Pump-Valve Coordination Control
5.4 Multi-Variable Control Design
Considering the distinguishing configuration of pump-valve coordinate control between resistive loads and overrunning loads, the multi-variable controllers are designed respectively for the following two conditions.
5.4.1 Multi-Variable Controller Under Resistive Loads
Figure 5.5 exhibits the difference between the PP_MI and PF_MO modes in design of the multi-variable controller. In detail, PP_MI mode employs a triple-input and triple-output (TITO) controller. The command voltage of pump controls the supply flow by pressure feedback, which makes the supply pressure beyond the load pres- sure by the preset pressure margin pm. The MI valve is employed to regulate meter-in valve the cylinder velocity to distribute the supply flow, while the meter-out valve controls the backpressure to reduce the outlet pressure losses and avoid cavitation simultaneously. In comparison, PF_MO mode employs a dual-input and triple-output (DITO) controller without the input of a preset pressure margin. The pressure feed- back is cancelled out and the supply flow is regulated based on the input velocities of all actuators. The MO valve controller is designed as follows: 1) the meter-in valve opens as much as possible to reduce the inlet pressure losses; 2) the meter-out valve controls the flow or pressure of each cylinder. Next, the detailed multi-variable controllers for PP_MI and PF_MO modes are designed in Fig.5.5.
The pump controller consists of two layers. The inner layer is utilized to regu- late the pump displacement, in which the swivel and valve controllers is employed to control the pump swash-plate angle with the feedbacks of swivel angle and valve position. The input reference swivel angle of the inner layer controller is acquired by an outer layer controller. In the outer layer, PP or PF control mode of the pump is implemented. PP controller includes a PI regulator to track the reference pressure margin. However, the PI parameters influence the pump dynamics, which means that an unsuitable value may weaken the response and stability. To reduce the dependence on PI parameters and improve the pump dynamic, a feedforward unit is introduced to calculate the theoretical swivel angle, such that the PI regulator only outputs a small
Fig. 5.5 Multi-variable control block diagrams
5.4 Multi-Variable Control Design 85 value around the reference swivel angle. PF controller only employs a feedforward unit to calculate the reference swivel angle, which cancels out the pressure feedback loop. The feedforward unit is based on a mapping from pump flow to swivel angle in Eq. (5.1), where supply pressure and rotation speed are involved. Then, the leakage flow pertaining to the swivel angle and supply pressure can be compensated.
up = θθs,max s,r e f = ∑qi,r e f nmV+p Cp ps (5.1)
The valve controller consists of two closed loops: velocity and pressure control loops, which are both based on the pressure feedback. In the velocity control loop, a calculated flow feedback controller is employed to track cylinder velocity. Taking PP_MI mode as example (Fig. 5.5a), a PID regulator is used to obtain the control signal of the meter-in valve according to the difference qe between the reference flow qref and the actual flow qv.
As mentioned in Chap. 4, the actual flow qv can be acquired by a non-linear flow mapping of the valve orifice in Eq. (5.2). The flow mapping has been calibrated offline as a hydraulic conductivity coefficient Kv:
QV = KV (uV , ∆pV )√
∆pV (5.2)
where the hydraulic conductivity coefficient Kv is subject to spool displacement, temperature, and pressure drops. The calculated flow feedback controller makes the cylinder velocity load-independent, such that the cylinder can precisely track the reference velocity under uncertain and time-varying loads.
In the pressure control loop, a PID regulator is also employed to make the outlet pressure maintain a minimum pressure pref by feeding the pressure difference pb,e between reference one pref and actual one pb. Thereby, it will not only reduce the outlet pressure losses but also avoid cavitation.
In PF_MO mode, it is noted that all meter-in valves open as much as possible to reduce the outlet pressure losses. However, another issue is how to obtain precise motions for different actuators only by the meter-out valves control. For heavy loads, the meter-out valve employs pressure control to reduce the supply pressure. For light loads and other loads under HPR mode, the meter-out valve utilizes flow control to distribute the supply flow. Thus, the flow of heavy load is determined by the subtraction between supply flow and light load flow. In this case, excessive supply flow between regulated supply flow and required one can be accepted by the heavy load actuator, which eliminates the over-matching issue in pump PF mode.
5.4.2 Multi-Variable Controller Under Overrunning Loads
Figure 5.6 exhibits the detailed multi-variable controller under overrunning loads. In LPR mode, the meter-out valve utilizes a calculated flow feedback controller to track
(a) LPR mode (b) NO mode
Fig. 5.6 Multi-variable control under overrunning load
the motion of the actuator. The meter-in valve is endeavored to open fully, which makes the inlet pressure losses as low as possible. Meanwhile, the capacity to avoid cavitation can be enhanced. If the operating condition is beyond the mode capability, the cylinder should switch to NO mode. The pump employs a pressure controller to track the preset pressure margin of 0.3 MPa, which is beyond the threshold of cavitation. The valve controller is almost the same as LPR mode except that the meter-out valve adopts a PI regulator rather than a PID one.
5.4.3 Pressure Matching
In the absence of a command signal, the valves hold on the load. To reduce the viscous drag losses, the pump should maintain a relatively low standby pressure which is much lower than the load pressure. Whenever the cylinder is commanded to move, the actuator would fall down suddenly owing to the maximal opening of the meter-in valve. To address the issue, the pump pressure must increase to the load pressure
p
LSp
sp
sp
LS1 0
Pump ON Pressure
t
t
1 0
Pump ON
p
LSp
sp
sp
LSValve ON Pressure
t
t
Fig. 5.7 Logics between the pump and valves of pressure matchings