Development of a Robust Controller for Electro ...

ISSN 1674-8484 CN 11-5904/U

汽车安全与节能学报, 2016 年, 第 7 卷 第 1 期 J Automotive Safety and Energy, 2016, Vol. 7 No. 1

13/15 100 — 107

Development of a Robust Controller for Electro-hydraulic Variable Valve Actuation System HUANG Chao 1, HUANG Yanjun 2, ZHANG Jian 1, Amir KHAJEPOUR 1,2 (1. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China; 2. University of Waterloo, Waterloo N2L3G1, Canada)

Abstract: Hydraulic oil viscosity has significant influence on the performance of hydraulic variable valve actuation (VVA) systems. The optimal valve timing and lift should be quickly reached under any operating condition to improve the efficiency of internal combustion engines. A mathematical model was built for an electro-hydraulic VVA using AMESim software and then validated to study the influence of hydraulic oil viscosity on the VVA performances. An average model of the VVA was developed based on the energy conservation concept. A sliding mode controller (SMC) was designed by using the average model in Matlab/Simulink. The simulation results show that the proposed SMC can adapt the valve lift by adjusting hydraulic pump speed. The SMC controller can improve the working aceuracy by 9.3%. Therefore, this SMC can eliminate the disturbances caused by the variation of hydraulic oil viscosity. Key words: internal combustion engine (ICE); variable valve actuation (VVA); viscosity of hydraulic oil; average model; sliding mode controller (SMC)

电控液压可变气门驱动系统鲁棒控制器的设计 ( 英文 ) 黄  超 1，黄岩军 2，张  健 1，Amir KHAJEPOUR1, 2 （1. 湖南大学 机械与运载工程学院，长沙 410082, 中国；2. 滑铁卢大学，滑铁卢 N2L3G1，加拿大）

摘  要：液压油粘度的变化会对液压可变气门系统（VVA）性能产生重要影响，为提高内燃机的性能， 应根据发动机的运行工况调整最佳的气门正时及升程。该文建立了全可变气门机构的 AMESim 仿真 模型，分析了液压油粘度对气门升程的影响。基于能量守恒定律建立了系统平均模型，利用 Matlab/ Simulink 设计了滑模控制器。仿真结果表明：所设计的滑模控制器通过调节液压泵的转速，调节气 门升程，使气门工作精度提高了9.3% 左右。因此，该控制器降低了液压油粘度变化带来的扰动影响。 关键词：内燃机 (ICE) ；可变气门机构 (VVA) ；液压油粘度；平均模型；滑模控制 (SMC) 中图分类号：U 411+.2

文献标识码：A

DOI: 10.3969/j.issn.1674-8484.2016.01.013

收稿日期 / Received ：2015-11-01 基金项目 / Supported by ：国家自然科学基金资助项目 (11202077) ；湖南自然科学基金资助项目 (14JJ3060) 第一作者 / First author ：黄超（1990 －），男（汉），湖南，硕士研究生。E-mail: [email protected] 通讯作者 / Corresponding author ：Amir Khajepour，男，加拿大，教授。E-mail: [email protected]

HUANG Chao, et al: Development of a robust controller for electro-hydraulic variable valve actuation system In order to create a less polluted and safer environment, many automobile manufacturers are subjected to increasingly stringent emissions standards and fuel consumption regulations, which encourages automobile researchers to develop more efficient and less polluting vehicles [1]. The advanced variable valve timing and lift is a useful technology that could improve engine power, fuel economy and reduce emission. With variable valve actuation (VVA) systems, engine valve timing and lift can be freely adjusted according to engine operating conditions [2, 3].

an accumulator, a high pressure spool valve (HPSV), a low pressure spool valve (LPSV), two identical phase shifters, and a cylinder with a piston shown in Figure 1. During an engine working cycle, the engine valve opening and closing events are driven by the high pressure hydraulic oil inside the cylinder chamber. As shown in Figure 2, the rotary spool valve (HPSV/ LPSV) is used to control the flow between the hydraulic cylinder and high/low pressure oil sources (accumulator/oil tank). The HPSV and LPSV are responsible for charging and discharging the hydraulic cylinder, when the spooling shaft of the high pressure valve is lined up with its casing port, the hydraulic fluid flows to the cylinder from the accumulator, which pushes the piston down. As the LPSV is open, the trapped hydraulic oil flows back to the tank, then, the engine valve starts to close because of the spring force. The two phase shifters are used to control the rotary valve’s opening and closing time to achieve the desired valve timing. Above all, the VVA system can be a substitute for the conventional valve train as long as the required valve timing and lift can be accurately achieved. The phase shifters are used to control the rotary valve opening and closing time to adjust the valve timing. In QHPSV

Accumulator

ECU

In most of the electro-hydraulic camless valvetrain, a precise control strategy is necessary since the engine performance is highly influenced by lift and timing. Several studies have been conducted [7,8], the opening interval of the high pressure spool valve is manipulated to realize lift control. Anderson in [7] has introduced an adaptive pole-placement control method to achieve the maximum lift. However, the engine valve timing and lift should not only change with the varying working conditions of the engine but also must account for external disturbances. This paper concentrates on studying and eliminating the disturbance brought by the viscosity change of hydraulic oil due to the variation in working temperature. In the past few decades, several types of approaches and control strategies have been developed and implemented to improve the performance of VVA systems. In this paper, an average model of the proposed VVA system is developed based on energy conservation principles, and an SMC is designed because of its robustness and lesser sensitivity to system uncertainties and disturbances for the valve operation.

1

Hydraulic Cylinder

E-motor

P2

GB

P1

HPSV QLPSV

Gear Pump

Poppet Valve

E-motor LPSV Engine

Oil Reservoir

Figure 1  Schematic Drawing of the VVA System [9]

Valve Casing Port Casing Spool Spool Shaft

1  Modeling and Validation of the VVA System

φc

Spool Part

Casing Port

φ

s

rc

rs

1.1  The Structure and Working Principle of the VVA The structure and working principles of the hydraulic VVA system are briefly introduced as follows [9]: The VVA system consists of seven main components: an oil pump,

Phase Shifter

M

In general, VVA systems are divided two main categories: camless and cam-based valvetrains. Some cam-based valvetrains have been already developed by several companies, such as Vanos system employed in BMW, Valvetronic system by BMW, VTEC system employed in Honda [4], due to their limited flexibility and high mechanism complexity, many manufacturers and researchers focus on camless valvetrains. Electro-magnetic and electro-hydraulic are all in this category, the electro-magnetic valve actuators have more flexibility than cam-based valve valvetrains, due to high non-linearity in magnetic force characteristics, the system have many difficulties include: high landing velocity, high power losses and high sensitivity to in-cylinder gas pressure[5,6]. However, the electro-hydraulic valve actuation can overcome some difficulties such as high landing velocity and slow actuator response.

101

θs

w

l Spool Shaft Spool

θc

Valve Casing 1

Spool Part

Figure 2  The Structure of the Proposed Rotary Spool Valve

[9]

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other words, engine timing is achieved by both rotary spool valves (high pressure spool valve (HPSV) and low pressure spool valve (LPSV)) by changing the angular position of the spooling shafts of the HPSV and LPSV.

2.3  Verification of the AMESim Model

2.2  Modeling of the VVA System in AMESim In order to study the influence of different viscosities on the performance of the VVA system, a model is built in AMESim software. The whole structure of the model is shown in Figure 3. In this model, the HPSV and LPSV are modeled by two variable hydraulic restrictors, which are controlled by valve opening and closing events. In order to simplify the model, the engine valve and hydraulic piston masses are lumped into a single mass, where the motion of the piston is based on Newton's second law and the design parameters use the optimized values calculated through many simulations, as shown Table 1. During the simulation, the compression and expansion process of the stored air in the accumulator can be considered as a polytropic process, and the polytropic coefficient is n = 1.3.

Accumulator

Actuator

HPSV LPSV

Pump

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The simulation results of this AMESim model are compared with those of a validated model proposed in [9] under the same condition, and the validated Simulink model is evaluated experimentally. For the sake of convenience, the comparison results for the scenario of initial pressure of accumulator (5.6 MPa) and engine speed (1 000 r/min) is provided. The comparison between the validated model and the AMESim model is shown in Figure 4. In the first plot, the comparison of the engine valve lift during one cycle is shown, where the maximum engine valve lift is about 8.5 mm and the difference between results of the two models does not exceed 5%. On the other hand, when the engine lift arrive at maximum value (8.5 mm), some fluctuation appear. This is because driving force fluctuations exists in hydraulic systems, although the accumulator can reduce fluctuation but cannot eliminate. In addition, valve spring force will cause fluctuations too. The second plot shows the hydraulic oil pressure in the accumulator while the initial pressure is set at 5.6 MPa, and the pressure agrees with that of the validated model. The pressure in accumulator is decreasing when the HPSV starts open, since the hydraulic oil from accumulator went to hydraulic cylinder. Plot 3 describes the pressure of the oil inside the actuator (the cylinder), and the AMESim model result matches that of the validated model quite well. In the last plot, the simulation result of the valve velocity also fits that of the validated model. There are also other verifications, such as HPSV flow rate, valve acceleration, etc. All the comparisons prove the AMESim simulation model is accurate and can be used for further studies.

2  Viscosity of the Hydraulic Oil Figure 3  The Structure of VVA System Model in AMESim

Table 1  Simulation Parameters Engine speed

Nengine / (r·min-1) -1

1000

Pump displacement volume

Vdisp / (mL·rev )

2.1

Engine valve moving mass

m / kg

0.376

-1

Valve return-spring stiffness

Ks / (kN·m )

10.5

Engine valve return-spring preload

Fpre / N

344

Coulomb friction force

Ffric / N

104.3

Rotary port opening area

2

50

Engine piston area

2

Ap / mm

164

Engine valve opening angle

CAopen / (°)

0

Engine valve closing angle

CAclose / (°)

210

Hydraulic cylinder volume

V2 / mL

10

Oil dynamic viscosity

μ / (mPa·s)

51

Oil density

Arotary / mm

-3

ρ / (g·cm )

0.87

The piston is the main part of a hydraulic VVA system, which drives the engine valve. The engine valves are always suffering from high temperature gas flushing and a poor heat transfer condition. The accumulated heat will be conducted to the piston and then to the oil above such that the temperature and the dynamic viscosity of the oil will be changed. Consequently, the valve timing and the maximum lift will be influenced. Therefore, it is necessary to identify the temperature variation range of the hydraulic oil at the top of the engine valve, so that it could also provide guidance toward the selection of hydraulic oils. LIN Fenggong and his team have done some research on the temperature field distribution of valves, and the studies show that the maximum temperature of a valve is approximately 959 ℃ , which appears at the bottom of the exhaust valve, while the minimum temperature of 80 ℃ appears at the top of the hydraulic piston [10]. Considering the leakage problem of the hydraulic system and the temperature of the environment, the 46# turbine hydraulic oil is selected in this paper. Hydraulic oil viscosity is mainly influenced by temperature and pressure. The working pressure is around 10 MPa in the hydraulic system, so the influence of pressure change can be neglected [11], whereas, the influence of the

HUANG Chao, et al: Development of a robust controller for electro-hydraulic variable valve actuation system 10 Accumulator pressure, ρ1 / MPa

Valve lift, x / mm

15

10

5

0

-5

0

180

CA / (°)

360

540

180

CA / (°)

360

4 Valve velocity, v / (m·s-1)

Cylinder pressure, ρb / MPa

5

0

4

2

0

-2

103

0

180

CA / (°)

360

Validated model AMESim model

2

0

-2

-4

540

540

180

0

CA / (°)

360

540

Figure 4 Comparison between Validated and AMESim Model

where, u, A and

Recommended range 20 12 10 8

0 15 VG 00 O 1 68 46 2 3 2 2 5 1

.

100

IS

In fact, a viscous resistance, which is proportional to the fluid viscosity, velocity and contact area based on Newton's law of viscosity [13], is always considered in the hydraulic system. The resistance force can be illustrated as follows:

1 000

mm2/s or cSt

3  Influence of Viscosity on Performance of VVA System

10 000

Viscosity

temperature change is significant and the correlation between temperature and viscosity is shown in Figure 5. Regardless of the hydraulic oil type, it is usually recommended that the working range of the viscosity be 12~100 mm 2·s-1 [12]. However, given that the engine’s cold-start temperature is -10 or even lower, the actual working range of the hydraulic oil should be from 5 to 1 390 mm 2·s-1, which is also the range studied in this paper.

6 4

(1)

are fluid dynamic viscosity, contact

area, and velocity gradient, respectively. Since the viscosity is susceptibility to the variation of oil temperature, and it tends to decrease as the temperature increases, the system’s performance will be severely affected by the dramatic change of fluid dynamic viscosity, especially during the cold-start period. As the dynamic viscosity of hydraulic oil changes, the engine’s maximum valve lift will vary. The simulation is done

-40

-20

0

20

40

60

80

100

120 140

ISO reference temperature θ/℃

Figure 5  The Correlation between Viscosity Oil and Temperature [12]

in an arbitrary operating condition (e.g. Nengine = 1 000 r/min) to demonstrate this phenomenon. Figure 6 shows that some conclusions could be drawn: as long as the viscosity changes

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between 10 and 150 mm 2·s-1, the viscosity has little influence on the engine valve maximum lift, but with the value beyond 150 mm 2·s-1, the valve lift decreases distinctly due to the high viscosity, poor responsiveness of the hydraulic piston, and the greater resistance of the hydraulic flow. On the other hand, the viscosity also has an effect on valve timing because of the slower response.

4  Controller Design As analyzed above, the hydraulic oil viscosity will influence valve timing and lift. Therefore, an urgent step is to develop a controller to achieve the desired valve timing and maximum lift such that the engine efficiency will be improved [14].

4.1  Valve Timing Control As discussed in the previous sections, the angular position of the spool shaft of the rotary valve can be adapted arbitrarily by the phase shifter. The valve displacement and the angular position of the spool shaft were measured precisely as feedback signals to the controller. Then, some delay and advance caused by disturbances can be compensated by manipulating the phase shifter based on the actual angle error measured in the previous cycle. The timing could be controlled by a PI controller. Some arbitrary valve timings can be achieved as shown in Figure 7. As a result, the delay or advance caused by the viscosity variation of the hydraulic oil can be addressed.

15

Valve lift, x / mm

v / (mm2·s-1) 10 50 150 300

10

5

0

-5

180

0

CA / (°)

360

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540

4.2  Valve Lift Control

Figure 6  The Valve Lift Comparisons between Different Viscosities

In addition to valve timing control, valve lift control can be used to improve engine performance [15, 16]. Different approaches

15

15 Delayed crank angle / (°)

0 15 30

5

Valve lift, x / mm

Valve lift, x / mm

Advanced crank angle / (°) 10

0

-5

10

0 15 30

5

0

0

360

180

540

CA / (°)

-5

0

360

180

540

CA / (°)

(a) Advanced Angle Achieved with Controller (b) Delayed Angle Achieved with Controller Figure 7  Controlled Engine Valve Timing

and control strategies have been used to control engine valve lift [7, 8]. In some electro-hydraulic camless valvetrains, a method that controls the high pressure servo-valve precisely can achieve the engine lift within every cycle. In this paper, a discrete sliding mode controller is designed based on an average model. The sliding mode control is a powerful control technique, and it is especially useful in nonlinear systems with disturbances. 4.2.1  The Average Model of the VVA As known, the input energy is equal to the output energy in a

system based on energy conservation principles. Therefore, the hydraulic energy produced by the pump is identical to the output energy existing in the high pressure hydraulic oil that is used to overcome the return spring resistance and gas force to actuate the valve. The energy consumed can be approximated by: .

(2)

Where, Esystem, xmax are the total energy consumed by the valve system and valve maximum lift. Based on the pressure and flow rate of the hydraulic oil passing through the HPSV, the

HUANG Chao, et al: Development of a robust controller for electro-hydraulic variable valve actuation system

105

Where, e is a lift tracking error:

valve system energy consumption can be also defined by: .

.

(3)

Where, P1, Qv are the pressure and flow rate of the hydraulic oil passing through the HPSV. So, by substituting (3) in (2), the valve lift is determined as follows: .

(14)

The equivalent control law ueq is responsible for maintaining the system on the S plane, while the feedback control law brings the system to the S plane. The control law is as follows: .

(4)

th

Using the above lift equation, the valve lift at (k+1) cycle can be calculated by: .

(5)

(15)

The signum function results in a severe chattering problem. To solve this problem, a sliding surface with boundary layer formulation can be employed. In this method, the sliding surface is replaced with a boundary layer with a thickness of ε,

So, from (4) and (5), the equation can be written as:

.

≤

(16)

The signum function is also replaced with the saturation function as below: .

(6)

However, the air compression and expansion process can be considered as isothermal, and the gas force can be neglected in one cycle, so, equation (6) can replaced by: .

(7)

,

so the air volume change in the accumulator can be written as follows: . can be approximately replaced by

(8)

, and to this

end, the developed non-linear dynamic system in a discrete time domain is achieved for valve lift as follows: .

(9)

Where, ,

,

.

,

(17)

.

The pump flow rate is considered as the control signal, and the hydraulic pump flow rate can be approximated as follows: .

(18)

.

(19)

4.3  Co-simulation model of AMESim and Simulink Since Simulink has the ability of numerical processing and logical operation, the controller is designed into Simulink. As shown in the Figure 8, the AMESim model sends the engine speed signal, valve position and speed signal to Simulink. The AMESim model receives control signals including the pump speed and opening and closing signals of HPSV and LPSV from Simulink.

(10)

(11)

(12)

4.2.2  Development of a Discrete Sliding Mode Controller In this VVA system, the pump speed is usually manipulated to achieve the precise engine valve lift under different operating conditions. A sliding mode control strategy is applied for lift control due to its robustness toward external disturbances and uncertainty in model parameters [17]. A sliding surface is defined as: .

;

In the above equation, Npump, Vdisp and η are pump speed and displacement volume, and volumetric efficiency. The desired hydraulic pump speed is determined by:

Where, P1,0, V1,0 are the precharge air accumulator pressure and volume. A four-stroke engine cycle duration is

,

(13)

Pa HPSV N_spe LPSV Angular Controller Fgas Val_disp Pump_spe Val_ve

Figure 8  AMESim Model of the VVA System with the Proposed Controller

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5  Simulation Results and Discussion From the analysis above, it is found that the engine valve timing and valve lift are affected greatly by the viscosity of the hydraulic oil. The comparative results in Figures 9 and 10 show that the desired valve lift can be achieved with the proposed controller. The required pump speed at various engine speeds for a desired maximum valve lift can be written as follows: .

15

（20）

Without SMC

Valve lift, x / mm

With SMC 10

Reference

5

312.4 r/min calculated by Equation 20. Nevertheless, when the hydraulic oil viscosity goes beyond 120 mm 2 · s-1, the reference lift cannot be achieved under the current pump speed. This highlighted the need for a controller to adjust the hydraulic pump speed based on the actual lift. The pump adjustment is large in the first three cycles due to large error between the actual valve lift and reference value. As the valve lift has been close to the reference value, the variation is becoming small but does not disappear due to the high speed of the valve. Therefore, the pump speed has fluctuation too. However, with the designed controller, the engine can achieve the reference lift in the next several cycles when the viscosity changes. The sliding mode controller parameters (λ and k) are given in Table 2, which have been tuned through many simulations under different scenarios. Table 2  The SMC Parameters Tuned through Experiment

0

-5

0.2

0.0

0.4

0.6

t/s

0

k

0.125

ε

0.5

A new variable valve actuation was introduced and its numerical model was built in AMESim and Simulink. The simulation results showed that the engine valve lift is influenced by some disturbance such as hydraulic oil viscosity. However, this study aimed at developing a robust controller for a VVA system to get rid of the effect brought by the disturbances and the conclusions can be drawn as follows:

350 Without SMC 340

With SMC

1) The proposed valve variable actuation system adopts two rotary spool valves instead of two solenoid actuated servovalves. In this way, it can overcome some problem such as response time comparing to other electro-hydraulic valve actuators.

330

320

310

λ

6  Conclusion

Figure 9  Valve Lifts with and without SMC

Pump speed, Npump / (r·min-1)

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0.0

0.2

t/s

0.4

0.6

Figure 10  Pump Speeds

Figure 9 presents the valve lift with and without SMC under the situation that the viscosity is 150 mm2 · s-1 (the oil temperature is about -5 ℃ ). Under the current scenario, the reference valve lift is set as 8 mm, the engine valve lift could only reach 7.26 mm instead of the reference lift owning to the high hydraulic oil viscosity. With the proposed sliding mode controller, the lift cannot achieve the reference value immediately but gradually within five cycles. The associated pump speeds are shown in Figure 10, the reference could be reached using the pump speed calculated by Equation 20 when the viscosity at 120 mm 2 · s-1. When the reference lift is 8mm, the pump speed is about

2) In electro-hydraulic system, the viscosity of hydraulic oil affects the performance of the VVA systems. The engine maximum valve lift will decrease with the viscosity increasing and the valve closing delay time will increase. That is why a robust controller is proposed in this paper to get rid of this type of adverse effects. 3) By using the proposed robust controller, influences caused by external disturbance such as variations of the temperature of hydraulic oil can be diminished. Desired engine maximum lift could be achieved by adjust the hydraulic pump speed within several cycles. Besides, the phase shifter is only responsible for engine valve timing control. Therefore, this reduces the sliding mode controller complexity and the cost. 4) In the future, the accuracy of the model will be improved and some experiments will be conducted to verify the performance of the whole system with the proposed controller.

HUANG Chao, et al: Development of a robust controller for electro-hydraulic variable valve actuation system

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