1. SIMULATION OF SEMI-ACTIVE SUSPENSION OF QUARTER CAR MODEL OF AN AUTOMOBILE

2. Introduction:- Vehicle Suspension Systems:
A good Suspension systems is designed to maintain contact between a vehicle’s tires and the road.
To isolate the frame of the vehicle from road disturbances.
Dampers, or shock absorbers reduce the effect of a sudden bump by smoothing out the shock.
Vehicle Suspension Systems:
1.Passive Suspension Systems:
They are composed of conventional
springs, and single or twin-tube oil
dampers with constant damping
properties.
Fig.1: Passive suspension spring and damper
It uses springs,dampers,strut..
When people think of automobile performance, they normally think of horsepower, torque and acceleration.
But all of the power generated by engine is useless if the driver can’t control the car.
To provide a comfortable ride, through isolation of the vehicle body from road irregularities.

3. 2.Semi-active Suspension Systems:
Since first proposed by Crosby and Karnopp (1973), semi-active suspension systems continue to gain popularity in vehicle suspension system.
Damping properties can be adjusted to some extent by applying a low-power signal.
They have either a solenoid valve as an adjustable orifice or a MR-fluid Dampers.
Fig 2: MR damper
>Semi-active (also known as adaptive-passive) suspension systems are essentially passive systems in which the
>They are commercialized recently by means of either a solenoid valve as an adjustable orifice, or MR-fluid Dampers.
Leading automotive manufacturers such as GM and Volvo have started the implementation of these semi-active suspension systems for their high-end automobile.
The MR dampers have still some crucial issues, such as MR degradation with time, temperature sensitivity, and sealing problems.
A magnetorheological damper  is a damper filled with magneto rheological fluid, which is controlled by a magnetic field, usually using an electromagnet.
This allows the damping characteristics of the shock absorber to be continuously controlled by varying the power of the electromagnet.
The system is fitted on a few vehicles including some Cadillac models (Imaj, Seville, SRX, XLR, STS, DTS), the ChevroletCorvette and most recently the Audi TT, the Audi R8 and the Ferrari 599 GTB.

4. 3. Active Suspension Systems
Active suspension system uses an active power source to actuate the suspension links by extending or contracting them as required (Gillespie, 2006).
In an active suspension, controlled forces are introduced to the suspension by means of hydraulic or electric actuators, between the sprung and unsprung-mass of the wheel assemblies (Brown, 2005).
Karnopp (1983) studied the effect of adding an active damping force to the suspension system. A variable force is provided by the active suspension at each wheel to continuously modify the ride and handling characteristics.
Sensors, as essential elements of an active suspension, are used to measure the suspension movements at different points.
The electromagnetic dampers (as actuators) have the potential to be used in active suspension systems.
The suspension system that commonly applied on the vehicle is a passive suspension system in which its spring stiffness and damping value is constant. In the passive suspension system damping settings does not gives a high performance where its vibration amplitude still high and the time required to damp out the vibrations is quite longer. To overcome this condition, a semi-active suspension with skyhook control is suggested. Unfortunately the active suspension system requires larger energy and less economical, so then the semi-active suspension becomes a better choice to keep the quality of the car comfortable on any road condition.
Fig 4: electromagnetic damper by Suda (2004).
Converts the transverse motion of the vibration between the car body and wheels into the rotating motion of the DC motor.
The Bose® linear electromagnetic suspension designed by Dr Amar Bose, which is based on a linear electric motor and power amplifier instead of a spring and a damper.

5. Vehicle Models:
The choice of the suspension system models depends on the vibration mode and the simplicity of the analysis involved.
Basic vehicle models that have been reviewed in the literature are the quarter-car one-degree-of-freedom (1DOF) model to study the bounce mode, the quarter-car 2DOF model to study the wheel-hop as well as the bounce mode.
The half-car 4DOF model for bounce and pitch modes, and the full-car 7DOF model for bounce, pitch and roll modes (Deo. et al, 2007)
Fig.3. One and two degree of
freedom Quarter car model
(Nima Eslaminasab, 2008))
This model is a good approximation of a real suspension system only for long wavelength and low frequency inputs.
Quarter-car models are perfect for a vehicle with a longitudinally independent suspension and a symmetric mass distribution in the vehicle body, where the front and rear suspension is decoupled (Mitschke et al, 1961).
However, it contains the most fundamental features of the real suspension system, such as suspension system forces, which are properly applied between a vehicle’s wheels and body.

6. Semi-active suspension Control Strategies:
1 .Skyhook Control Method :
The damping force provided by the
damper, Csky, is always opposite to
the absolute velocity of
Figure 4: A schematic of the Skyhook
control system (Eslaminasab N., 2008)[8]
According to the Skyhook working principle, the semi-active on-off control law for a 2 Degree of freedom system is
The common goal of these initiatives is to achieve a higher level of vibration isolation or to find practical and easy implementation methods, or both. Leading automotive companies such as General Motors and Volvo have started to use semi-active actuators in the suspension systems of high-end automobiles, such as the Cadillac Seville and Corvette, to improve the handling and ride performance in the vehicle. In this section, the most conventional methods are briefly introduced.
In general, a controlled system consists of a plant, which is the subject of control; sensors; actuators; and a control method.
The problem in implementing the Skyhook is that in some applications, especially in the automotive industry, the absolute velocity is impossible to measure. Many researchers, including Hedrick (Hedrick et al., 1994) and Shen (Shen et al., 2006), have concentrated on this problem.

7. 2. Rakheja-Sankar (R-S) Control Method
The absolute acceleration of the mass based on this equation can be formulated as
This equation shows that the damping force in a passive damper tends to increase the mass acceleration when the damping force and the spring force are acting in the same direction.
Where α is a gain factor.
For this study Skyhook control has been implemented.
>>Fd Fkand are damping and spring forces.
**If an ideal semi-active damper is able to produce no damping force, or at least a minimum amount of damping force, when the spring and damping forces are acting in the same direction and produce damping force equal to the spring force when they are acting in different directions, then the mass acceleration and, as a result, the acceleration transmissibility will be minimum.
In practice, it is difficult to have the damping force properly follow the spring force; therefore, the original control strategy developed by Rakheja-Sankar (R-S) (1985) is implemented in the real applications in a modified version.[8]

8. ANALYSYS OF PASSIVE SUSPENSION SYSTEM
MODELING AND ANALYSIS OF SINGLE DOF SYSTEM USING Simulink®:
Assumptions:
• Only vertical displacement of the car is considered (no roll or pitch);
• The springs and dampers are assumed to be mass-less;
• The tire has no mass or dampening properties associated with it.
Figure 5: An automobile passing through a pothole

9. y= hstart= 22.5m, hend= 22.55m Given Parameters: Sprung mass =500 kg
Stiffness of spring =1000 N/m
Damping coefficient C=10 N-s/m
Car’s vertical displacement (hole depth) = 0.15 m
Governing Equation:
Input:
Displacement of tire y=
hstart= 22.5m, hend= 22.55m
…..(3.3)
hstart and hend correspond to the time instants at which the tire starts entering the hole and comes out of it.

10. Fig.6. Simulink model of 1degree of freedom passive suspension system

11. Results:: Input step signal:
Sprung mass displacement: The simulink model is simulated for given
parameters and
sprung mass
displacement (x)(mm))
vs. time(sec)
This figure shows how a lack of dampening would result in an uncomfortable ride.
it takes 7 seconds for sprung mass to come to stable condition.

12. Sprung mass acceleration:
Figure 3.7: Sprung mass acceleration (m/s2) vs. time(s)

13. Influence of damping(c)- When the dampening coefficient is increased, the oscillations that occurs in the system are decreased.
1. Parameters: k=1000 N/m, c=300 N-s/m
Figure 3.7(a): Sprung mass acceleration (m/s2) at c=300N-s/m vs. time(s)

14. This large dampening leads to hardly any reverberations and small displacement.
From fig 3.7(a), (b), (c), it can be observed that the required damping is 800N-m/s for given parameters under this type of road excitations but the damping cannot be changed after setting the parameters initially for passive system which is the main disadvantage of passive mode.

15. MODELING AND ANALYSIS OF 2 DOF SYSTEM USING Simulink®
Figure 7: 2 DOF Quarter car
model of passive suspension system (Image: Florin et al. 2006)
Equations (3) and (4) are a second-order differential equations of a passive suspension system. Solving these systems of equations is difficult so we can use Matlab Simulink software.
Sprung mass-m1
466.5 (kg)
Unsprung mass-m2
49.8 (kg)
Stiffness of tyre-k1
5700 (N/m)
Stiffness of suspension-k2
(N/m)
Coefficient of damper-c1
650 (N/m/s)
Coefficient of damping of tire –c2
1400 (N/m/s)

17. Figure 8: step input signal (y) vs. time(s)
Results:
Road profile: Road input signal is given by step input function which represents a bump on the road with amplitude of 0.10 m.
Figure 8: step input signal (y) vs. time(s)
Sprung mass displacement:The simulink model is simulated for 20 seconds under step input road signal and the deflection of sprung mass or car body (x1) is plotted
Figure 9: Sprung mass
displacement (x1) (m)
vs. time(s)
This road excitation is chosen because road bump gives maximum discomfort to the passenger and this is used in standard road testing also.

18. Figure 10: Sprung mass acceleration (m/s2) vs. time(s)
The simulink model is simulated for 20 seconds under step input road signal and the velocity of sprung mass or car body is plotted as shown in fig.
Figure 10: Sprung mass acceleration (m/s2) vs. time(s)
Initially acceleration of the car body is at zero but as soon as it hits the bump accelerates up to 4.75 m/s2.After 5 seconds the acceleration reduces to zero because of damping effect
Initially acceleration of the car body is at zero but as soon as it hits the bump accelerates up to 4.75 m/s2.After 5 seconds the acceleration reduces to zero because of damping effect. To analyse the ride comfort sprung mass acceleration is the main criteria. The sprung mass acceleration reaches to its maximum value within milliseconds as shown in fig.3.13 that creates unwanted jerks which can be felt by passenger. So, this system needs improvements in parameters to achieve good ride comfort.

19. Figure 11: Unsprung mass displacement (x2) vs. time(s)
Unsprung mass displacement and acceleration:
Figure 11: Unsprung mass displacement (x2) vs. time(s)
Figure 12: Unsprung mass acceleration (x2’’)(m/s2) vs. time(s)
When tire reaches bump of amplitude 0.10m at 5th second, it deflects up to 0.12 m. Due to high stiffness of tire, the wheel comes to its equilibrium position within 3 seconds as shown in fig The vibrations in the tire are less.

20. Figure 13: Suspension deformation (x1-x2)(m) vs. time(s)
Initially deformation of the suspension is at zero but as soon as it hits the bump deflects up to .05m. After 6 seconds the deflection reduces to zero because of damper and spring.
Figure 13: Suspension deformation (x1-x2)(m) vs. time(s)
Initially deformation of the suspension is at zero but as soon as it hits the bump deflects up to .05m. After 6 seconds the deflection reduces to zero because of damper and spring. If the suspension deformation is more, it has good handling but poor ride comfort.

21. Conclusions:
In this chapter, we modelled the 2 degree of freedom quarter car model passive system and simulated in matlab simulink. A step type signal (road bump) was used for a broad application of the suspension system.
To analyse the road holding and comfort, car body acceleration and suspension deformation graphs were plotted. The parameters of a passive suspension system are generally fixed, being chosen to achieve a certain level of compromise between ride comfort and handling. So, in next chapter semi-active suspension system is proposed and analysed for ride comfort and handling.

22. SEMI-ACTIIVE SUSPENSION SYSTEM
The spring for the suspension is assumed
to be linear and the tire is also modelled
as linear spring component.
The model has a sprung mass which is
¼ of vehicle’s mass, unsprung mass is the
wheel mass, k2 is the suspension spring
stiffness, k1 is tire stiffness and Co is variable
damping coefficient.
Equations of motion:
……..4.1
…….(4.2)
Figure 4.1: Two DOF quarter car model of Semi-active suspension system
Semi-active suspension system is mostly same as passive suspension system. It also has spring and damper but damper may be hydraulically or electrically actuated and controlled by electronic controller. In passive system the damping characteristics are fixed but in semi-active suspension damping characteristics i.e. damping coefficient and stiffness of spring can be varied to achieve better ride and handling. In this chapter, semi-active suspension quarter car is modelled in simulink and skyhook control strategy is implemented.
Equation 4.1 and Equation 4.2 can be modelled in simulink using blocks from simulink library as shown in fig This simulink model is given input parameters and is later connected to skyhook control model.

23. Figure 4.2: Simulink model of semi-active suspension
m1,m2,k1,k2,co

24. Skyhook Control:
Skyhook control strategy is used so that damping force can be varied and sprung mass acceleration can be reduced to achieve comfort.
Semi-active dampers allow for the damping coefficient, and therefore the damping force, to be varied between high and low levels of damping.
First define the velocity of the suspended mass relative to the base, V12, to be positive when the base and mass are separating (i.e., when V1 is greater than V2) for both systems
Now assume that for both systems, the suspended mass is moving upwards with a positive velocity V1. If we consider
the force that is applied by the skyhook damper to
the suspended mass, we notice that it is in the
negative x1 direction,
Fsky = - Csky* V 1
A typical diagram that describes the implementation of conventional semi-active controllers in a 1DOF system is depicted in Figure 4.2.
Another approach to achieving skyhook damping is to use semi-active dampers.
Once it is decided that semi.-active damper will be used, determine how to modulate the damper such that it emulates a skyhook damper
Where FSKY is the skyhook force. Where FCONTROLLABLE (Fc) is the force applied to the suspended mass.

25. Next, we need to determine if the semi-active damper is able to provide the same force.
If the base and suspended mass in are separating, then the semi-active damper is in tension. Thus, the force applied to the suspended mass is in the negative X1 direction
Fc × Cc= - V 12
Since we are able to generate a force in the proper direction, the only requirement to match the skyhook suspension is
Cc=
We can apply the same simple analysis to the other two combinations of V1 and V12, resulting in the well-known semi-active skyhook control policy
………………..Eqn.(4.3)
Since the semi-active damping force cannot possibly be applied in the same direction as the skyhook damping force, the best that can be achieved is to minimize the damping force.

26. According to the Skyhook working principle, the semi-active on-off control law for a 2 Degree of freedom system is
………………Eqn.(4.3)
Modeling of skyhook controller using Simulink:
Figure 4.4: Simulink model of Skyhook Controller
Where is the controllable damping coefficient.
The problem in implementing the Skyhook is that in some applications, especially in the automotive industry, the absolute velocity is impossible to measure. Many researchers, including Hedrick et al. and Shen et al. have concentrated on this problem.
We can give different values of Cfirm(Cmax), Csoft(Cmin) and Csh on double clicking the Skyhook controller block.

27. Incorporating skyhook controller model in semi-active suspension model:

28. 5.SIMULATION RESULTS AND ANALYSIS OF SEMI-ACTIVE SUSPENSION SYSTEM
5.1. Simulation of the Semi-active Suspension with skyhook control:
Assuming road profile as step input with amplitude 0.10 m which represents the road bump, the semi-active suspension model with skyhook control is simulated for 5 sec and various graphs are plotted.
TABLE 4.4: System parameters used
Sprung mass-m2
240 kg
Unsprung mass-m1
36 kg
Stiffness of tyre-k1
N/m
Stiffness of suspension-k2
16000 N/m

29. Road profile input: For this study step input road profile signal is used with amplitude of 0.10 m is given and different results will be obtained.
Figure 5.2: Road profile input (m) vs. time (s)

30. 5.1.2. Sprung mass displacement:
. Initially car body displacement or sprung mass displacement is zero but after 1 sec when it meets the bump, the displacement increases. The oscillations reduce in 1.5 seconds due to damping effect.
Figure 5.3: Sprung mass displacement (m) vs. time(s)

31. Sprung mass velocity: Initially velocity of the car body is at zero but when it experiences a bump, reaches to amplitude of 1.15 m/s. The vibration reduces due to damping and sprung mass velocity becomes zero after 3 seconds.
Figure 5.4: Sprung mass velocity (m/s) vs. time(s)

32. 5.1.4. Sprung mass acceleration:
it can be seen that sprung mass acceleration is high at starting but reduces to zero after 2.5 seconds.
Figure 5.5: Sprung mass acceleration (m/s2) vs. time(s)
So this suspension system is capable of reducing the vibrations of car body very quickly than passive suspension system.

33. 5.1.5. Unsprung mass displacement (m) vs. time(sec)
5.1.6 Unsprung mass velocity (m/s) vs. time(sec)
Initially unsprung mass displacement or sprung mass displacement is zero but after 1 sec when it meets the bump, the displacement increases. The oscillations reduce in 1.5 seconds due to damping effect.

34. 5.1.8. Skyhook control force (N) vs. time(sec)
Skyhookdamping (N-s/m) vs. time(sec)
Skyhook control force (Fd) varies according to input given and it tries to reduce the body acceleration. It depends on the Skyhook damping coefficients i.e. Csoft, Cfirm and Csh. Skyhook control force can be varied to suit the comfort and performance of suspension system by changing these values. Skyhook control force graph is shown in fig. 5.9.
Skyhook damping varies with time according to motion of sprung mass and can be adjusted to lower the sprung mass displacement. From fig.5.10, it can be observed that skyhook damping coefficient is varying at different time step which is the major drawback in passive suspension system. The maximum damping is set to 4000 N-s/m2 and minimum damping is 1000 N-s/m2 as set in the controller.

35. Figure 5.11: Suspension deformation (m) vs. time(s)
Suspension deformation: Suspension deformation is high at starting but reduces very quickly. From fig. 5.1 simulink model is simulated for 5 sec and suspension deformation (z2-z1) is plotted
Suspension oscillations reduce to zero after 2 seconds so this system has good damping characteristics and road holding.
Figure 5.11: Suspension deformation (m) vs. time(s)
Suspension deformation is high at starting but reduces very quickly. From fig. 5.1 simulink model is simulated for 5 sec and suspension deformation (z2-z1) is plotted as shown in fig Suspension oscillations reduce to zero after 2 seconds so this system has good damping characteristics and road holding.

36. Comparison between semi-active suspension system and passive suspension system:
Both semi-active and passive systems are simulated for same step input road profile of amplitude 0.10m and for same sprung mass, unsprung mass and tire stiffness. Then sprung mass acceleration and suspension deformation graphs are plotted to understand the damping characteristics of both the systems.
Passive system has constant damping of 1400 N-s/m2 throughout the simulation and semi-active suspension has variable stiffness from 1000 N-s/m2 to 4000 N-s/m2. Minimum and maximum damping of semi-active are set in skyhook control model and it calculates the required damping force and damping coefficient at different time step so that body oscillations and suspension deformations are minimum.
Both semi-active and passive systems are simulated for same step input road profile of amplitude 0.10m and for same sprung mass, unsprung mass and tire stiffness. Then sprung mass acceleration and suspension deformation graphs are plotted to understand the damping characteristics of both the systems.
Passive system has constant damping of 1400 N-s/m2 throughout the simulation and semi-active suspension has variable stiffness from 1000 N-s/m2 to 4000 N-s/m2. Minimum and maximum damping of semi-active are set in skyhook control model and it calculates the required damping force and damping coefficient at different time step so that body oscillations and suspension deformations are minimum.

37. Passive and semi-active suspension simulink model

38. 5.2.1. Sprung mass acceleration:
It takes 6 seconds for passive system to reduce oscillations to zero. Semi-active suspension system with skyhook control has less car body acceleration magnitude and it takes only 2 seconds to reduce body acceleration.
Figure 5.13: Sprung mass acceleration in Semi-active suspension mode and passive suspension mode
The simulink model is simulated for 10 seconds under step input road excitation and sprung mass acceleration is plotted in matlab for both passive and semi-active system with skyhook control as shown in fig When wheel reaches to bump after 1 sec, sprung mass acceleration for passive suspension is more than semi-active system.
From fig.5.13 it can be observed that semi-active system with skyhook control has better ride comfort compared to passive suspension system.

39. 5.2.2. Suspension deformation:
. Initially deformation of the suspension is at zero but as soon as tire hits the bump passive suspension deflects up to .12 m and semi-active suspension deflects up to 0.05 m. Suspension oscillation reduces to zero after 6 seconds in case of passive system. There are more oscillations in passive mode till it reaches to zero.
Figure 5.14: Suspension deformation in Semi-active suspension mode and passive suspension mode
In case of semi-active system with skyhook control, suspension deformation is less than passive system and it reaches to zero much faster than passive mode. So, semi- active system has better road holding and better ride comfort compared to passive mode for same input parameters.

40. Figure 5.15: Road profile input (pot hole)
Now another step-input function is given as input of amplitude (-0.10) m which represents the pothole in the road.
Figure 5.15: Road profile input (pot hole)

41. 5. 3. 1. Sprung mass acceleration:
Sprung mass acceleration: . It takes 4 seconds for passive system to reduce oscillations to zero. Semi-active suspension system with skyhook control has less car body acceleration magnitude and it takes only 2.5 seconds to reduce body acceleration.
Figure 5.16: Sprung mass acceleration in Semi-active suspension mode and passive suspension mode
The simulink model is simulated for 10 seconds under step input road excitation and sprung mass acceleration is plotted in matlab for both passive and semi-active system with skyhook control as shown in fig When wheel reaches to pothole after 1 sec, sprung mass acceleration for passive suspension is more than semi-active system. It takes 4 seconds for passive system to reduce oscillations to zero. Semi-active suspension system with skyhook control has less car body acceleration magnitude and it takes only 2.5 seconds to reduce body acceleration.

42. Suspension deformation: Initially deformation of the suspension is at zero but as soon as tire reaches to road bump passive suspension deflects up to -.15 m and semi-active suspension deflects up to 0.13 m. Suspension oscillation reduces to zero after 4 seconds in case of passive system. There are more oscillations in passive mode till it reaches to zero.
Figure 5.17: Sprung mass deformation in Semi-active suspension mode and passive suspension mode (Pothole road input)
In case of semi-active system with skyhook control, suspension deformation is less than passive system and it reaches to zero much faster than passive mode. So, semi- active system has better road holding and better ride comfort compared to passive mode for same input parameters.

43. 5.4. Summary of the results:
In order to evaluate the semi-active suspension, simulation tests were performed with sinusoidal road profile. Evaluation of the new suspension was done by comparing the passive and semi-active suspension modes.
Therefore, each test was performed once in the passive mode and then, in the semi-active mode. The achieved data from these tests in the two suspension modes were analyzed.
These results were plotted in Matlab Simulink. The sprung mass acceleration and suspension deformation were analyzed to evaluate the vibration characteristic of the suspension system.
Car body (sprung mass) accelerations of the car body were measured, and the influence of the new suspension system on the ride comfort capability of quarter car model was evaluated by comparing the results of the passive and semi-active suspension modes.
Semi-active suspension system is better in both ride comfort and suspension performance.
In evaluation of the semi-active suspension, the ride comfort capability of the car was considered as the first criterion. For this purpose,

44. 6. Conclusion and Future Scope:
6.1. Conclusion: The research presented in this report is directed to the simulation and modeling of a semi-active suspension. Although based on the well-known physical models for investigating the vertical dynamics of suspension systems,
It is expanded with an extensive set of simulations based on Simulink modeling and benchmark road profiles employed in real industrial tests.
The skyhook control strategy is evaluated by means of multiple criteria, i.e., the comfort and handling.
In addition, it can be seen that skyhook control improves, in a significant way, comfort characteristics in comparison with the passive system
However, the technology is still an emerging one, and elaboration and more research work on different theoretical and practical aspects are required. This thesis is an attempt to develop an understanding of some of those aspects, such as the effect of the semi-active dampers response-time on the performance of the control strategies through analytical and numerical methods.

45. The main conclusions that may be derived are :
A control approach based on skyhook algorithm for semi-active suspension systems has been implemented in the Simulink environment.
In order to show the effectiveness of the proposed procedure, performance comparison with passive system has been presented.
Extensive simulation tests have been performed on the quarter-car linear models, which provide an accurate enough description of the dynamic behavior of a vehicle equipped with constant damping or varying damping control.
On the basis of the results, it can be concluded that the inclusion of the skyhook algorithm in a semi-active control system improves the comfort index of semi-active suspensions systems.

46. The possible extensions for this work are listed below:
6.2. Future scope:
The possible extensions for this work are listed below:
1. Development of a full car model of semi-active suspension system with skyhook control is an important aspect of future work.
2. Development of different control strategies such as modified skyhook, PID control and fuzzy logic control for suspension system.
3. In this thesis, a step input response analysis of the suspension system has been conducted. As the real-life excitations to a vehicle are varied random inputs, more research on the nonlinear system response to a general random input is an important area for further study of suspension system design.

47. References:
[1] Babak Ebrahimi,(2009),Ph.D. thesis on ‘Development of Hybrid Electromagnetic Dampers for Vehicle Suspension Systems’ University of Waterloo, Canada [2] Karnopp D., (2007)Active damping in road vehicle suspension systems, Vehicle System Dynamics, 12, (1983) [3] Gillespie T., (2006) Development of semi-active damper for heavy off-road military vehicles, M.Sc. Thesis, University of Waterloo [4] Johnsson et al, (2003).Methods for road texture estimation using vehicle Measurements, Luleå University of Technology [5] Karnopp et al,(1974) Vibration control using semi-active force generators, Transaction of ASME, Journal of Engineering for Industry, 96, [6] Guglielmino et al,(2008). Semi-active Suspension Control, springer, ISBN [7] Nima Eslaminasab,(2008) Ph.D. thesis on ‘Development of a Semi-active Intelligent Suspension System for Heavy Vehicles’ University of Waterloo, Canada [8] Yi, K.S., Song, B.S. (1999), Observer design for semi-active suspension control. Vehicle System Dynamics, vol. 32, p , DOI: /vesd [9] Carter et al, (1998).Master’s thesis, Application of Magnetorheological Dampers For vehicle Seat Suspensions, etd [10] Turnip, A.et al,(2008) Control of a semi-active MR-damper suspension system: A new polynomial model. Proceedings, The International Federation of Automatic Control. Seoul, p [11] Jazar, R. (2009). Vehicle Dynamic: Theory and Application, Springer, New York. [12] Abramov, S. et al, (2009), Semi-active suspension system simulation using Simulink, International Journal of Engineering System Modelling and Simulation, vol. 1, no. 2/3, p [13] Rill, G., (2009)Vehicle Dynamics, University of Applied Science, Regensburg,. [14] Popp, et al. (2010). Ground Vehicle Dynamics. Springer, Berlin, DOI: / [15] Kuznestov et al.,(2011). Optimization of improved suspension system with inerter device of the quarter-car model in vibration analyses. Archive of Applied Mechanics, vol. 81, no. 10, p [16] Karnopp, D.,(1995) "Active and Semiactive Vibration Isolation," Journal of Vibrations and Acoustics, Vol. 117, No. 3B, pp

48. THANK YOU !!!