Modelling static friction the velocity deadband method

7 Modelling static friction the velocity deadband method 

Section 22.6 has accounted for one important nonlinearity, namely the velocity limit of the valve. Another nonlinearity that can cause control problems is static friction, sometimes referred to as stiction, although more properly known as Coulomb friction. Static friction acts to prevent or impede relative motion by opposing the force applied. Its effect on valve movement may be measured as the difference between the valve s demanded travel (equal to the normalized controller output) and the actual valve travel seen on the plant. This difference will lie normally in the normalized range 0.001 to 0.005 (0.1 to 0.5% of total valve travel) for valves fitted with a valve positioning system, although the author has had experience of an important control valve with a value measured at 

The situation is generally significantly worse for pneumatic valves not fitted with a positioning system, where the likely range is 0.005 to 0.05. 

Experiments have shown that a force applied to two initially static objects in touching contact will encounter a countervailing frictional force that will prevent relative motion until a limiting value is reached. Motion will occur once this value has been exceeded, but it will still be opposed by a frictional force. This frictional force will be independent of velocity and will be only slightly less than the limiting value. 

The conditions in equation (22.56) are presented in terms of both the difference tenn, c — jc, and the current valve travel, x, with the latter being often a more convenient form for application. 

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