Modeling and Controller Development of Active Pneumatic Engine Mount (APEM) System
Introduction
An engine mount system has two basic functions: One is to support the weight of the engine and the other is to isolate engine vibrations. In vehicles, there are two significant vibration sources, vibrations from the engine and vibrations from the ground, which should be reduced to enhance the comfort of passengers. The engine vibrations typically contain frequencies in the range of 20-200 Hz with amplitudes generally less than 0.3 mm. On the other hand, the main part of chassis vibrations involves frequencies under 30 Hz with amplitudes greater than 0.3 mm.
A hydraulic mount (hydro-mount in short) system is naturally required to have a high dynamic stiffness to support the engine weight. However, it also should transmit as less vibration from the engine to the chassis as it can. To achieve this (i.e., vibration isolation), the engine mount system should also satisfy a low dynamic stiffness. It is difficult to meet these conflicting demands with a passive engine mount system. To resolve this problem, an innovative hardware design as well as an efficient vibration control technique is needed. To reduce the time in designing a new engine mount for various types of cars, it is necessary to have a mathematical model to predict the behavior of the system before it is physically assembled. A good model is also a key element when designing an efficient control algorithm for the system. The closer the response of a mathematical model is to the real plant, the higher achievement of control performance.
A hydraulic mount (hydro-mount in short) system is naturally required to have a high dynamic stiffness to support the engine weight. However, it also should transmit as less vibration from the engine to the chassis as it can. To achieve this (i.e., vibration isolation), the engine mount system should also satisfy a low dynamic stiffness. It is difficult to meet these conflicting demands with a passive engine mount system. To resolve this problem, an innovative hardware design as well as an efficient vibration control technique is needed. To reduce the time in designing a new engine mount for various types of cars, it is necessary to have a mathematical model to predict the behavior of the system before it is physically assembled. A good model is also a key element when designing an efficient control algorithm for the system. The closer the response of a mathematical model is to the real plant, the higher achievement of control performance.
Modeling of a Hydro-Mount
A hydro-mount and its cross-section used in this research are depicted in Fig. 1(a) and Fig. 1(b), respectively. It has two mounting brackets: one for the engine and the other for the chassis. The hydro-mount consists of a primary rubber, four chambers with different volumes (the upper, working, air, and lower chambers), and the first and secondary orifices. From Fig. 1(b), the functionalities of the hydro-mount are recapitulated in Fig. 2. Let x ( t ) be the displacements of the engine, and let F ( t ) and F
T ( t ) be the engine excitation force and the transmitted force to the chassis, respectively. Let P ( t ) and A
p be the pressure and the equivalent area of the upper chamber. The stiffness characteristics of the primary rubber is divided into two spring constants: the main spring constant k
r and the bulge spring constant k
p. Since the primary rubber supports the engine, the stiffness characteristics in the vertical deformation of the rubber at an equilibrium position is modeled as the main spring constant, whereas the variation of the stiffness characteristics of the primary rubber due to the pressure variation in the upper chamber is modeled as the bulge spring constant. Hence, the bulge spring constant becomes a function of the pressure in the upper chamber. The first orifice connects the upper chamber to the lower chamber and the second orifice connects the upper chamber to the working chamber, in which the orifices will equalize the pressures in individual chamber in the steady state. Also, to make the hydro-mount stiff in high frequency vibrations of the engine, a decoupler between the working chamber and the air chamber is used. The decoupler is made of a rubber or a fabric diaphragm. It can move freely in the passage connecting the two chambers.
Now, the hydraulic flows through the first and second orifices can be modeled as a second-order mass-spring-damper system as in Fig. 3. Let the cross-sectional areas of first and second orifices be A
1 and A
2, respectively. The amount of fluids flowing through two orifices are modeled as equivalent masses m
1 and m
2, respectively, with damping coefficients c
1 and c
2, respectively, and spring constants k
1 and k
2, respectively. Let x
p ( t ) and x
1 ( t ), and x
2 ( t ) be the displacements of the primary rubber, the equivalent mass in the first orifice, and the equivalent mass in the second orifice, respectively.
Fig. 4 shows a scheme for the active pneumatic engine vibration control considered in this work (two regular rubber mounts and one hydro-mount will be used). The actuator in Fig. 4 is a pneumatic system. The air pressure (control force) in the air chamber in Fig. 1(b) is generated by opening and closing a solenoid valve. Due to the difference between the ambient air pressure and the pressure in the vacuum tank, the air will flow in when the valve is open. Because of the decoupler, the forces generated in the air chamber can be transmitted to the engine or to the chassis.
Feedforward Control Algorithm of the APEM System
Feedforward controller uses knowledge of the given plant to improve the command response which implies that the command signal is processed using the model of the plant and the disturbance source ahead of the control law. Through this process, feedforward controller calculates a best guess of the command signal to produce the ideal response of the plant. This improved command response of the feedforward controller reduces response time to the desired output, while accurate modeling of the plant and the disturbance source is required to achieve this goal. Feedforward controllers are able to completely cancel out the disturbances fast under the assumption of the accurate modeling of the plant and disturbance source.
Fig. 5 shows the block diagram for feedforward control algorithm, where W ( s ) is the transfer function of the feedforward controller, M ( s ) B ( s ) is the transfer function of an actuator, A ( s ) is the transfer function of the engine mount, x ( i ) is the disturbance, is the reference signal correlated to x ( i ) and F T( i ) is the forces transmitted to the chassis. The operation of the APEM system can be seen in the flowchart of the APEM system (Fig. 6).
Fig. 5 shows the block diagram for feedforward control algorithm, where W ( s ) is the transfer function of the feedforward controller, M ( s ) B ( s ) is the transfer function of an actuator, A ( s ) is the transfer function of the engine mount, x ( i ) is the disturbance, is the reference signal correlated to x ( i ) and F T( i ) is the forces transmitted to the chassis. The operation of the APEM system can be seen in the flowchart of the APEM system (Fig. 6).