The Control of an Active Seat Suspension Using an Optimised Fuzzy Logic Controller , Based on Preview Information from a Full Vehicle Model

The use of suspension preview information obtained from a quarter vehicle model (QvM) to control an active seat has been shown by the authors to be very promising, in terms of improved ride comfort. However, in reality, a road vehicle will be subjected to disturbances from all four wheels, and therefore the concept of preview enhanced control should be applied to a full vehicle model. In this paper, different preview scenarios are examined, in which suspension data is taken from all or limited axles. Accordingly, three control strategies are hypothesized—namely, front-left suspension (FLS), front axle (FA), and four wheel (4W). The former utilises suspension displacement and velocity preview information from the vehicle suspension nearest to the driver’s seat. The FA uses similar preview information, but from both the front-left and front-right suspensions. The 4W controller employs similar preview information from all of the vehicle suspensions. To cope with friction non-linearities, as well as constraints on the active actuator displacement and force capabilities, three optimal fuzzy logic controllers (FLCs) are developed. The structure of each FLC, including membership functions, scaling factors, and rule base, was sequentially optimised based on improving the seat effective amplitude transmissibility (SEAT) factor in the vertical direction, using the particle swarming optimisation (PSO) algorithm. These strategies were evaluated in simulation according to ISO 2631-1, using different road disturbances at a range of vehicle forward speeds. The results show that the proposed controllers are very effective in attenuating the vertical acceleration at the driver’s seat, when compared with a passive system. The controller that utilised suspension preview information from all four corners of the car provided the best seat isolation performance, independent of vehicle speed. Finally, to reduce the implementation cost of the “four suspension” controller, a practical alternative is developed that requires less measured preview information.


Introduction
Vehicle drivers are frequently exposed to vertical vibration over a low frequency range, which is transmitted to the driver's seat from road roughness through the vehicle suspension and body.This vibration reduces ride comfort and can cause long-term health problems, as the human body is most sensitive to vertical vibration in the frequency range of 4-8 Hz [1,2].Consequently, seat suspensions are practicable and cost-effective solutions that are used in vehicles to overcome these effects.
Three configurations of seat suspension exist in this field: passive, semi-active, and active.Passive systems are simple and cost-effective, consisting of spring and damper elements with fixed characteristics.Due to this, they have limited vibration attenuation performance.Semi-active suspensions are also comprised of spring and damper elements, but the properties of these elements can be adjusted using minimal power consumption.Thus, their vibration attenuation performance is superior to passive systems.However, their performance is still compromised, because they can only dissipate energy from the system [3].Conversely, active seat suspensions, which apply an external force based upon a control strategy, can significantly reduce vibration over a broadband frequency range, and therefore can be considered as an alternative to costly vehicle active suspension systems that are called upon to optimise both ride comfort and handling.
It was Bender who first presented the concept of preview information in vehicle suspensions [30], suggesting that employing preview information can effectively improve vehicles' performance.Preview information from the road disturbance is used in the control approach, before the road disturbances act on the vehicle body.This approach can decrease the controller and actuator response times, hence improving the suspension performance [31,32].There are two approaches to preview control.The first is "look ahead", where the road disturbances are sensed as preview information for the controller of the active suspension, before these disturbances act on the vehicle.The second is the "wheelbase", where instead of acquiring preview information from the road disturbances, the disturbances are sensed from the dynamic changes of the front wheels, and later used as preview information to control the active rear suspension.However, both approaches have some drawbacks; for instance, the real implementation of the look-ahead approach is costly and complicated, as it requires expensive sensory systems to accurately predict road profiles [27,31,32].Whilst the "wheelbase" option seems more practical than the "look ahead" alternative, the preview information is only accessible to control the rear suspension, and road excitations at the rear axle cannot be always correctly predicted from those encountered by the front axle, especially during cornering [33].In a previous study by the authors [34], a simple and cost-effective controller approach with a linear Quarter Vehicle Model (QvM), which uses preview information from the vehicle suspension, was applied to control an active seat suspension.Both simulation and experimental results showed that this approach can significantly attenuate the vertical vibration at the driver's seat.To make the application more realistic and investigate the benefits that could be gained from this principle, a full vehicle model is utilised here.To cope with vehicle suspension non-linearities and physical constraints in both the seat suspension travel and actuator force capacity, a fuzzy logic control (FLC) approach was used.One of the main drawbacks of FLC is the construction of the rule base (RB) and the fuzzification process, including membership functions (MFs) and scaling factors.Moreover, there is no standard method to set the number and type of the MFs.In addition, the RB depends on expert knowledge about the system behaviour, which is influenced by the type and number of both the input and output variables, as well as their corresponding scaling factors.It is challenging to hypothesise the RB for a complicated system [35], such as that required for an active seat suspension.A trial and error approach has been widely used to tune either the parameters of the MFs or the scaling factors under a suggested RB [14,15,18], but this is both time-consuming and an inefficient way of finding a global optimum solution [36].
In contrast, other researchers have used evolution optimisation algorithms, such as genetic algorithms (GA) [37][38][39] or the Particle Swarm Optimisation (PSO) algorithm [16,35,40].Rajeswari and Lakshmi [41] employed both GA and PSO to optimise the scaling factors, MFs and RB of an FL controller for an active suspension system.They concluded that the PSO is more effective in optimising the FLC structure when compared with the GA.The PSO technique is simple and can be easily applied.Moreover, its convergence characteristics are stable and computationally efficient [42][43][44].
This paper presents the design of three optimal FL controllers for an active seat suspension, which use measurable and low-cost preview information from the vehicle suspension states, considering hard constraints related to both allowable seat stroke and actuator force capacity.These controllers are front-left suspension (FLS-FLC), front axle (FA-FLC), and four wheels (4W-FLC).The first utilises suspension displacement and velocity information from the nearest corner to the active seat.The FA-FLC uses similar preview information, but from both the front left and right suspensions.The 4W-FLC, employs preview information from all four vehicle suspensions.The optimal structure of each of the FLCs, including the MFs, scaling factors, and RB were sequentially designed using PSO.

Integrated Model
The vehicle and seat simulation model used in this study consists of a full linear vehicle model, a passive seat suspension, and a driver's body model, as shown in Figure 1.The full vehicle model is the "seven degree of freedom" model presented in [45].The vehicle body mass M s (sprung mass) is assumed to be a rigid body with bounce, pitch, and roll motions denoted by x s , θ, and φ, respectively.In this study, we have neglected any lateral or yaw body motions that would be appropriate in the analysis of vehicle handling.
Each wheel of the front and rear axles, represented by the un-sprung masses m 11 , m 12 , m 21 , and m 22 , has a single degree of freedom in the vertical direction, denoted by x 11 , x 12 , x 21 , and x 22 , respectively, while the road disturbances at these wheels are represented by x r11 , x r12 , x r21 , and x r22 .For simplicity, this model involves only the driver's seat, with a linear lumped mass-spring-damper of one degree of freedom (DOF) in the vertical direction, denoted by x se .Further development of the model could include the extension of this study to multiple suspension seats, where the cross coupling would be explicitly modelled.Moreover, the driver's body is represented by a one DOF in the vertical direction, denoted by x b .The tyre springs and suspension spring elements of the front and rear axles are presumed to be linear.Assuming small pitch and roll angles, the dynamic equations of the integrated model are given as follows: (1) Vehicle body motion: where F sij is the suspension dynamic force at each vehicle suspension, given by: while f V sij is the dry friction force of the suspension damper at each wheel, F se is the seat suspension force, and F a is the controller force.(b) Pitch (2) Un-sprung masses m ij ..
(3) Seat suspension . Each of the vehicle suspension dampers includes a non-linear dry friction force f (V s ) that depends on the velocity across the suspension V s and a viscous band ε [15], as presented in Figure 1.
Vibration 2018, 2, x FOR PEER REVIEW 4 of 21 (3) Seat suspension (4) Driver's body Each of the vehicle suspension dampers includes a non-linear dry friction force ( ) that depends on the velocity across the suspension and a viscous band [15], as presented in Figure 1.

Fuzzy Logic Controller
Generally, an FLC consists of four parts, as shown in Figure 2 [46]: (1) A fuzzification interface, which changes the controller inputs to linguistic variables that can be utilised in the inference mechanism.(2) A rule-base (RB), which is a set of linguistic ("if-then") rules that stores the knowledge of how to control the process.(3) An inference mechanism, which uses the linguistic inputs and the RB to produce the control decision.(4) A defuzzification interface, which converts the linguistic outputs into crisp ones.
Put simply, the output of each proposed FLC is the control force.However, the total number of inputs for each FLC is different.For instance, the FLS-FLC has only two inputs, as presented in Figure 3a.The FA-FLC requires four inputs, namely the displacements and velocities of the front left and right suspensions.Conversely, the number of inputs to the 4W-FLC are eight.However, the number of rules of the FLC depends on the number of input and output variables, as well as the number of their MFs.For example, assume that each input variable of the FA-FLC consists of five MFs, then a total of 625 rules are required to design its RB, and hence, there is an increase in the optimisation processing time and controller complexity.
Alternatively, the FA-FLC and 4W-FLC are assumed to be composed of sub-FLCs [38], such that each sub-FLC requires only two inputs, as shown in Figure 3b,c, respectively.Thus, the FA-FLC consists of two sub-FLCs, namely FA1-FLC and FA2-FLC, in which the former uses the preview information from the front-left vehicle suspension and generates the sub-control force .The latter utilises similar preview information, but from the front-right suspension, and produces the sub-

Fuzzy Logic Controller
Generally, an FLC consists of four parts, as shown in Figure 2 [46]: (1) A fuzzification interface, which changes the controller inputs to linguistic variables that can be utilised in the inference mechanism.(2) A rule-base (RB), which is a set of linguistic ("if-then") rules that stores the knowledge of how to control the process.(3) An inference mechanism, which uses the linguistic inputs and the RB to produce the control decision.(4) A defuzzification interface, which converts the linguistic outputs into crisp ones.
Put simply, the output of each proposed FLC is the control force.However, the total number of inputs for each FLC is different.For instance, the FLS-FLC has only two inputs, as presented in Figure 3a.The FA-FLC requires four inputs, namely the displacements and velocities of the front left and right suspensions.Conversely, the number of inputs to the 4W-FLC are eight.However, the number of rules of the FLC depends on the number of input and output variables, as well as the number of their MFs.For example, assume that each input variable of the FA-FLC consists of five MFs, then a total of 625 rules are required to design its RB, and hence, there is an increase in the optimisation processing time and controller complexity.
Alternatively, the FA-FLC and 4W-FLC are assumed to be composed of sub-FLCs [38], such that each sub-FLC requires only two inputs, as shown in Figure 3b,c, respectively.Thus, the FA-FLC consists of two sub-FLCs, namely FA1-FLC and FA2-FLC, in which the former uses the preview information from the front-left vehicle suspension and generates the sub-control force F a1 .The latter utilises similar preview information, but from the front-right suspension, and produces the sub-control force F a2 , while the resultant control force is the sum of these forces.Similarly, the 4W-FLC has four sub-FLCs, each corresponding to each vehicle suspension.However, each sub-FLC has its own RB, thereby decreasing the computational time and reducing the overall RB size.control force , while the resultant control force is the sum of these forces.Similarly, the 4W-FLC has four sub-FLCs, each corresponding to each vehicle suspension.However, each sub-FLC has its own RB, thereby decreasing the computational time and reducing the overall RB size.control force , while the resultant control force is the sum of these forces.Similarly, the 4W-FLC has four sub-FLCs, each corresponding to each vehicle suspension.However, each sub-FLC has its own RB, thereby decreasing the computational time and reducing the overall RB size.

Optimisation Process
The optimum FLC knowledge base is obtained sequentially through two stages, as shown in Figure 4a.Initially, the RB and scaling factors are optimised using assumed MFs.Then these are used in stage 2 to modify the parameters of the initial MFs.Hence, the output of the each proposed FLC is limited by the actuator force capacity.Thus, the output scaling factor S 3 of the FLS-FLC is constrained to be 1500.0N.This ensures that the demand control force does not exceed the actuator force capacity, which is important in terms of stability and real-life implementation.However, this is not the case for the sub-FLCs, either in the FA-FLC or the 4W-FLC, which consist of different sub-FLCs.Nevertheless, the sum of all the output scaling factors of all the sub-FLCs in the main FLC is limited within the maximum allowable force.Moreover, the output of each FLC is filtered by a low-pass filter with a cut-off frequency of f n = 25 Hz, in order to emulate the dynamics of the active force actuator, and also to reduce the effect of road-induced high-frequency content in the preview signal.
The MFs used in this study are of triangular shape, due to their simplicity and ease of adjustment, as well as offering the greatest output results with respect to other MF types [47].Each input variable is assumed to be comprised of five linguistic degrees: negative big (NB), negative small (NS), zero (ZE), positive small (PS), and positive big (PB).The output fuzzy function consists of seven degrees: negative big (NP), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM), and big (PB), as shown in Figure 4b.Consequently, the RB of the FLS-FLC or any sub-FLCs is composed of 25 rules.
The rules and the scaling factors are formulated based on the PSO.For example, in stage 1 the size of the position vector of each particle in the PSO is 27, corresponding to the total number of design variables.The first 24 positions are assigned integer numbers from (1 to 7), which are equivalent to the linguistic degrees of the output variable.The remaining three design variables are allocated to the input and output scaling factors, respectively.

Optimisation Process
The optimum FLC knowledge base is obtained sequentially through two stages, as shown in Figure 4a.Initially, the RB and scaling factors are optimised using assumed MFs.Then these are used in stage 2 to modify the parameters of the initial MFs.Hence, the output of the each proposed FLC is limited by the actuator force capacity.Thus, the output scaling factor of the FLS-FLC is constrained to be 1500.0N.This ensures that the demand control force does not exceed the actuator force capacity, which is important in terms of stability and real-life implementation.However, this is not the case for the sub-FLCs, either in the FA-FLC or the 4W-FLC, which consist of different sub-FLCs.Nevertheless, the sum of all the output scaling factors of all the sub-FLCs in the main FLC is limited within the maximum allowable force.Moreover, the output of each FLC is filtered by a lowpass filter with a cut-off frequency of = 25 Hz, in order to emulate the dynamics of the active force actuator, and also to reduce the effect of road-induced high-frequency content in the preview signal.
The MFs used in this study are of triangular shape, due to their simplicity and ease of adjustment, as well as offering the greatest output results with respect to other MF types [47].Each input variable is assumed to be comprised of five linguistic degrees: negative big (NB), negative small (NS), zero (ZE), positive small (PS), and positive big (PB).The output fuzzy function consists of seven degrees: negative big (NP), negative medium (NM), negative small (NS), zero (ZE), positive small (PS), positive medium (PM), and big (PB), as shown in Figure 4b.Consequently, the RB of the FLS-FLC or any sub-FLCs is composed of 25 rules.
The rules and the scaling factors are formulated based on the PSO.For example, in stage 1 the size of the position vector of each particle in the PSO is 27, corresponding to the total number of design variables.The first 24 positions are assigned integer numbers from (1 to 7), which are equivalent to the linguistic degrees of the output variable.The remaining three design variables are allocated to the input and output scaling factors, respectively.The optimum RB and scaling factors are obtained in Stage 1 using the assumed MFs; then, in stage 2, the parameters of these MFs are modified, using the optimum RB and scaling factors.These parameters are adjusted based on the assumptions given in [38].Thus, each input and output variable has six and eight MF parameters to be adjusted, respectively, as illustrated in Figure 4b.
Ride quality is related to both the magnitude and frequency content of the vertical vibration sensed by the human body, particularly over a frequency range of 4-8 Hz.Thus the seat effective amplitude transmissibility (SEAT) factor in the vertical direction was selected as the objective function in the optimisation process.It is defined as the ratio between the frequency-weighted root mean square (RMS) acceleration at the seat to that at the seat base [48], as follows: x se,w rms ..
x s,w rms (9) The subscript w in the previous formula indicates that the acceleration values are weighted according to the frequency weighted function W k , as suggested by ISO 2631-1 [49] and shown in Figure 5.This scheme weights the human body's most sensitive frequency range (4-8 Hz) more heavily than other frequencies.The optimum RB and scaling factors are obtained in Stage 1 using the assumed MFs; then, in stage 2, the parameters of these MFs are modified, using the optimum RB and scaling factors.These parameters are adjusted based on the assumptions given in [38].Thus, each input and output variable has six and eight MF parameters to be adjusted, respectively, as illustrated in Figure 4b.
Ride quality is related to both the magnitude and frequency content of the vertical vibration sensed by the human body, particularly over a frequency range of 4-8 Hz.Thus the seat effective amplitude transmissibility (SEAT) factor in the vertical direction was selected as the objective function in the optimisation process.It is defined as the ratio between the frequency-weighted root mean square (RMS) acceleration at the seat to that at the seat base [48], as follows: The subscript in the previous formula indicates that the acceleration values are weighted according to the frequency weighted function , as suggested by ISO 2631-1 [49] and shown in Figure 5.This scheme weights the human body's most sensitive frequency range (4-8 Hz) more heavily than other frequencies.Reducing the seat acceleration results in large seat suspension strokes, which are physically bounded [2].Thus, this constraint is considered in the optimisation problem, such that the maximum allowable seat suspension travel ( , ) was assumed to be 45 mm.The system was modelled using Simulink, and the optimisation problem was formulated in MATLAB and solved off-line, using the PSO and Fuzzy Logic toolboxes with a time step size of 0.001 s.Due to the fact that most road unevenness is best described by random profiles, which include the frequency range most sensitive to the human body in the vertical direction, a random road profile was selected in the optimisation process.The random road profile used in this study is of class E (very poor) road roughness according to the ISO-8606 standard [50], which was previously used by the authors in [34] with a vehicle forward speed of 60 km/h.In the optimisation process, the default MATLAB setting parameters of the PSO algorithm were used with a swarm size of 14.The type of fuzzy system used in this study is a Mamdani-type, and the centre of gravity method is used in the defuzzification process.Reducing the seat acceleration results in large seat suspension strokes, which are physically bounded [2].Thus, this constraint is considered in the optimisation problem, such that the maximum allowable seat suspension travel (x se,max ) was assumed to be 45 mm.
The system was modelled using Simulink, and the optimisation problem was formulated in MATLAB and solved off-line, using the PSO and Fuzzy Logic toolboxes with a time step size of 0.001 s.Due to the fact that most road unevenness is best described by random profiles, which include the frequency range most sensitive to the human body in the vertical direction, a random road profile was selected in the optimisation process.The random road profile used in this study is of class E (very poor) road roughness according to the ISO-8606 standard [50], which was previously used by the authors in [34] with a vehicle forward speed of 60 km/h.In the optimisation process, the default MATLAB setting parameters of the PSO algorithm were used with a swarm size of 14.The type of fuzzy system used in this study is a Mamdani-type, and the centre of gravity method is used in the defuzzification process.
Moreover, the full vehicle model was excited at the left and right front wheels with different disturbances [51].The disturbances at the rear wheels were similar to those at the front, with a time delay that depended on the vehicle wheel base and the vehicle speed.
To achieve realistic dynamic responses, the characteristics of the passive seat suspension (m se , k se and c se ), as well as the driver's body (k b and c b ), were determined from experimental tests of a passive seat suspension with a dummy [34].The parameters of the full vehicle model and the characteristics of the passive seat suspension, as well as those of the driver's body, are listed in Table 1.After solving the optimisation problem for each FLC, the resulting optimum controller maps are presented in Figure 6.In addition, the demand control force of both the FLS-FLC and the FA-FLC were plotted, using contour plots as shown in Figure 7a,b, respectively.These maps encompass a very wide range of suspension operating conditions that are unlikely to be experienced during normal operation.From these figures, it can be observed that the output map of the FA1 is very similar to that of the FLS-FLC, with only small differences in the output force.In addition, the output force of the FLCs is zero when both the vehicle suspension displacement and velocity are zero.
The interpretation of these maps is not easy, as the control force is based on the vehicle suspension states and applied to the seat suspension, which is influenced by all four vehicle suspensions and vehicle body dynamics.Nevertheless, some cases can be explained; for example, in the case of FLS-FLC, when the vehicle suspension displacement and velocity are both NB (negative big) and the vehicle suspension is largely compressed, the seat suspension is also compressed, and a large positive actuator force is required to cancel this effect on the seat suspension, as shown in Figure 7a.Also, this is evident for the FA-FLC, as shown in Figure 7b.
To clarify these results further, the control force from FLS-FLC and the seat suspension force are compared when the vehicle is excited by a random road profile over a whole range of vehicle speeds, from 20 to 100 km/h (Figure 8).It is clear that when the vehicle suspension displacement and velocity is positive big, the control force is negative big, and vice versa.The same is true of the relationship between the seat suspension states and the control force.

Random Road
In this analysis, the full vehicle model was excited using an artificial random road profile of class E (very poor) according to the ISO 8608 standard, which has a road roughness of 256 × 10 −6 m 3 .For more details, refer to [34]. Figure 9 shows an example of this road input in the time domain at a vehicle speed of 60 km/h.For the sake of brevity, only the time domain responses of the active and passive seat suspensions at low and high forward vehicle speeds are presented, as shown in Figure 10.Moreover, the RMS values of the seat acceleration and seat suspension travel over the whole range of vehicle speeds are presented in Figure 11; due to the random nature of the road excitation, the simulations were performed 10 times for each vehicle speed over a time period of 20 s, and then an average was taken.

Random Road
In this analysis, the full vehicle model was excited using an artificial random road profile of class E (very poor) according to the ISO 8608 standard, which has a road roughness of 256 × 10 −6 m 3 .For more details, refer to [34]. Figure 9 shows an example of this road input in the time domain at a vehicle speed of 60 km/h.For the sake of brevity, only the time domain responses of the active and passive seat suspensions at low and high forward vehicle speeds are presented, as shown in Figure 10.Moreover, the RMS values of the seat acceleration and seat suspension travel over the whole range of vehicle speeds are presented in Figure 11; due to the random nature of the road excitation, the simulations were performed 10 times for each vehicle speed over a time period of 20 s, and then an average was taken.

Random Road
In this analysis, the full vehicle model was excited using an artificial random road profile of class E (very poor) according to the ISO 8608 standard, which has a road roughness of 256 × 10 −6 m 3 .For more details, refer to [34]. Figure 9 shows an example of this road input in the time domain at a vehicle speed of 60 km/h.For the sake of brevity, only the time domain responses of the active and passive seat suspensions at low and high forward vehicle speeds are presented, as shown in Figure 10.Moreover, the RMS values of the seat acceleration and seat suspension travel over the whole range of vehicle speeds are presented in Figure 11; due to the random nature of the road excitation, the simulations were performed 10 times for each vehicle speed over a time period of 20 s, and then an average was taken.From these figures, it can be seen that the controllers more effectively reduce the seat acceleration when compared with the passive system, with the 4W-FLC delivering the best performance, followed by the FA-FLC and the FLS-FLC, respectively.However, this improvement in the ride quality comes at the expense of increased seat suspension travel, although constraints for both this and the actuator force are satisfied.
It can be observed from Figure 12 that the active seat suspensions provide lower power spectral density (PSD) acceleration when compared with the passive system over a broadband frequency range, especially over the human body sensitive frequency range (4-8 Hz).However, this performance deteriorates at lower frequencies during high vehicle forward speeds.In general, the 4W-FLC demonstrates the best performance over a broadband frequency range, irrespective of the vehicle speed followed by the FA-FLC and the FLS-FLC.
Figure 13a,b shows that the proposed active seat suspensions significantly attenuate the vibration at the seat, as well as reduce the weighted RMS seat acceleration when compared with the passive seat suspension.At high speed, the active systems perform less well, although they are as good as the passive system throughout the speed range.The 4W-FLC provides the best vibration isolation performance, in which the transmitted vibration and the weighted RMS seat acceleration are reduced by at least 20% regardless of the vehicle speed, as shown in Figure 13c,d  From these figures, it can be seen that the controllers more effectively reduce the seat acceleration when compared with the passive system, with the 4W-FLC delivering the best performance, followed by the FA-FLC and the FLS-FLC, respectively.However, this improvement in the ride quality comes at the expense of increased seat suspension travel, although constraints for both this and the actuator force are satisfied.
It can be observed from Figure 12 that the active seat suspensions provide lower power spectral density (PSD) acceleration when compared with the passive system over a broadband frequency range, especially over the human body sensitive frequency range (4-8 Hz).However, this performance deteriorates at lower frequencies during high vehicle forward speeds.In general, the 4W-FLC demonstrates the best performance over a broadband frequency range, irrespective of the vehicle speed followed by the FA-FLC and the FLS-FLC.
Figure 13a,b shows that the proposed active seat suspensions significantly attenuate the vibration at the seat, as well as reduce the weighted RMS seat acceleration when compared with the passive seat suspension.At high speed, the active systems perform less well, although they are as good as the passive system throughout the speed range.The 4W-FLC provides the best vibration isolation performance, in which the transmitted vibration and the weighted RMS seat acceleration are reduced by at least 20% regardless of the vehicle speed, as shown in Figure 13c,d.Whilst the 4W-FLC is shown to be the best preview based controller for use in an active seat suspension, its real implementation is somewhat costly, as it requires instrumentation at each corner of the car.This can be partially overcome in a new controller, denoted as the "practical four wheel" (P4W) FLC, which is similar to the 4W-FLC, but uses fewer states.Specifically, this controller employs the same optimum sub-fuzzy logic controllers as the 4W-FLC.However, it requires only the states from the front suspensions as the required states from rear suspensions are hypothesised as a time delayed version of the measured states at the front, as illustrated in Figure 14.It should be noted that, due to this assumption, the performance of P4W-FLC in some maneuvers such as hard cornering will be compromised.Whilst the 4W-FLC is shown to be the best preview based controller for use in an active seat suspension, its real implementation is somewhat costly, as it requires instrumentation at each corner of the car.This can be partially overcome in a new controller, denoted as the "practical four wheel" (P4W) FLC, which is similar to the 4W-FLC, but uses fewer states.Specifically, this controller employs the same optimum sub-fuzzy logic controllers as the 4W-FLC.However, it requires only the states from the front suspensions as the required states from rear suspensions are hypothesised as a time delayed version of the measured states at the front, as illustrated in Figure 14.It should be noted that, due to this assumption, the performance of P4W-FLC in some maneuvers such as hard cornering will be compromised.Figure 15 compares the seat acceleration PSD of the P4W-FLC and 4W-FLC active seats to those of the passive system.Clearly, the P4W-FLC is almost identical to the 4W-FLC regardless of the vehicle speed.Moreover, as shown in Figure 16, the P4W-FLC provides very similar vibration attenuation performance and weighted RMS seat acceleration to the 4W-FLC at the full range of vehicle speeds.Figure 17 shows the frequency-weighted RMS acceleration of the active and passive seat suspensions with respect to the threshold limit values (TLVs), as suggested by the American Conference of Government Industrial Hygienists [53].It can be seen that the active seat suspension, using any of the developed controllers, delivers a lower frequency-weighted RMS seat acceleration over the human body-sensitive frequency range, whereas the passive system exceeds the 16-hour working daily exposure limit.Once again, the performance of both the LFS-FLC and FA-FLC are reduced at high vehicle speeds, at which the FA-FLC performs very similarly to the FLS-FLC.In fact, the 4W-FLC provides the best performance regardless of vehicle speed, while the P4W-FLC delivers Figure 17 shows the frequency-weighted RMS acceleration of the active and passive seat suspensions with respect to the threshold limit values (TLVs), as suggested by the American Conference of Government Industrial Hygienists [53].It can be seen that the active seat suspension, using any of the developed controllers, delivers a lower frequency-weighted RMS seat acceleration over the human body-sensitive frequency range, whereas the passive system exceeds the 16-hour working daily exposure limit.Once again, the performance of both the LFS-FLC and FA-FLC are reduced at high vehicle speeds, at which the FA-FLC performs very similarly to the FLS-FLC.In fact, the 4W-FLC provides the best performance regardless of vehicle speed, while the P4W-FLC delivers almost identical results to the 4W-FLC at a reduced cost, in terms of state measurements.Figure 17 shows the frequency-weighted RMS acceleration of the active and passive seat suspensions with respect to the threshold limit values (TLVs), as suggested by the American Conference of Government Industrial Hygienists [53].It can be seen that the active seat suspension, using any of the developed controllers, delivers a lower frequency-weighted RMS seat acceleration over the human body-sensitive frequency range, whereas the passive system exceeds the 16-hour working daily exposure limit.Once again, the performance of both the LFS-FLC and FA-FLC are reduced at high vehicle speeds, at which the FA-FLC performs very similarly to the FLS-FLC.In fact, the 4W-FLC provides the best performance regardless of vehicle speed, while the P4W-FLC delivers almost identical results to the 4W-FLC at a reduced cost, in terms of state measurements.

Parameter Uncertainties
In order to investigate the robustness of the proposed active seat suspension systems, the systems' performance was evaluated when subject to variations in the system parameters and operating conditions.The most varying parameters for an active seat suspension are the vehicle speed and the driver's weight, and thus the performance of the developed FLCs' active seat suspension under the variation in these parameters was examined in terms of the SEAT factor and the weighted RMS seat acceleration.Due to the nature of a random road, the simulations were carried out 10 times over a period of 20 s, and the average values were taken.Figure 18 shows the sensitivity maps of the SEAT factor for the passive and active seat suspension systems, subject to variations in the vehicle speed and the driver's weight.It is clear that the isolation performance of the passive seat suspension is sensitive to changes in both parameters.Notably, heavy drivers are exposed to less vibration energy than lighter ones, regardless of the vehicle speed.On the other hand, the vibration isolation performance of the developed FLCs is less sensitive to passenger weight variations, in which the 4W-FLC and P4W-FLC provide the highest robustness level.
Figure 18 also reveals that the ride comfort level of the passive seat suspension is highly sensitive to variations in both the driver's weight and the vehicle speed, in which light drivers are subject to the most discomfort when driving at high speeds.In comparison, the FLCs were only slightly affected by these changes, especially at low and intermediate vehicle speeds.Once again, the 4W-FLC and P4W-FLC provide the highest robustness level, compared with the FLS-FLC and FA-FLC.
FLC and P4W-FLC provide the highest robustness level.
Figure 18 also reveals that the ride comfort level of the passive seat suspension is highly sensitive to variations in both the driver's weight and the vehicle speed, in which light drivers are subject to the most discomfort when driving at high speeds.In comparison, the FLCs were only slightly affected by these changes, especially at low and intermediate vehicle speeds.Once again, the 4W-FLC and P4W-FLC provide the highest robustness level, compared with the FLS-FLC and FA-FLC.

Road "Bump" Input
Figure 19a shows the bump road profile used to excite the full vehicle model [54].Figure 19b,c shows the superior ability of the proposed controllers to reduce the seat acceleration when compared with the passive system, without exceeding the seat suspension travel limit.However, the active seat suspension using the P4W-FLC shows a peak acceleration value at approximately 0.5 s, which may be due to the fact that the suspension states from the rear axle used in this controller are approximated from the front axle, which introduces compromises in the controller that are reflected in high frequency seat actuator force inputs and associated seat accelerations, especially when using a very severe bump road profile.
Once again, the 4W-FLC and P4W-FLC show very similar results, reducing the RMS value of seat acceleration from 1.031 m/s 2 with the passive system to be less than 0.75 m/s 2 , as presented in Table 2.

Road "Bump" Input
Figure 19a shows the bump road profile used to excite the full vehicle model [54].Figure 19b,c shows the superior ability of the proposed controllers to reduce the seat acceleration when compared with the passive system, without exceeding the seat suspension travel limit.However, the active seat suspension using the P4W-FLC shows a peak acceleration value at approximately 0.5 s, which may be due to the fact that the suspension states from the rear axle used in this controller are approximated from the front axle, which introduces compromises in the controller that are reflected in high frequency seat actuator force inputs and associated seat accelerations, especially when using a very severe bump road profile.
Once again, the 4W-FLC and P4W-FLC show very similar results, reducing the RMS value of seat acceleration from 1.031 m/s 2 with the passive system to be less than 0.75 m/s 2 , as presented in Table 2.

Conclusions
In this paper, three novel and cost-effective FL controllers for an active seat suspension have been developed, which use inexpensive and available preview information from the vehicle suspensions while satisfying the physical system constraints at a range of different operational conditions.The simulation results indicated that the controllers significantly improve ride comfort compared with the passive system.The 4W-FLC shows the best performance regardless of the vehicle speed.Interestingly, the P4W-FLC performs very similarly to the 4W-FLC, and requires fewer measured system states, thus it is a practical and cost-effective system that improves ride comfort and reduces driver fatigue.

Symbol Description a v
Frequency-weighted RMS acceleration W i Frequency-weighting value at the centre frequency ..
x s,w rms Weighted root mean square vertical acceleration at the seat's base ..
x se,w rms Weighted root mean square of the vertical seat acceleration (x se − x s ) max Maximum seat stroke (x se − x s ) min Minimum seat stroke ..

x s
Vertical acceleration of the sprung mass ..
x se Vertical acceleration of the seat

( 4 )
Driver's body m b .. x b = k b (x se − x b ) + c b .

Figure 4 .
Figure 4. (a) Optimisation process of the FLC structure and (b) the membership functions (MFs) adjusting parameters.

Figure 4 .
Figure 4. (a) Optimisation process of the FLC structure and (b) the membership functions (MFs) adjusting parameters.

Figure 7 .
Figure 7. Contour plots of (a) the FLS-FLC map and (b) the FA-FLS map.

Figure 8 .
Figure 8. Contour plots of the seat suspension and control force of the FLS-FLC.

Figure 8 .
Figure 8. Contour plots of the seat suspension and control force of the FLS-FLC.

Figure 8 .
Figure 8. Contour plots of the seat suspension and control force of the FLS-FLC.

Figure 9 .
Figure 9. Road profile at a vehicle speed of 60 km/h.

Figure 10 .
Figure 10.Time responses at low and high vehicle speeds.

Figure 9 .
Figure 9. Road profile at a vehicle speed of 60 km/h.

Figure 9 .
Figure 9. Road profile at a vehicle speed of 60 km/h.

Figure 10 .
Figure 10.Time responses at low and high vehicle speeds.

Figure 10 .
Figure 10.Time responses at low and high vehicle speeds.

Figure 11 .
Figure 11.Comparison of ride comfort for passive and active seat suspension systems at different vehicle speeds. .

Figure 11 .
Figure 11.Comparison of ride comfort for passive and active seat suspension systems at different vehicle speeds.

21 Figure 12 .
Figure 12.Power spectral densities (PSDs) of the seat acceleration at different vehicle speeds.

Figure 12 .
Figure 12.Power spectral densities (PSDs) of the seat acceleration at different vehicle speeds.

Figure 12 .
Figure 12.Power spectral densities (PSDs) of the seat acceleration at different vehicle speeds.

Figure 13 .
Figure 13.SEAT factor, weighted RMS seat acceleration and percentage improvements at different vehicle speeds.

Figure 13 .
Figure 13.SEAT factor, weighted RMS seat acceleration and percentage improvements at different vehicle speeds.

Figure 15
Figure15compares the seat acceleration PSD of the P4W-FLC and 4W-FLC active seats to those of the passive system.Clearly, the P4W-FLC is almost identical to the 4W-FLC regardless of the vehicle speed.Moreover, as shown in Figure16, the P4W-FLC provides very similar vibration attenuation performance and weighted RMS seat acceleration to the 4W-FLC at the full range of vehicle speeds.

Figure 15
Figure15compares the seat acceleration PSD of the P4W-FLC and 4W-FLC active seats to those of the passive system.Clearly, the P4W-FLC is almost identical to the 4W-FLC regardless of the vehicle speed.Moreover, as shown in Figure16, the P4W-FLC provides very similar vibration attenuation performance and weighted RMS seat acceleration to the 4W-FLC at the full range of vehicle speeds.

Figure 15 .
Figure 15.PSDs of the seat acceleration at different vehicle speeds.Figure 15.PSDs of the seat acceleration at different vehicle speeds.

Figure 15 .
Figure 15.PSDs of the seat acceleration at different vehicle speeds.Figure 15.PSDs of the seat acceleration at different vehicle speeds.Vibration 2018, 2, x FOR PEER REVIEW 15 of 21

Figure 16 .
Figure 16.Seat effective amplitude transmissibility (SEAT) factor, weighted RMS seat acceleration, and percentage improvements at different vehicle speeds.

Figure 16 .
Figure 16.Seat effective amplitude transmissibility (SEAT) factor, weighted RMS seat acceleration, and percentage improvements at different vehicle speeds.

Figure 16 .
Figure 16.Seat effective amplitude transmissibility (SEAT) factor, weighted RMS seat acceleration, and percentage improvements at different vehicle speeds.

Figure 17 .
Figure 17.Health risk assessment of the passive and proposed active seat suspensions at different vehicle speeds.

Figure 17 .
Figure 17.Health risk assessment of the passive and proposed active seat suspensions at different vehicle speeds.

Figure 18 .
Figure 18.Sensitivity of the passive and active seat suspension performance to variations in the driver's weight and vehicle speed.

Figure 18 .
Figure 18.Sensitivity of the passive and active seat suspension performance to variations in the driver's weight and vehicle speed.

Figure 19 .
Figure 19.Time responses under a bump road profile.

Table 2 .
Time responses characteristics of the proposed controllers under a bump road profile.

Table 2 .
Time responses characteristics of the proposed controllers under a bump road profile.
Lateral distance from the driver's seat to C.G R y Longitudinal distance from the driver's to C.G V sij Vehicle suspension velocity, i and j = 1, 2 V o , V Forward vehicle speed D sij Vehicle suspension displacement, i and j = 1, 2 c s Damping coefficient of the vehicle suspension c se Damping coefficient of the seat suspension k s