Recently, fractional-order proportional–integral–derivative (FOPID) controllers are demonstrated as a general form of the classical proportional–integral–derivative (PID) using fractional calculus. In FOPID controller, the orders of the derivative and integral portions are not integers which offer more flexibility in succeeding control objectives. This paper proposes a multi-objective genetic algorithm (MOGA) to optimize the FOPID controller gains to enhance the ride comfort of heavy vehicles. The usage of magnetorheological (MR) damper in seat suspension system provides considerable benefits in this area. The proposed semi-active control algorithm consists of a system controller that determines the desired damping force using a FOPID controller tuned using a MOGA, and a continuous state damper controller that calculates the input voltage to the damper coil. A mathematical model of a six degrees–of–freedom seat suspension system incorporating human body model using an MR damper is derived and simulated using Matlab/Simulink software. The proposed semi–active MR seat suspension is compared to the classical PID, optimum PID tuned using genetic algorithm (GA) and passive seat suspension systems for predetermined chassis displacement. System performance criteria are examined in both time and frequency domains, in order to verify the success of the proposed FOPID algorithm. The simulation results prove that the proposed FOPID controller of MR seat suspension offers a superior performance of the ride comfort over the integer controllers.
AldairAAWangJW (2010) Design of Fractional Order Controller Based on Evolutionary Algorithm for a Full Vehicle Nonlinear Active Suspension Systems. International Journal of Control and Automation3: 33–46.
2.
BarbosaRSMachadoJATJesusIS (2010) Fractional PID control of an experimental servo system. Computers & Mathematics with Applications59: 1679–1686.
3.
BiswasADasSAbrahamADasguptaS (2009) Design of fractional-order PID controllers with an improved differential evolution. Engineering Applications of Artificial Intelligence22: 343–350.
4.
BoileauPRakhejaS (1998) Whole-body vertical biodynamic response characteristics of the seated vehicle driver; Measurement and model development. International Journal of Industrial Ergonomics22: 449–472.
5.
ChoiSBHanYM (2007) Vibration control of electrorheological seat suspension with human-body model using sliding mode control. Journal of Sound and Vibration303: 391–404.
6.
ChoiSBNamMHLeeBK (2000) Vibration control of a MR seat damper for commercial vehicle. Journal of Intelligent Material Systems and Structures11: 936–944.
7.
ChoiSChoiJLeeYHanM (2003) Vibration control of an ER seat suspension for a commercial vehicle. Journal of Dynamic Systems, Measurement, and Control (Transactions of the ASME)125: 60–68.
8.
CohonJL (1978) Multi-objective Programming and Planning, New York: Academic Press.
9.
DasSSahaSDasSGuptaA (2011) On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA Trans50: 376–388.
10.
DuHLamJSzeK (2003) Non-fragile output feedback H∞ vehicle suspension control using genetic algorithm. Engineering Applications of Artificial Intelligence16: 667–680.
11.
DuHSzeKLamJ (2005) Semi-active H∞ control of vehicle suspension with magneto-rheological dampers. Journal Sound and Vibration238: 981–996.
12.
FialhoIBalasG (2002) Road adaptive active suspension design using linear parameter-varying gain-scheduling. IEEE Transactions on Control Systems Technology10: 43–54.
13.
GadSMeteredHBassuinyAAbdel GhanyAM (2015) Ride Comfort Enhancement of Heavy Vehicles using Magnetorheological Seat Suspension. International Journal of Heavy vehicle System22: 93–113.
14.
GucluR (2005) Fuzzy logic control of seat vibrations of a non-linear full vehicle model. Nonlinear Dynamics40: 21–34.
15.
GuoDHuHYiJ (2004) Neural network control for a semi-active vehicle suspension with a magnetorheological damper. Journal of Vibration and Control10: 461–471.
16.
HostensIDeprezKRamonH (2004) An improved design of air suspension for seats of mobile agricultural machines. Journal of Sound and Vibration276: 141–156.
17.
International Standard Organization (1997) Evaluations of human exposure to whole-body vibration, part 1: General requirements. ISO-2631/1.
18.
JiangCMaYWangC (2006) PID controller parameters optimization of hydroturbine governing systems using deterministic-chaotic-mutation evolutionary programming (DCMEP). Energy Convers Manage47: 1222–1230.
19.
KarnopDCrosbyMJHarwoodRA (1974) Vibration control using semi-active force generators. Journal Engineering Industry96: 619–626.
20.
LaiCYLiaoHW (2002) Vibration Control of a Suspension System via a Magnetorheological Fluid Damper. Journal of Vibration and Control8: 527–547.
21.
LiangCChiangC (2006) A study on biodynamic models of seated human subjects exposed to vertical vibration. International Journal of Industrial Ergonomics36: 869–890.
22.
LiangCChiangC (2008) Modeling of a seated human body exposed to vertical vibrations in various automotive postures. Industrial Health46: 125–137.
23.
MaciejewskiIMeyerLKrzyzynskiT (2010) The vibration damping effectiveness of an active seat suspension system and its robustness to varying mass loading. Journal of Sound and Vibration329: 3898–3914.
24.
Metered H and Šika Z (2014) Vibration Control of a Semi-active Seat Suspension System using Magnetorheological Damper. In: 10th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA 14), September 10–12, Senigallia, Italy.
25.
Metered H, Bonello P and Oyadiji SO (2009) Vibration control of a seat suspension system using magnetorheological damper. In: ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. 30 August–2 September, San Diego, California, USA (DETC2009-86081).
26.
Metered H, Bonello P and Oyadiji SO (2010) An investigation into the use of neural networks for the semi-active control of a magnetorheologically damped vehicle suspension. In: Proceedings of the Institution of Mechanical Engineers, Part D: Automobile Engineering 224: 829–848.
27.
PodlubnyI (1999) Fractional-Order Systems and PID Controllers. IEEE Transaction on Automatic Control44: 208–214.
28.
RakhejaSAfeworkYSankarS (1994) An analytical and experimental investigation of the driver-seat suspension system. Vehicle System Dynamics23: 501–524.
29.
ShiPBoukasENguangSGuoX (2003) Robust disturbance attenuation for discrete-time active fault tolerant control systems with uncertainties. Optimal Control Applications and Methods24: 85–101.
30.
ShiPMahmoudMYiJIsmailA (2006) Worst case control of uncertain jumping systems with multistate and input delay information. Information Sciences176: 186–200.
31.
SimsNDStanwayRPeelDJBulloughWA (1999) Controllable viscous damping: an experimental study of an electrorheological long-stroke damper under proportional feedback control. Journal of Smart Materials and Structures8: 601–615.
32.
Sun L, Cai X and Yang J (2007) Genetic algorithm-based optimum vehicle suspension design using minimum dynamic pavement load as a design criterion. Journal of Sound and Vibration 301: 18–27.
33.
SunWLiJZhaoYGaoH (2011) Vibration control for active seat suspension systems via dynamic output feedback with limited frequency characteristic. Mechatronics21: 250–260.
34.
TiemessenIJHulshofCTJFrings-DresenMHW (2007) An overview of strategies to reduce whole-body vibration exposure on drivers: A systematic review. International Journal of Industrial Ergonomics37: 245–256.
35.
WangZQiaoH (2004) H∞ reliable control of uncertain linear state delayed systems. Journal of Dynamical and Control Systems10: 55–76.
36.
WangZHuangBUnbehauenH (1999) Robust reliable control for a class of uncertain nonlinear state delayed systems. Automatica35: 955–963.
37.
WangZYangFHoDLiuX (2006) Robust H∞ filtering for stochastic time-delay systems with missing measurements. IEEE Transactions on Signal Processing54: 2579–2587.
38.
WeiLGriffinM (1998) Mathematical models for the apparent mass of the seated human body exposed to vertical vibration. Journal Sound and Vibration212: 855–874.
39.
YangGLamJWangJ (1998) Reliable H_ control for affine nonlinear systems. IEEE Transactions on Automatic Control43: 1112–1117.
40.
YiKSongBS (1999) A new adaptive sky-hook control of vehicle semi-active suspensions. Proc. IMechE, Part D: Journal of Automobile Engineering213: 293–303.
41.
YildirimŞ (2004) Vibration control of suspension systems using a proposed neural network. Journal Sound and Vibration277: 1059–1069.
42.
YingZNiYKoJ (2005) Semi-active optimal control of linearized systems with multi-degree of freedom and application. Journal Sound and Vibration279: 373–388.
43.
ZhaoYSunWGaoH (2010b) Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay. Journal of Sound and Vibration329: 4335–4353.
44.
ZhaoYZhaoLGaoH (2010a) Vibration control of seat suspension using H∞ reliable control. Journal of Vibration and Control16: 1859–1879.
45.
ZhihuanCXiaohuiYBinJPengtaoWHaoT (2014) Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Convers Manage84: 390–404.
