This chapter describes briefly about the semi-active suspension system and the magnetorheological damper used in the system. A detail explanation emphasizing the semi-active magnetorheological damper suspension system is explained and an overview on semi-active suspension system available in the market is presented. This chapter also focuses on the research works done by researchers on semi-active suspension system specifically on the development of magnetorheological damper model. Gaps in research are identified and justification for the research is presented.
Function of Vehicle Suspension System
A vehicles suspension system, which is located between the wheel axles and the vehicle body frame, has four main functions.
The presence of suspension system allows the vehicle to travel over rough surface with minimum up-and-down body movement, depending on the performance of the springs and the shock absorbers used. The suspension system also allows the vehicle to corner with minimum roll by minimizing the tendency of wheels to lose traction with the road surface. This will ensure continuous cushioning action so that road harshness or road shock only has a minimal effect on the occupants.
Semi-active Suspension System and Magnetorheological Damper
As described in the previous chapter, a semi-active suspension system is a system consists of a conventional spring and a variable damping damper (or shock absorber). The semi-active suspension is much less complex than a fully active suspension system and can be produced at a lower cost. In terms of the performance, the semi-active suspension system can produce road comfort and handling approaches to the performance of a fully active system (Elmadany and Abduljabar, 1991)
A semi-active system is a close loop system where a number of sensors are required to measure vehicle's attitude. Accelerometers are used for this purpose and they are located on the sprung and unsprung masses of the vehicle. Semi-active suspension system can be designed to response either in high bandwidth category or low bandwidth category systems. High bandwidth systems are focusing in improving suspension's rattle space response (10-12 Hz) and tire hop response (3-4 Hz). However majority of semi-active suspension system are low bandwidth system and only improve the tire hop frequency (Chen et al., 2000).
As emphasized previously, variable damping damper or shock absorber is the important part, which makes semi-active suspension system differs from conventional passive suspension system and fully active suspension system. There are two types of variable damping damper used in semi-active suspension system; hydraulically based damper and magnetorheological (MR) fluid-based damper.
In hydraulically based damper, the variable damping characteristics are achieved by varying the total area of valves area within the shock absorber. Ferrari and Maserati are the keenest users of this type of adaptive damping damper. Mondial T, F355, 456GT, 550M, 360M, Shamal, Quattroporte and 3200GT are among the models that employed this type of damper. In most of the time, the damper is in "soft" setting to benefit ride comfort. In case the car goes in action, it is set to "stiff" mode for stable handling and minimize body roll.
For magnetorheological fluid-based damper, the variable damping characteristics were achieved by magnetizing the MR fluid using the wire coil within the damper. When the coil is energized ("on" state), the magnetic field causes the iron particles in MR fluid to align into fibrous structures in the direction of the magnetic flux. The strength of the bond between the particles in the structures is proportional to the strength of the magnetic field. When the coil is not energized ("off" state), the MR fluid is not magnetized. During this state, the MR fluid will behaves like a conventional fluid damper. As a result, a variable resistance to fluid flows within the damper piston, which provides a variable damping capability is generated in the damper. Delphi introduces the first commercialize MR damper in 1998 known as Magneride. It was first used by General Motors in the Chevrolet Corvette C5 and Cadillac Seville and STS, and is also now used in the Ferrari 599, the Audi TT and in some Holden Special Vehicles models.
2.4 Research Review on Magnetorheological Fluid Technology
Magnetorheological fluid technology has existed for more than 50 years. Although this technology was introduced in 1940's by Rabinow (Carlson, 2001), the interest on applying the technology was very small and soon died out. The action taken by Lord Corporation in introducing 'Motion Master' which used MR technology has triggered the interest among researchers in MR fluid devices. Nowadays, MR fluid technology is not only restricted in vehicle's damper (or shock absorber) it is also being used in building stabilization during earthquake, gun control recoil in Naval turret, prosthetic leg and also in polishing machine (Poynor, 2001).
Although the MR fluid technology has been successfully applied for commercial used, the research on this technology is still going on. Through literature review on MR technology research, the research focused can be categorized into 4 categories:
Research on MR fluid composition.
Research on MR fluid mathematical and numerical simulation modeling.
Research on design and development of MR devices.
Research on the MR devices control strategies.
Research on MR Fluid Composition
In this category of MR technology research, the research interests are on describing the properties of MR fluid, its content and its application.
Carlson and Jolly (2000) has defined MR fluid, MR elastomers and MR foams. MR fluid are the liquids (contains iron particles) whose flow or shear properties are easily controlled to enable a variety of unique torque transfer or vibration control devices while MR elastomers are rubber materials whose stiffness may be controlled to provide tunable or adjustable mounts and suspension devices. It is also stated that MR foams are controllable fluid that contains an absorptive matrix, used to provide a convenient way of realizing the benefits of MR fluids in highly cost sensitive applications.
Chen and Yeh (2002), studied macroscopic behaviors of MR fluid when exposed to magnetic field. The research focused on the stress generated under the magnetic field effect and the mechanism of energy dissipation.
Li et al., (2002) studied the creep behaviors of magnetorheological fluid under constant shear stress and it was later found out that MR fluids behave as linear viscoelastic bodies at small stresses and changed as the magnetic field increased with increasing constant stresses, nonlinear viscoelastic, and viscoplastic.
Simon et al., (2001) shown the effective magnetic behavior of magnetorheological composite as a function of the interparticle distance. The research focused on the effect of nonmagnetic layer due to additive added into MR fluid to keep the iron particles in the MR fluid from touching each other. A formula used to predict the behaviors of MR fluid by considering these effects was proposed.
Research on MR Fluid Dynamic Characterization Modeling
Researchers have proposed various modeling methods to characterize the dynamic behavior of MR fluid devices and the effort is still continued until today. The modeling of MR fluid devices' dynamic behavior can be grouped into two; parametric modeling and non-parametric modeling.
2.4.2.1 Parametric Modeling
In parametric modeling, the dynamic behaviors of MR fluid are represented by mathematical function whose coefficients are determined based on the experimental data i.e. the parameter values are adjusted until the quantitative results match closely with the experimental data. The next sections are the lists of parametric modeling approach developed by researchers.
a Bingham Model
The Bingham model is the most common model used to represent the dynamic behavior of MR fluid. An ideal Bingham body behaves as a solid until a minimum yield stress is exceeded and then exhibits a linear relation between the stress and the rate of shear. The shear stress developed in the fluid is given by
(2.1)
where is the shear rate and is the plastic viscosity of the fluid i.e. Newtonian viscosity at zero field (Gavin et al., 1996a). Stanway et al., (1987) proposed a mechanical model, commonly referred to as the Bingham model, where it combines viscous and Coulomb friction. In this model (Figure 2.1), the force F generated by the MR device is given by
(2.2)
where presents the velocity due to the damper excitations, and the damping coefficient and the frictional force are related to the fluid's viscosity and the field dependant yield stress respectively (Spencer et al., 1997). An example of the comparison between the predicted force-velocity characteristic of MR damper using Bingham model and the experimental result conducted by Spencer et al., (1997) is shown in Figure 2.2
Figure 2.1 Bingham Model
Figure 2.2 Comparison of experimental data ( ) and predicted of Bingham model( )
b Extended Bingham Model
Gamota and Filisko (1991) proposed an extension of the Bingham model to describe the MR fluid behavior in the pre-yield and in the post-yield region as well as the yield point. This extended model consists of a series of three-parameter elements as shown in Figure 2.3.
Figure 2.3 Extended Bingham Model
The force generated in this system is given by equation (2.3) where represents damping coefficient and is the frictional force in the Bingham model that account for the plastic viscosity and the yield stress. The parameters , and are the field dependant parameters (Gamota and Filisko 1991, Spencer et al., 1997)
(2.3)
Figure 2.4 shows an example of comparison between the predicted model of extended Bingham model with the experimental data. It can be seen that the extended Bingham model qualitatively describes the hysteretic response of MR fluid device (Spencer et al., 1997).
Figure 2.4 Comparison of experimental data ( ) and predicted of extended Bingham model ( )
c Three Element Model
Powell (1994) has proposed three-element model to characterize the behavior of MR fluid damper. It is a mechanical analogue consisting of a viscous damper, a non-linear spring and a frictional element arranged in parallel (Figure 2.5).
Figure 2.5 Three-element model
The force generated by the MR device following this model is given by;
(2.4)
with
(2.5)
and
(2.6)
where is Coulomb friction force, which is modeled with static and dynamic friction coefficients and respectively, is the displacement transmitted to the rheological device,and denotes the velocity and the acceleration respectively and is the non-linear force of a spring. In the three element model, the values of the damping parameters,,,, and as well as the elastic parameters and are fitted to the experimental results. An example of comparison between the predicted and the observed behavior of MR fluid is shown in Figure 2.6.
Figure 2.6 Comparison between the predicted (a) and the experimental data (b) of force velocity characteristic for three elements model
d Bingmax Model
Makris et al., (1996a and 1996b) proposed a discrete element model in order to characterize the behavior of MR fluid. It consists of a Maxwell element in parallel with a Coulomb friction element as shown in Figure 2.7
Figure 2.7 Bingmax Model
In this proposed model, the generated force is given by
(2.7)
where, is the quotient o the damping constant and the spring stiffness, K. The notations denotes the permanent friction force.
e Bouc-Wen Model
Spencer et al., (1997) presented a model named as the Bouc-Wen model, used to characterize the behavior of MR fluid damper. The concept of the model is based on an approach due to Wen (1976), where this model is supposed to reproduce the response of hysteretic systems to random excitations.
Figure 2.8 shows the mechanical analogue of the Bouc-Wen model. The force generated from this model is given by
(2.8)
where the hysteretic component satisfies
(2.9)
By adjusting the parameter values ,,and , it is possible to control the shape of the force velocity characteristic of MR fluid damper. The initial displacement of the spring element (representing the accumulator) is .
Figure 2.8 Bouc-Wen Model
An example of the comparison of this model with an experimental data is shown in Figure 2.9. It can be seen that the model is well suited for numerical simulation, since it is less stiff than the extended Bingham model. But as can be seen in Figure 2.9, this model cannot reproduce the characteristic in the yield region i.e. for velocities with a small absolute value.
Figure 2.9 Comparison of the Bouc-Wen model ( ) and the experimental data ( )
f Modified Bouc-Wen Model
To better predict the response of the MR damper in the yield region point, Spencer et al., (1997) proposed an extension of the Bouc-Wen model as depicted in Figure 2.10. The equations for the force in this system is given by
(2.10)
where
(2.11)
and
(2.12)
The hysteretic component, accounts for the time history of the response (Dyke et al., 1997). The spring and its initial displacement are for both the additional stiffness and the force offset produced by the presence of an accumulator.
Figure 2.10 Modified Bouc-Wen Model
The notations of , and in equations (2.10), (2.11) and (2.12) are defined as in equations (2.13), (2.14) and (2.15) respectively. Equations (2.13), (2.14) and (2.15) are assumed to depend on the voltage applied to the current driver in order to obtain the parameter values in equations (2.10), (2.11) and (2.12), which are valid for varying magnetic field strength.
(2.13)
(2.14)
(2.15)
where is governed by
(2.16)
The parameters ,, , , and are constants where the values are determined from experiment. An example of comparison between the predicted force-velocity of MR damper and the data collected from the experiment is depicted in Figure 2.11. It can be seen from the comparison that the model is able to accurately reproduce the MR fluid behavior, even over a broad range of operating conditions (Spencer et al., 1997). More over, its parameter values are independent of the applied voltage and need not to be estimated anew for different field strength.
Figure 2.11 Comparison between modified Bouc-Wen model ( ) and experimental data ( )
g Non-linear Viscoelastic-Plastic Model
Kamath and Werely (1997a) has presented viscoelastic-plastic model, which combines two linear shear flow mechanism with non-linear weighting functions in order to characterize the response of MR fluid damper.
Figure 2.12 Viscoelastic-plastic model.(a) Viscoelastic mechanism (b) Viscous mechanism.
In this model, the MR fluid's behavior in pre-yield region is simulated by the three-parameter elements as depicted in Figure 2.12(a). The viscoelastic force is generated by
(2.17)
where , and denote the parametric damping and stiffness constant respectively, and X is the displacement transmitted to the damper. In the post-yield region the MR fluid response is represented by
(2.18)
where the damping coefficient is related to the apparent viscosity of the fluid (Figure 2.12b). The transition from the pre-yield to the post-yield regime is performed by nonlinearly combining the viscoelastic and viscous component and to the net force
(2.19)
where and are the shape function parameters and represented by
(2.20)
and,
(2.21)
where , and are the non-dimensional velocity, yield parameter and a smoothing parameter respectively. The proposed model is found to be able to reproduce nonlinear effects of the MR fluid. Furthermore, the proposed model is also numerically robust due to the linearity of the shear flow mechanism (Kamath and Werely 1997a).
h Augmented Non-Linear Viscoelastic-Plastic Model
Kamath and Werely (1997b) has extended the non-linearity of the viscoelastic-plastic model mentioned previously. In this extended model, in the pre-yield region, the friction force is weighted by a shape function, . The shape function was added to allow the Coulomb-like effects to be observed at low velocities. Thus, the force generated in the pre-yield is given by
(2.22)
where
(2.23)
and is a smoothing factor. The viscoelastic component is given by equation (2.17). In order to consider the viscous and inertial mechanism, Kamath and Werely (1997a) introduced the viscous and inertial mechanism as depicted in Figure 2.13. The force is given by
(2.24)
Figure 2.13 Inertial mechanism of augmented viscoelastic-plastic model
Both of these two shear flow mechanisms are combined by two non-linear weighting functions and yielding the non-linear network as depicted in Figure 2.14
Figure 2.14 Scheme of the augmented viscoelastic-elastic model
The total force F generated by this model is given by
(2.25)
The comparison made between the results generated from the model and the experimental model is shown in Figure 2.15. From the comparison, it can be seen that the model precisely depicts the behaviour of the considered MR fluid. The added mechanisms, such as the friction component , largely depend on the design of the considered damper, but they can be manually adjusted by choosing suitable parameter values (Kamath and Werely, 1997b).
Figure 2.15 Comparison between simulation and experimental results for augmented viscoelastic-plastic model.
2.4.2.2 Non-Parametric Modeling
For non-parametric modeling, the modeling method involves experimental data on a specific magnetorheological device, and used to model the dynamic behavior of MR fluid device. The experiment is generally being conducted by observing the device by varying operating condition i.e. supplied current. The data collected from the experiment are used to predict the rheological device under random excitations. Below are the lists of the non-parametric models have that been proposed by researchers.
a Chebyshev Polynomial Fit
Ehrgott and Masri (1992) used a Chebyshev polynomial fit to approximate the force generated by MR device. For fixed magnetic filed strength and fixed exciting frequency, the restoring force of the MR device is predicted by an analytical function constructed by Chebychev polynomials
(2.26)
where the denote the two dimensional Chebyshev coefficients, and is the degree of polynomial. The values and are obtained by normalizing the displacement, and the velocity that are associated with the external excitation to the internal [-1,1]. In the same way, the force can be determined as a function of velocity, and acceleration .
Gavin et al., (1996b) extended this curve fitting method to three dimensions. The restoring force of MR fluid damper is related to the displacement, the velocity and the magnetic field strength E by
(2.27)
where the denote the Chebyshev coefficients, and and are normalized values.
Figure 2.16 shows the comparison of the force-velocity characteristic estimated by the Chebyshev polynomials with the experimental results conducted by Ehrgott and Masri (1992). The predicted MR response resembles the corresponding experimental data. However the force plot from Ehrgott and Masri (1992), partly exhibit oscillatory behaviour frequently observed for polynomial interpolation.
Figure 2.16 Comparison between the predicted (……) and the experimentally obtained ( ___ ) force-velocity characteristic for a Chebyshev polynomial fit.
b Neural Networks
Burton et al., (1996) studied the performance of a multilayer neural network to predict the rheological effect response. Neural network consists of several processing unit (neurons) whose input are weighted and passed to an activation (signal) function producing one single output. The weighting depends on the neurons' interconnections and can be adjusted by a kind of learning process. The network presented by Burton et al., (1996) was constructed by an algorithm known as the Dependence Identification Algorithm, which is attributed to Moody and Antsaklis (1996).
Makris et al., (1996b) extended the use of neural networks in combination with mechanical models mention earlier. As the latter were assumed to reproduce most of the linear rheological response, the network was trained on a different signal between the response predicted by the parametric models and actual response of the damper.
Burton et al., (1996) found that the performance of the neural network model of MR damper is better than the element models such as the Bingham Model. When the neural network is combined with the simple mechanical model, the network's prediction is superior to the results achieved with the parametric method alone. A comparison between experimental data and a prediction obtained from the neural network combined with the parametric model is shown in Figure 2.17.
Figure 2.17 Comparison between the predicted ( ____ ) and the experimentally obtained (----- ) force-velocity characteristic for a neural network combined with the Maxwell model.
2.4.3 Research on Design and Development on MR Devices
Gordaninejad and Kelso, (2000) designed a MR damper to be used on off-high-payload, off-road vehicles. The designed MR damper was tailored to cater for a wide range of dynamic loading with the capability to operate at a different rebound and compression. The design is based on the original shock absorber as the reference. The author used Bingham model to design its MR damper and also conduct experimental studies to verify the design. The results from the studies show that the experimental results demonstrate good correlations with the simulation results.
Ahmedian, (2000) from Advanced Vehicle Dynamics Laboratory, Virginia Tech has applied the MR fluid technology to design the MR damper for bicycle applications. The author used two approaches in order to study the effectiveness of MR damper in providing comfort for the bicycle users. The first method is by only retrofitting the MR valves inside the original damper while for the second method the author made a new design for the bicycle by considering the easiness of fabrication and assembly. The author also considered the new characteristic of the designed damper to envelope the original damper. The results from this studies are that, a properly designed MR dampers can provide significant dynamic improvement in terms of comfort, as compared with a conventional passive bicycle damper.
Ahn et al., ( 1999) had modified a conventional fluid mount and replaced the original fluid of the mounting with MR fluid. The dynamic behaviour of MR fluid when subjected to magnetic field was used to control the fluid flow inside the mounting. The behaviour of MR fluid was used as a switch to control the openings of fluid passage of the mounting. A simple control scheme was used to control the operation of the MR fluid and it was found that the application provides a good improvement for the mount's isolation effect.
Simon and Ahmedian, (1999) studied the effect of magnetorheological damper as a primary suspension in improving ride comfort on heavy truck vehicle. For this purpose, a set of controllable magnetorheological damper was fabricated. An embedded controller was used to determine the damping level for the semi-active suspension based on the skyhook control scheme.
Pare' (1998) has studied the effectiveness of magnetorheological damper in improving vehicle's ride comfort by testing the developed magnetorheological damper on a full scale quarter car model, constructed at the Advanced Vehicle Dynamics Laboratory at Virginia Technology. The author evaluated the response of the developed damper on the vehicle suspension using different control algorithms namely skyhook, groundhook and hybrid skyhook-groundhook. The comparison between semi-active system and passive system were also studied using the developed quarter car rig. Very promising results were shown in terms of ride quality improvement that can be produced by the semi-active magnetorheological damper.
Poynor (2001) has researched several different applications of magnetorheological fluid technology. The developed magnetorheological dampers were for automotive suspension system application and for military purposes. The dampers developed for the automotive suspension system were mono-tube based damper and hybrid-tube based. In the military application, the magnetorheological dampers was developed to be used in gun recoil system in order to reduce the impact of back-thrust during firing.
Another research work on the development of magnetorheological fluid technology is by Gravatt, (2003). In his master's thesis, the magnetorheological dampers were developed to be used in super bike's suspensions system. The developed MR dampers were designed and fabricated based on the original manufacturers dampers and installed in the super bike's suspension system. The author used skyhook control algorithm to control the operation of the developed damper in order to improve the super bike's ride comfort and results from the installation are very promising.
2.4.4 Research on MR Device Control Strategies
In this section, control strategies that were used to control the operation of magnetorheological damper will be discussed involving the most common control strategies of semi-active suspension system to the most advanced control strategies that were only tested via simulation.
2.4.4.1 Basic Control Strategies In Semi-Active Suspension System
This section described the most common control strategies used to control the operation of variable damping damper in semi-active suspension system. The control strategies are skyhook control strategies, groundhook control strategies and hybrid skyhook-groundhook control strategies.
a Skyhook Control System
Skyhook control system is the most basic and most common algorithm used in semi-active suspension system for disturbance rejection control. The algorithm was introduced by Karnopp et al., (1974). In skyhook control system, an imaginary damper is inserted between the sprung mass and the stationary sky as shown in Figure 2.18 as an effort to reduce or eliminate the motions of sprung mass when the vehicle is subjected to road inputs such as road harshness or bumps.
In essence, the skyhook configuration adds more damping to the sprung mass and takes away damping from the unsprung mass. The skyhook configuration is ideal if the primary goal is to isolate the sprung mass from base excitations, even at the expense of excessive unsprung mass motion.
The control policy of skyhook system can be summarized as follows: if the product of the sprung mass velocity, and relative velocity between the sprung mass and unsprung masses, is positive, the semi-active force is proportional to the velocity of sprung mass. Else, the semi-active damping force is set to zero. The equation governing skyhook control is given by:
If then
If then (2.28)
Figure 2.18 Skyhook control system
b Groundhook Control System
Groundhook control system was proposed by Novak and Valasek (1996) in order to eliminate the excessive unsprung mass motion and improves tyre force dynamics. In ground hook control, an additional fictitious damper is added between the unsprung mass and the ground. If in skyhook control system, the improvements are focused in reducing the sprung mass oscillations and isolate it from the base excitations, the ground hook control system is focused in improving unsprung mass oscillations from base excitations.
Groundhook control system is more suitable to be used to control semi-active force in semi-active suspension system for heavy vehicle because the algorithm in Groundhook control improves tire force dynamics which will reduce the effect of road damage which might possibly cause by the heavy vehicle's suspension system (Valasek and Kortum, 1998a and 1998b). The configuration of Groundhook control is shown in Figure 2.19. The equations governing Groundhook control are as follows:
If then
If then (2.29)
Figure 2.19 Groundhook control system
c Hybrid Skyhook-Groundhook Control System
Hybrid skyhook-groundhook has been proposed by Ahmedian (1997). The control system which takes benefit both of skyhook and groundhook systems gives the users the ability to specify how closely the controller emulates the skyhook or groundhook. The hybrid skyhook-groundhook system has two dampers connected to some inertial reference in the sky and in the ground as depicted in Figure 2.20.
The hybrid control strategy is a linear combination of skyhook control system and groundhook control system and can be written as
If then
If then
(2.30)
If then
If then
where and are the skyhook damping force and groundhook damping force respectively. The parameters and are the skyhook and groundhook damping constant. The variable is the relative ratio between the skyhook and groundhook control, and G is a constant gain.
Figure 2.20 Hybrid Skyhook-groundhook Control System.
2.4.4.2 Advanced Control Strategies For Semi Active Suspension System
In this section, brief descriptions on alternatives control strategies that are used to control the operations of the variable damper are discussed with most of the control strategies involve complex algorithms.
a Sliding Mode Control
Lam and Liao (2001) and Yokoyama et al., (2001) studied the application of sliding mode control (SMC) with semi-active magnetorheological damper. The controller which considers the loading uncertainties and the undesirable non-linear properties of magnetorheological damper was reported to reduce significantly the sprung mass acceleration. It was also reported that the use of SMC with magnetorheological damper also improves sprung mass peak response and the root-mean-square values of the studied parameters (i.e. acceleration, vertical displacement).
b Fuzzy Logic Control
Fuzzy Logic control is known to be very effective in disturbance rejection control of semi-active suspension system (Brown and Harris, 1994). The concept of a fuzzy logic set is introduced by first defining membership functions. In order to develop a fuzzy logic system for control application, a functional form of the membership function is needed. This membership function describes the degree of certainty that an element belongs to a fuzzy set.
There are many shapes of membership functions proposed, and the most widely used membership functions are the triangular-type, trapezoidal-type, Gaussian-type and the singleton membership function. The mathematical form of a standard rule-based fuzzy system is given by
(2.31)
where and represents the membership function, fuzzy parameter, number of rule and output membership function for i-th rule respectively.
The output of the fuzzy system is used to calculate the desired damping coefficients for semi-active suspension system (Al-Holou and Shaout,1994) or to calculate the desired force required by the active suspension system (Barr and Ray, 1996). It is reported via numerical studies that the use of fuzzy logic are able to improve the vehicle model's ride comfort (Sireteanu et al., (2001), Chen et al., (2001 and 2003) and Zhang et al., (2004)). In real world application for semi-active suspension system, the implementation of fuzzy logic control had been performed by Fang et al., (1999), Craft et al., (2003) and Rui et al., (2004) and the results are very promising with the controller could effectively reduce sprung mass vertical oscillation and improve ride comfort and handling stability.
c H Control System
H∞ control system is known for its robustness when operating under different environment. It is a control method that considers uncertainties, including the model's uncertainties, model parameters and disturbances. H control system of semi-active suspension system with magnetorheological damper has been studied by Du et al., (2005). In this study, the dynamic behavior of magnetorheological was first simulated using a polynomials model based on the experiments carried out on the developed magnetorheological damper. Then the magnetorheological damper model was used in a quarter car model along with the H control system. The H controller used the suspension deflection and the sprung mass velocity as the feedback signals. The scheme was further studied via numerical simulation under random excitations. Simulation results showed that the designed H controller could provide good performance for the semi-active suspension system.
d Neural Network Control
Yiming and Xiangying (2004) investigated the performance of semi-active suspension system with magnetorheological damper controlled by neural network controller. The study was carried out via simulation model by using a quarter car model. Neural network control of magnetorheological with experimental assessment using a quarter car test rig was reported by Chen et al. (2000). The results from both of these studies show that the neural network control system excel in improving the suspension performance.
e Linear Quadratic Regulator (LQR) Control
The LQR control system for semi-active suspension system has been studied by ElMadany and Abduljabar (1999) using a simple quarter car model. Hrovat (1991) studied the scheme on a full car model while Krtolica and Hrovat (1992) on a half car model. The strength and advantage of LQR approach is that the elements of the performance index can be weighted according to the designer's desires or other constraint. With this advantage, an optimal result can be achieved when all the criteria of performance are taken into account (i.e. body acceleration, relative velocity and dynamic tyre load)
2.5 Conclusions
Through the review of the magnetorheological fluid technology, it is clear that researchers are focusing on studying the behavior of the MR fluid and try to model it via a simulation model. There are various version of simulation models to simulate the dynamic behaviour of magnetorheological device that has been proposed. The researched also focused on the implementation of the magnetorheological fluid technology involving the design and development of magnetorheological device to be applied in various fields i.e. automotive application. The researchers are also focusing their researched on the control scheme to control the operation of magnetorheological device optimally.
It is shown from the literature that most of the studies on magnetorheological damper emphasize on the modeling the dynamic characteristic of magnetorheological fluid and the control algorithm to control magnetorheological device. The work on the design and development of magnetorheological device is not clearly explained or exposed to the readers especially the detail calculations on how the magnetorheological damper been designed.
The simulations that have been carried out by researchers on the semi-active suspension system used only one control algorithm without any attempts to compare with other control algorithm that affect the performance of magnetorheological damper and hence effect the overall performance of vehicle's ride comfort.
This thesis will unwrap the development of magnetorheological damper model for vehicle's suspension system through the model-based-design approach and shows how two control algorithms that are used to control the operation of magnetorheological damper can effect the overall performance of vehicle's ride comfort.
