-
a 0 a tA
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′
L q A 2 s
and Ba are equivalent mass, stiffness and visco-damping
coefficient of accumulator, and Aa, Ba0, ktA are respectively area of cross section in accumulator, visco-damping
where
L L
B′ = BL + AL2/ktL.
coefficient of liquid part and gain of flow rate to pressure at inlet of accumulator, as well as pa0 and Va0 are the initial value of the pre-charge gas. The visco-damping coefficient Ba0 is small but the gain ktA is large for the reason of low
By Eqs. (7)–(8), (12)–(16), reduction yields the structure
diagram of the model of the whole system as depicted in Fig. 7 and built in MATLAB. Here
A sG
viscosity of water comparing to oil hydraulics. So the
N11
= − 1 A ,
1−G1GA
(17)
damping ratio
a = Ba/(2 ) « 0.1
and is under
damped seriously. It is necessary to reduce the gain ktA to depress the overshoot and oscillations.
The continuity of water flow and force balance equations
N12
= − Cip GA ,
1−G1GA
(18)
CHINESE JOURNAL OF MECHANICAL ENGINEERING ·423·
N21 =
A3 sG′ ,
′
(19)
error for step response is obvious by reason of the resistance of throttle valves, injector, pipes, etc. The
N22
1+ G2GL
C G′
= ip2 L , 1+ G2G′
(20)
steady-state error can be reduced and the capacity of resisting disturbance can be enhanced, by closed-loop control of load pressure with integral compensation and PID control. As shown in Fig. 7, the proportional relief
valve is a key component in the pressure control system.
N = GL ,
3 ′
L
(21)
The poor control performance of the valve due to severe nonlinearity and low accuracy makes the linearization of the control loop very difficult. But the frequency response
N4 =
1 ,
ms2 + Bs
pB
(22)
bandwidth of the water hydraulic proportional pressure relief valve, generally below 10 Hz, is much lower than the natural frequency of the WAIM system. So in the opinion
of linear controller design and system simulation, the
N5 = ,
U
(23)
transfer function of the proportional relief valve can be simplified as a three-order loop like
G = V1s + C ,
(24)
1 ip1
e
pB =