′

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   =