Analysis of Active Suspension Systems using the Quarter Car Model

This report investigates the performance of active suspension systems, contrasting them with passive and semi-active systems, using a quarter car model. The study begins with an introduction to vehicle suspension systems, highlighting the importance of ride comfort and handling. It then delves into the classifications of suspension systems, including passive, semi-active, and active systems, explaining their components and functionalities. A comprehensive literature review explores controller implementation techniques, actuation systems, and modeling using Bond graphs, with specific focus on the quarter car model. The report examines the application of various control strategies like PID control, LQR control, and fuzzy sliding mode control, as well as the use of hydraulic actuators. Furthermore, the report discusses the benefits of active suspension systems in improving ride comfort and vehicle stability, while acknowledging the challenges and complexities involved, such as power consumption. The study concludes with a comparative analysis of the active suspension system with a passive system. The report emphasizes the potential of active suspension systems to enhance vehicle performance, providing insights into the design and control of these systems.

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Investigation of Quarter Car active suspension behavior based on Bond graph
Student’s Name
Institutional Affiliation
Date

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Contents
1 Introduction........................................................................................................................................3
1.1 Passive suspension systems.........................................................................................................4
1.2 Semi-active suspension system...................................................................................................5
1.3 Active suspension system............................................................................................................6
1.4 Problem definition.......................................................................................................................7
2 Literature review................................................................................................................................7
2.1 Controller Implementation in different types of suspension systems.........................................7
2.2 Actuation systems......................................................................................................................10
2.3 Modeling using Bond graphs.....................................................................................................12
2.4 The quarter car model...............................................................................................................13
2.5 Controller design and Simulink model.......................................................................................15
6 References........................................................................................................................................18

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1 Introduction
A key issue in the design and manufacture of modern automobiles is passenger
comfort and satisfaction. A vehicle suspension system is a mechanism that physically isolates
the body of the vehicle from its wheels. Road or trajectory irregularities such as bumps and
potholes can cause a lot of vibrations making the ride very uncomfortable. Vibrations have
harmful effects on the passenger, including induced back pains, hyperventilation, and
osteoarthritis. They also have detrimental effects on the vehicle itself such as disc slipping.
The achievement of a high performance suspension system requires the consideration of
several performance characteristics related to force distribution, suspension and body
movement (Yerrawar, and Arakerimath 2017). The ideal suspension system should be
capable of isolating the vehicle’s body from the road and inertial disturbances related to
cornering, accelerating and braking (Mitra, Jawarkar, Soni, and Kiranchand 2016). In
addition, the suspension mechanism should be capable of minimizing the vertical force
transmitted to the passenger’s seat. To achieve this objective, it is necessary to minimize the
vertical acceleration of the vehicle. An excessive wheel travel results in non-optimum altitude
of the tires relative to the ground, leading to poor contact. The maintenance of good vehicle
handling properties requires maintaining the optimum contact between the tires and the
ground. Conventional vehicle suspension systems have conflicting characteristics and
therefore fail to meet all the requirements.
According to Deng & Lai (2010), suspension systems can be classified into three
broad categories. These include passive, semi-active and full-active suspension systems.
Passive suspension systems are constructed from conventional components with spring and
damping characteristics that are time-invariant. Springs are passive elements and they can
only store energy corresponding to a part of the suspension cycle while dampers dissipate
energy. Passive suspension systems have no direct supply of external energy. Semi-active

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suspension mechanisms utilize springs and damping elements whose characteristics can be
altered using an external controller (Reddy et al. 2016). Fully active or simply active systems
utilize actuators to produce the desired forces in the suspension mechanism. The actuators
used are usually hydraulic cylinders that derive power from an external supply. The figure
below shows the three types of suspension mechanisms.
Figure 1: The different vehicle suspension mechanisms
1.1 Passive suspension systems
The control of the dynamics of many vehicles’ vertical motion, roll (tilting) and pitch
(spinning) is achieved through the use of passive suspension mechanisms. Passive is a term
that suggests that the elements used in the suspension mechanism do not provide energy to
the system. The system is made up of a spring and a damper which are then mounted at each
of the vehicle’s wheels. The purpose of the spring is to support the body of the vehicle and to
absorb and store energy. The damper on the other hand (also called shock absorber) has the
task of dissipating the vibrational energy stored in the spring and to control impulses from the
road that are transmitted to the vehicle. In addition, the suspension mechanism isolates the
sprung mass from the unsprung mass vibration which provides directional stability during
cornering (Reddy et al. 2016).

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1.2 Semi-active suspension system
The semi-active suspension system represents an improvement in the passive
suspension system. The two mechanisms have some similarities but the semi-active can
produce better performance characteristics. This type of suspension mechanism has a spring
and a damper that can be controlled to dissipate energy. According to Deng & Lai (2010),
some semi-active systems utilize a controllable spring and a passive damper due to the
limited ability of the controllable damper to yield a controlled force while dissipating energy.
An advantage of the semi-active system is its lower operating cost compared to the active
system since it consumes only a small amount of energy. Figure 2 below shows a semi-
active suspension system with a controllable damper.
Figure 2: Semi-active suspension system
The semi-active suspension system with a controllable damper can only alter the damping
coefficient of the shock absorber and has no ability to add energy to the system (Hanafi,
2010). The most commonly used semi-active control devices include magneto-rheological
(MR) dampers. These devices are capable of yielding high damping forces while consuming
very little energy.

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1.3 Active suspension system
As can be observed in figure 1 above, in the active suspension system, both the
passive components (spring and damper) are replaced with a force actuator. The force
actuator is cable of both energy dissipation and energy addition into the system, unlike a
passive damper mechanism. With this mechanism, a force can be applied independently of
the relative displacement or the velocity. According to Yerrawar, and Arakerimath (2017),
this model yields better results even with a compromise between vehicle stability and ride
comfort, as long as the correct control strategy is adopted. The figure below shows a
comparison of the performance of both passive and active suspension systems.
Figure 3: A comparison of the response characteristics of passive and active suspension
systems
The control for active suspension systems can be achieved through the use of four different
types of control mechanisms. These include the use of magneto-rheological damper,
electromagnetic control, solenoid actuation, and hydraulic actuation. The fully active
suspension system thus requires different components or elements such as actuators, sensors,

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accelerometers, control units, servo valves, and high pressure tanks for the control fluid. This
makes fully active systems more expensive than either the semi-active or passive systems.
However, their performance is superior as demonstrated in figure 3 above. The active
suspension system can be configured in two different ways depending on the linking between
the active part (controller) and the passive part (spring and damper). If the active and passive
components are linked in parallel, this results in the high-bandwidth configuration. On the
other hand, series linking results in a low-bandwidth configuration. The major advantage of
the high-bandwidth over low-bandwidth configuration is the ability to achieve control over
the suspension system in case the actuator fails to work satisfactorily.
1.4 Problem definition
Most commercial vehicles utilize passive suspension systems to control vehicle
dynamics such as pitch, roll and vertical motion. The suspension system controls the motions
of the vehicle’s body and wheels by limiting their relative velocities to a value that yields
satisfactory ride characteristics. However, passive suspension systems have conflicting
requirements regarding stability during vehicle handling and damping properties which
makes the system less effective. This problem may be addressed through the use of active
suspension systems which offer better performance with their superior ride and roll stability,
their ability to reduce the braking effect which may result in nose-diving or acceleration
which may cause the vehicle skid. This project investigates the application of active
suspension systems based on a quarter car model.
2 Literature review
2.1 Controller Implementation in different types of suspension systems
There are many studies on the application of active suspension systems using different
control techniques. These include proportional-integral-derivative (PID) control, LQR control

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and fuzzy sliding mode control (Yerrawar, and Arakerimath 2017). Lian (2012) showed
experimentally that active suspension systems offer superior performance compared to
passive systems. Their study also showed that the performance of the active system
deteriorates at higher frequencies (1 Hz and above). This is because force tracking becomes
more difficult at higher frequencies. Mohammadpour and Scherer (2012) investigated a
quarter car model using an analysis method based on parameter variation. Their simulation
results of the parameter variations established that the system’s resonance frequency was
highly dependent on the damping parameters. This means that the parameters of the damping
system have a great impact on ride comfort. They showed that comfort could be improved
through the use of a controller for the damper. Using a non-linear quarter car model, Dong,
Yu, Liao, and Chen (2010) showed that it was very difficult to maintain a high level of ride
comfort, handling, and control of the vehicle's body simultaneously using the conventional
suspension system.
Singh and Aggarwal (2017) used a vehicle model with 7 degrees of freedom and
active control to investigate the performance of a model utilizing a PID controller with the D
term of roll and pitch angles and he PID terms of suspension deflections. They showed that
the PID controller significantly improved the attitude control of the vehicle by lowering the
pitching and rolling motion in braking and cornering maneuvers. Ma and Chen (2011)
presented the use of adaptive active suspension mechanisms as a novel approach through
combined nonlinear backstepping techniques and parameter varying control. The lower level
adaptation control shapes the nonlinear properties of the suspension system a function of road
disturbances while the higher level control applies switching between the different nonlinear
properties considering conditions on the road.
Many studies have been conducted to investigate different methods that can be used
to improve the comfort of rides as well as improve mobility performance over wide terrain

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conditions (Agharkakli, Sabet, and Barouz 2012). Bhise, Desai, Yerrawar, Mitra, and
Arakerimath (2016) used a proportional-integral controller (PID) in combination with an
active suspension for a quarter car model of a passenger car in an effort to boost the vehicle’s
holding ability and ride comfort. The results of the study showed an improvement in the
system's response in terms of reduced overshoot of the sprung mass acceleration and
displacement in comparison with a passive system. They concluded that the performance of
the active system was better than that offered by a passive system. Kuber (2014) used
computer simulation (MATLAB and Simulink) to model the performance of an active quarter
car suspension system. To improve the performance of the system they used a PID controller
with manual tuning. They compared the performance specifications of the active system to
that of a passive system and concluded that PID control with proper tuning has the ability to
reduce the settling time for equivalent road inputs and the ability to lower the vertical
displacement of the body.
Ahmed, Ali, Ghazaly, and El-Jaber (2015) designed a PID controller for an active
quarter car model based on a hydraulic actuator for a passenger car. The aim was to improve
the vehicle’s holding ability and the ride dynamics, their results showed that the active
system was capable of improving ride comfort even at the resonant frequency. Using a step
input of 0.8 m, a reduction of about 25 % in the displacement of the sprung mass was
observed. This indicated an improvement in the ride dynamics as well as the acceleration of
the sprung mass which reduced by about 74.64 %. A major problem of this system was its
power consumption. Results showed that power consumption was at its minimum when
driving on a smooth road. Driving through rough roads was observed to demand more power
from the system as the hydraulic pump worked much harder.
According to Kuber (2014), active suspension systems offer much superior dynamic
performance compared to passive systems, with simulation results indicating that PID control

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is an effective control scheme. Gaur and Jain (2013) designed and applied PI and PID
controllers in the control of the suspension system of a quarter car model. They used
Simulink to compare the system’s response using Pi and PID controllers. The PI controller
achieved a peak overshoot of 0.0067 with a settling time of 5 seconds. The PID controller’s
performance was superior with an overshoot of 0.0048 and a settling time of 2 seconds. The
open loop system had an overshoot of 0.81 and a settling time of 38 seconds, which is quite
long. In another study, Wang, Chen, and Yu (2016) investigated the performance of active
and passive suspension systems for vehicle applications using a feedback controller for the
active system. To validate the model, they used both the quarter car and full car models. The
results confirmed the superior performance of the active system over the passive system.
They identified power consumption as the major practical difficulty in the implementation of
active suspension systems.
2.2 Actuation systems
According to Kuber (2014), the actual implementation of active suspension systems using
force actuators may be very complicated and it is not possible to neglect the interaction
between the actuator and the body of the vehicle. In addition, it is quite difficult to produce
an actuator force that approaches the magnitude of the reference force without the application
of force tracking techniques or inner loop control.
The active control mechanism in active suspension systems can be implemented
through various techniques which include hydraulic, pneumatic or electromagnetic systems.
These are usually mounted in parallel with a damper and a spring. Sim, Lee, Yoon, Choi, and
Hwang (2017) studied a hydro-pneumatic active suspension system for a full vehicle model.
Their aim was to investigate the effect of hydro-pneumatic actuation in active suspension
systems on the quality of vehicle rides compared to conventional passive systems, through

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simulation. The results showed that the performance of the hydro-pneumatic system was
superior as a result of its initial larger bandwidth which improves the ride comfort.
Patil, and Joshi (2014) both experimentally and through simulation, analyzed an
active quarter car suspension model with based on a hydraulic actuator. The active system
showed significant improvement in the comfort properties in terms of overshoot and settling
times over a wide range of excitation frequencies in the region close to resonance. However,
they noted the complexity of the system as its major drawback. Zhang, Smith, and
Jeyakumaran (2010) developed an active hydraulic suspension system utilizing oil as the
energy source to yield hydraulic pressure that counters the externally acting forces on the
vehicle. This gave the system the ability to control the movement of the vehicle continuously
and freely. The flexibility of this control technique enabled the provision of higher ride
comfort. In addition, the vehicle dynamics achieved were superior to those obtained using
conventional systems. According to Shafie, Bello, and Khan (2015), hydraulic actuators
exhibit nonlinear characteristics that develop from the effects of unwanted back pressure due
to reciprocal action that is observed between the hydraulic actuator and the vehicle
suspension. The nonlinear properties may also develop from the transient response of the
servo valve.
Klimenko, Batishchev, Pavlenko, and Grinchenkov (2015) developed an active
suspension system based on an electromechanical actuator for use in passenger car vehicles.
Their aim was to address the problems associated with pneumatic actuators. Using unit and
system tests on a model vehicle, they demonstrated the effectiveness of the actuator and the
possibility for use in high-speed train suspension systems. According to Klimenko,
Batishchev, Pavlenko, and Grinchenkov (2015), pneumatic systems face several drawbacks
which makes them unsuitable for application in economy vehicles. These include the demand

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for large amounts of compressed air and poor frequency response which may lead to
excessive vibrations in the vehicle.
2.3 Modeling using Bond graphs
According to Dridi, Salem, and Amraoui (2017) the quarter car suspension is can be a
heterogeneous system with mechanical, electrical and mechatronic components. This makes
the modeling of the dynamic behavior of such a system quite complex. For the representation
of the models and control laws for such a system, using the bond graph is the best approach.
This approach is based on the notion of energy transfer between subsystems (Najafi 2010). It
combines two variables namely effort and flow. A bond graph consists of four major groups
of elements. These include active, passive, power conserving and detector elements (Najafi
2010). Active components are the sources of effort represented by Se and flow represented by
Sf . These are the sources of input power into the system. Passive elements are grouped into
two categories, energy dissipating elements such as resistors and energy storage elements
such as capacitors. The power conserving elements consist of effort conservation junction ‘1’
and flow conservation junction ‘0’. These elements include transformers and gyrators.
Detectors or sensors are represented by De for effort sensors and Df for flow sensors (Emami,
Mostafavi, and Asadollahzadeh 2011). The figure below shows the highlighted bond
elements,