By S. Braun [title, etc., at back]
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The logic for the on±off groundhook control policy is similar to the on±off skyhook control policy, except that control is based on the unsprung mass. When the relative velocity of the damper is positive, the force of the damper acts to pull up on the axle; when the relative velocity is negative, the force of the damper pushes down on the tire mass. When the absolute velocity of the axle is negative, however, it is traveling downward and the maximum value of damping is desired to pull up on the axle, while the minimum value of damping is desired to continue pushing down on the axle.
That is the system of eqn  can be written as a set of first-order decoupled equations by simply applying the Jordan transformation. In the physical space, the attempt to look for a transformation that decouples the equations of motion amounts to looking at whether or not the mass weighted eigenvectors of the stiffness matrix can be used as system eigenvectors. The existence of modally decoupled control laws depends on the conditions under which two matrices share common eigenvectors. This condition is that two symmetric matrices share the same eigenvectors if and only if they commute.
The control schemes that are commonly used for vehicle suspensions include: . . . on±off skyhook control continuous skyhook control on±off groundhook control hybrid control fuzzy logic damping control The succeeding paragraphs describe these control methods in more detail. On±Off Skyhook Control Figure 3 Schematics of a driver-adjustable suspension. In on±off skyhook control, the damper is controlled by two damping values. Illustrated earlier in Figure 7A, these are referred to as maximum and minimum damping.
Encyclopedia of Vibration by S. Braun [title, etc., at back]