Pu 1988; Wikander 1988).
First commercial products were available in the 1980s (Bala et al. 1986;
Pu and Weston 1988; Virvalo 1995a:12). It took almost two decades to de-
velop this technology to a point were off-the-shelf controlled pneumatic
drives can be regarded as standard components that do not require special
training in control system design to be operated successfully (Zhou 1995).
The achievable accuracy is less than those of electric drives but suffices
for many applications. Muijtjens (1998) gives a repeatability of ± 0.05 mm
for electric drives with ball screws and a repeatability of ± 0.15 mm for
those with tooth belts while pneumatic servo drives achieve ± 0.1 mm.
Howe (2004) states that electric drives are capable of an accuracy of
± 0.025 mm and that accuracies of commercial pneumatic systems can be
as good as ± 0.81 mm with a repeatability of ± 0.13 mm.
This chapter begins with models for control system design, presents dif-
ferent control strategies and finally gives some measurements of a com-
mercial drive. The presentation follows mostly the dissertations from
Schwenzer (1983), Pu (1988), Wikander (1988) and Virvalo (1995a).
Industrial process control systems that also use air as medium face other
problems and are described in Chap. 19.Figure 18.1 shows all components that are necessary to operate a posi-
tion controlled pneumatic drive successfully. Air supply, 1 to 3, and load,
6, can have a substantial effect on the performance (Virvalo and Mäkinen
1999). However, in the following these components will be taken as ideal
to not further increase the complexity of the system.
A number of variations of this configuration have been studied. Ruster-
holz and Widmer (1985) and Rusterholz (1986) point out that this structure
has serious drawbacks for longer cylinders. Therefore they use two 3/2-
way proportional directional control valves which can be mounted direct at
the cylinder ends to avoid the problems caused by long lines between
valve and cylinder. Wikander (1988) also studies a system with two 3-port
valves to reduce the dependence of the natural frequency on the position of
the piston.
 To reduce costs the replacement of proportional control valves by
switching valves has been studied by many researchers (Hippe 1988). An-
other approach is the use of pressure control valves as actuators for posi-
tioning loops (Baoren and Zhuangyun 1997).
18.1 Mathematical Model for Control System Design
In previous chapters mathematical descriptions of the processes in pneu-
matic cylinders, proportional control valves and lines are given. These
highly non-linear models are very well suited to simulate the response of a
system on a digital computer. Due to the fact that most controller design
methods require linear models these non-linear equations have to be line-arised and simplified. In the first work1 covering this field extensively
Shearer (1954:57) starts with the following assumptions:
1. The supply pressure is constant.
2. The supply temperature is constant.
3. Heat transfer between working gas and its surroundings is negligible.
4. The working gas obeys the ideal gas equation of state:  T R p ⋅ ⋅ ρ = .
5. The temperature of the gas flowing between the valve and the ram is
at all times equal to supply temperature.
6. The ram moves only small distances from its centre position.
7. The ram pressures pA and pB vary by only small amounts from an
initial steady value pi.
8. The control valve is symmetrical and the describing parameters do
not vary with valve opening.
9. Valve opening does not exceed its maximum design value.
10. Passages connecting valve and ram are very short and offer negligi- 气动系统英文文献和翻译(2):http://www.youerw.com/fanyi/lunwen_1308.html