Dynamic Model of a Pneumatic Proportional Pressure Valve
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2001 IEEUASME International Conference on Advanced Intelligent Mechatronics Proceedings 8-12 July 2001 Como, Italy
Dynamic Model of a Pneumatic
Proportional Pressure Valve
Massimo Sorli O, Giorgio Figliolini '", Stefan0 Pastorelli O
Dept. of Mechanics, Politecnico di Torino Corso Duca degli Abruzzi 24,10129 Torino, Italy email sorli@polito.it, pastorellis@ polito.it
O0 DiMSAT, University of Cassino
Via G. Di Biasio 43 03043 Cassino (Ft), Italy
e-mail : figliolini @r ing.unicas.it
Abstract - A dynamic non linear model of a commercial proportional pressure valve, type heifer Honeywell EPP3 5-21- U-100-10, is formulated in order to simulate its behavior in time- domain under several operating conditions. The mechatronic design of the valve and its static and dynamic characterktics are analyzed carefully. Then, the modeling of the valve is carried out by taking into account its main internal devices, which are integrated all together inslde the valve in order to aUow the pressure control through an input electric signul. Fin@, some diugrams given by a computer simulation con+ the validity of the proposed dyMmic non linear model for thLr tjpe of proportional valve.
NOMENCLATURE
AR, &
bl, b2 bs, b cc Compensator
C1, C2
CS, Cv Upper and lower areas of plunger 1 Critical pressure ratios for valves V1 and V2 Critical ratios for supply and exhaust orifices
Conductance of valves V1 and V2
Conductance for supply and exhaust orifices
Pre-load of spring acting on plunger 2
Friction forces on plungers 1 and 2 Spring force on plunger 2
Gravity acceleration Outlet mass flow-rate
Mass flow-rate entering in the servo-chamber
Mass flow-rates through supply and exhaust
Mass flow-rates across VI and V2
Static gain of Vl and V2 equivalent valve
Static gain of proportional pressure valve
Spring stiffness
Stiffness of seals 3 and 4
Polytropic exponents
Masses of plungers 1 and 2
Outlet and control abs. pressures
Outlet and control rel. pressures
Reference conditions of abs. pressures
Reference pressure
Supply and vent abs. pressures
Thermodynamic constant of air
Reaction forces on plungers 1 and 2
Standard abs. temperature Tc0, TRo Reference conditions of abs. temperature
Ts, Tv Abs. temperature of air in supply and exhaust
Vc, VR Volumes of exhaust and control chambers
VO Dead volume in the servo-chamber
VI? Voltage error
VEc Compensated error
VREP Reference input voltage
Vpwi
x, x, x
y, y, y
p12, p2
'yl. 'y2 PANR Standard air density PWM control signals for valves V1 and V2,
(i = 1,2)
Displacement, velocity and acceleration of
plunger 1
Displacement, velocity and acceleration of
plunger 2
Damping coefficients of seals 3 and 4
Viscous friction coefficients for plungers 1 and 2
I. INTRODUCTION
The pneumatic proportional pressure valves convert an input
electric signal in outlet pressure. These valves can be used in
several applications, as processes and servo-systems, for
which different static and dynamic performances are
required. Usually, in the first case very narrow time
responses are not required, while high flow capacity can be
necessary. A typical example is given by gate valves with a
position control, which are generally used in petrochemical
and alimentary industries, or for gas network. The
servomechanisms are instead provided of small sizes of
valves with high band-width, which is necessary for force
and torque control. The following analysis is addressed to
these components,
Three-way proportional pressure valves have supply,
exhaust and outlet ports and they can be provided of
different actuation and control systems. In particular, the
actuation system can be composed by two plungers and the
first design of the valve is very similar to standard relief
valves. The pressure acting within a servo-chamber above
the main plunger controls the opening and closing of the
valve. This pressure can be controlled by means of a pair of
two-way modulated digital valves. Usually, an electric
0-7803-6736-7/01/$10.00 0 2001 IEEE 630
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feedback is obtained by a suitable internal pressure sensor.
The effects of main parameters on the characteristics of a
diaphragm type pressure proportional valve were analyzed in
theoretical and experimental way in [ll. A pneumatic
braking system for Parisian metro was modeled in [2], while
a non-linear dynamic model and experimental analysis of a
commercial proportional pressure valve was described in [3].
The dynamic model of a pressure control system was
proposed in [4]. In particular, a second order linear model was formulated for the used proportional pressure valve and
