydraulic damper. It rather is an energy 'transfer' from one form to another. So the generated 'correcting' force is not simply proportional to the error between INPUT and OUTPUT. It's also reduced proportionately to the rate of change in lean angle (its speed), which corresponds to a dampening function.

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