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The whole purpose of the suspension system as a whole, is to basically separate the body of the vehicle from sudden shocks or vibrations (speed bumps, holes, etc.) that would be transferred to the passengers. The suspension system must also keep the tires of the car on the road, regardless of the roads surface. Any basic S.S. consists of the following: springs, axles, shock absorbers, arms, rods, and ball joints. The spring acts as the elastic component of the S.
S., with basic types of springs such as leaf springs, coil springs, or even torsion bars.
Almost all of the vehicles being used by civilians as transportation usually use light coil springs. Other commercial vehicle use heavier springs than those used for the passenger vehicles, and can also contain coil springs for frontal use and leaf springs for rear use. Other heavy vehicles frequently use leaf type springs, or even air suspension. Wheels on each side of the vehicle are connected using either solid or beam axles, meaning that the movement on one side of a vehicles wheel, is then transferred to the wheel on the parallel side.
Independent suspension on the other hand, moves the wheels independently of each other, and this reduces the movement of the body. The independent suspension prevents any wheel by being affected by movement from the initial wheel, which also reduces movement of the car body. When a wheel on a vehicle hits a speed-bump, a reaction force takes place, and that energy is then transferred onto the spring, which then oscillates, but oscillation that is not contained may cause the vehicles wheels to loss traction with the road.
In this case, shock absorbers act as dampers for the oscillation that occurs on the springs, by forcing oil introduced, using small holes. The oil that is introduced, heats up when it absorbs the motions energy, and the heat that is generated is then transferred throughout the body of the absorbers into the atmosphere. Whenever a vehicle hits an obstacle, depending on the un-sprung mass at every wheel assembly, the size of the reaction force occurs. The sprung mass denotes the parts of the vehicle that are supported on the springs, including the body, engine, frame and many other associated parts.
Other parts such as the wheels, brakes, tired, suspension parts are the un-sprung mass, meaning they are not supported by the installed springs. Whenever the un-sprung mass is low the vehicle handling and the ride as a whole, improves, and the opposite is true. Wheel and brake units that are small and light follow the road contours without a large effect on the rest of the vehicle.  The three types of suspensions that exist are the passive suspension system (which refers to the dampers and springs being used), semi-active suspension systems, and active suspension systems.
Suspension system: Is a mechanical system of springs and shock absorbers that connect the wheels and axles to the chassis of a wheeled vehicle. (7)
Semi Active suspension system includes a sensor that identifies bumps on the road and movements of the vehicle, and a controller that control the damper on each wheel. The semi active suspension can react to even minor variations in road surface and to cornering.  A well-controlled suspension system will provide high vehicle handling, decent driving pleasure, and great comfort for passengers, and good separation from road noise and vibration. In order to improve the comfort and handling of light-weight transportation vehicles, the semi-active suspension systems is a considerable issue and had been proposed in a number of papers. The semi-active suspension system requires fewer space than traditional suspension systems.
Therefore, it is appropriate for a compact car body known as light vehicles. Moreover, the system complication and maintenance caused by difficulty of assembly will be condensed. 
The concept of a semi-active suspension is to replace active force producers with continually adaptable elements which can vary/or change the rate of energy dissipation in reaction to an immediate condition of motion. 
A method that can be used to remove the balance between the resonance control and the high frequency isolation, requires a slight change in the configuration setup of the entire suspension system. As seen in figure 4 below, the damper is moved from between the mass and the base to the new location shown. From the figure below, the damper is now connected to a reference which in this case is a ceiling which will remain fixed vertically, that is relative to the ground reference. The following configuration is a fictional one, since the damper has to be attached to a reference in the sky, which will remain in the vertical direction, but will also be able to render within the horizontal direction too.
The traditional suspension system is a passive system that once mounted in the car, its character barely change. Alternatively an active suspension system is capable of continuously monitoring and regulating itself to the changes in the road conditions, thus changing its character on an ongoing basic. Using sensors and microprocessors to feed itself all the time its character remains flexible, circumstantial and shapeless. The active suspension systems provides remarkable handling, responsiveness and safety. An active suspension system is comprised of an electronic control unit, adjustable springs and sensors across the body of the car and the wheels, and an actuator.
Such components differ marginally from company to company, but these are the main components that an active suspension system consists of. As the car is moving down the road surface, the active suspension continually senses changes in the surface of the road and sends these information using the ECU to the remote components. Simultaneously the system starts to adjust its shock stiffness, spring rate and other parameters to improve the receptiveness, drivability and the overall ride performance. The human body could be used as an analogy of the active suspension system, the sensors see, feel, hear and taste the road surface then sends these information the ECU which would represent a human mind, which then gather, sort, understand, evaluate the sensory input and send the orders to the components of the system. In our system the wires act as the central nervous system, delivering the orders from the ECU – mind- to the rest of the components.
Finally the servos and actuators resemble the muso-skelatal of the human body. They carry the commands given to them by the ECU to adapt to the road. In a car with a conventional suspension, potholes present a problem to the suspension system. The potholes could even set the system up in an oscillation loop-a scenario where the car starts moving up and down higher and higher and gets out of control. In a car with an active suspension system that is turning left the sensors on the right side of the turn would begin to pick up yaw and transverse body motion, sense the extreme vertical travel and then deliver that data back to the ECU.
The ECU then compiles and analyzes the date in an average time of 10 milliseconds and sends a command to the servo atop the right front coil spring to increase its stiffness. An oil pump working at almost 3000 pounds per square inch feeds additional oil to the servo to increase the tension, thus decreasing the body roll, yaw and spring oscillation. Another command is sent to the servo atop the right rear coil springs making it increase its stiffness but to a lesser extent. Simultaneously another group of actuators briefly increases the rigidity of the suspension dampers on the right front and rear corners of the car, making the vehicle slide through the turn smoothly and comfortably. 
An active suspension system is capable of decreasing the acceleration of sprung mass along with minimizing the suspension deflection, which improves the tire grip with the road surface thus improving brake, traction control and vehicle maneuverability. Conventional suspension systems shown in Fig 6 can either attain driver’s luxury or good road holding since these two standards require different spring and damper characteristics. Semi-active suspension systems have variable damping characteristics and low power consumption thus providing an improvement when compared to the conventional systems; however an active suspension system fig 2 offers a noteworthy improvement, which produces suspension forces to acquire the desired performance. 
The active suspension model shown in fig 8 is made up of three plates, each of them slides along stainless steel shafts using linear bearings and is supported by a set of springs. The uppermost plate symbolizes the car’s body that is supported above the suspension, it is also known as the sprung mass. The central plate resembles the vehicle’s tire, also known as the un-sprung mass. The bottommost plate mimics the road surface.
The uppermost plate is attached to a DC motor using a capstan to imitate an active suspension system that consistently make up for the fluctuations presented by the road. The bottom most plate is also driven by a DC motor that is attached to a lead screw and a cable transmission system. It is used to mimic different road profiles. 
Only quarter of the car is considered in this preliminary modelling of the different suspension systems. The elasticity of the tire was considered as a spring connected to the wheel mass, which is then connected to one of the three suspension systems discussed. The passive suspension system consists of a fixed spring and a fixed damper, while the semi-active suspension system consists of a fixed spring and a controllable damper that varies with time, by using skyhook control system. This is done by the help of sensors in order to identify the road profile.
Regarding the active suspension system, it consists of a fixed spring, da force generator. The force generator is used to oppose the force exerted by the damper and thus allowing for better control according to the road conditions.  The three types of suspension systems were modelled and the free body diagram for each of them was drawn. Using Newton’s Second Law (F = ma) the equations of motion were derived and then the Laplace transform of each was solved for. Using Matlab, the Laplace transform equations are used to get the response in the time domain.
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