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Design of genetic-fuzzy control strategy for parallel hybrid electric vehicles

Control Engineering Practice 16(2008)861–873

Amir Poursamad,Morteza Montazeri

Department of Mechanical Engineering,Iran University of Science and Technology,Narmak,Tehran 16844,Iran

Received 15September 2006;accepted 12October 2007

Available online 26November 2007

Abstract

Hybrid Electric Vehicles (HEVs)generate the power required to drive the vehicle via a combination of internal combustion engines and electric generators.To make HEVs as ef?cient as possible,proper management of the different energy elements is essential.This task is performed using the HEV control strategy.The HEV control strategy is the algorithm according to which energy is produced,used and saved.This paper describes a genetic-fuzzy control strategy for parallel HEVs.The genetic-fuzzy control strategy is a fuzzy logic controller that is tuned by a genetic algorithm.The objective is to minimize fuel consumption and emissions,while enhancing or maintaining the driving performance characteristics of the vehicle.The tuning process is performed over three different driving cycles including NEDC,FTP and TEH-CAR.Results from the computer simulation demonstrate the effectiveness of this approach in reducing fuel consumption and emissions without sacri?cing vehicle performance.r 2007Elsevier Ltd.All rights reserved.

Keywords:Hybrid electric vehicle;Control strategy;Fuzzy logic;Genetic algorithms

1.Introduction

Because of the potential of hybrid electric vehicles (HEVs)to reduce fuel consumption and environmental pollution,HEVs have become one of the most viable alternatives to conventional vehicles,which are driven by internal combustion engines (ICE).HEVs encompass two energy converters to generate the power required to drive the vehicle and operate other accessories.Typically,the architecture of these vehicles includes an ICE with an associated fuel tank and an electric machine with an associated energy storage system (battery).

Proper management of power ?ow or distribution of torque is a critical issue for the implementation of HEVs.This task is performed by HEV control strategy.The HEV control strategy determines which power source is used according to the driver’s torque demand and the speci?c features of the driving situation.In other words,the control strategy is the algorithm according to which energy is produced,used and saved.

It has been demonstrated that fuzzy logic control could be applied successfully to the design of the HEV control strategy (Baumann,Washington,Glenn,&Rizzoni,2000;Cerruto,Consoli,Raciti,&Testa,1994;Farrall &Jones,1993;Hyeoun-Dong et al.,2000;Kheir,Salman,&Schouten,2004;Schouten,Salman,&Kheir,2002,2003;Won &Langari,2002).The main idea of these control strategies is commonly based on the concept of load-leveling,which attempts to operate the ICE in an ef?cient region and uses the electric motor (EM)as a load-leveling device.The structure and parameters of all these fuzzy control strategies are designed based on the designer’s knowledge of the problem.However,due to the complex nature of HEVs,fuzzy control strategy that has been designed based on engineering intuition frequently fails to achieve satisfactory overall system ef?ciency.To confront this dif?culty,optimization algorithms can be used to achieve an optimal fuzzy logic controller (FLC).Moreover,the driving perfor-mance characteristics of the vehicle have not been considered in fuzzy control strategy design in previous works.

Usually,the design of FLC is converted into an optimization problem and an optimization algorithm is

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E-mail address:amirpoursamad@mail.iust.ac.ir (A.Poursamad).

used to determine the rules and/or to change shapes of the fuzzy sets.However,since popular FLCs contain fuzzy inference mechanisms(MIN,MAX operators),gradient-based algorithms are dif?cult to use because they require the approximate computation of the gradient or mathe-matically differentiable MIN and MAX operators. Furthermore,in most of the applications,the objective function is a highly nonlinear function with several peaks and valleys.In such cases,many of the conventional search algorithms face the danger of approaching local extrema as the solution.

Genetic algorithms(GAs),?rst formulated by Holland (1975),are search algorithms based on natural genetics, which provide robust search capabilities in complex spaces; as a result,GAs offer a valid approach to problems requiring ef?cient and effective search processes.GA was used?rst by Karr(1991)in the design of FLCs to determine membership functions(MFs).Karr applied GA to the design of FLC for the cart-pole problem.Since then,

several approaches have been introduced to the design of FLC using GA(Cordona,Gomide,Herrera,Hoffmann,& Magdalena,2004).

In this paper,a genetic-fuzzy control strategy for parallel HEVs is proposed.The genetic-fuzzy control strategy is a fuzzy control strategy,which is tuned of?ine using GA. First,an FLC is designed,whose rule base is extracted based on expert knowledge.The parameters de?ning the MFs are then tuned via GA.The main objective is to minimize fuel consumption and emissions.In addition,we will demonstrate that the control strategy parameters highly affect the driving performance of the vehicle.To obtain a satisfactory control strategy,the parameters should be tuned such that the driving performance characteristics are not sacri?ced when minimizing fuel consumption and emissions.To this end,the driving performance characteristics of the vehicle are imposed as constraints and are handled using penalty functions.The tuning process is performed for three different driving cycles,including NEDC(European cycle),FTP(US uni?ed cycle)and TEH-CAR.TEH-CAR is a driving cycle that was developed based on the experimental data collected from real traf?c conditions in the city of Tehran.The simulations are?nally conducted to investigate the effec-tiveness of the approach and effect of the driving cycle on optimization of the HEV control strategy.

2.HEV con?gurations

Generally,there are two accepted basic con?gurations for HEV:series and parallel.A dual or multi-mode type is also considered as a third type that combines the features of both series and parallel hybrids(Chau&Wong,2002). The series HEV con?guration incorporates a fuel converter(ICE),a generator,battery,and an electricmotor (EM),as shown in Fig.1.In this case,the fuel converter does not drive the vehicle shaft directly.Instead,it converts mechanical power into electrical energy using a generator.The electrical energy is also saved in the energy storage system(i.e.battery).In this con?guration,the torque required to drive the vehicle is supplied by the EM.The series con?guration is usually used for heavy duty vehicles. In parallel HEV,both ICE and EM may deliver power to the vehicle wheels as shown in Fig.2.The EM may also be used as a generator to charge the battery by either regenerative braking or absorbing excess power from the ICE when its output is greater than that required to move the wheels.One advantage of the parallel HEV over the series type is that parallel HEV requires a smaller ICE and EM to provide similar performance.This feature makes parallel HEV more suitable for passenger cars.

In the combined series-parallel hybrid,the con?guration involves an additional mechanical link compared to the series hybrid and an additional generator,as compared to the parallel hybrid that makes the dual HEV a relatively more complicated and costly version.

3.Driving cycles

Driving cycles are de?ned as test cycles that are used to standardize the evaluation of vehicle fuel economy and emissions.Driving cycles are speed-time sequences that represent the traf?c conditions and driving behavior in a speci?c area.Driving patterns may vary from city to city and from area to area;therefore,the use of a driving cycle obtained for certain cities or countries is not necessarily applicable to other cities.

To evaluate fuel consumption and emissions in this study,three driving cycles were used.These cycles are shown in Fig.3,including the cycle currently used in the United States(FTP cycle)and European community (NEDC cycle).A recent driving cycle was also developed for the city of Tehran,based on the experimental data collected from real traf?c conditions.This driving cycle is named TEH-CAR and is depicted in Fig.3c(Montazeri-Gh &Naghizadeh,2003).

Fig.1.Series HEV con?guration.

Fig.2.Parallel HEV con?guration.

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A driving cycle consists of a mixture of driving modes including idle,cruise,acceleration,and deceleration.The maximum,minimum and average speeds are also con-sidered as the cycle characteristics.Table 1compares the parameters of the three driving cycles.Signi?cant varia-tions can be expected depending on the type of the driving cycle.

4.Parallel HEV control strategy

As mentioned before,a parallel HEV incorporates two power drives,including ICE and EM.Therefore,it is the responsibility of the parallel HEV control strategy to determine how to distribute the driver’s required torque between the ICE and EM.For negative torque request

(car braking),the engine torque is 0and the sum of the motor and brake torques would be equal to the driver’s request.However,for positive torque requests,the sum of the engine and motor torques should be equal to the driver’s torque request.

The HEV control strategy is aimed at several simulta-neous targets such as minimization of fuel consumption (FC)and exhaust emissions (HC,CO,and NO x ).These aspects are often in con?ict with each other.For instance,the typical loci of optimal operating points in a spark ignition (SI)engine map is shown in Fig.4(Johnson,Wipke,&Rausen,2000).It is clear from this ?gure that the minimum fuel consumption does not necessarily result in the minimum emissions,which implies the need for a trade-off solution.

The bottom line for control strategy is that the vehicle must follow the driver’s request.This means that the total torque delivered by the ICE and EM must be determined such that the driver’s torque requests (from brake and accelerator pedals)are satis?ed consistently.The driver’s request is equivalent to the driving cycle.Therefore,control strategy must perform such that the driving cycle is tracked adequately.

Another aim for control strategy is to maintain or enhance vehicle performance measures,such as gradeabil-ity,acceleration,etc.In this study,partnership for the next generation of vehicles (PNGV)passenger car constraints (Moore &Lovins,1995)are used to ensure that the vehicle performance is not sacri?ced during the control strategy design.These constraints are listed in Table 2.It should be

500

10001500

050

100

TEH-CAR

Time (sec)

0500

1000

1500

2000

2500

050

100

FTP

0200

400

600

800

1000

1200

050

100

NEDC

S p e e d

(k m /h )

Fig.3.FTP,NEDC and TEH-CAR driving cycles.

Table 1

Characteristic parameters of TEH-CAR,FTP,and NEDC driving cycles

TEH-CAR

FTP NEDC Time (s)179724771225Dist.(km)13.4217.6710.87Vmax (km/h)83.9390.72119.3Vavg (km/h)26.8725.6731.91Acc.max.(m/s 2) 1.71 1.47 1.05Decc.max.(m/s 2)à2.71à1.47à1.38Acc.avg.(m/s 2)0.450.510.54Decc.avg.(m/s 2)à0.56à0.57à0.78Idle Time (%)

16.81

38.8

27.67

E n g i n e t o r q u e

Fig.4.Loci of optimal operating points for an SI engine.

Table 2

PNGV passenger car performance constraints Constraint Description

Gradeability At 88.5km/h,for 20min,with 272kg added mass X 6.5%

Acceleration time

Time for 0–97km/h p 12s Time for 64–97km/h p 5.3s Time for 0–137km/h p 23.4s Maximum speed X 137km/h Maximum acceleration X 0.5g’s Distance in 5s

X 42.7m

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mentioned that the initial state of change (SOC)is 0.65when calculating acceleration times,maximum speed,maximum acceleration and distance in 5seconds.

One of the other constraints for control strategy is to remain charge-sustaining.This constraint has been intro-duced to force the battery SOC to recover its initial value by the end of the driving cycle.

It should be noted that in addition to the above constraints,there are also some physical constraints such as constraints on engine torque limits,motor torque limits,and battery power limits.These limits are hard constraints that cannot be violated all the time.In this study,these constraints are imposed on models of the components.5.Fuzzy logic control strategy

In this section,the fuzzy control strategy is described.The main objective of this controller is to cause the ICE to work in the vicinity of its optimal operating points.The optimal operating points are determined based on ICE parameters at the current vehicle speed,so as to minimize instantaneous fuel consumption and emissions.At any particular point in time,the speed of rotation for the ICE is determined based on the powertrain con?guration and the current gear ratio.This is the speed at which instantaneous optimization is performed.For the current speed,all possible torques provided by the ICE are considered.Afterwards the fuel consumption and emissions for all torques at the current speed are taken from the engine

maps and the following cost function is calculated for all points:

j ?1123w 1FC FC tw 2HC tNO x HC tNO x tw 3CO

(1)in which FC,HC tNO x ,CO are the target values used to normalize each variable.The target value for fuel consumption can be de?ned by the designer and for the target value of emissions,the standards of tailpipe emissions can be used.w i ’s are relative weights assigned to each parameter based on the level of importance.This is one large degree of freedom and the weights must be selected based on the design objectives.For instance,when the main objective is the minimization of the vehicle fuel consumption,the FC weight is set to 1and the weights of emissions will be set to 0.

The optimal operating point at the current speed is the one with the lowest value of cost function.If the optimal operating points are plotted for all speeds,the optimal curve will be achieved.The optimal curve for particular weights of this work is shown in Fig.5.It is worth mentioning that this optimal curve is obtained for a particular ICE temperature.When the ICE temperature varies,the maps are corrected based on the new temperature,and the shape of the optimal curve changes.The calculated optimal operating point is an ideal operating point.However,the actual torque delivered by the ICE should be determined in a manner such that the driver’s torque requests (from brake and accelerating pedals)are satis?ed consistently,and the battery is suf?ciently charged at all times.Therefore,the actual torque of the ICE is computed by the FLC based on the previously calculated optimal operating point of the ICE,driver’s torque request and the battery SOC.This is the FLC command to the ICE.It should be noted that the actual output torque of the ICE delivered to the torque coupler could be very different from the FLC command (e.g.due to manifold ?lling dynamics and air-to-power delay).The remaining torque at that speed,required to meet driver’s command,is provided by the EM.The EM may produce either positive or negative torque.A schematic of this control strategy is shown in Fig.6.5.1.Overview of fuzzy logic control

A fuzzy logic controller,?rst proposed by Zadeh (1973),uses fuzzy rules to form a controller that can approximate

1000

2000300040005000

6000

405060708090Engine speed (rpm)

E n g i n e t o r q u e (N .m

)

Fig.5.Optimal curve for an SI engine.

ICE Speed Fig.6.Schematic of fuzzy control strategy.

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expert reception and judgment.A typical FLC has four basic components:

1.Rule base(RB):The RB is composed of a set of

if–then rules,from which an inference mechanism is formed.A standard form of RB with m rules is presented as:

where x1,y x n are state variables,y is the control variable,A i1,y,A in and B i,i?1,y,m are respectively the linguistic variables of x1,y,x n and y in the universe of discourse.

2.Data base(DB):The DB is formed by the speci?c MFs

of linguistic variables,in order to transform crisp inputs into fuzzy ones.

3.Inference engine:The operators within the logic rules

form the inference engine.Generally,logic rules use AND or OR as connecting operators between state variables.

4.Defuzzi?cation:Defuzzi?cation is the synthesis of

inference results of all activated logic rules into crisp outputs for decision making.

5.2.Structure of the FLC

When designing an FLC,two main parts must be determined:structure(input and output variables,structure of fuzzy rules,the number and type of MFs,the type of inference mechanism,operators,and defuzzi?cation method) and parameters(parameters relating to MFs and fuzzy rules). In this study,the FLC is a Mamdani type fuzzy system. The required torque and SOC at each time are considered the inputs of the FLC.It should be noted that the optimal torque is not an input for the FLC and is used only to scale the MFs at each time step.FLC output is the scaled value of the actual output torque from the ICE that must be scaled back later.

The logical AND has been implemented with the minimum operator,the implication method is minimum, the aggregation method is maximum,and the defuzzi?ca-tion method is centeroid.

5.3.Membership functions

Each input and output has3MFs,implying a total of9 rules.The required torque is scaled from0to1,0indicating zero torque,0.5indicating the calculated optimal torque, and1indicating the maximum ICE torque at the current speed.To perform the scaling of the required torque,it is compared to the calculated optimal torque at each time step.The calculated optimal torque at the current speed is scaled to0.5.It should be noted that the calculated optimal torque(value0.5)varies at every time step.

Similarly,SOC is scaled from0to1,0corresponding to the lowest SOC limit and1corresponding to the highest SOC limit.The lowest and the highest SOC limits are determined according to the characteristics of the battery pack.It is desirable to maintain the SOC near a target value during the driving cycle.This target value is selected to be as close as possible to the minimum charge and discharge resistances of the battery.The lowest and highest SOC limits should be close to this target value.For instance,the charge and discharge resistance curves of the lead-acid battery used in this study are shown in Fig.7.For this case,the target value is set to0.65,the lowest SOC to 0.6and the highest SOC to0.7.In SOC scaling,0.5 represents the target value.

The MFs for the output torque are exactly the same as those for the required torque.The justi?cation is that MFs of the required torque are de?ned based on ICE characteristics and the output of FLC is the output

00.20.40.60.81

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

SOC

(

)

Fig.7.Charge and discharge resistances of the battery.

Rule1:IF x1is A11AND x2is A12ANDáááx n is A1n THEN y is B1

Rule2:IF x1is A21AND x2is A22ANDáááx n is A2n THEN y is B2

...

Rule i:IF x1is A i1AND x2is A i2ANDáááx n is A in THEN y is B i

...

Rule m:IF x1is A m1AND x2is A m2ANDáááx n is A mn THEN y is B m

A.Poursamad,M.Montazeri/Control Engineering Practice16(2008)861–873865

torque of the same ICE.The initial MFs are depicted in Fig.8.

5.4.Rule base of the FLC

Using these MFs,the rule base is de?ned by a set of 9rules,as listed in Table 3.The general logic behind these rules is the idea of load leveling,in which the EM is used to assist or generate,while running the ICE near optimal operating point.In fact,the optimal operating point of the ICE is varied based on SOC constraints.

For instance,consider a case (the last rule in the rule table)when the required torque is above the optimal operating point and the SOC is high.It is favorable to bring the ICE operating point near the optimal operating point (for that speed).This would mean a lower torque output by the ICE relative to what is required to meet the driver’s demand.This requires that the EM be run as a motor to make up for the remaining torque,provided there is enough battery charge.Since there is suf?cient charge in this case,the ICE is allowed to operate near the optimal operating point.

Let us consider another case (the ?rst rule in the rule table),when the desired torque is sub-optimal,and the battery SOC is low.It is desirable to increase the ICE torque output to near optimum.This would require load-leveling by the EM (functioning as a generator),so as to output only what the driver demands.This is possible only if the SOC is not high.Here,the SOC is low,and thus,the EM can be run as a generator,while running the ICE at the optimum.In this case,the EM torque is negative,generating some energy into the battery pack.In both the cases,the EM torque is represented by the difference between the required torque and ICE output torque.6.Tuning of the FLC by GA

The FLC described in the previous section was designed based on intuition the problem,and therefore,it does not necessarily work optimally.This is due to the complex nature of the HEV control problem.In this section,the application of GA to construct a genetic-fuzzy control strategy will be described.The genetic-fuzzy control strategy is an FLC that is tuned of?ine by GA.In the tuning phase,parameters of the FLC are modi?ed by GA so as to minimize an objective function.In the application phase,the tuned FLC is used to control the HEV.Fig.9shows a schematic of this process.

As mentioned before,to design an FLC,the degrees of freedom are the structure and parameters of the FLC,which must be determined optimally.In this process,fuzzy rules and the parameters de?ning the MFs are of crucial importance.Therefore,in the FLC design problem,the structure is usually ?xed and one is only concerned with ?nding the optimal parameters.

To obtain optimal FLC parameters using GA,all parameters de?ning the fuzzy rules and MFs are coded into a chromosome that is handled by GA.Increasing numbers of parameters that are handled result in greater chances of obtaining a global optimum.However,one of the main drawbacks of this approach is the rapid increase in the length of the chromosome as the number of parameters and fuzzy rules increases.A lengthier chromo-some usually implies the need for a larger population size and a larger number of generations to achieve a global

0.2

0.40.60.81

00.5

Required Torque

D e g r e e o f m e m b e r s h i p

Low

Optimal

0.2

0.4

0.60.81

00.5

SOC

D e g r e e o f m e m b e r s h i p

Low Normal

High

Fig.8.The initial MFs of the FLC.

Table 3

Rule base of the FLC to determine ICE output torque

Required torque Low

Optimal High SOC Low Optimal High High Normal Low Optimal High High

Low

Optimal

Requested torque

SOC

Requested torque

SOC

Fig.9.The schematic of genetic-fuzzy control strategy;(a)Tuning phase,(b)application phase.

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optimum,resulting in greater computational times.An-other drawback is the dif?culty in interpreting the?nal FLC obtained by GA;that is,there may be a number of rules that are not consistent with each other or cannot be interpreted using expert knowledge.To tackle these dif?culties,a compromise between the use of expert knowledge and the number of parameters handled by GA (degrees of freedom)is proposed in his https://www.sodocs.net/doc/022416739.html,ing this approach,some degrees of freedom are sacri?ced to obtain an interpretable FLC through a computationally more ef?cient process.

The designed FLC is simple with2inputs,3MFs for each input and9fuzzy rules.The number of rules in the designed FLC is low and the rules can be optimally developed based on expert knowledge about the problem and by means of trial and error.Therefore,in this study,the fuzzy rules will be?xed in addition to the structure of the FLC,and parameters of the MFs are tuned by GA.Furthermore,the minimum number of parameters that mainly affect the MFs is used and the MFs are coded such that the meaning of the linguistic labels(low,normal, etc.)does not change during the tuning process.The outcome is that the fuzzy rules designed in the previous section remain exactly the same at the end of tuning process and are interpreted as discussed in the previous section.

6.1.Formulation of tuning as an optimization problem Here,the tuning problem of the FLC is formulated as an optimization problem and GA is applied to solve this optimization problem.The aim of the previously designed FLC is to minimize an instantaneous cost function. However,it is favorable to optimize the FLC to minimize a long-term objective,while satisfying driving performance constraints.The long-term objective is the integral of fuel consumption and emissions over the entire driving cycle,as follows:

JexT?

w1tw2tw3

?w1

Z T DC

d t

tw2

Z T DC

HCtNO x

d ttw3

Z T DC

d t

e2T

in which all parameters are similar to those of the instantaneous cost function,x is a vector containing all parameters used to de?ne the MFs,and T DC is the duration of driving cycle.

To provide further insight into the order of magnitude of this objective function,it is worth mentioning that sensitivity analysis reveals that the weights and target values of this objective function are such that a0.05 decrease in the objective value is equivalent to a1L/100km decrease in fuel consumption.

The optimal selection of MF parameters for FLC is formulated as a constrained optimization problem as follows:

MinimizeJexT

x2X

s:t:h iexTp0;i?1;2;...;n con,e3Twhere x is a solution to the problem within the solution space X.X de?nes the lower and upper bounds of the parameters.Moreover,J(x)is the objective function and each inequality h i(x)p0represents one of the PNGV constraints discussed before.Finally,n con is the number of constraints.It is worth mentioning that if it is desired to keep the emissions within standard limits rather than to further reduce them,the emissions can also be included in the constraints.

6.2.Overview of GA

GAs are probabilistic global search and optimization methods that mimic the metaphor of natural biological evolution.GA operates on a population of individuals (potential solutions),each of which is an encoded string (chromosome)containing the decision variables(genes). The structure of a GA is composed of an iterative procedure with the following?ve main steps(Man,Tang, &Kwong,1996):

1.Creating an initial population(P0).

2.Performance evaluation of each chromosome(c i)from

the population by means of a?tness function.

3.Selection of chromosomes for generating a new popula-

tion.

4.Application of genetic operators:Crossover and Muta-

tion.

5.Iteration of steps2–4until a termination criterion is

ful?lled.

6.3.Coding the parameters of the MFs

The de?nition and number of decision variables are critical issues of the optimization process.These variables are coded into chromosomes to be used by GA.As discussed before,when using GA,one should avoid increasing the length of chromosomes.The main reason for this is that when the length of chromosomes increases, one should increase the number of chromosomes in a

Fig.10.Variables de?ning MFs.

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population and,consequently,the total number of genera-tions to increase the probability of achieving a global optimum.This will result in increased simulation time and decreased computational ef?ciency.Therefore,it is bene-?cial to adopt the minimum number of variables that can fully de?ne the MFs.Fig.10shows the MFs for required torque and the?ve variables used to de?ne these MFs. As depicted in the?gure,a variable is used to de?ne the triangular MF and two variables are used to de?ne each trapezoidal MF.The centre of the triangular MF is?xed at 0.5so that the meaning of its linguistic variable(‘optimal’) is not changed during the tuning process.The inside corners of trapezoidal MFs are also?xed at0.5to guarantee adequate overlap of MFs.The bounds of variables de?ning trapezoidal MFs are limited such that they remain compatible with the meaning of their labels. The outside corners of trapezoidal MFs(x1and x5)can exceed0and1because the required torque may be negative or may be more than the maximum torque of ICE.These MFs are also used for the output torque of ICE without any change,except that the output torque is limited to the minimum and maximum torque of the ICE at the current speed by a limiter.

To de?ne the MFs of SOC,?ve other variables(x6,y, x10)are used similarly.Again,the centre of a triangular MF is?xed at0.5to be consistent with the de?nition of target SOC and trapezoidal MFs can exceed0and1 because SOC may have a value less or more than its lower or upper limits during driving.

Using this approach,the dimension of the solution space is10.These10variables are coded in a chromosome using a binary coding scheme as follows:

x?ex1;x2;...;x10T.(4) To start the algorithm,an initial population of chromo-somes is de?ned.Here,the GA is con?gured such that it creates a?xed number of initial individuals at random from the whole solution space.

An important parameter in initialization is the popula-tion size.In general,the population size affects both the ultimate performance and the ef?ciency of GA.The larger population usually requires more evaluations per genera-tion and implies a better solution and longer running time. On the other hand,a small population encourages premature convergence to suboptimal solutions.

6.4.Fitness function

To apply GA to the tuning of MFs,a?tness function is required to evaluate the status of each solution.In this study,the?tness function is considered to be the inverse of the objective function described by Eq.(2).Using this approach,the driving performance requirements are then considered constraints.However,as GA is directly applic-able only to unconstrained optimization problems,the constraints are handled by using penalty functions that penalize the infeasible solutions,thus reducing their?tness values(Carlos&Coello,2002).Here,a penalty value is added into the violating solutions taking the number of violated constraints and their distance from feasibility into account.In this case,the?tness function will take the following form:

FexT?

JexT

X n con

i?1

a i?G iexT,(5)

where F(x)is the?tness function,J(x)is the objective function,G i(x)is the penalty function related to the i th constraint,and a i is a positive number that determines the degree to which the i th constraint is penalized,usually called penalty factor.These penalty factors are treated as constants in this work and their values are obtained by trial and error.

6.5.Genetic operators

Following the evaluation of?tness of all chromosomes in the population,the genetic operators are applied to generate a new population.During this process,a number of genetic operators are used.The most important genetic operators are selection,crossover,and mutation,which are brie?y described here.

Selection is the mechanism for selecting the individuals with high?tness to produce new individuals for the next population.The selection function adopted here is the roulette wheel method,in which the probability of choosing a certain individual is proportional to its?tness, as follows:

Prob c i is selected

? ?

Fec iT

Fec kT

.(6)

Crossover is the method of merging the genetic information of two individuals(parents)to produce new individuals(children).In the simplest case,this process is realized by cutting two chromosomes at a randomly chosen position,with a probability of p c,and swapping the two tales,as is visualized in Fig.11(a).

The parameter p c is called the crossover rate and controls the rate at which solutions are subjected to crossover.The higher the value of p c,the quicker the new solutions

crossover

mutation

children

Fig.11.Genetic operators:(a)crossover,(b)mutation.

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introduced into the population.As p c increases,however,a solution can be disputed faster than selection can exploit them.Typical values of p c are in the range of0.5–1.0. Mutation is a probabilistic random deformation of an individual’s genetic information.The positive effect of mutation is the preservation of genetic diversity.The local maxima can be avoided.This process can be handled by altering each bit randomly with a small probability,p m,as depicted in Fig.11(b).

For parameter p m,which is called mutation rate,large

values will transform the GA into a purely random search algorithm.However,values that are too small will cause the premature convergence of GA to suboptimal solutions. Typically,p m is chosen in the range of0.005–0.1.

The process of reproduction continues until the termina-tion criterion is ful?lled.In this work,the termination criterion is the maximum number of generations;that is, reproduction continues until the number of generations reaches a speci?ed maximum limit.Fig.12shows the ?owchart of the whole optimization process via GA.

7.Simulation results

As discussed before,some important parameters affect the optimization process by GA.In this work,these parameters are determined through a series of experiments and algorithm performance comparisons.These para-meters are listed in Table4.

The advanced vehicle simulator,ADVISOR,(Markel et al.,2002)was used for simulation studies in this work. ADVISOR employs a combined forward/backward facing approach for the vehicle performance simulation.The vehicle components,models and speci?cations have been set for a parallel HEV,as listed in Table5.Sizes of the ICE and EM and the number of battery modules are obtained from a previous study using the GA approach(Montazeri-Gh&Poursamad,2005).

Fig.13shows the optimization process history(the best objective value in the population vs.generation number) for the TEH-CAR driving cycle.The resulting tuned MFs

Fig.12.Operation of a typical GA.Table4

Parameters of GA

Parameter Value Population size40 Number of generations50 Crossover rate(p c)0.6 Mutation rate(p m)0.05

Table5

HEV components models and speci?cations

Parameter Value

Vehicle characteristics

Rolling resistance coef.0.009

Aerodynamic drag coef.0.335

Vehicle front area(m2) 2.0

Wheel radius(m)0.282

Glider mass(kg)592

Cargo mass(kg)136

Transmission characteristics

Type Five speed manual gearbox

Gear ratios 2.84,3.77,5.01,5.57,and13.45

Ef?ciency(%)95

EM characteristics

Type Westinghouse AC induction motor Maximum power(kW)14

Maximum speed(rpm)10000

Speci?c power(W/kg)824

Peak ef?ciency(%)92

Energy storage system characteristics

Type Hawker Genesis VRLA battery Number of modules14

Module’s mass(kg)11

Voltage(V)12

Energy capacity(Ah)25

ICE characteristics

Type Geo Metro1.0L SI engine Maximum power(kW)41

Speci?c power(W/kg)313

Peak ef?ciency(%)34

Catalyst converter Close-coupled conventional converter

A.Poursamad,M.Montazeri/Control Engineering Practice16(2008)861–873869

for this cycle are depicted in Fig.14.As mentioned before,the MFs for output torque are exactly the same as those for required torque.In addition,Fig.15shows the control surface obtained for the TEH-CAR cycle.

Fuel consumption and emissions of the vehicle over TEH-CAR cycle,using the initial and tuned FLC,are compared in Table https://www.sodocs.net/doc/022416739.html,paring the value of objective function,it is clear that the tuned FLC outperforms the initial one.It is apparent from this table that there is an increase in CO emission after tuning the FLC.This is because GA aims to minimize the entire objective function rather than each component.In addition,the driving

performance characteristics of the vehicle are listed in this table,which reveal that HEV performance is improved by the tuned FLC.It is clear from the table that the control strategy parameters highly affect the driving performance characteristics of the vehicle and these driving character-istics should be included in the design process of control strategies.

As mentioned before,the bottom line for the control strategy is that the vehicle must follow the driver’s request,which is equivalent to the driving cycle.To show that this constraint is adequately satis?ed by the tuned FLC,the achieved speed and the difference between required and achieved speed (missed speed)are plotted in Fig.16.It is clear that there is an excellent agreement between the achieved and target speeds.

However,it should be mentioned that this constraint is not handled during the optimization process.The reason is that the torques required to produce the accelerations for satisfying the driving cycle are less than those required to satisfy the PNGV constraints;if the control strategy is

203040

1.47

1.4751.481.4851.491.4951.51.5051.51

1.515Generation number

V a l u e o f o b j e c t i v e

Fig.13.Trace of objective value during the optimization for TEH-CAR.

0.5

Required Torque

D e g r e e o f m e m b e r s h i p

Optimal

0.2

0.4

0.60.81

0.5

SOC

D e g r e e o f m e m b e r s h i p

Low

Low High

Normal

High

Fig.14.Final MFs tuned for TEH-CAR cycle.

00.20.40.60.8R O u t p u t t o r q u e

Fig.15.Control surface for TEH-CAR.

Table 6

Results for the tuned FLC over TEH-CAR cycle

Initial FLC

Tuned FLC FC and emissions FC (L/100km) 5.7851 5.6841HC (g/km)0.34880.31908CO (g/km)0.9516 1.1079NO x (g/km)0.27480.19027Objective

1.6251 1.4724Performance characteristics Gradeability (at 88.5km/h) 5.2951 6.56320–97time (s)1

2.830610.331664–97time (s)7.0383 5.27630–137time (s)34.679121.8773Max.speed (m/s)

151.3282153.4785Max.acceleration (m/s 2) 4.9507 4.9507Dist.in 5s (m)

49.1764

51.8251

A.Poursamad,M.Montazeri /Control Engineering Practice 16(2008)861–873

870

tuned such that the PNGV constraints are satis?ed,the constraint for tracking the driving cycle will be satis?ed consequently.

As discussed before,another constraint is the charge sustaining requirement.In this work,the difference between ?nal and initial SOC is forced not to exceed 0.5%of the initial SOC,by means of an iterative algorithm;that is,the simulation run is repeated until the difference between initial and ?nal SOC is in a 70.5%tolerance band.Fig.17shows the history of SOC during TEH-CAR cycle.This ?gure demonstrates that the charge sustaining requirement is satis?ed.Furthermore,the tuned FLC forces the SOC to be very close to the target SOC and this is a very useful feature of the controller,resulting in a longer battery life and a sustained SOC level,when extending the use to real world driving.

To investigate the effectiveness of the proposed ap-proach and study the impact of the driving cycle on the optimization of the fuzzy control strategy,the tuning process is also performed over FTP and NEDC driving cycles.

It should be mentioned that when noise is added to the TEH-CAR cycle such that the cycle characteristics do not change drastically,the tuned MFs obtained by GA do not vary.However,due to signi?cant differences among TEH-CAR,FTP and NEDC characteristics,the optimal

parameters obtained for FTP and NEDC cycles are different from those obtained for TEH-CAR cycle.This supports the theory that the driving cycle affects control strategy optimization and an optimal FLC,tuned for a speci?c driving cycle,is not necessarily optimal for other driving cycles.The tuned MFs for the NEDC driving cycle are depicted in Fig.18.Fuel consumption and emissions,together with driving performance characteristics of the HEV,controlled by the FLC,tuned over FTP and NEDC cycles are summarized in Table 7.

Another important point is the effect of the weighting factors in the objective function on FLC optimization.The weighting factors in the objective function were all set to 1

0200

400

600

800

10001200140016001800

050

100

A c h i e v e d s p e e d (k m /h )

200

400

600

800100012001400160018000

0.5

11.52x 10

-12

Time (sec)

M i s s e d s p e e d (k m /h )

Fig.16.Achieved and missed speeds over TEH-CAR driving cycle.

020*******

800100012001400160018000.63

0.64

0.65Time (sec)

S O C

Fig.17.SOC history over TEH-CAR driving cycle.

0.5

Required Torque

D e g r e e o f m e m b e r s h i p

Low High

-0.2

0.2

0.40.6

0.8

0.5

SOC

D e g r e e o f m e m b e r s h i p

Low High

Normal

Optimal Fig.18.Tuned MFs for NEDC driving cycle.

Table 7

Results for the tuned FLC over FTP and NEDC cycles

FTP NEDC Initial

Tuned Initial Tuned FC and emissions FC (L/100km) 6.0689 5.8221 5.8228 5.835HC (g/km)0.27570.268850.40030.36297CO (g/km)0.87010.90346 1.0566 1.3669NO x (g/km)0.22490.214530.33540.22236Objective

1.4131

1.38 1.8431 1.6794Performance characteristics Gradeability 5.2951 6.3382 5.2951 6.93140–97time (s)1

2.829210.359212.830110.318864–97time (s)7.0369 5.30027.0378 5.27140–137time (s)34.664622.001534.674121.7985Max.speed (m/s)151.3445161.8926151.338175.6567Max.accel.(m/s 2) 4.9507 4.9507 4.9507 4.9507Dist.in 5s (m)49.1758

51.8318

49.1762

51.8787

A.Poursamad,M.Montazeri /Control Engineering Practice 16(2008)861–873

871

to achieve a trade-off between FC and emissions.However,the optimal curve for ICE changes when these weights vary,and hence different tuned MFs are expected.For example,if the main objective is to minimize the vehicle FC,the weighting factor for FC in the objective function is set to 1and the other weighting factors are set to 0.This case is called FC-targeted optimization.Similarly,CO-targeted and (HC+NO x )-targeted cases can be de-?ned.The optimal curve of the ICE varies for these cases as depicted in Fig.19.The tuned MFs for FC-targeted optimization over TEH-CAR are shown in Fig.20and the FC and emissions of this case are compared to those of the trade-off case (where all weights are 1)in Table https://www.sodocs.net/doc/022416739.html,paring Fig.20with Fig.14,it is apparent that

different tuned MFs are obtained as the weighting factors vary in the objective function.In addition,it is seen from Table 8that FC is reduced in the FC-targeted optimiza-tion,while all emissions are increased with respect to the trade-off case.8.Conclusion

Genetic-fuzzy control strategy for parallel HEVs is proposed.The genetic-fuzzy control strategy is an FLC,which is tuned using GA.The objective is the fuel consumption and emission minimization and maintenance of driving performance characteristics within standard limits.

The tuning process is conducted to maintain computa-tional ef?ciency,utilizing expert knowledge and interpret-ability,together with diversity of solution space and global optimality.To this end,the rule base of the FLC is designed based on the knowledge of experts.Furthermore,the coding is performed such that the length of the chromosomes is minimized by using the most effective MF parameters and also the tuned MFs remain consistent with the meaning of their linguistic https://www.sodocs.net/doc/022416739.html,ing this approach,the performance of the tuned FLC is easily interpretable.

The simulation results show the effectiveness of this approach in terms of reducing the value of objective and improving the driving performances.An important result is that the parameters of the fuzzy control strategy affect HEV driving performance characteristics and the control strategy should be designed such that driving performance is not sacri?ced.The simulations are run over three different driving cycles.The results reveal that the tuning process is affected by the driving cycle;that is,an optimal set of MFs for a driving cycle or driving situation is not necessarily optimal for other driving situations.In view of this fact,an additional extension that can be added in the future to increase the effectiveness of the proposed genetic-fuzzy control strategy is designing an adaptation algorithm that recognizes the driving situation and adapts the parameters such that the FLC works optimally in the current driving situation.

Moreover,it should be mentioned that the fuel economy,as well as emissions and performance,of HEVs also depends on optimal gear shifting strategy.Therefore,future works can also include developing an optimal gear

1000

2000300040005000

6000

010203040506070

8090Engine speed (rpm)

E n g i n e t o r q u e (N .m )

Fig.19.Optimal curves for different weighting factors.

0.2

0.4

0.60.81

1.2

00.5

Required Torque

D e g r e e o f m e m b e r s h i p

Low High

0.5

SOC

D e g r e e o f m e m b e r s h i p

Low Normal

High

Optimal Fig.20.Tuned MFs for FC-targeted optimization over TEH-CAR.

Table 8

Comparison of trade-off and FC-targeted results over TEH-CAR cycle

Trade-off

FC-targeted FC (L/100km) 5.6841 5.5466HC (g/km)0.319080.3376CO (g/km) 1.1079 1.1155NO x (g/km)0.190270.2622Objective

1.4724

1.6176

A.Poursamad,M.Montazeri /Control Engineering Practice 16(2008)861–873

872

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Design of genetic-fuzzy control strategy for parallel hybrid electric vehicles

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