In this paper, based on the previous research experiences in the lumped parameter modeling and study of active control mounts (ACM) model, an analytical model of active ACM in powertrain is developed and implemented in MATLAB. In order to validate this newly developed model in this work, a finite element analysis (FEA) method is conducted in ANSYS and the results of FEA is compared with analytical model for validation. After the validation, the control strategy is integrated into the analytical model by using the linear quadratic regulator (LQR) method. Numerical results show a good control performance. Furthermore, this work examines the application of genetic algorithms (GA) in optimizing the weight matrices of LQR. An optimal configuration is obtained and thus this approach could help the practical design of ACM systems

Ming Li

Pak-Kin Wong

Yucong Cao

Zhengchao Xie

English

Journal of Vibroengineering

  © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716 3273 
1417. A numerical investigation on active engine 
mounting systems and its optimization 
Zhengchao Xie1, Pak-Kin Wong2, Yucong Cao3, Ming Li4 
1, 2, 3Department of Electromechanical Engineering, Faculty of Science and Technology,  
University of Macau, Macau, China 
4Department of Thermal Engineering, Jilin University, Changchun, China 
1Corresponding author 
E-mail: 1zxie@umac.mo, 2fstpkw@umac.mo, 3mb15479@umac.mo, 4limingtiger@jlu.edu.cn 
(Received 1 October 2013; received in revised form 9 December 2013; accepted 16 December 2013) 
Abstract. In this paper, based on the previous research experiences in the lumped parameter 
modeling and study of active control mounts (ACM) model, an analytical model of active ACM 
in powertrain is developed and implemented in MATLAB. In order to validate this newly 
developed model in this work, a finite element analysis (FEA) method is conducted in ANSYS 
and the results of FEA is compared with analytical model for validation. After the validation, the 
control strategy is integrated into the analytical model by using the linear quadratic regulator 
(LQR) method. Numerical results show a good control performance. Furthermore, this work 
examines the application of genetic algorithms (GA) in optimizing the weight matrices of LQR. 
An optimal configuration is obtained and thus this approach could help the practical design of 
ACM systems. 
Keywords: test bench model, finite element analysis, linear quadratic regulator, genetic algorithm, 
optimization. 
1. Introduction 
During the last decade, the noise, vibration and harshness (NVH) has received attention in 
several publications. As a result, engine mounts are becoming more important as being not only 
engine vibration isolation but also a part of engine support. One of the main functions of the 
automotive vehicle engine mounting system is to support the engine body and provide comfort 
ride for passengers by reducing vibration caused by engine excitation. There is much literature in 
which extensive investigations have been conducted on different kinds of engine mounting 
systems, from elastomeric to hydraulic mounts, from passive to semi-active and active mounts. 
Although elastomeric mounts have been successfully used for automotive industry for many 
years, but the conventional elastomeric mounts do not meet all the requirements, it just can only 
provide a small dampingand a solution between static deflection and vibration isolation [1]. 
Hydraulic engine mounts (HEM) can offer a better performance than traditional elastomeric 
mount in the low frequency. Hydraulic mounts have been promising alternatives to conventional 
elastomeric mounts because of their ability to create frequency-dependent damping. 
Hydraulic mounts have been used in the automotive industry since 1985 in General Motors 
(GM). Today, almost all passenger cars are installed hydraulic mounts. The basic idea of the 
hydraulic mounts is to use highly elastic rubber for vibration isolation and to use a hydraulic device 
(inertia track and decoupler) to generate the large damping at a constant frequency for vibration 
control. The lumped parameter of a floating-decoupler type hydraulic mount (the most common) 
is as illustrated in Fig. 1, and consists of two fluid-filled chambers separated by a metallic plate 
containing the decoupler and inertia track. ܭ௥ and ܤ௥ are the equivalent stiffness and damping of 
the rubber spring. The volumetric compliance of the upper chamber and lower chamber are 
modeled as ܥଵ and ܥଶ. Also, the pressures in the upper and the lower chambers are captured by ଵܲ 
and ଶܲ. ܣ௣ is the effective piston area, and the flow through the inertia track ܳ௜ and the decoupler 
ܳௗ . ܫ௜ , ܴ௜  representing the effective inertia and resistance of inertial track. Similarly, effective 
inertia and resistance of decoupler are ܫௗ and ܴௗ. 
During low-frequency high-amplitudes vibrations, the ideal mount should exhibit large 
1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
3274 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716  
stiffness and damping characteristics to reduce relative displacement transmissibility whereas for 
high-frequency low-amplitude vibrations the ideal mount should have low stiffness and damping 
[2]. For that the characteristics of passive elastomeric mount or semi-active mount can hardly meet 
the requirement of broad frequency band of engine vibration and noise reduction. One of the 
effective methods to reach ideal vibration isolation is using active control engine mounts (ACM). 
A typical active control engine mount (ACM) consists of a passive hydraulic mount, an active 
actuator, a vibration sensor, and electronic controller. The structure of the ACM is illustrated in 
Fig. 2 (ܭ௥ and ܥ௥ are the equivalent stiffness and damping of the rubber spring. ܫ௜, ܴ௜ representing 
the effective inertia and resistance of inertial track. Similarly, effective inertia and resistance of 
decoupler are ܫௗ and ܴௗ). 
 
Fig. 1. Lumped parameter model of a  
floating-decoupler type hydraulic mount 
 
Fig. 2. Structure model of an active control mount 
Fig. 2 shows thestructure model of the ACM, which is an amalgamation of the structure of the 
hydraulic mount and an actuator system. But the role of the decoupler is changed to a piston 
because of the actuator, so that it transmits the force from the actuator to the engine and chassis 
through the upper chamber. The role of the inertia track is also changed: in hydraulic engine 
mounts, the inertia track generates frequency dependent stiffness and damping. However, in the 
active control engine mount, it just relieves the static pressure in the upper chamber. 
Because passive hydraulic mount has superior isolation ability in the low frequency range, and 
active actuator can provide highly efficient vibration control performance in relative high 
frequency range, so the active engine mount can isolate the vibration of engine in much wider 
frequency range. At the same time, the numerical simulation shows that the active control engine 
mount is capable of significantly reducing the vibration transmission. 
2. Analytical modeling 
The modeling of the active engine system is restricted to three degrees of freedom. However, 
note that the assumptions are made for this system [3]. 
1) The displacement is small compared to system dimensions. 
2) The spring force is linear around the working point. 
3) The upper plate (engine body) on the vibration isolation system is a rigid body. 
4) Fluid is incompressible, and fluid density in chambers and fluid track is the same. 
5) Mass of rubber spring, upper and lowerconnectors are negligible. 
6) Damping of both lower diaphragm and decoupler membrane are negligible. 
7) Leakage path tending to short-circuit fluid track is ignored. 
These assumptions are used to model the vibration system in this work and Fig. 3 shows the 
coordinate system [3]. 
1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716 3275 
 
Fig. 3. Coordinate system [3] 
The state space format for the equations of motion of vibration system is: 
ݔሶ = ܣݔ + ܤݔ, (1)
ݕ = ܥݔ + ܦݑ, (2)
where matrix ܣ, ܤ, ܥ and ܦ are defined as: 
ܣ =
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ 0 1 0 0 0 0
− 4
ሺ݇ + ݇௔ሻ
݉ −
4ܦ௔
݉ 0 0 0 0
0 0 0 1 0 0
0 0 − ܮଶ
ଶ ሺ݇ + ݇௔ሻ
ܬ௫௫
− ܦ௔ܮଶ
ଶ
ܬ௫௫
0 0
0 0 0 0 0 1
0 0 0 0 ߙ ߚے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
, 
ܤ =
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ 0 0 0 01
݉
1
݉
1
݉
1
݉
0 0 0 0
− ܮଶ2 −
ܮଶ
2
ܮଶ
2
ܮଶ
2
0 0 0 0
−ܽ + ܮଵ2 ܽ −
ܮଵ
2 ܽ −
ܮଵ
2 −ܽ +
ܮଵ
2 ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
, 
ܥ =
ۏ
ێ
ێ
ێ
ێ
ۍ− 4
ሺ݇ + ݇௔ሻ
݉ −
4ܦ௔
݉ 0 0 0 0
0 0 − ܮଶ
ଶ ሺ݇ + ݇௔ሻ
ܬ௫௫
− ܦ௔ܮଶ
ଶ
ܬ௫௫
0 0
0 0 0 0 ߙ ߚے
ۑ
ۑ
ۑ
ۑ
ې
, 
ܦ =
ۏ
ێ
ێ
ێ
ێ
ۍ 1݉
1
݉
1
݉
1
݉
− ܮଶ2 −
ܮଶ
2
ܮଶ
2
ܮଶ
2
−ܽ + ܮଵ2 ܽ −
ܮଵ
2 ܽ −
ܮଵ
2 −ܽ +
ܮଵ
2 ے
ۑ
ۑ
ۑ
ۑ
ې
, 
ߙ = − ቆܮଵଶ݇ + ሺ−4ܽܮଵ + 4ܽଶ + ܮଵଶሻ
݇ܽ
ܬ௬௬
ቇ, 
1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
3276 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716  
ߚ = − ܦ௔
ሺܮଵଶ − 4ܽܮଵ + 4ܽଶሻ
ܬ௬௬
, 
where ݇௔ is the actuator spring constant, ܦ௔ is the damping parameter. 
3. Validation of the mathematical model 
In order to validate this newly analytical model in this work, in this section, the analytical 
model is validated using a finite element model set up in ANSYS which is a widely accepted 
commercial FEM software [4]. A finite element analysis (FEA) method is conducted in ANSYS 
and compared with analytical model for validation. 
Table 1 shows the modal frequency of the vibration system from both the finite element model 
in Fig. 4 and the mathematical model by state space method. 
Table 1. Validation of the mathematical model by comparing to the finite element model  
in MATLAB and ANSYS 
Modes Frequency (Hz) Finite element model 
Frequency (Hz) 
Mathematical model Difference (%) 
The first modal 6.84 6.84 0 
The second modal 11.69 11.84 1.3 
The third modal 11.73 12.76 8.0 
It can be seen that both modal frequency are very close to each other, so that it can said the 
model implemented in this work is reliable [5]. With the validated active mounting system model, 
it is possible to conduct the control strategy modeling and the design optimization using GA. 
Fig. 4. The finite element model 
Table 2. Model parameters 
Parameter Value 
ܦ௔ damping 20 Ns/m 
݇௔ stiffness 8902 N/m 
݉ upper mass 19.274 kg 
ܮଵ 0.348 m 
ܮଶ 0.3 m 
ܽ 0 m 
ܬ௫௫ inertia of ݔ-axis 0.1446 Kg/m4s 
ܬ௬௬ inertia of ݕ-axis 0.1676 Kg/m4s 
 
4. Control strategy 
In this section, the control strategy will be analyzed by using the linear quadratic regulator 
(LQR) method, which is a well-known design technique that provides practical feedback gains [6]. 
The LQR controller in Simulink/MATLAB for this feedback active vibration control is shown in 
Fig. 5, where step is disturbance input, ݑ is the control vector. By implementation of the LQR 
controller, we find that the vibration isolation takes place attenuating the disturbance coming form 
engine. 
Transmitted acceleration with and without control are presented in Fig. 6 and Fig. 7 in time 
domain. 
Figs. 6 and 7 show the response of system under the disturbance in time domain. It can be seen 
form Fig. 6 and Fig. 7 that the active engine mounting vibration system takes place right from the 
very beginning when subjected to step disturbance signal input. As input of the step disturbance 
activates, the transmitted acceleration has been increase to a greater range. This increase in the 
1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716 3277 
transmitted acceleration at engine mount decreases passenger comfort and smooth ride, working 
condition such as a vehicle through a rough road in a very short time. 
The second line and the third line in Fig. 6 and Fig. 7 show that the response of the longitudinal 
acceleration is much faster and the lateral acceleration weakens a lot with LQR controller. It can 
be noticed that at the time interval of 0-0.5 sec, transmitted accelerationat active engine is reduced 
from 0.05 to 0.01 m/s2 (approximately). The first line in Fig. 6 and Fig. 7 shows that the 
attenuation of the vertical acceleration is more outstanding for LQR controller. It can be seen that 
at time interval of 0-0.3 sec, the transmitted acceleration has been attenuated to a value of 
0.02 m/s2. The magnitude of the transmitted acceleration using LQR controller is reduced from 
0.04 to 0.02 m/s2 from time interval 0.3 sec. At the same time, the LQR controller can also weaken 
the heel and pitching direction of rotation. 
 
Fig. 5. Implementation of LQR controller in Simulink/MATLAB 
 
Fig. 6. Control response without LQR controller 
1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
3278 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716  
By comparing the simulation results, it is quite clear that LQR controller is effective in 
restricting the transmitted force to the chassis. It is observed that the vibration attenuation is 
obtained for a period less than 0.3 second. The result confirmed that the model with LQR control 
algorithm is able to reduce significantly the vibration transmission. 
By implementing LQR controller in Fig. 7, the value of gain ܭ is calculated by adjusting the 
ܳ and ܴ weights matrix. By doing various iterations the values for ܴ and ܳ are set, so that optimal 
results are obtained. There are various methods of selecting values of the weights which will lead 
to the optimal control of an associated system. These methods are cheap control, expensive control 
and terminal control. In this paper, each of the methods was used to obtain our weights and the 
one leading to optimal control of our system was chosen. 
 
Fig. 7. Control response with LQR controller 
5. Optimization via GA 
 
Fig. 8. Fitness function value in GADST 
The selection of weight matrices in LQR is very importance and it straight affects the control 
performance. But the weight matrices are usually set by experience of designer and so the optimal 
1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716 3279 
control performance could not be obtained. The genetic algorithm (GA) is an optimization and 
search technique based on evolution, and it has been applied to many optimization problems [7, 8]. 
This work examines the application of genetic algorithms in optimizing the weight matrices of 
linear quadratic regulator [9]. The objective function for GA is: 
Minimize ܮ = ܧܣሺݔሻܧܣ݌ܽݏ +
ܲܣሺݔሻ
ܲܣ݌ܽݏ +
ܴܣሺݔሻ
ܴܣ݌ܽݏ, (3)
where ܧܣ is the engine body vertical acceleration, ܲܣ is the pitching acceleration, ܴܣ is the roll 
acceleration, pas is the passive acceleration. The result of the GA objective function in 
MATLAB/GADST GA toolbox is shown in Fig. 8. 
6. Conclusions 
In this paper, the vibration control performance of a selected active control engine mount 
system with LQR controller is evaluated. Then, an analytical model which includes the hydraulic 
engine mount and active control technique are implemented and analyzed [10]. This newly 
proposed model is validated by compared with FEA. In addition, the LQR controller is integrated 
into the model in order to achieve better vibration reduction as shown in numerical examples. Also, 
the application of GA for optimization design of LQR weight matrices is studied as well to have 
the optimal configuration of control strategy. For future work, different control techniques can be 
examined for the disturbance rejection such as LQG and robust control methods, which probably 
could provide more effective ways of dealing with disturbance reduction. 
Acknowledgements 
This project is supported by MYRG155(Y2-L2)-FST11-XZC which is funded by Research 
Committee of University of Macau. 
References 
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1417. A NUMERICAL INVESTIGATION ON ACTIVE ENGINE MOUNTING SYSTEMS AND ITS OPTIMIZATION.  
ZHENGCHAO XIE, PAK-KIN WONG, YUCONG CAO, MING LI 
3280 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. NOV 2014, VOLUME 16, ISSUE 7. ISSN 1392-8716  
[10] Xie Zhengchao, Lou Inchio, Ung Wai Kin Freshwater algal bloom prediction by support vector 
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Zhengchao Xie received B.Sc. degree from Jilin University and M.Sc. degree from 
Huazhong University of Science and Technology, both degrees are on automotive 
engineering. Dr. Xie got his Ph.D. degree from University of Alabama and his research 
interests include vibration control, finite element method, and design optimization. 
 
Pak-Kin Wong received the Ph.D. degree in Mechanical Engineering from The Hong 
Kong Polytechnic University, Hong Kong, China, in 1997. He is currently a Professor in 
the Department of Electromechanical Engineering and Associate Dean (Academic 
Affairs), Faculty of Science and Technology, University of Macau. His research interests 
include automotive engineering, fluid transmission and control, engineering applications 
of artificial intelligence, and mechanical vibration. He has published over 152 scientific 
papers in refereed journals, book chapters, and conference proceedings. 
 
Cao Yucong received the B.S. degree in Electromechanical Engineering from Jilin 
University, China. Now he is a master student in Electromechanical Engineering, 
University of Macau. His current research interests include automotive engineering, 
vibration control, and design optimization. 
 
Li Ming received his B.Sc., M.Sc., and Ph.D. degrees from Jilin University, and all these 
degrees are on automotive engineering. His research interest is mainly on the thermal 
transfer modeling and analysis and automotive engineering. 
 


A numerical investigation on active engine mounting systems and its optimization

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A numerical investigation on active engine mounting systems and its optimization

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