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                                                            ELECTROHYDRAULIC MOTION CONTROL SYSTEMS  477
                                  Under non-saturated conditions, the performances of pre-compensated and post-
                             compensated configurations of multi circuit hydraulic systems are very similar. When the
                             pump capacity is saturated, the post-compensator configuration backs-off the flow-demand
                             from each line proportionally and tries to maintain even flow delivery based on demand
                             to each circuit. Whereas in pre-compensated multi circuits, when the pump saturates, the
                             circuit which has the largest load pressure gets less flow and may eventually get zero flow.
                             In three or more function circuits, the higher load pressure circuits get progressively less
                             flow and only the lowest pressure circuit gets most of the flow. The orifice in the pressure
                             feedback line from the load has increased the dampening effect (in addition to the added
                             hydraulic resistance) so that high frequency pressure spikes are filtered from the feedback
                             signal to the compensator valve.
                                  The pressure compensated flow control valves work on the basic operating principle
                             of maintaining constant flow despite pressure variations. Examining Equation 7.193 shows
                             that for a given spool displacement, the flow rate will change as a function of pressure
                             differential across the valve which may vary as a function of load and supply pressure
                             variations. The basic principle is to change the valve opening A(x ) by shifting the spool
                                                                                  s
                             as a function of pressure feedback. As a result, the effective spool displacement is not only
                             a function of the current but also the pressure drop. Hence, if the pressure drop increases,
                             feedback moves the spool to reduce the orifice area. Similarly, if the pressure drop reduces,
                             feedback moves to increase the orifice area. The end result is to maintain an almost constant
                             flow for a constant current signal under varying load conditions. The feedback mechanism
                             to shift the spool as a function of pressure drop can be implemented by hydro-mechanical
                             or electronic means. Normally, a pressure compensated flow control valve is implemented
                             with two valves in series: one valve is the proportional directional flow control valve and
                             the other valve is the pressure compensator valve. Examples of such implementations are
                             shown in Figures 7.55–7.57. It should be noted that if two pressure sensors were available at
                             the input and output ports of the proportional valve, the solenoid current could be controlled
                             to perform the function of the second valve, while at the same time metering the flow. In
                             other words, the control algorithm that decides on the solenoid current to shift the spool can
                             take not only the desired command signal but also the two pressure signals into account.
                             Hence, we can implement a pressure compensated flow control valve using a solenoid
                             controlled proportional valve, two pressure sensors, and digital control algorithm.


                             The Need for Pressure Compensation in Multi Function Circuits
                             When a load-sensing pump is used used to supply two or more parallel hydraulic cir-
                             cuits, the flow distribution between the circuits is load dependent (Figure 7.58). More flow
                             will go to the circuit with lower load resistance. Load check valves in each circuit are used
                             to make sure that the load does not drive the flow back to the pump when the load pressure
                             is larger than the supply pressure. Let us assume that both circuits have the same valve size
                             and cylinders. The flow across each valve is given by

                                                                      √
                                                     Q v1  = C ⋅ A (x ) ⋅  p − p l1            (7.208)
                                                                         s
                                                               v1
                                                                  v1
                                                           d
                                                                      √
                                                     Q v2  = C ⋅ A (x ) ⋅  p − p l2            (7.209)
                                                                  v2
                                                           d
                                                               v2
                                                                         s
                             where
                                             Q = Q  v1  + Q v2  ; for p < p relief  (Q relief  = 0.0)  (7.210)
                                                                  s
                                              s
                             Since the valves are the same size, and assuming that both valve spools are displaced to
                             the same value (same valve orifice openings), C A (x ) = C A (x ), the flow rate that
                                                                                 v2
                                                                                     v2
                                                                      v1
                                                                   d
                                                                               d
                                                                         v1
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