Design and Control of a Full-Scale Quarter Car Test Rig for Semi-Active Suspension System

- Passive hydraulic dampers are commonly used in the automotive suspension system. Nevertheless, they are suffering from a significant drawback owing to the changing of its characteristics at high-frequency; as a result, decreasing the ride quality due to the increase of the transmitted force, especially at high frequency excitations. The present work developed a semi-active suspension system to solve this problem with its effect. A Sky-hook control strategy is used to suppress the positional oscillation of the sprung mass in the presence of road irregularities via the use of the electrohydraulic (EH) damper, as an objective. In order to apply the control strategy used herein, a full-scale quarter-car test platform has been designed and constructed to offer increased testing flexibility at a reasonable cost not found commercially. MATLAB Simulink is applied for modeling the semi-active suspension system. The control strategy using a Sky-hook control was used to enhance the comfort due to the simplicity of this method that can easily be implemented in a real-time embedded application. The control strategy is evaluated for its performance under the road bump excitation. The experimental results were compared with the simulated ones for both passive and semi-active suspension systems, the comparison includes time response analysis of body vertical displacement, and vertical displacement of quarter car structure.


Introduction
The primary function of the suspension system is to isolate the frame of the vehicle from road irregularities.A distinctive car with a suspension system is needed to maintain a regular contact between the road and the tires of the vehicle.The damper is considered as a highly significant element of this system.It decreases the results of an unanticipated bump on the road via reducing the roughness of shock.In the majority of absorbers of shock, the energy of vibration is first changed to heat and then dispelled into the surrounding.In a viscous damper, the energy is transformed into heat by a viscous fluid.In the hydraulic cylinders, the fluid becomes hot [1].Vibration control techniques are widely categorized into three types of controls, including passive, semi-active, and active controls.A passive system of suspension is a control system considered as an open loop to conduct only a specific state, therefore the characteristics of this kind of suspension are fixed and cannot be modified by any mechanical component, and road irregularities are transformed considerably.Although considering the tire damping has a slight effect on the wheel-hop vibration, the ignorance of damping in tire models compelled the misleading conclusions that at the wheel hop frequency.Moreover an active suspension possesses an enhanced suspension performance by getting a force actuator, which is a control system having a closed-loop [2].The semi-active suspension system gains popularity in the automotive suspension system due to its higher efficiency and advantageous features over the passive one.Within the systems of semi-active suspension, the properties of damping of a damper are modified to a certain extent.The modified properties in the semi-active dampers are performed through a diversity of technologies, as piezoelectric actuators, electrorheological (ER) and magnetorheological (MR) fluids, and solenoid valves.It has been broadly recognized that a system of semi-active suspension gives higher efficiency than a passive type system [1].In recent years, the popularity of semi-active suspension attracted much interest to many researchers, e.g., the semi-active system that used the magnetorheological damper (MRD) that has the adjustable controlled force that varies with the current.Other kinds of semi-active control algorithms are, e.g, sky-hook control, state-based control algorithms [3], which successfully applied to vibration control of vehicle suspension systems.Other researchers tackled the nonlinearity of MR damper dynamics by using different control strategies such as neural networks, fuzzy logic, and sliding mode control [4,5].The main objective of the present work is to design and manufacture a test rig platform to check the performance of the automotive semiactive suspension system.The control strategy used was a Sky-hook control to suppress the positional oscillation of the sprung mass in the presence of road irregularities via the use of the electrohydraulic (EH) damper.

Manufacturing of Test Rig
The purpose of the manufactured test rig is to construct a full-scale platform test rig to study the performance of the independent automotive suspension system.Figure 1 shows a SolidWorks model of the test rig with its primary components.The dimension of the base plate used in this design is 110 cm × 70 cm × 10 cm; the purpose of it is to build a steel base plate for the rig.The base has a trolley guide slot that carries the bump, which allows it to move in a linear motion.The trolley is connected to a pneumatic cylinder and moved by a specific distance along with the piston.

Measuring Devices
There are two reasons for using accelerometers.Firstly, an acceleration signal is used as an indicator for ride comfort.Secondly, the car body and wheel unit velocity need to be measured and used in feedback control.Theoretically, a velocity signal could be obtained from an acceleration signal by an analog or digital integrator.

Determining Damping Coefficient
The damping coefficient is determined by relating the damper forces characteristics with their compression and extension velocities.However, the essential parameters stated by these characteristics is by correlating it with the ride and handling quality, which represents an overall mean damping coefficient [6].As the electrohydraulic (EH) manufacturer data was not available, a test rig was constructed to determine the damping coefficient experimentally.This test rig is shown in Figure 2, and Figure 3 shows the experimental results.

Quarter Car Mathematical Model
In this paper, the theoretical analysis is based on a 2-DOF quarter car model; the model considered linear behavior within the suspension spring and damper forces that have a vital influence on the responses of the suspension when excited by completely different road inputs [7].Consider a simple model of quarter car, shown in Figure 4, made up of a sprung mass (m s ) and an unsprung mass (m us ).Spring with the stiffness coefficient k s and a semi-active damper connected both masses.
A spring modeles the wheel tire with the stiffness coefficient k t .In this model, z 1 and z 2 are the vertical position of m us and m s , respectively.In Figure 4, the free body diagram leads to the following mathematical equations of motion: This can be used to get a state-space representation [8] described in the following section.
Of which State space equation can be written as form, where,

Control Methods
Better controller design significantly improves the vehicle ride and handling.In this paper, the sky-hook control strategy is used to adjust the damping force so that improving the suspension dynamics.The Sky-hook control is the most widely used controlling algorithm insensible and covers some types of scientific domains [9].

Sky-hook Control Method
The sky-hook control is one of the most effective control algorithms due to its simplicity.The skyhook can reduce the resonant peak of the vehicle sprung mass significantly; as a result improved ride quality, this is performed by adjusting the skyhook damping coefficient as the vehicle body velocity, and other conditions are changing, the adjustable damping ranges between hard and soft envelopes [10,11].The approximation to an ideal sky-hook can be expressed by the following control logic [12][13][14].
Where,   is the force applied to the sprung mass.As the force in the proper direction can be

Numerical Simulation
The effectiveness of the suggested control strategy is studied using MATLAB; the purpose is to explore the effect of different system parameters on the sky-hook control law.The main objective is to increase or to evaluate the passenger ride comfort during the traveling of the vehicle under bump type road excitation.
Simulation by MATLAB m-file was achieved in the time domain for both passive and semi-active (controlled) of the quarter car suspension systems using On/Off Sky-hook controllers.The simulation run time was set to 10 s, and the vehicle traveling speed is considered to be 20 km/h, as shown in Figure 5.   Figures (8 -9) show the experimental results of the semi-active suspension using the control technique Sky-hook.Figure 8 illustrates the sprung mass displacement representing the body of the car, where the maximum overshoot is 0.023/m at the time of 4.6 seconds, and the maximum undershoot is -0.008m at the time of 5 seconds.Because of the continuous Sky-hook on/off control method note the descent of the line is a breaker unlike the semi-active system without control.Also, the system stability time is 5.3 seconds less than the time of the semi-active system without control.Figure 9 demonstrates, the acceleration amplitude, the peak value is reduced to 39% percent and also the settling time is reduced, giving better ride performance.Figure 10 shows the comparison between a semiactive controlled suspension system and the other semi-active suspension system without control experimentally.It was observed through the form that the control technique used reduced the maximum overshoot to 20% and also reduced the stability of the semi-active suspension to 27%.

Conclusion
The conventional sky-hook offers the best performance at low frequencies close to the first mode of resonance and reasonably good performance at higher frequencies as well.From the result of the simulation, the semi-active suspension reduced the peak amplitude and settling time to 53% and 67%, respectively than the passive suspension.Also, the performance of the semi-active suspension under the control effect gives better performance than the semiactive uncontrolled system.

Figure 1 :
Figure 1: Quarter Car Test Rig

Figure 10 :
Figure 10: Comparison between experiment and theoretical results.

Table 1 : Test results of deep beam specimens
X 1 =Z 1 , X 2 =Z 2 , X 3 =Z 1 ' , X 4 =Z 2 ' , then the system state equation can be expressed as: