Compound control of rail pressure in dual common rail injection system based on a dual regulating valve

To improve the performance of fuel injection in high power diesel engines, high pressure dual common rail system (HPDCRS) is made to match high power diesel engine, proportional-integral-derivative (PID) compound control for rail pressure is proposed based on dual regulating valve: pressure balance valve (PBV) and pressure control valve (PCV), a PID hybrid neural network (PID-HNN) is provided to complete tuning and match of PID coefficient automatically, simulation control modelling of rail pressure is made by MATLAB software, pressure control comparison of dual common rail is made with PID compound control method. The pressure control effects illustrated that PID compound control of dual regulating valves can rapidly trace different target pressure and reduce rails pressure wavelet, and feasibility of compound control is verified in dual common rail pressure.


Introduction
The high pressure common rail injection system is one of advanced fuel injection system in diesel engines currently, its advantages are smaller installation space and flexible control of fuel injection parameter.It has become a main technical means to enhance the diesel engine performance and wide application in small-power diesel engines [1][2][3].With an ever-growing optimization demand for injection performance in high-power diesel engines, high pressure dual common rail system (HPDCRS) becomes the first choice [4].HPDCRS utilizes the advantages of single rail system, and resolves the problems of long rail arrangement in high-power engine: two common rails are arranged in parallel and series next to the cylinder bank and connected using a three-way valve or fuel pipe.There are two advantages of dual rail system: one is installation and manufacture convenience, the other is fast pressure response, but there exists some shortage, such as the two-pressure unevenness and pressure wavelet.Closed-loop control and its algorithm are main paths to overcome these shortages, the existing research literatures on closed-loop control focuses on impacting on single common rail pressure control.Liu X B et al. [5] added neural networks into proportional-integralderivative (PID) control system to simplify tuning work, Xu L et al. [6] presented PID control based on T-S type self-adapted neural fuzzy reasoning system, Huang Y et al. [7] conducted research on starting pressure control strategy and parameter optimization of common rail in diesel engine, Xu W Y et al. [8] presented a common rail injection system and pressure impact analysis on V8 diesel engines.Because the dual common rail injection system is single input, multi output hydraulic circuit, and exacerbates the pressure disturbance between the two common rails, the simple PID control has some difficulties to improve the response and the consistency of dual common rail pressure, an improving control scheme is proposed based on the two dual regulating valves, the pressure control effect of PID hybrid neural network was verified in order to provide a reference for the pressure control of HPDCRS.

Common rail pressure control scheme
Turbocharged diesel engine with six-cylinder V-type water-cooled is selected as object, a dual common rail fuel injection system is constructed.A compound control scheme of the common rail pressure is presented based on dual regulating valves, which is composed of two control circuits in series, as shown in Figure 1.The first loop is a target pressure control (called control I), fast tracking of the target rail pressure is achieved by regulating pressure control valve (PCV) on the high-pressure fuel pump, the second loop is a pressure balancing control (called control II), which counters the pressure of two common rails by controlling pressure balance valve (PBV).PBV is made up of a balance valve core 1, proportional electromagnet 2, reset spring 3, valve body 4, fuel inlet 5, left fuel outlet 6 and right fuel outlet 7, as shown in Figure 2 b), two common rails are connected with PBV.The valve core is a multi-cylindrical structure that forms a self-balancing valve with the valve body cavity [9].The displacement of the valve core is controlled by adjusting the solenoid duty cycle proportionally.There are three positions in PBV: when the control duty cycle is 10-45%, the balance valve core is in the left position, the outlet 6 opening gradually increases and the outlet 7opening slowly decreases.When the control duty cycle amounts to 45-50%, PBV is in the middle position to make outlet 6 and outlet 7 to keep same opening.When the control duty cycle increases to 50-80%, the outlet 7 opening gradually increases and the outlet 6opening gradually closes.

Control principle
The control I is a digital positional PID, the control II has two modes: 1) Open-loop constant value control, it maintains the same opening of two common rail fuel circuits; 2) Digital positional PID control, it finely finishes the pressure regulations of a single common rail to reduce pressure wavelet.
For specific error e(k), e(k-1) in the sample time k and k-1, the control output u (k) of digital PID is as in Equation (1) [10]: According to the working characteristics of the dual common rail fuel injection system, when the target pressure PID control is working, the dynamic tracking of the common rail pressure target value is achieved.The dynamic tracking error is defined as e=p ave -p tar , the control I threshold range is prescribed as ± 5MPa, the pressure equalizing error of two common rails is defined as ed =p rai -p tar , and the control II threshold range of is set to ± 2MPa.Based on the relationship between the dynamic tracking error and the pressure equalizing error, the pressure balance control mode is selected.
(1) When the target pressure changes significantly and the dynamic tracking error is greater than ± 5MPa, Control I dynamically tracks the target value of actual common rail pressure by adjusting the PCV.Control II adopts fixed value control to maintain the PBV in the two output fuel supply positions.
(2) When the target pressure does not change much and the dynamic tracking error approaches ± 5MPa, Control I continues to adjust the PCV to make the two rails pressure approach the target quickly.Control II starts working under the condition that dynamic tracking error is greater than the pressure equalizing error e d , the pressure difference between the two common rails is reduced by means of regulating the PBV.
(3) When the targets pressure remains basically unchanged and the dynamic tracking error is less than ± 5MPa, control I keeps the target pressure tracking unchanged.When the dynamic tracking error is less than the pressure equalizing error e d , control II regulates the opening of the PBV to equalize the pressure between dual rail.
The transfer function of single common rail is selected from reference [11], and the transfer function is shown in Equation ( 2 (2)

PID coefficient tuning
To ensure engine power and emissions to meet the required values, the targets of rail pressure are different in the full operating profile.PID coefficient of common rail pressure control needs to be different in order to have a small overshoot and difference of dual rail pressure [9].Confronting different requirements for pressure difference, multiple sets of PID coefficient tuning bring about a significant increase in coefficient tuning workload.Therefore, a PID hybrid neural network (PID-HNN) is adopted to achieve automatic tuning of dual PID coefficients [12].
PID hybrid neural network.Hybrid neural network is composed of two neural network structure PIDs, which are independent and parallel.The PID hybrid neural network consists of three layers: input layer, hidden layer, and output layer, as shown in Figure 3.There are four neurons in input layer, these inputs are pressure control targets r 1 and r 2 of two PIDs and the control output y 1 and y 2 of controlled object respectively.r 1 and y 1 respectively represent the pressure target value and the flow target value of control I, while r 2 and y 2 represent the pressure target value and the flow output of control II, respectively.The outputs of the input layer are as in Equations ( 3)-( 4): (3) (4) The hidden layer in each neural network structure PID has three neurons, and the output functions of each neuron are different from each other, output functions complete the operations of proportional (P), integral (I), and differential (D) coefficients, PID coefficients operations are fulfilled in the hidden layer of the network.
The every neuron input of hidden layer is gotten from Equation ( 5): ∑ ∑ , j 1,2,3,4,5,6 (5) The output function of every neuron is listed in Equations ( 6) to ( 8): Proportional The two output of the PID-HNN is completed in output layer, these outputs are obtained from inputs in Equation ( 9): Where, is neuron weight from input layer to hidden layer, is neuron weight from hidden layer to output layer.
PID neural network calculation.Considering the significant difference of the input magnitude in closed-loop control, in order to prevent union data from being redundant by more significant data, the input data is normalized according to the following formula in Equation ( 10) [13].(10) Where, x min and x max are the minimum and maximum values in each group of data, x and X ' are the values before and after normalization for each group of data.
The weight from input layer to hidden layer is listed in Equation ( 11): The minimum mean square error J between target r and actual value y is computed from Equation ( 12): The gradient descent method is a simple and common method for back-propagation (BP) neural networks, when the learning step is set toη.After n steps of learning, the weights from hidden layer to output layer can be calculated using the following formula in Equation (13): The appropriate learning step size is extremely important to the network's convergence speed and learning times.Introducing adaptive learning step size calculation, to make the learning step size change significantly, the change in learning step size ∆η(n) Calculate according to Equations ( 14) to (16): η n 1 η n Δη n (16) Where, α is a momentum factor parameter (0 ≤α≤ 1), σ is an incremental constant (0.01 ≤σ< 0.1), λ is a sign constant.
When λ is greater than zero, the learning step size increases, if the learning error ε is given, the PID-HNN can automatically correct the calculated weight (PID coefficient) and adjust the controlled object to continuously approach its target value r.

Modelling and simulation
A common rail pressure control modeling is completed with MATLAB/Simulink software, its model is shown in Figure 4. Algorithm training model of PID hybrid neural network is programmed in m language and encapsulated into the control simulation model [14].The PID-HNN training is proceeded as follows steps: 1) initial state parameter e, r, y are known, initial weight is set to w 1 j (0)= ± 1, and w 2 j (0)= -1; 2) Learning error ε is given, learning step η is preset to be fixed; 3)The pressure control target value r is given initial value; 4) In each control cycle, when J is greater than ε , back-propagation modifying of the network is started, the network modifies weight value w and enters the learning process to decrease the difference between the target and actual; 5) When J is less than ε, then two PID control outputs u are obtained, and PID coefficients of two PID controls are determined automatically.
In the conditions of sampling time 100ms, target values of common rail pressure is set as 100 MPa, 140MPa separately, four learning errors are chosen to confirm the desired count of learning step, the rail pressure variety of four learning errors is listed in Table 1.Results in Table 1 imply that when the learning error reduces, the more learning count requires, and the variety range of the rail pressure is smaller.When the learning error is less than 0.042 and 0.033, the variety range of rail pressure is within the limit of ± 5MPa and ± 2MPa respectively, therefore the learning errors of the first and second loop are taken as 0.042 and 0.033 respectively, corresponding to common rail pressure 100MPa and 140MPa.

Rail pressure tracking control
When control II is set to a fixed value control, which maintains the same opening of the left and right valve cores of the pressure equalization valve, the target common rail pressure tracking control is completed by control I.When the target pressure of common rail changes from 50MPa to 110MPa, tracking curve of dual common rail pressure is shown in Figure 5.As Figure 5 shows, for the first target pressure of 50MPa, the time t of tracking pressure of two common rails to the target value is about 0.7s, and for the second target pressure of 110MPa, the time t to the target value is 1.9s.Although continuous adjustment is made, the pressure fluctuation range of two common rails is between 100-120MPa with an error of 10MPa from the pressure target value.Moreover, the pressure fluctuation values of two common rails are inconsistent.There are two main reasons: firstly, the feedback pressure adopts the measured average value of two common rails pressure, which causes a certain dynamic difference between the feedback pressure and the actual pressure of corresponding common rail, and large fluctuations in the adjustment pressure range are resulted in.Secondly, because a fixed value control is used in control II, the PBV has an equal opening and becomes a threeway valve [15].The fuel circuits of two common rails are connected at the same time, the pressure fluctuations generate reflections in two common rails and produces different pressure values of two common rails.

Single common rail pressure stabilization control
When the control pressure of control I approaches the target 110MPa, control II begins the PID control. in the condition of an initial control duty cycle of 40% and a learning error of 0.04, the pressure of common rail 1 is adjusted and controlled by control II.The pressure changes in rail 1 are shown as Figure 6 before and after pressure control.As Figure 6 shows, pressure change is above 5MPa to target pressure of 110MPa before control II starts, when continuous adjustment is acted by control II, the pressure change range of rail 1 is between 107MPa and 111MPa, with an error of 2MPa to the pressure target.Compared the pressure changes before control, there exists significantly reduction in pressure wavelets after using control II adjustment.This indicates that it can effectively attenuate the pressure wavelets of common rail 1 and achieve the rail pressure control accuracy to 2MPa.

Dual common rail pressure equalization control
In the condition of fuel supplied to the injector alternately by the common rail 1 and 2, PID control to two common rails is continuously regulated by control II, the target pressure and learning error is set to 110MPa and 0.033 respectively, and the PID coefficient of control I are K P =30, K i =15, K d =0.01, while PID coefficient of control II are K P = 7, K i =10, K d =0.5, the control effect of dual rail pressure is shown in Figure 7.As Figure 7 shows, when injection fuel once is made by fuel injector connected to common rail 1, control II changes the PBV opening to common pipe 1, so that the pressure of common rail 1 quickly closes to target pressure, then fuel injection once is completed by another fuel injector attached to common rail 2, the control II continuously regulates the PBV opening to common rail 2, the pressure of common rail 2 gradually gets close to target pressure too.Control II continuously regulates the pressure of common rail 1, 2, pressure wavelet difference is reduced to 2MPa between two rails [16].

Conclusions
1) A compound control of dual common rail pressure has been constructed by adding pressure balance valve control on the basis of original pressure control valve, this compound control can finish the fast-tracking of common rail pressure and refinement adjustment of pressure balance.
2) According to the requirements of rail pressure compound control, a PID hybrid neural network is introduced to determine PID coefficient tuning in two loops, it can automatically complete PID coefficient tuning by back propagation algorithm of neural network and reduce the tuning workload.
3) PID control method of hybrid neural network has a better control effect on common rail pressure with the MATLAB simulation results, its good control effect is mainly focused on the improvement of pressure difference in dual common rail system, the further study will be made in real experimental control of real system and diesel engine.

Figure 1 .
Figure 1.Compound control of dual common rail pressure.

Figure 2 .
Figure 2. a) Pressure control valve; b) Pressure balanced valve.PCV consists of ball valve 1, armature 2, proportional electromagnet 3, and return spring 4 in Figure 2 a), it is integrated into the high-pressure fuel pump, and the fuel flow rate to the common rail is regulated by changing the opening of the solenoid controlled ball valve.PBV is made up of a balance valve core 1, proportional electromagnet 2, reset spring 3, valve body 4, fuel inlet 5, left fuel outlet 6 and right fuel outlet 7, as shown in Figure2 b), two common rails are connected with PBV.The valve core is a multi-cylindrical structure that forms a self-balancing valve with the valve body cavity[9].The displacement of the valve core is controlled by adjusting the solenoid duty cycle proportionally.There are three positions in PBV: when the control duty cycle is 10-45%, the balance valve core is in the left position, the outlet 6 opening gradually increases and the outlet 7opening slowly decreases.When the control duty cycle amounts to 45-50%, PBV is in the middle position to make outlet 6 and outlet 7 to keep same opening.When the control duty cycle increases to 50-80%, the outlet 7 opening gradually increases and the outlet 6opening gradually closes.

Figure 4 .
Figure 4. Simulation model of rail pressure PID control.

Figure 5 .
Figure 5. Tracking curve of dual common rail pressure by control I.

Figure 6 .
Figure 6.Control effect of rail pressure by control II.

Figure 7 .
Figure 7.Control effect of dual rail pressure by control II.

Table 1 .
Rail pressure variety of four learning errors.