1721
Fuzzy and PID Controlled Active Suspension System and Passive Suspension System Comparison
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]
,Abstract
Suspension system mainly is referred to the system of springs, shock absorbers and linkages that connects a car to its wheels Suspension systems perform a dual purpose firstly maintain the vehicle's road holding /handling and braking for good active safety secondly keeping vehicle ride comfort by isolating the passenger from road noise bumps and vibrations etc. This research is aim to design quarter vehicle active suspension control model subjected to vibration excitation from a random road profiles using fuzzy logic control and PID. The vehicle active suspension system in this paper is controlled using fuzzy and PID controls for a quarter vehicle model. The active suspension systems performance is compared with the passive one to show the improvements. The performance of the Fuzzy and PID controlled suspension systems are evaluated mathematically using the MATLAB and SIMULINK toolbox. It is found that fuzzy active suspension system controlled and PID suspension system controlled give improvements in the ride comfort compared with passive suspension. Finally, the results showed in time domain, frequency domain, and power spectral density and root mean squares values also showed.
Keywords: Quarter car model, Active suspension System, Fuzzy control, Road profile.
1. Introduction
Vehicle ride comfort and handling represent two important criteria in a passenger vehicle which is related to driver discomfort, and safety. The suspension systems main function is to reduce the vibration excitations then, improve ride performance [1, 2]. Conventional passive suspension system consists of spring and damping.
The components of passive suspension system are fixed and cannot be adjusted by any mechanical part. The problem of passive suspension is, that a lot of road vibrations will be transferred to the passengers [3]. Also, in order to improve the passenger ride comfort, the passive the elements (springs and dampers) must be selected carefully in soft part, but to increase the comfort of the passenger the passive elements must be selected in harder part [4,5]. So, the suspension specifications of the suspension systems must be varied to face the road conditions.
Therefore, several semi-active, and fully active suspension approach have been designed and built to solve this problem.
The preview control of quarter car active vehicle suspension model improves the ride performance [6]. Also, the optimal control used for a quarter car semi-active suspension system was presented [7]. Various control strategies recently, are applied to control active suspension system.
Linear Quadratic Gaussian control, adaptive control, robust control, and non-linear control are designed, developed and proposed to deal the occurring problems [8, 12]. Recently, Control systems such as H2, H8, GL2, GH2, GA, etc. used in vehicle suspensions attracts more attention [13: 15].
Fuzzy logic control and PID controller approach has been fruitful research area with semi-active and active suspension system [16: 21]. The aim of this paper is to study the performance of automotive active suspension system using different control systems such as, Fuzzy and PID control and compared them by passive suspension only.
Firstly construct a mathematical model for the passive and active quarter car suspensions systems subject to vibration from a road profile using Fuzzy and PID control.
The evaluation of vehicle suspensions systems depend on two main parameters, the first is providing good road handling and the second is improving Passenger comfort. The performance of the Fuzzy,
PID controlled car active suspension system is compared with the passive one. The performance of this controller will be determined using computer simulations programs such as, the MATLAB SIMULINK toolbox.
Figure 1.Quarter car model (a) Passive suspension (b) Active suspension
2. Mathematical Modelling of Active Suspension
Adding hydraulic actuators to the passive components is to obtain the active suspension systems of suspension system as shown in Figure 1. The advantage of such a system is that, if the control system stopped, the passive components perform the action. The equations of motion are written as,
(1) (2)
Active suspension system:-
(3)
(4)
Where ua is the control force from the hydraulic actuator 3. Road Profile
In this paper 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.
K
sK
tC
sMb
M
wX
bXw
X
0K
sK
tC
sU
a MbM
wX
bXw
X
01723
0 1 2 3 4 5 6 7 8 9 10
-4 -3 -2 -1 0 1 2 3 4 5 6x 10-3
Time,s
S,m
Figure 2 Road roughness
Table: 1 Passive and active suspension system parameters.
No Symbol Value
1 Mb 320 kg
2 Mus 40 kg
3 Ka 17000 N/m
4 Ca 1000 N.sec/m
5 Kt 170000 N/m
6 Β 1 sec-1
4. Passive Suspension System
The Simulink model of passive suspension system is shown in Figure-3.
Figure 3 Simulink of passive suspension system.
5. Controller Design 5.1 PID controllers
The PID controller is the most common control of feedback found in all fields where a control is used, as shown in Figure 4. The PID algorithm is described by:
(5)
Where, y is the measured process variable, r is the reference variable, u is the control signal and e is the control error ( ). The reference variable is often called the set point ( ).
The control signal is thus a sum of three terms: the P-term (which is proportional to the error), the I- term (which is proportional to the integral of the error), and the D-term (which is proportional to the derivative of the error). The controller parameters are proportional gain K, integral time , and derivative time ( ) . In general form the PID algorithm can be represented by the transfer function below:
(6)
Figure 4 Block of the quarter car PID controller 5.2 FUZZY logic controller
Fuzzy logic control (FLC) algorithm feeds a means of converting a linguistic control technique and it is commonly employed in vehicle applications. In this work, the application of fuzzy logic technique to plan a controller for the active vehicle suspension system to improve the suspension system performance is presented.
The steps in designing fuzzy logic controller are as follows: Gaussian membership functions are defined for each variable that are used to fuzzify inputs and output of suspension system. Linguistic variables assigned to these fuzzy sets are, NB, NM, NS, ZE, PS, PM and PB. Total 49 rules are made. Mamdani type inference method and centroid defuzzification method are used. Output of fuzzy controller is actuator force based on two inputs i.e. the sprung mass acceleration error and the corresponding rate of change of velocity of the suspension system. Fuzzy control rules are made in the form of table II of the designed fuzzy logic controller.
Table 2 Fuzzy control rules
Acceleration (error)
PB PM PS ZE NS NM NB
Velocit y (error rate)
PB PB PM PM PM PM PS ZE
PM PM PM PM PS PS ZE NS
1725
PS PM PM PM ZE ZE NS NM
ZE PM PM PS NS NS NM NM
NS PS PS ZE NM NM NM NM
NM ZE ZE NS NM NM NM NM
NB ZE NS NM NM NM NM NM
6. SIMULINK Model on Matlab
Simulink model of suspension system passive and active suspensions are shown in Figure 5.
Figure 5 Passive and active suspension system using Fuzzy and PID control Simulink model.
7. Results and Discussions
Simulation based on the mathematical model for quarter vehicle using MATLAB/SIMULINK software will be performed. The vehicle ride comfort parameters will be observed. The parameters are the suspension working space, wheel deflection, and the body acceleration for quarter vehicle model. The aim is to reduce value for suspension travel, wheel deflection and the body acceleration. Figures from 6 to 14 represent the acceleration, suspension working space and dynamic tyre deflection in time domain, frequency domain and power spectral density. From Figures, the active suspension system using fuzzy control gives better ride comfort than active suspension system with PID control. Also, the active suspension system with Fuzzy and PID controller give better ride comfort than passive suspension system.
Figure 6 Sprung mass acceleration in time domain
Figure 7 Sprung mass acceleration in frequency domain
Figure 8 Sprung mass acceleration in power spectral density
Figure 9 Suspension working space in time domain
1727 Figure 10 Suspension working space in frequency domain
Figure 11 Suspension working space in power spectral density
Figure 12 Tyre deflections in time domain
Table: 3. Reduction in r.m.s values different parameters (random road)
No Parameter Passive Active (PID) Active (Fuzzy) % Reduction Fuzzy PID 1 Car body acceleration 1.791 m/s^2 0.9021 m/s^2 0.6295 m/s^2 65 50
2 Suspension travel 0.02118 m 0.0197 m 0.01275 m 40 7
3 Wheel deflection 0.006038 m 0.005564 m 0.005484 m 40 45
Figure 13 Tyre deflections in frequency domain
Figure 14 Tyre deflections in power spectral density
The r.m.s values for the passive and active suspension systems, as in table (3) indicates that active suspension system using sliding mode control gives better ride performance than passive suspension system. Active suspension system using Fuzz and PID control give better performance in comparison with passive suspension system.
8. Conclusions
A controller was designed for active suspension for a passenger car to improve the performance of the system with respect to passive suspension system. A two degree of freedom model for passive and active suspension system are used as a mathematical model. Fuzzy and PID control design approach has been applied and examined for the active suspension system. It is found that the active
1729 suspension system provide a better ride comfort compared with passive one. Also the fuzzy active suspension system gives better ride comfort than the PID controlled active suspension system.
References
1. Robert L.W. & Kent L.L., “Modeling and Simulation of Dynamic System”, Second Edition, Prentice-Hall, 1997.
2. Chen H.Y. & Huang S.J., “Adaptive Control for Active Suspension System” International Conference on Control and Automatic. June. Budapest, Hungary: 2005.
3. Aldair, A & Wang, W. J. “Design an Intelligent Controller for Full Vehicle Nonlinear Active Suspension Systems, International Journal on Smart Sensing and Intelligent Systems, 2011, ,vol.
4, no. 2, 224-243.
4. Fatemeh Jamshidi. & Afshin Shaabany. “Robust Control of an Active Suspension System Using H2 & H∞ Control Methods, Journal of American Science, 2011, 7(5), pp.1-5.
5. Nouby M. Ghazaly, Ahmad O. Moaaz “The Future Development and Analysis of Vehicle Active Suspension System” IOSR Journal of Mechanical and Civil Engineering, Volume 11, Issue 5 Ver. V (Sep- Oct. 2014), PP 19-25.
6. Karnopp, D. (1986). Theoretical limitations in active vehicle suspensions, Vehicle System Dynamics, Vol. 15, pp. 41-54, ISSN 0042-3114.
7. S. Mouleeswaran, Development of Active Suspension System for Automobiles using PID Controller, Proceedings of the World Congress on Engineering 2008 Vol II WCE 2008, July 2 - 4, 2008, London, U.K.
8. V. S. Deshpande, S. B. Phadke, "Sliding Mode Control of Active Suspension Systems Using an Uncertainty and Disturbance Estimator", Computational Intelligence and Information Technology, Volume 250 of the series Communications in Computer and Information Science, pp. 15-20, November 7-8, 2011, doi: 10.1007/978-3-642-25734-6_3.
9. Zhou, Q., Research and Simulation on New Active Suspension Control System. 2013.
10. Bin Nawawi,Zulkifli.“Vibration investigation for passenger car with different damping characteristic on car suspension systems”, Faculty of Mechanical Engineering Universiti Malaysia Pahang, B.Sc. Thesis, 2012
11. Šehović, Jasmin and Pikula, Boran.“Analysis of effects of vehicle suspension system stiffness and damping on oscillatory comfort”, International Journal of Engineering & Scientific Research, Volume 3, Issue 12, 2015
12. Lajqi,Shpetim andPehan, Stanislav.“Designs and Optimizations of Active and Semi-Active Non- linear Suspension Systems for a Terrain Vehicle”, Strojniškivestnik - Journal of Mechanical Engineering 58(2012)12, 732-743, 2012
13. M. M. M. Salem and A. A. Aly, “Fuzzy control of a quarter-car suspension system,” World Acad. Sci. Eng. Technol., vol. 53, pp. 258-263, 2009.
14. J. Fengi, J. Li, F. Yui, “GA-based PID and fuzzy logic control for active vehicle suspension system,” International Journal of Automotive Technology, vol. 4, pp. 181-191, 2003
15. D. Lee, J. Allan, H. A. Thompson, and S. Bennett, “PID control for a distributed system with a smart actuator,” Control Eng. Pract., vol. 9, pp. 1235-1244, 2001.
16. I. Eski and Ş. Yıldırım, “Vibration control of vehicle active suspension system using a new robust neural network control system,” Simul. Model. Pract. Theory, vol. 17, pp. 778-793, 2009.
17. J. Wang and D. A. Wilson, “Mixed GL2/H2/GH2 control with pole placement and its application to vehicle suspension systems,” Int. J. Control, vol. 74, pp. 1353-1369, 2001.
18. W. Abbas, O. B. Abouelatta, M. El-Azab, M. El-Saidy, and A. A. Megahed, “Optimal Seat Suspension Design Using Genetic Algorithms,” J. Mech. Eng. Autom., vol. 1, pp. 44-52, 2011.
19. Nouby M. Ghazaly, Abd El-Nasser S. Ahmed, Ahmed S. Ali and G.T. Abd El- Jaber “H∞
Control of Active Suspension System for a Quarter Car Model" Int. J. Vehicle Structures &
Systems, 8(1), 35-40, 2016.
20. S. Chantranuwathana and H. Peng, “Adaptive robust force control for vehicle active suspensions,” Int. J. Adapt. Control Signal Process., vol. 18, pp. 83-102, 2004.
21. H. Pan, W. Sun, H. Gao, T. Hayat, and F. Alsaadi, “Nonlinear tracking control based on extended state observer for vehicle active suspensions with performance constraints,”
Mechatronics, vol. In Press, Corrected Proof, Available online 27 August 2014, 2014.
