Physics-Based Model of Control Valve Stiction
- PDF / 391,589 Bytes
- 8 Pages / 441 x 666 pts Page_size
- 45 Downloads / 187 Views
Physics-Based Model of Control Valve Stiction
In this book, stiction in control valves is modelled using two approaches. One is physics based and the other is data driven. A physics-based model is outlined in this chapter, while Chap. 13 will present a data-based model that has the same input– output behaviour. The physics-model discussed in this chapter was published in Choudhury et al. (2005a).
12.1 Introduction Friction in the valve arises principally in the packing (See Fig. 10.1). It is the packing that stops process fluid from leaking out of the valve but the valve stem nevertheless has to move freely relative to the packing. There is a trade-off because too tight packing reduces emissions and leaks from the valve but at the same time increases the friction. Loose packing reduces friction but there is a potential for process fluids to leak. Other effects that cause excessive friction are corrosion of the valve stem, which makes it rough or nonsmooth, and deposits on the valve seat, which can make the valve plug stick in the seat. Sticking control valves have deadband and stick–slip behaviour (stiction) caused by excessive static friction. Friction effects have been thoroughly studied in the literature, for instance by Karnopp (1985), Dewit et al. (1995), Olsson (1996), Kayihan and Doyle III (2000) and Choudhury et al. (2005a, 2005b).
12.2 Physical Modelling of Valve Friction 12.2.1 Physics of a Control Valve The purpose of this section is to understand the physics of valve friction and reproduce the behaviour seen in real plant data.
M. A. A. S. Choudhury et al., Diagnosis of Process Nonlinearities and Valve Stiction, c Springer-Verlag Berlin Heidelberg 2008
153
154
12 Physics-Based Model of Control Value Stiction
For a pneumatic sliding stem valve, the force balance equation based on Newton’s second law can be written as: M
d2x = Forces = Fa + Fr + Ff + Fp + Fi , dt 2 ∑
(12.1)
where M is the mass of the moving parts; x is the relative stem position; Fa = Au is the force applied by pneumatic actuator, where A is the area of the diaphragm and u is the actuator air pressure or the valve input signal; Fr = −kx is the spring force where k is the spring constant; Fp = −A p ΔP is the force due to fluid pressure drop, where A p is the plug unbalance area and ΔP is the fluid pressure drop across the valve; Fi is the extra force required to force the valve to be into the seat and Ff is the friction force (Fitzgerald, 1995; Kayihan and Doyle III, 2000; Whalen, 1983). Following Kayihan and Doyel III, Fi and Fp will be assumed to be zero because of their negligible contribution to the model.
12.2.2 Friction Model The friction model is adopted from Karnopp (1985) and Olsson (1996). It includes static and moving friction. The expression for the moving friction is in the first line of Eq. (12.2) and comprises a velocity-independent term Fc known as Coulomb friction and a viscous friction term vFv that depends linearly upon the velocity. Both act in opposition to the velocity, as shown by the negative signs. ⎧
Data Loading...
