Fuzzy Control of Active Suspension System using Full Car Model

S u m m a r y Fuzzy logic technique has been proposed to control full car model based active suspension system. The full car model has been used to simulate the mathematical model of active suspension system. The performance of proposed controller mainly depends on body displacement, acceleration, roll and pitch angle of full car model. But the roll and pitch angle cannot be measured in quarter car model of active suspension system. The dynamic nature of suspension system and complex nonlinear characteristics of actuating system has increased the difficulty of creating mathematical model for active suspension system. In real time, the controller designed based on analytical method will not give better result due to its complex mathematical model. The fuzzy logic technique has able to give better performance for active suspension system irrespective of the complex nature of mathematical model of suspension system. This paper describes mathematical model of suspension system with fuzzy controller in order to obtain vehicle response for range of road input. The result of simulation will confirm the performance of fuzzy logic controller for active suspension system.


Introduction
A suspension system consists of spring and oil damper connected between vehicle body and tire to control the vertical moment of car body.The main purpose of suspension system is to reduce the effect of road disturbance on vehicle body by minimizing the displacement and acceleration of vehicle body.The main objective of suspension system is to provide ride comfort for passenger which depends on soft suspension system and better road handling capacity which depends on hard suspension.Design of suspension involves an optimization process where the design elements are selected by compromising on soft and hard suspension.A suspension system classified into passive suspension, semi active suspension and active suspension.A passive suspension system does not require any external energy source and its damping coefficient values are almost constant.In active suspension, force actuator placed in between wheel and vehicle body along with suspension system.The active suspension systems are closed loop systems where the suspension travel of suspension system measured to predict the actuator force needed for active suspension system.Nowadays, many researcher focusing research on active suspension systems [1] due to its ability to operate wide range frequency.The development of computer and microprocessor improved practical implementation of active suspension [2][3] in automotive industries.
A quarter car model consists of one fourth of vehicle mass, spring and damper connected between wheels' mass has been used to design a controller for active suspension system.The quarter car model is a simplified model of car with two degree of freedom by using that the vertical motion of car body and wheel has been measured for active suspension.The quarter car model will be used to represent heave motion of one fourth of vehicle mass.Initially, the controller for quarter car active suspension system designed without considering the dynamics of actuator.But it cannot be used to measure the pitch motion of front wheel and rear wheel.Alleyne et al [4] proposed a nonlinear control technique for hydraulic operated quarter car active suspension.A nonlinear control law formulated to control dynamic nature of hydraulic actuator.
Half car model with four degree of freedom will be used to represent pitch and heave motion of vehicle body.Vehicle body coupled between front and rear wheel by cen-tre of gravity.Nurkan Yagiz [5] proposed sliding mode control combined with Fuzzy logic for nonlinear half car model.The effect of chattering in sliding mode control can be eliminated completely by adding fuzzy controller for half car model.Both quarter car and half car model does not model the actual system for practical application.Accurate model of the actual system need full car model with seven degree of freedom.A full car model of active suspension system is developed by considering seven degrees of freedom namely four vertical motion of wheel, pitch, roll and heave motion of vehicle body.H infinity controller [6] introduced for full car model to suppress the effect of road disturbances and parameter uncertainty in actuator dynamics.A preview controller for full car model [7] based active suspension introduced with two control approach.The first controller optimizes the displacement of actuator whereas the second controller control the pitch, heave and roll motion of vehicle body.The complexity of mathematical model of full car and nonlinear behaviour of actuator has increased the difficulties of applying conventional control schemes to active suspension system.Hence a model free controller based on intelligent control schemes like fuzzy logic, neural network is gaining more importance in recent times and they are applied success fully to control suspension system in real time.
The Fuzzy logic introduced by Lotfi Zadeh in his seminar paper fuzzy set theory [8] in 1965.Fuzzy logic is based on multi value logic where the true values lies in between 1 and 0. The performance of fuzzy depends on type and nature of linguistic variable whereas the values of variable graded using membership function.Fuzzy rules are written based on knowledge of system and then it will be converted in to equivalent mathematical model of a system.Fuzzy controller is simple and flexible hence it can handle imprecise data very well.Fuzzy logic can easily model the nonlinear function of any system.
Mamdani [9][10] introduced fuzzy logic in control system for practical application.The control rules in fuzzy logic is written based on the knowledge of expert.Fuzzy logic has ability to develop controller without any mathematical model of a system.The complex nonlinear behaviour of actuator and its dynamics has been controlled effectively using fuzzy logic controller.Fuzzy logic controller for quarter car active suspension [11] proposed with inputs as suspension deflection and its change and the output as the change of the control signal.An active suspension system proposed for a half-car model where the active control is the sum of two kinds of control.Fuzzy logic algorithm [12][13][14] for quarter car model was developed for better ride comfort using hybrid intelligent algorithm.
Expert's knowledge and experience plays an important role in creating fuzzy rules for conventional fuzzy logic controller.So, there is no proper guideline for selecting rules and parameter for fuzzy controller.Quarter car model based active suspension with Self-organizing fuzzy sliding mode controller (SFSC) created using sliding surface [15] and its change as input to fuzzy controller.The stability of system improved by adaptive law of SFSC.Type-2 fuzzy controller is proposed to resolve nonlinear control problems of active suspension systems [16][17][18][19][20][21] which integrates the Takagi-Sugeno (T-S) fuzzy model, interval type-2 fuzzy reasoning method.A fuzzy sliding-mode controller for active suspensions [22] of a nonlinear half-car model is introduced to remove non chattering effect in sliding-mode control.In this method, sliding mode controller combined with a single-input-single-output fuzzy logic controller to improve its performance for active suspension system.
The remaining part of this paper is organised as follow: Section 2 describes mathematical model of full car model with governing equation.The design of intelligent controller using fuzzy logic carried out in section 3. Section 4 present the result of simulation carried out for different road profile.Conclusion of the work will be presented in section 5.The distance of CG from front and rear end of vehicle indicated by symbol a and b respectively.Tf and tr indicates front and rear treat of vehicle body.The actuator arranged vertically between sprung and unsprung mass has been used to provide actuator force to active suspension system.The full car model has ability to measure the pitch and roll motion of car boy which cannot be possible to measure in quarter car model of vehicle suspension system.A hydraulic actuator is placed on each suspension between sprung and unsprung mass.In this work, the dynamics of actuator is neglected for simulation of full car model.The values of parameter used in full car model listed in Table 1.The equation of motion for full car model [23] derived from newton's second law of motion using the schematic diagram of full car model.The equation for heave z, pitch angle, roll angle of vehicle body described in equation ( 1), ( 2) and (3):

Table 1 Values of parameter used in full car model
.
The four vertical motion of tire on each corner for an external disturbance can be described in equations (4-7):     ) .
In the above equation, vertical displacement of car body at corner 1, 2, 3, 4 can be described in equation ( 8) using heave z, pitch angle, roll angle of vehicle body. Where:

Controller design
Fuzzy logic controller has ability to handle complexity, nonlinearity and unpredictable behaviour of actuator dynamics in active suspension system.The overall layout of fuzzy controller used in full car modelled active suspension system is shown in Fig. 2. The actual suspension travel of each wheel act as control parameter for fuzzy controller.

Fig. 2 Overall layout of Fuzzy controller
The fuzzification stage converts the error e(k) and error change ec(k) of suspension deflection into fuzzy values with help of membership function.The fuzzy rules which are designed based on expert knowledge has been applied in inference mechanism.

Fig. 3 Membership function for Fuzzy controller
The triangular membership function with five linguistic variable represented in in Fig. 3.These membership function converts the real input data into fuzzy values.A classic interpretation of Mamdani [24] 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 2. Minimizing the vertical displacement of the automobile body is the basis of constructing the fuzzy control rules.Defuzzification process converts the fuzzy values obtained membership function into real output data as control voltage which drives servo valve.Among the many defuzzification methods, centroid method is simple and easy to use for control application [25].The centroid defuzzification technique can be expressed as: where: ZCOG is the crisp output, μA(z) is the aggregated membership function and z is the output variable.

Simulation
The simulation was carried out for active suspension system using full car model described in section 2. The performance of proposed fuzzy controller measured against passive and Proportional Integral Derivative (PID) control of Active suspension system.The variables namely body displacement, suspension travel, control force, body Acceleration of each wheel measured find the performance of proposed fuzzy controller.
The road input for each wheel of full car model [26][27][28] indicated in equations (9-11).There will be small change in height of road Zr1 and Zr2 in order to measure the roll angle of full car model.
The response of front wheel at corner 1 for given road profile is represented in Fig. 4 which indicates the response of passive, PID and fuzzy active suspension for various suspension parameter.Table 3 lists the root mean squared values of suspension parameters used for simulation of full car model.The Passive suspension of corner 1 has displacement of 2.94 cm and long settling time compare to fuzzy controller which has wheel displacement of 2.44 cm and less settling time.The acceleration of fuzzy controlled suspension is 0.7252 m/s 2 which is far better than 1.01 m/s 2 of passive suspension.Hence a fuzzy controller reduces the body displacement and acceleration of corner 1 better than passive suspension system.
The response of front wheel at corner 2 for given road profile is represented in Fig. 5 which indicates the response of passive, PID and fuzzy active suspension for various suspension parameter.The Passive suspension of corner 2 has displacement of 2.23 cm and long settling time compare to fuzzy controller which has displacement of 0.79 cm and less settling time.The acceleration of fuzzy controlled suspension is 0.5063 m/s 2 which is far better than 0.7984 m/s 2 of passive suspension.Hence a fuzzy controller reduces the body displacement and acceleration of corner 2 better than passive suspension system.
The response of front wheel 3 at corner 3 is represented in Fig. 6.The suspension travel of passive suspension of corner 3 is 0.7513 cm whereas suspension travel of fuzzy controller is 0.2407 cm.The acceleration of fuzzy controlled suspension is 0.4786 m/s 2 which is better than 0.6226 m/s 2 of passive suspension.So, fuzzy controller reduces suspension travel and acceleration better than passive suspension system.
The response of front wheel 4 at corner 4 for given road profile is represented in Fig. 7 which indicates the response of passive, PID and fuzzy active suspension for various suspension parameter.The Passive suspension of corner 4 has displacement of 2.04 cm and long settling time compare to fuzzy controller which has displacement of 1.674 cm and less settling time.The acceleration of fuzzy controlled suspension is 0.4865 m/s 2 which is far better than 0.6406 m/s 2 passive suspension.Hence a fuzzy controller reduces the body displacement and acceleration better than passive suspension system.
Table 3 lists root mean squared values of displacement, suspension travel and acceleration of corner at 1, 2, 3, 4 respectively.It also indicates displacement, pitch angle, roll angle of whole body for passive, PID and fuzzy controlled suspension system.This result indicates that fuzzy controller reduces suspension travel and vertical acceleration amplitude of suspension significantly compare to passive and PID suspension.It indicates that the ride comfort of the passengers is improved greatly by using the proposed Fuzzy logic controller.The whole body vertical motion about CG indicated by body displacement.The vehicle body motion for given road profile is represented in Fig. 8.The body displacement of fuzzy controlled suspension is 1.442 cm which is less than 1.710 cm of passive suspension.The acceleration of vehicle body in Fig. 9 indicates that fuzzy controlled suspension has acceleration of 0.4288 m/s 2 which is less than passive suspension system.This simulation results shows that fuzzy controlled suspension for full car model provide better ride comfort and stability than passive suspension system.The performance of proposed controller mainly depends on body displacement, acceleration, roll and pitch angle of full car model.But the roll and pitch angle cannot be measured in quarter car model of active suspension system.

Conclusions
The seven-degree-of-freedom full car model based suspension has nonlinear characteristics as a result of its hydraulic components has increased the difficulty of creating mathematical model for active suspension system.In real time, the model based controller do not give better result due to its nonlinear behaviour of actuators used in active suspension system.The proposed fuzzy controller results have demonstrated that the magnitudes of the body displacement and acceleration are decreased as well as the resonance peak due to vehicle body is eliminated significantly compare to model based controller.The simulation of proposed fuzzy controller for active suspension system has confirmed improvement of the ride comfort in vehicles.

Fig. 1
Fig. 1 Schematic representation of 7 DOF full car model A full car model with 7 degree of freedom (DOF) is shown in Fig. 1.The full car model consists of Vehicle body mass ms and four tires of mass mu1, mu2, mu3 and mu4 respectively.The four corners of vehicle body represented by z1, z2, z3 and z4 respectively in order to measure the vertical displacement of vehicle body at each corner.A spring of stiffness k and damping coefficient b along with actuator force u is placed in between vehicle body and tire on each corner.The vertical motion of tire is indicated by zu1, zu2, zu3 and zu4 respectively.The stiffness of tire at each corner is modeled by spring of stiffness kt.The up and down motion of vehicle body along pitch axis is represented by symbol θ.Similarly, α represent rolling motion of vehicle body along roll axis.The displacement of road for each tire on each corner is indicated by road profile zr1, zr2, zr3 and zr4.The 7 Degree of freedom of full car model are represented as four vertical tire displacement (zu1, zu2, zu3, zu4) , heave Z, Pitch θ, Roll α of an vehicle body.

2 Ir 2 b1b
mass of the car body kg mu1 mass of the front wheel at corner 1 kg mu2 mass of the front wheel at corner 2 kg mu3 mass of the front wheel at corner 3 kg mu4 mass of the front wheel at corner 4 kg Ip Pitch moment of inertia kgm Roll moment of inertia kgm Damping coefficient of front suspension at corner 1 Ns/m b2 Damping coefficient of front suspension at corner 2 Ns/m b3 Damping coefficient of rear suspension at corner 3 Ns/m b4 Damping coefficient of rear suspension at corner 4 Ns/m k1 Stiffness of front suspension at corner 1 N/m k2 Stiffness of front suspension at cor-Distance between rear end to CG of Vehicle body 1.65 m tf Front treat 0.505 m tr Rear treat 0.557 m

Fig. 4
Fig. 4 Response of wheel 1 for road profile

Fig. 5
Fig. 5 Response of wheel 2 for road profile

Fig. 7
Fig. 7 Response of wheel 4 for road profile

Fig. 8
Fig. 8 Response of body displacement