Abstract. The main objective of this paper is to investigate the performance of activesuspensionsystem, using suspension deflection of the vehicle body as the principal criterion of control and fuzzy-logic as the control scheme. This work describes the application of fuzzy logic technique to the control of a continuously damping automotive suspensionsystem. Activesuspension systems are multivariable dynamic systems for which it is difficult to derive mathematical models. Therefore, analytical control schemes based on such models are complex to construct and generally do not perform well in practice. Hence intelligent control schemes like fuzzy logic controllers that can control the un modelled part of the suspension dynamics are simple to realize and can yield accurate control. This paper has described a proposed fuzzycontrol scheme for suspensions of the vehicle, because of its inherent ability to represent dynamics, the controller is easy to adapt for control tasks. The paper also describes the model and controller used in the study and discusses the vehicle response results obtained from a range of road input simulations. The simulation results obtained have confirmed the feasibility of the proposed fuzzycontrol scheme in Activesuspensionsystem.
A fuzzycontrolsystem is a system which emulates a human expert. Creating machines to emulate human expertise in control gives a new way to design controllers for complex plants whose mathematical models are hard to specify. The knowledge of the human operator would be put in the form of a set of fuzzy linguistic rules. The fuzzy logic controller consists of three steps: fuzzification, fuzzy inference and defuzzification. Fuzzification is a Process of defining the fuzzy sets, and determination of the degree of membership of crisp inputs in appropriate fuzzy sets. Fuzzy inference is a process of evaluation of fuzzy rules to produce an output for each rule and aggregation or combination of the outputs of all rules. Defuzzification is a process of conversion of aggregate output fuzzy set to real-number (crisp) output values .
 presented a more complex activesuspensionsystem controller using fuzzy reasoning and a disturbance observer applied to a quarter vehicle model. The activecontrol force is released by actuating a pneumatic actuator. The excitation from the road profile is estimated by using a disturbance observer, and denoted as one of the variables in the precondition part of the fuzzycontrol rules. The experimental result indicated that the proposed activesuspensionsystem controller improved the vibration suppression of the vehicle model. Adaptive fuzzy logic (AF) and active force control (AFC) strategies are applied to a quarter vehicle model by . They proposed a controlsystem which essentially comprises three feedback control loops.
The triangular membership function with five linguistic variable represented in in Fig 4 to 6. These membership function converts the real input data into fuzzy values in order to reduce the complexity and processing time of fuzzy controller. A classic interpretation of Mamdani  was used as rule basis. The range of input variable and output variable were determined by the simulation results in different conditions. The rules table for fuzzy logic control is shown in table II. The fuzzy controller has 25 control rules. Singleton method and centre of gravity method were selected for fuzzification and defuzzification, respectively. Minimizing the vertical displacement of the automobile body is the basis of constructing the fuzzycontrol rules.
The controlled suspensionsystem is now widely applied such as semi-activesuspension [6, 7], and activesuspension [8, 9]. Chen  proposed a new method on design and stability analysis of semi-activesuspensionfuzzycontrolsystem. Based on the Lyapunov stability theory, each fuzzy subspace's stability of close loop system is analyzed. And then stable condition of whole fuzzycontrolsystem is obtained. The result of experiment and simulation shows that fuzzycontrolsystem of semi-activesuspension is effective and stable and improves the ride performance. Pang  studied the problem of stability analysis and fuzzy-smith compensation control for semi-activesuspension systems with time delay. Based on the Lyapunov stability analysis, the necessary and sufficient condition of the critical time delay for the semi-activesuspension is derived, and the numerical computation method of solving the asymptotic stability area for the suspensionsystem is given. Finally, the results show the ride comfort is improved. Although many scholars explored various semi-active vehicle suspensions to improve ride performance, the activesuspension is widely utilized for luxurious vehicle since it can effectively improve the ride comfort as well as stability. However, a challenging problem for activesuspension design is determined by a control strategy to improve the system performance. During the past two decades, many control strategies have been proposed by many researchers. A half car model with activesuspension was presented by . They utilized a dual loop PID controller strategy to improve dynamic performance. A nonlinear optimal control law is developed, and applied on a half-car model for the control of activesuspension systems to improve the tradeoff between ride quality and suspension travel compared to the passive suspensionsystem . An effective and robust proportional integral sliding mode control strategy is proposed in the activesuspensionsystem . Control strategies are investigated for activesuspension systems with control concepts of look-ahead and wheelbase preview. The corresponding controllers were designed and the suspensionsystem performance was improved . A robust fuzzy sliding-mode controller for an activesuspensionsystem was applied in a half-car model. The feasibility was verified . The uncoupled half car model is constructed such as Karnopps’ work . He presented a passive and activecontrol of road heave and pitch motions for approximately uncoupled motions. Wong’s work  considered a two DOF vehicle model to study the heave and pitch motions neglecting the vehicle suspension dynamics.
The semi-activesuspension modelling was done in simulink using linearized equations of variable damping force. Semi-activesuspensionsystem is controlled by PI, neural network and ANFIS and analysed for performance parameters that is relative suspension deflection, relative tyre force and body acceleration. It is seen that relative suspension deflection, is always less than 1, in all the cases of PID controller, Neural Network and ANFIS, which indicates that suspension will always travel in its rattle space without providing any physical damage to the system. Relative tyre force is very less than one, in every case, which ensures that dynamic force on tyre will not overtake the static tyre force on the tyre. Body acceleration is less in all the cases but with the change of control techniques. It was also observed that the body acceleration showed a drastic change in its value
For the nonlinear system, Ozgur Demir et al. used fuzzy logic combined with a PID controller for a suspension design of a half-car model . Fuzzy logic improves the control of the nonlinear system, and in the robust nonlinear system, the fuzzy logic system can react fast and has great performance . Qu Wenzhonga et al. have shown the advantage of fuzzy logic over filtered- X LMS algorithm . They proved that use of fuzzy logic can be advantageous over an algorithm like filtered-X LMS, which is simple to use and requires low computational load but is more suitable for linear control problems. Shiuh-Jer et al.  have designed an adaptive fuzzy controller using the sliding mode controller, where a smaller rule base is required, but they implemented online learning to compensate the system’s time-varying and nonlinear behavior. Jinpeng Li et al.  elaborated on the coupling of fuzzy logic and sliding mode controller where they designed an adaptive fuzzysystem for a semi-activesuspensionsystem.
The main purpose of this study is to design an active vehicle suspension ensuring high vibration isolation efficiency and stability though the limited consumption of external energy. Active systems used in vehicle suspensions widely employ parallel (full active) structures. It shall be analysed and tested experimentally. The major part of the study summarises the laboratory experiments carried on a designed active vehicle suspension in the form of a quarter car model. Apart from the vibration isolation efficiency offered by the designed and engineered suspension, other considered performance indicators include the system’s stability and external energy demand. A laboratory model of the suspension is described and laboratory tests are outlined that were performed to check the adequacy of various control algorithms. An attempt is made to evaluate the energy demand for the given structure and to determine the power ratings of the source supplying the active vibration isolation system. Inter alia quarter-vehicle full activesuspension, vibration displacement transmissibility in the function of frequency, transmissibility function from the input to the output for various types of actuator’s controllers, comparison of instantaneous power absorbed from the power-supplying unit for various types of actuator’s controllers, comparison of instantaneous power intake from the supplying unit for various types of controllers are presented in the paper.
A damper (shock absorber) is a mechanical device designed to smooth out or damp shock impulse, and dissipate kinetic energy. MR damper technology was originally developed by General Motors for use in the Cadillac and Chevrolet Corvette in 1998. In recent years, a flurry of interest has been shown for a relatively old technology called magneto- rheological fluids, or MR fluids. Multiple types of devices have been designed to implement this versatile fluid, including linear dampers, clutches, work-piece fixtures, and polishing machines. The devices have been used in automobiles, washing machines, bicycles, prosthetic limbs, and even smart structures. The MR dampers provided a more stable ride than that of the OEM dampers. By reducing suspension displacement, settling time, and suspension oscillations, the MR dampers were able to reduce suspension geometry instability. A MR damper consists of a hydraulic cylinder containing MR fluid that, in the presence of a magnetic field, can reversibly change from a free- flowing, linear viscous fluid to a semisolid with controllable yield strength in fraction of a second. Magneto-rheological damper (MR damper) has been expected to control the response of civil and building structures in recent years, because of its large force capacity and controllable force characteristics.
Sharp and Crolla  has described road surfaces, modeling vehicles and setting up performance criteria to passive, active and semi-activesuspension systems. They also elaborated methods of deriving control laws for active systems. D.A.Crolla , in his review paper reviews the contributions of vehicle dynamics theory to practical vehicle design. Dean Karnopp  shows, using simple linear two degree-of-freedom suspensionsystem model that even using complete state feedback, there still are limitations to suspension performance.
Talib and Darus (2014) implemented a semi-activesuspensionsystem using FLC and PID controllers. Per- formance of both the controllers is optimized by the PSO algorithm for mean square error. Optimized FLC, PID controllers are compared with a passive suspensionsystem for body displacement, acceleration, tyre dis- placement for bump, and hole disturbances. It is ob- served that the FLC controller gave better results as compared to the PID controller. Celin and Rajeswari (2012) implemented type-2 FLC to the activesuspensionsystem. Sprung mass displacement, RMS acceleration, suspension space, and tyre deflection criterions were used to study the FLC and passive suspensionsystem. GA-coded FLC outperforms the FLC and passive sus- pension system. D’Amato and Viassolo (2000) presented the activesuspensionsystem to reduce the body acceler- ation to improve comfort. FLC is used to control where parameters are tuned by GA optimization. This method- ology improves ride comfort thus was effective in case of a quarter car suspensionsystem. Li and Du (2006) pre- sented a GA-based approach to optimize rule base and scaling factors. The parameters were coded into real-coded strings and treated as chromosomes during optimization. The GA-based optimization approach im- proves the performance of FLC. Liu et al. (2016) had suc- cessfully optimized the membership functions of FLC to a maximum power point tracking (MPPT) algorithm using PSO algorithm to improve averaged tracking error and fit- ness value. Bouarroudj et al. (2017) had presented the comparative analysis of Mamdani FLC with Gaussian membership functions for MPPT of PV system using GA and PSO approach. It was observed that PSO and GA op- timized FLC gives better results in terms of performance.
Automotive manufacturers often compete against each other to develop dependable and comfortable drive characteristics while at the same time also producing best stability during braking and cornering. With passive suspension however, it could just provide one of the stated features or at most compromise between handling and ride comfortability. Nevertheless, selected companies do offer adjustable suspensionsystem options which can be tuned according driver comfortability needs. Because of this, researchers had proposed and employed several semi-active and active vehicle suspension systems both in theoretical and experimental terms . These systems main benefit is that they simultaneously permits eliminating most road interferences from pitch control as well as active roll.
Optimal vehicle handling, good driving pleasure, best comfort for passengers, effective and efficient isolation of road noise and vibration in suspension systems has been a key research area .This paper presents the application of different controllers to control the vibration occurred in the car suspensionsystem. When the suspensionsystem is designed, a ¼ model of car is used to simplify the problem to a one dimensional mass spring- damper system. Its open-loop performance on the basis of time response is observed which depicts that the car suspension has oscillations with large settling time. To overcome this problem, closed-loop system is used. Despite continuous advancement in control theory, Proportional –Integral (PI), Proportional-Integral- Derivative (PID) IMC, FUZZY, Fuzzy PID Control method are the popular technique to control any process. In this paper, PID, Fuzzy and Fuzzy -PID controllers are used to control the vibrations to give smooth response of the Car suspensionsystem and carry-out their comparison on the basis of time and frequency using Matlab environment.
I hereby, declared this report entitled “ActiveControl of Quarter-Car SuspensionSystem using Linear Quadratic Regulator” is the results of my own research except as cited in references. The report has not been accepted for any degree and is not concurrently submitted in candidature of any other degree.
The designer of heavy goods vehicles (HGVs), today are more aware of the needs to design suspensionsystem that satisfies an additional criterion, namely road friendliness that reduces road damage caused by heavy goods vehicles. The forces of interaction between the tires and the road surface induce stresses on the pavement, which ultimately will lead to road failure (Tsampardoukas et al., 2008; Yarmohamadi and Berbyuk, 2012). For passenger vehicles the contact forces between tires and road are too small to cause significant pavement damage (Valasek et al., 1998). The high cost of maintenance of highways and road networks, because of premature road failure due to heavy traffic has caused global concern. Fluctuating component of tire-road force is the main contributor to road damage along with other environmental factors (Pable et al., 2007). For HGVs the contact forces between tires and road are considerable and hence for these vehicles, suspension parameters need to be selected to reduce road damage.
Fig. 1: Conflicting effects of bogie suspensionsystem on vehicle performance. One of the early stages in this project is to develop a suitable vehicle model for the multiobjective optimisation and activecontrol design problems of the bogie suspensionsystem. Some aspects have to be addressed when developing a vehicle model for such analysis. The model should not be too simple as it might fail to represent the realistic dynamics behaviour and it also should not be too complicated as it would be difficult and time costly to study. Here, a one-car railway vehicle model with 50 degrees of freedom (DOFs) developed in the multibody dynamics software SIMPACK is chosen for the analysis. The structural parameters used to develop the vehicle model are provided by the Bombardier Transportation, Västerås, Sweden. Since the abovementioned vehicle model is too complicated for the activecontrol design, a simple half- car railway vehicle model with 7 DOFs is also considered in this thesis for that particular purpose.
Most previous researches concerning automotive have employed the linear model of activesuspensionsystem (Hrovat 1990, 1997, Xue et al., 2011). In this model the spring, the damper and the actuators were arranged in a 90 degree vertical arrangement. The new model of the MacPherson suspension has been proposed by (Hong et al., 1999, and Fallah et al,. 2008). In this new model the spring, the damper and the actuators were not arranged in 90 degree vertical where this phenomenon created a nonlinear characteristics. However, the number of studies from previous researchers did not consider the issues pertaining to uncertainties, and nonlinearities in the parameters of MacPherson activesuspensionsystem. Furthermore, the self-steer that takes place in the MacPherson activesuspensionsystem causes unbalanced tyre forces and moments, suspension geometry, as well as unbalanced force line position, Nishizawa et al. (2006). The vertical acceleration of sprung mass and the angular acceleration of the control arm in the MacPherson strut are the parameters have been applied to minimize the self-steer. The self-steer, hence, can be minimized by controlling the angular acceleration of the control arm in the MacPherson strut. Therefore, a robust control strategy is essential to control the MacPherson activesuspensionsystem due to its nonlinear, uncertain and self- steer characteristics toward achieving a virtuous measurement on ride comfort and road handling performances.
The dynamic load and vibration caused by landing impact and the unevenness of runway will result in airframe fatigue, discomfort of crew/passengers and the reduction of the pilot’s ability to control the aircraft. The semi-activesuspensionsystem can provide good performance of both landing impact and taxi, and has the ability for adapting to various ground and operational conditions. This current paper designs Proportional Integral Derivative controller based on Bees Intelligent Algorithm as the optimization technique for nonlinear model of semi-active landing gear system that chooses damping performance of system at touchdown as object function. Optimal setting of controller parameters to achieve favorable time response using numerical software method based on Bees Algorithm is more simple and more effective than other traditional methods such as Ziegler-Nichols and experimental because it does not need high experience and complex calculations and leads to better results. This research develops nonlinear two-dimensional mathematical model to describe landing gear system with oleo- pneumatic shock absorber and linear tire. Based on this model, the dynamic equations are used to investigate the behavior of an aircraft semi-active landing gear system subject to runway disturbance excitation and the stability conditions of the landing system around static equilibrium position is studied. SIMULINK simulation software is applied to validate the theoretical analysis of system stability. Results of system numerical Simulation with optimized controller using Bees Algorithm in MATLAB software shows that the transmitted impact load to airframe, the vertical vibration of aircraft and time to return static equilibrium position at touchdown are significantly improved.
Abstract- The purpose of this paper is to construct an activesuspensioncontrol for a quarter car model subject to excitation from a road profile using an improved sliding mode control with an observer design. The sliding mode is chosen as a control strategy, and the road profile is estimated by using an observer design. The objective of a car suspensionsystem is to improve the riding quality without compromising the handling characteristic by directly controlling the suspension forces to suit the road and driving conditions. However, the mathematical model obtained suffers from few uncertainties. In order to achieve the desired ride comfort, road handling and to solve the uncertainties, a sliding mode control technique is presented. A nonlinear surface is used to ensure fast convergence of vehicle’s vertical velocity. The nonlinear surface changes the system’s damping. The effect of sliding surface selection in the proposed controller is also presented. Extensive simulations are performed and the results obtained shows that the proposed controller perform well in improving the ride comfort and road handling for the quarter car model using the hydraulically actuated suspensionsystem. The main motivation for designing an activesuspensionsystem is to improve the ride comfort by absorbing the shocks due to a rough and uneven road.
Active air suspension controls the vertical movement of the wheels with an on-board system and air bags both which provide more complex ability to the system. The normal coil spring is not used in this suspension, thus eliminating its vibration and improving riding comfort. The spring function has been replaced by the air bags but emergency springs are also used. The pressure control range has been widened to maintain a flat vehicle position even while turning. The sensors used are pressure sensors and height sensors.