Semi-Active Suspension System Control Using Skyhook and Groundhook Controller

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ISSN: 2005-4238 IJAST 424

Semi-Active Suspension System Control Using Skyhook and Groundhook Controller

Ahmad O. Moaaz¹ and Nouby M. Ghazaly²

1

Mechanical Eng. Dept., Faculty of Engineering, Beni-suef University, Egypt

2

Mechanical Eng. Dept., Faculty of Engineering, South Valley University, Qena- 83523, Egypt

*Corresponding Author E-mail: [email protected]

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Abstract

The purpose of this research paper is to analyze the effect of skyhook and groundhook control strategies on a semi-active suspension system. Computer simulation of the quarter-vehicle model is conducted through MATLAB/SIMULINK. The ride comfort and handling characteristics of the suspension system are predicted for random road input by the mathematical model. The passive suspension system performance is compared with skyhook and groundhook controlled semi-active suspension system. The result shows that the groundhook control offers better ride comfort and handling as compared to skyhook and passive suspensions. Also, the results showed in the time domain, frequency domain, power spectral density, and root mean squares values.

Keywords:Quarter car model, semi-activesuspension System,skyhookcontrol, groundhook.

1. Introduction

Vehicle suspensions aim to isolate the vehicle body from road irregularities and to provide good road holding. The isolation of the vehicle body from road irregularities concerns the problem of how to achieve comfort to vehicle occupants.

Good road holding is concerned with the area of handling analysis. The handling is the ability of a car to accelerate, brake and corner safely [1-4]. The design aimed to decrease both the body acceleration and the dynamic tire load while operating within the constraints of suspension working space for a given suspension parameter set. The traditional passive suspension systems try to compromise between ride and handling. A very high damped suspension provides good handling, but cause passenger discomfort, that is unacceptable. On the other hand, a low damped suspension improves the ride comfort, but it reduces the vehicle stability A good control policy used in the active suspension system, the compromise between comfort and stability can be achieved [3].

Although, there is a large power required for active suspensions that make them too expensive for widespread commercial use. Semi-active dampers can change their damping characteristics using a small amount of external power. Semi-active suspensions are popular in commercial cars because of less complexity, more reliability, and cheaper than active suspensions. Semi-active suspensions were first introduced by Karnopp [7]. Many kinds of research have been carried out since then

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in the quarter, half and full car models. Semi-active control strategies researches focused primarily on linear systems, such as optimal control [6] and skyhook control [5-10], further nonlinear techniques also been applied by different researches [12].

This paper aims to investigation semi-active suspension systems with different controller’s approaches. The mathematical quarter-vehicle model under the random road is simulated using MATLAB/SIMULINK. The ride comfort and handling characteristics of the suspension system are obtained. The comparison between the passive suspension system performance using skyhook and groundhook controlled for semi-active suspension system are evaluated.

2. Quarter Vehicle Semi-Active Suspension Model

In this research a 2 DOF model is used to test the performance of skyhook, and groundhook on the semi-active suspension system.A semi-active damper vehicle suspension system showed in Figure 1. The assumption simulation parameters are mentioned in Table 1.The main equations of motionthat is considered in the mathematical model as following:-

𝑀_𝑤𝑥 _𝑤+ 𝑘_𝑠 𝑥_𝑤− 𝑥_𝑏 + 𝐶_𝑠 𝑥 _𝑤− 𝑥 _𝑏 + 𝐾_𝑡 𝑥₀− 𝑥_𝑤 = 0.0 (1) 𝑀_𝑏𝑥 _𝑏 + 𝑘_𝑠 𝑧_𝑤− 𝑧_𝑏 + 𝐶_𝑠 𝑥 _𝑤− 𝑥 _𝑏 = 0.0 (2)

Figure 1. A semi-active damper vehicle suspension system

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Table: 1 simulation parameters.

No Symbol Value

1 Mb(Body Mass) 320 kg

2 Mw(Wheel Mass) 45 kg

3 Ka 22000 N/m

4 Cs 1500 N.sec/m

5 Kt 192000 N/m

3. RoadProfile

In this research random road input are simulated as random road profile. A white noise road input signal should represent the real road condition when a vehicle drives on the road. Many researchers showed that when the vehicle speed is constant, the road roughness is a stochastic process that is subjected to Gauss distribution, and it cannot be described accurately by mathematical relations. The road profile in time domain is shown in the Figure 2.

Figure.2 Road roughness signal Simulink model

4. Controller Methods 4.1 SkyhookControllers

The damper is connected to the sky. If the suspension damper is expanding and the sprung body is moving towards, then Skyhook control turns the damper on and the damper pulls down on the sprung body. The difference between Skyhook and passive is that the Skyhook controller varies the damper force such that the damper force is equal to,

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𝐹_𝑠𝑎 = 𝐺_𝑠𝑘𝑦 ∗ 𝑥_𝑠 ; 𝑖𝑓 𝑥_𝑠 𝑣_𝑠𝑢 > 0

𝐹_𝑠𝑎 = 0 ; 𝑖𝑓 𝑥_𝑠 𝑣_𝑠𝑢 < 0 (3) Where,

𝐹_𝑠𝑎 = Desired damping force, N 𝑥_𝑠 = Sprung-mass velocity, m/s

Vsu = 𝑥_𝑠 - 𝑥_𝑢 ; Relative velocity between sprung & unsprung-mass, m/s 𝐺_𝑠𝑘𝑦 = Skyhook gain, N/m/s

4.2 GroundhookController

An alternative semi-active control policy, groundhook control to take advantage of the benefits of both. With groundhook control, the generated forces are added to the passive vehicle model which used as a reference on active suspension controller design.

𝐹_𝑔𝑎 = 𝐶_𝑔 ∗ 𝑥_𝑢 ; 𝑖𝑓 − 𝑥_𝑢 𝑣_𝑠𝑢 > 0

𝐹_𝑔𝑎 = 0 ; 𝑖𝑓 − 𝑥_𝑢 𝑣_𝑠𝑢 < 0 (4) Where,

𝐹_𝑔𝑎 = Desired damping force, N 𝑥_𝑢 = Unsprung-mass velocity, m/s

Vsu = 𝑥_𝑠 - 𝑥_𝑢 ; Relative velocity between sprung & unsprung-mass, m/s 𝐶𝑔 = Groundhook gain, N/m/s

5. Simulink Model on Matlab

Simulink model of suspension system passive and semi-active suspensionsare shown in Figure3.

Figure.3. Simulink ofpassive and semi-active suspension system using skyhook and groundhook control.

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6. Results and Discussions

Performances of the suspension system in terms of ride comfort and car stability will be shown. A random road disturbance is assumed to be the input for the system.

The vehicle ride Parameters are body acceleration, suspension working space, and the vehicle tyre load. The aim is to achieve a better vehicle ride comfort. Figures from 4 to 11 represent the body acceleration, suspension working space and dynamic tyre load in the time domain, frequency domain, and power spectral density. The figures showed that the semi-active suspension system using groundhook gives better ride comfort compared with a semi-active suspension system with skyhook control. Also, the semi-active suspension system with groundhook and skyhook controllers gives better ride comfort than the passive suspension system.

Fig.4. Body acceleration (Ride comfort) in time domain

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Fig.5. Body acceleration (Ride comfort) in frequency domain

Fig.6. Body acceleration (Ride comfort) in power spectral density

Fig.7. Suspension working space (road handling) in time domain

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Fig.8Suspension working space (road handling) in frequency domain

Fig.9. Suspension working space (road handling) in power spectral density

Fig.10. Tyre loadin time domain

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Fig.11. Tyre load in frequency domain

Fig.11. Tyre load in power spectral density Table: 2. Reduction in R.M.S values different parameters (random road)

No Parameter Passive Skyhook Groundhook % Reduction Skyhook Ghook 1 Car body

acceleration

0.622 m/s^2

0.378 m/s^2

0.33 m/s^2 24 29

2 Suspension travel

0.0052 m 0.004 m 0.0006 m 22 80

3 Wheel deflection

346.7N 203.1N 137.8N 40 60

The R.M.S values for the passive and active suspension systems, as in Table (2)indicates thatsemi-active suspension system using skyhook and groundhook controlgives better ride performance than passive suspension system.

7. Conclusion

Mathematical modelling has been performed using a two degree-of-freedom model of the quarter car model for passive and active suspension system considering only bounce motion to evaluate the performance of suspension with respect to various contradicting design goals. Skyhook and groundhook Control design approach has been examined for the semi-active system. Semi-active suspension using groundhook controller gives better ride comfort and stability than skyhook controller. The semi-active system using groundhook and skyhook controller gives better ride comfort and stability than passive suspension system.

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References

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[20] Md Kaleemullah, WaleedF. Faris, Nouby M. Ghazaly “Analysis of Active Suspension Control Policies for Vehicle using Robust Controllers” International Journal of Advanced Science and Technology Vol. 28, No. 16, (2019), pp. 836 – 855.