This paper uses a quarter model of an automobile having passive and semiactive suspension systems to develop a scheme for an optimal suspension controller. Semiactive suspension is preferred over passive and active suspensions with regard to optimum performance within the constraints of weight and operational cost. A fuzzy logic controller is incorporated into the semiactive suspension system. It is able to handle nonlinearities through the use of heuristic rules. Particle swarm optimization (PSO) is applied to determine the optimal gain parameters for the fuzzy logic controller, while maintaining within the normalized ranges of the controller inputs and output. The performance of resulting optimized system is compared with different systems that use various control algorithms, including a conventional passive system, choice options of feedback signals, and damping coefficient limits. Also, the optimized semiactive suspension system is evaluated for its performance in relation to variation in payload. Furthermore, the systems are compared with respect to the attributes of road handling and ride comfort. In all the simulation studies it is found that the optimized fuzzy logic controller surpasses the other types of control.
A suspension system of an automobile improves the ride quality by absorbing shock and other external disturbances under various operating conditions. While doing so, it has to support both static and dynamic loading of the vehicle as well. The external disturbances may arise from a variety of sources such as road surface irregularities, aerodynamics forces, nonuniformity of the tire/wheel assembly [
An active suspension system requires external power to function, which results in added complexity, cost, and weight, as well as reliability problems, though it improves the controllability [
Fuzzy logic control has been used in many applications including cruise control, automatic transmissions, Sendai subway operation, coldrolling mills, fish processing machine, robots, selfparking car, image stabilizer for video camera, and a fully automated washing machine [
Rao et al. [
Slaski and Maciejewski [
Given the proven diversity of fuzzy logic control, this technique is incorporated for control of a semiactive suspension system in the present paper. It is difficult to control the parameters of a fuzzy logic control system because it may not be possible to design the rules without the help of an expert or the process may be rigorous involving a number of iterations. Therefore, a biologically inspired optimization method is utilized in the tuning of the important scaling parameters of the controller. Specifically, particle swarm optimization (PSO) method is used, which gives better results both in terms of convergence and computation time in comparison with genetic algorithms (GA). PSO uses a mathematical model that somewhat mimics a flock of birds in search of food. Every bird is considered a particle and it keeps record of its best position and velocity. The best position and velocity of the complete flock are also recorded. In this manner a bird continuously orients itself in the best path based on its own experience and that of the entire flock. This technique has been widely used in engineering problems [
The present paper uses quarter car passive and semiactive suspension systems, which are modeled in Simulink. Fuzzy logic control is used in the semiactive suspension system. The inputs and the output of fuzzy logic controller are normalized and gain factors are incorporated into the system. These gain factors are evaluated by performing offline tuning using PSO in an optimal manner. Based on the optimized tuning parameters, the maximum output of the damper is determined. Various models are designed based on a variety of control algorithms, input parameters, damping coefficient limits, and membership functions. The models are compared for road handling and ride comfort. Two different types of road disturbance profile are considered in the present paper. The rest of the paper is organized as follows. Section
This section describes the modeling aspects of the considered systems. The block diagram fuzzy logic control system, which is through PSO, is presented in Figure
Block diagram of PSO tuned fuzzy logic control system.
The quarter car model of a passive suspension system is shown in Figure
Quarter car parameters.
Parameter  Symbol  Value  Units 

Sprung mass 

300  kg 
Unsprung mass 

36  kg 
Sprung mass damping coefficient 

1000  N s/m 
Spring stiffness 

16000  N/m 
Tire stiffness 

160000  N/m 
Quarter car model [
The mathematical model of the passive suspension system is described by (
Here,
In order to carry out a comparison between the passive and the fuzzylogicbased semiactive suspension systems, two types of road profiles are considered. The sinusoidal profile is given by (
Sinusoidal road profile.
The road disturbance is a combination of two different sinusoidal functions and hence the performance of the suspension systems can be clearly predicted for a variety of road profiles.
A step input of 0.5 m step height is considered as shown in Figure
Step road profile.
For a semiactive suspension model, the damping coefficient needs to be varied. In order to incorporate variability of the damping coefficient, a fuzzy logic controller is included in the design scheme.
A fuzzy logic controller involves fuzzification interface, fuzzy rule base, decision making logic, and defuzzification interface [
Membership function of relative velocity.
Membership function of relative displacement.
Membership function of damping coefficient.
Based on the three membership functions for each input, a maximum of nine rules may be formulated. These rules are given in Table
Fuzzy rule base (nine rules).
Relative displacement  

N  Z  P  
Relative velocity  N  M  L  L 
Z  S  S  S  
P  L  L  M 
PSO is inspired by the behavior exhibited by flocks of birds and schools of fish. The main approach of this algorithm is to search through an ndimensional problem to optimize an objective function. The PSO technique was selected because its implementation is relatively simple and the convergence behavior is good. Furthermore, it has the ability to reach the global optimum while avoiding local optima [
The swarm comprises a fixed number of particles. These particles collaboratively search for an optimal position. A cognitive component encourages the particles to improve upon their individual best position thus far, while a social component always pulls the particles toward the global best position thus far. A flow chart of the algorithm is given in Figure
Flow chart of PSO algorithm [
The objective function used in the present application is the suspension displacement with respect to the step road disturbance, which needs to be minimized. The best known position for each particle is tracked and memorized as
Here,
The proposed approach is implemented on the suspension system of a quartervehicle model, and computer simulations are carried out. This section describes this simulation exercise and analyzes the obtained results. Modeling and simulation are performed in Matlab 7.8.0 (R2009a). The fuzzy logic controller is designed using the Matlab Fuzzy Tool Box while simulations are performed in Simulink. The PSO algorithm is programmed in Matlab and executed to determine the three optimized gain parameters of the fuzzy logic controller. The reference algorithm is employed on an active suspension system while the present work implements the technique on a semiactive suspension system. The parameters used in the PSO algorithm are given in Table
Parameters of the PSO algorithm.
Parameter  Symbol 

Swarm size  30 
Number of iterations  30 
Unknown variables  3 
Cognitive acceleration  1.2 
Social acceleration  1.6 
Inertial weight  0.4 
Optimized values obtained through the PSO algorithm for the fuzzy semiactive suspension system are
Fuzzy skyhook system is designed using the theoretical background of skyhook system in which the relative velocity across the two masses and the absolute velocity of the sprung mass are monitored in order to modulate the damping value. In case of the fuzzy groundhook system, the absolute velocity of the sprung mass is replaced by that of the unsprung mass. The fuzzy hybrid system combines the strategy of fuzzy groundhook and skyhook systems. Figures
Tire load for various control algorithms (step input).
Suspension displacement for various control algorithms (step input).
Values of important performance parameters in different control algorithms are tabulated in Table
Performance comparison of various control techniques for step road profile.
Parameters  Control algorithms  

Optimized fuzzy  Passive  Fuzzy skyhook  Fuzzy groundhook  Fuzzy hybrid  
Tire load 



— 






− 

− 
—  − 

− 

− 


Suspension displacement 



— 








− 
—  − 

− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
The bold values indicate percentage overshoot while the italic values indicate the stabilizing time expressed in seconds. The same format is maintained throughout the tabular presentation of the performance parameters. The top two values in each grid correspond to the initial disturbance and the bottom ones correspond to the second part of the disturbance. Suspension displacement is a good indicator of the ride comfort while tire load is a measure of vehicle handling.
For a step road disturbance, the optimized fuzzy system outperforms all other systems, with regard to suspension displacement. There is no overshoot and the system gets stabilized at the earliest in relation to other systems in the comparison. It follows that the optimized fuzzy system gives the best ride comfort among all the control algorithms. The passive system does not stabilize at all and it gives the highest values of overshoot for the suspension displacement. Fuzzy hybrid approach combines the strategies of skyhook and groundhook. Therefore, it is better than each of the other control algorithms.
With regard to the tire load, the shortest stabilizing time periods are obtained by the optimized fuzzy logic system while groundhook offers the minimum percentage overshoot. However, the optimized fuzzy system is still comparable with the groundhook system, with regard to vehicle handling.
Figures
Tire load for various control algorithms (sinusoidal input).
Suspension displacement for various control algorithms (sinusoidal input).
The values of important performance parameters for various control algorithms are given in Table
Performance comparison of various control techniques for sinusoidal road profile.
Parameters  Control algorithms  

Optimized fuzzy  Passive  Fuzzy skyhook  Fuzzy groundhook  Fuzzy hybrid  
Tire load  − 


—  − 

− 

− 

− 



− 

− 

− 


Suspension displacement 


− 
— 


− 

− 



− 



− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
For a sinusoidal road disturbance, the optimized fuzzy system still provides the best performance by giving a zero overshoot for suspension displacement. However, the fuzzy hybrid gives the shortest stabilizing time periods. It is worth mentioning that the optimized fuzzy system performs better even for sinusoidal input, thereby validating its performance for different inputs.
Various systems are modeled on the basis of different combinations of input parameters of the fuzzy logic controller. Two different systems are modeled on the basis of relative velocity and relative displacement across the sprung mass and the unsprung mass. While the fuzzy input variables having three membership functions each give rise to a total of nine rules, the selection of two membership functions each leads to a total of four rules, as given in Table
Fuzzy rule base (four rules).
Relative displacement  

N  P  
Relative velocity  N  M  S 
P  L  M 
Figures
Performance comparison of various input parameters in fuzzy logic control for step road profile.
Parameters  Input parameters for fuzzy logic controller  

Relative velocity/ 
Absolute velocity/ 
Absolute acceleration/ 
Absolute velocity/ 
Relative velocity/  
Tire load 










− 

− 

− 

− 

− 


Suspension displacement 














− 

− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
Tire load for various input parameters (step input).
Suspension displacement for various input parameters (step input).
Various systems are designed based on the input parameters of the fuzzy logic controllers. The fuzzy systems that incorporate fuzzy inputs of relative displacement and relative velocity provide the best results for suspension displacement in response to a step road disturbance. This system is governed by nine rules (Table
The optimized fuzzy system gives better performance for the vehicle handling parameter of tire load while maintaining the combined factors of minimum overshoot and shortest stabilizing time. Figures
Tire load for various input parameters (sinusoidal input).
Suspension displacement for various input parameters (sinusoidal input).
Values of important performance parameters of the systems based on various input parameters are given in Table
Performance comparison of various input parameters in fuzzy logic control for sinusoidal road profile.
Parameters  Input parameters for fuzzy logic controller  

Relative velocity/ 
Absolute velocity/ 
Absolute acceleration/ 
Absolute velocity/ 
Relative velocity/  
Tire load  − 

− 

− 

− 

− 

− 

− 

− 

− 

− 


Suspension displacement 






− 

− 





− 

− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
The same fuzzy system outperforms all other systems even for sinusoidal road disturbance.
Various systems are modeled and simulated for analyzing the impact of payload variation on the performance parameters. The weight of each passenger is taken as 100 kg, which transforms to 25 kg in the quarter car parameter. Figures
Performance comparison of systems based on different payloads for step road profile.
Parameters  Variable payload (number of passengers)  

Only driver  1  2  3  
Tire load 








− 

− 

− 

− 


Suspension displacement 










− 

− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
Tire load for payload variation (step input).
Suspension displacement for payload variation (step input).
The optimized fuzzy system is analyzed for its performance under conditions of variable payload. For a step road disturbance, there is a slight variation in the ride comfort in relation to the number of passengers, while vehicle handling improves with the increase in the number of passengers. Figures
Tire load for payload variation (sinusoidal input).
Suspension displacement for payload variation (sinusoidal input).
Values of important performance parameters of the systems for various payloads are given in Table
Performance comparison of systems based on different payloads for sinusoidal road profile.
Parameters  Variable payload (number of passengers)  

Only driver  1  2  3  
Tire load  − 

− 

− 

− 

− 

− 

− 

− 


Suspension displacement 
















Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
For a sinusoidal road disturbance, both the ride comfort and the vehicle handling characteristics show improvement with the increase in the number of passengers. Therefore, the designed controller provides optimum results even with a variable payload.
Using the optimized value of damping coefficient, four systems are designed with variable damping coefficient limits of 1000, 2000, 3000, and 4000 N s/m. Simulation of these systems presents an insight into the parametric analysis of the variable damping coefficient limits. Figures
Tire load for maximum damping coefficient limit (step input).
Suspension displacement for maximum damping coefficient limit (step input).
Values of some important performance parameters of the systems based on maximum damping coefficient limit are given in Table
Performance comparison of systems based on maximum damping coefficient for step road profile.
Parameters  Maximum damping coefficient limit (N s/m)  

4000  3000  2000  1000  
Tire load 








− 

− 

− 

− 


Suspension displacement 










− 

− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
Selection of an appropriate damping coefficient limit is very significant performance consideration. Systems based on different damping coefficient limits exhibit different results as is evident from the tabulated values. A damping coefficient limit of 4000 N s/m (the optimized value is 3802.3) gives the best results for ride comfort and road handling under a step road disturbance. The performance deteriorates as the damping value decreases. Figures
Tire load for maximum damping coefficient limit (sinusoidal input).
Suspension displacement for maximum damping coefficient limit (sinusoidal input).
Values of important performance parameters of systems based on maximum damping coefficient limit are given in Table
Performance comparison of systems based on maximum damping coefficient for sinusoidal road profile.
Parameters  Maximum damping coefficient limit (N s/m)  

4000  3000  2000  1000  
Tire load  − 

− 

− 

− 

− 

− 

− 

− 


Suspension displacement 


− 

− 

− 
— 


− 

− 

− 

Bold cells give percentage overshoot.
Italic cells give stabilizing time in seconds.
For a sinusoidal road disturbance, a damping coefficient of 1000 N s/m yields a nonstabilizing behavior of the system with regard to the ride comfort parameters. A damping coefficient of 4000 N s/m yields the best results for suspension displacement, and with regard to the tire load it gives the shortest stabilizing time and comparable overshoot values.
This paper presented a successful application of a hybrid fuzzylogic technique in the design of a semiactive suspension system for an automobile. The relative displacement and the relative velocity of the suspension were the inputs to the fuzzy logic controller. The input and output membership functions of the fuzzy system were normalized using scaling factors. The incorporation of particle swarm optimization (PSO) to tune the controller parameters is a novel approach in the context of semiactive suspensions. Specifically, PSO performed offline tuning of the gain factors of the fuzzy logic controller of a quarter car suspension model. The PSO objective function was selected as the offset of the suspension displacement and the road disturbance, which was minimized. The developed algorithm generated a damping coefficient limit for the damper of the suspension system. The performance of the fuzzy logic controlled system was found to be much better than that of the passive system in terms of both road handling and ride comfort. Furthermore, by comparing the performance under different control algorithms, it was found that the optimized fuzzy logic system was superior. The designed semiactive system performed better within the entire range of payload variation. Furthermore, the fuzzy heuristic rules coped well with the changing disturbances.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors wish to express their gratitude to Professor Dr. Syed Riaz Akbar and Professor Dr. Sahar Noor for their valuable guidance and support in the successful culmination of the research presented in this paper.