Double anti-roll bar hardware-in-loop experiment for active anti-roll control system

3.1. PI-PD type fuzzy controller

For PI-PD type Fuzzy controller (PI-PD type FLC), the derivative action is placed at the measurement of the process feedback but not after the feedback error [15]. The basic concept of this controller is shown in Fig. 5.

Fig. 5Basic layout of PI-PD controller

In order to improve the controller’s compatibility to non-linear system, Veeraiah et al. (2004) implemented fuzzy logic to design PI-PD type FLC controller. The controller is designed to preserve the linear structure of conventional PI-PD controller and substitutes the coefficient gains with non-linear fuzzy functions. The output of PI-PD type FLC controller, $u_{PI-PD}\left(nT\right)$, is represented by:

where $u_{PI}\left(nT\right)$ and $u_{PD}\left(nT\right)$ are the equivalent outputs from Fuzzy PI and Fuzzy PD controllers respectively. By applying bilinear transformation, Fuzzy PI controller output (Muniandy et al., 2015) can be written as:

where $u_{PI}\left(nT\right)$ is the Fuzzy PI controller output, $T$ is the sampling period and $K_{uPI}$ is the Fuzzy PI control gain. Similarly, for Fuzzy PD controller, the equation will be:

which $u_{PD}\left(nT\right)$ is the fuzzy PD controller output and $K_{uPD}$ is the fuzzy PD control gain. Both $K_{uPI}$ and $K_{uPD}$ will be determined by fuzzy rules. This controller’s layout applied in active ARB is shown by the block diagram in Fig. 6.

Fig. 6Block diagram of PI-PD Type Fuzzy Logic controller of AARB system

Fig. 7Example of implementation of PI-PD Type Fuzzy Logic controller in Simulink model

Membership functions and rules will be applied to the fuzzy PI and fuzzy PD controllers can be referred in [11]. The inputs for both controllers will be in terms of roll angle signal. Earlier, it has been stated that fuzzy PI controller has two inputs, which are roll angle error signal, $e_p\left(nT\right)$ and rate of change of roll angle error signal, $e_v\left(nT\right)$. The fuzzy PI controller output, also called as incremental control output is denoted as$∆u_{PI}\left(nT\right)$. The inputs for fuzzy PD controllers are the roll angle, $d\left(nT\right)$ and rate of change of roll angle, $∆y\left(nT\right)$. Fig. 7 shows an example of actual construction of PI-PD Type FLC controller in Simulink software with the indication of actual placement for each controller parameter, which are $K_p$, $K_i$, $K_p^{\text{'}}$, $K_d$, $K_{uPD}$ and $K_{uPI}$. Despite the notations, these parameters act only as input sensitivity ratio in order to avoid undesirable noise in the output. The proportional, derivative and integral actions are expressed in the form of non-linear fuzzy functions.

3.2. Self-tuning fuzzy PID

Self-Tuning Fuzzy PID controller was implemented in AARB by Xinpeng and Duan [4] in their attempt to improve the ride and handling of a SUV. The controller algorithm uses conventional approach where the values of PID controller parameters are tuned online by Fuzzy controller depending on the feedback input received from the plant. This approach is more direct compared to the approach used in PI-PD type FLC controller. The general equation for the PID controller is:

where $e\left(t\right)$ is the body roll error with respect to the desired roll angle which is 0 at all time. The corresponding desired active anti-roll torque is $T_{ac}$. The body roll angle variety rate is denoted by $∆e\left(t\right)$ and the error sum is denoted by$\sum e\left(t\right)$. The terms $K_i$, $K_p$, and $K_d$ denote integral, proportion and derivatives coefficients respectively. The controller parameters $K_i$, $K_p$, and $K_d$ will be self-tuned by fuzzy controller according to the roll angle error, $e$ and roll angle error variety rate, $∆e.$ The self-tuning ability is well known for its promising results. Fig. 8 shows the general block diagram for the controller.

Fig. 8Controller structure proposed by Xinpeng and Duan (2007)

3.3. Self-tuning fuzzy PI–PD controller

By incorporating classical PI-PD configuration into self-tuning Fuzzy PID method, the STFPI-PD controller is expected to solve derivative kick problem [11]. This controller is designed as an attempt to upgrade the currently available Fuzzy PID controller used in AARB system. The general equation of PI-PD controller will be:

Note that there are 2 proportional actions; $K_p$ and$K_p\text{'}$, each for roll angle error, $e\left(t\right)$and the direct measurement of roll angle input, $\varnothing \left(t\right)$ repectively. The derivative action is applied at the measurement of roll angle. The performance of AARB system can be adjusted by tuning the parameter $K_p$, $K_p^{\text{'}}$, $K_i$, and $K_d$ of PI-PD controller to influence the system’s rise time, steady state error, overshoot and settling time. The tuning process of the controller parameters will be done by fuzzy controllers. These fuzzy controllers will receive roll angle error, $e\left(t\right)$ and error rate, $\dot{e}\left(t\right)$ as inputs to tune the value of $K_p$ and$K_i$; also, the fuzzy controllers that receive roll angle value, $\varnothing \left(t\right)$ and the roll rate value, $\dot{\varnothing }\left(t\right)$ as inputs will tune the values of $K_p^{\text{'}}$ and $K_d$. The fuzzy rules, membership functions and tuning procedures are reported in [11]. Fig. 9 shows the general block diagram of the proposed controller.

Fig. 9General Block diagram of Self-Tuning Fuzzy PI-PD controller

4.1. Slalom test

Slalom test was carried out at 2 different speeds. The test evaluates three major variables to show the performance of the three controllers. These variables are roll angle, roll rate and actuator force. For actuator force however, it is showcased in order to show the different trend on each controllers’ reaction. Having a low magnitude in force output does not mean advantage except low power usage. Fig. 10 shows roll angle response for 40 km/h slalom manoeuvre test.

From Fig. 10, it can be seen that STFPI-PD controller reduces roll angle to negligible state, with one visible spike at 5.5th second. It should be noted that problems regarding HIL setup discussed earlier applies to all tests. STFPID controller manages to reduce roll angle significantly when compared to passive system, but could not bring the roll motion closer to zero like the other two controllers. PI-PD Type FLC follows the trend of STF PID controller for the first three seconds and settles down at almost zero position until the 5th second where the roll angle spikes to a magnitude equal to passive result. This is due to the limitation of the controller that is unable to produce the direction of a desired force efficiently and causes the roll angle to increase abruptly until the controller reacts again. The weakness of PI-PD Type FLC in predicting the desired directions is maybe due to the use of small number of membership functions compared to other two controllers as reported in [11]. The lack of detailed membership functions promotes the controller to make various mistakes when comes to determining acting force direction. This can be seen at force distribution figure later. Fig. 11 shows the roll rate response for this test.

It can be observed that STF PID controller creates more oscillations compared to the other two controllers. This oscillation degrades ride comfort in comparison with passive system. While maintaining the roll rate at almost zero position, STFPI-PD controller only spikes once exceeding passive roll rate value at 5.5th second. This is because the actuator meets the stroke limit and could not extend/retract any further. When this situation appears, the vehicle roll angle starts to rise, following the direction similar to passive system as no additional active force acting to the system. The roll angle continues to rise until the steering wheel changes direction and causing the vehicle to roll in the opposite direction. The controller immediately takes action once the vehicle rolls at opposite direction and resets the roll angle back to zero position.

However, this sudden correction action by the controller causes roll rate to increase which is presented in Fig. 11. It is important to take note that this problem will seldom occur in real car application due to several reasons. One of the reasons are, the stroke length of the experimental actuator was determined based on simulation tests alone. The estimation itself may not be a problem, but the capability of the actuator to return back to its zero position is limited in HIL setup due to lack of actual body weight and vehicle main suspension system to return back the vehicle to its default position every time. In HIL setup, only ARB acts as a spring to push/pull back the actuator to its default position. It is crucial to know that a significant amount of force is required to push/pull back the actuator shaft to its default position even when there is no power running through it; although the actuator itself were designed not to self-lock. This is the nature of the high power linear electric actuator which incorporates very strong magnet in the motor. The failure of the actuator shaft to return back to its default position quickly causes the zero position to drift and the actuator reach maximum stroke point pre-maturely. Other than that, STF PI-PD controller manages to improve ride performance by keeping the roll rate at minimum. PI-PD type FLC exceeds the passive roll rate value twice and the magnitude is the largest compared to all tested controllers. Fig. 12 shows the active force response for the mentioned test.

Fig. 10Roll angle response for 40 km/h slalom test

Fig. 11Roll rate response for 40 km/h slalom test

It can be observed that STF PID controller creates more oscillations compared to the other two controllers. This oscillation degrades ride comfort in comparison with passive system. While maintaining the roll rate at almost zero position, STFPI-PD controller only spikes once exceeding passive roll rate value at 5.5th second. This is because the actuator meets the stroke limit and could not extend/retract any further. When this situation appears, the vehicle roll angle starts to rise, following the direction similar to passive system as no additional active force acting to the system. The roll angle continues to rise until the steering wheel changes direction and causing the vehicle to roll in the opposite direction. The controller immediately takes action once the vehicle rolls at opposite direction and resets the roll angle back to zero position. However, this sudden correction action by the controller causes roll rate to increase which is presented in Fig. 11. It is important to take note that this problem will seldom occur in real car application due to several reasons. One of the reasons are, the stroke length of the experimental actuator was determined based on simulation tests alone. The estimation itself may not be a problem, but the capability of the actuator to return back to its zero position is limited in HIL setup due to lack of actual body weight and vehicle main suspension system to return back the vehicle to its default position every time. In HIL setup, only ARB acts as a spring to push/pull back the actuator to its default position. It is crucial to know that a significant amount of force is required to push/pull back the actuator shaft to its default position even when there is no power running through it; although the actuator itself were designed not to self-lock. This is the nature of the high power linear electric actuator which incorporates very strong magnet in the motor. The failure of the actuator shaft to return back to its default position quickly causes the zero position to drift and the actuator reach maximum stroke point pre-maturely. Other than that, STF PI-PD controller manages to improve ride performance by keeping the roll rate at minimum. PI-PD type FLC exceeds the passive roll rate value twice and the magnitude is the largest compared to all tested controllers. Fig. 12 shows the active force response for the mentioned test.

Fig. 12Active force response for 40 km/h slalom test

All tested controllers show similar trend in terms of force distribution. PI-PD type FLC controller shows delay in response to change direction in comparison with the other two controllers. STF PID controller generates the lowest force and capable of making a smooth change in direction. However, the oscillations in its force distributions may cause further impact negatively on roll motion even if the force magnitude was increased. This can be seen in Fig. 11, even with less amount of force, the vehicle roll motion keeps on oscillating more than the passive system at the first three seconds. In fact, with higher active force, this oscillation will be worsened; hence the controller limits its response to continue provide lower force magnitude throughout the test. This is one of the features of self-tuning controllers which can act appropriately according to the sensed disturbances. However, STFPI-PD controller shows that its self-tuning capability is much more efficient as it can give higher forces with higher agility to overcome any fluctuations that may be rise from the steering angle input noises. Next, the roll angle response for 50 km/h slalom test is presented in Fig. 13.

Similar results are shown. Earlier discussion is more evident. Figs. 14 and 15 shows roll rate response and active force response for 50 km/h slalom test respectively.

Fig. 13Roll angle response for 50 km/h slalom test

Fig. 14Roll rate response for 50 km/h slalom test

Fig. 15Active force response for 50 km/h slalom test

As can be seen in Fig. 14, PI-PD Type FLC causes significant rise in roll rate at approximately the 7th second, exceeding the magnitude created by passive system. This will definitely impact ride comfort negatively. This may be due to the failure of the controller to provide active force in the negative direction at the 6th second as generated by the other controllers. The trend of STF PI-PD controller sets it apart from other controllers as the controller continues to give negative force until approximately the 6.5th second. At approximately the 7th second, in order to overcome the rising roll angle, the controller gives force at positive direction abruptly but failed to completely reduce the roll angle due to the actuator shafts reaches its limit. The evidence can be seen from 7th to 7.5th seconds where the force value stalls at almost constant as the actuator could not move any further. This kind of constant force values is not visible with the other tested controller outputs, further supporting the claim. The reason of this error can be also caused by quick change of the force direction with higher magnitude, which makes the actuator impossible to return to the default position in a very short time. The use of dampening element might be useful to overcome this problem, where in a real vehicle, the vehicle’s main dampers will assist to lessen this negative effect.

Following are the tables presenting the improvement made by the proposed controllers in comparison with the passive system. Tables 1 and 2 show the RMS value of the presented variables for 40 and 50 km/h slalom test respectively.

It is found that STFPI-PD controller improves both its roll angle and roll rate response in comparison with passive system. This result may be improved further if the STFPI-PD controller does not suffer from actuator stroke limitation. Table 1 shows both STFPID and PI-PD Type FLC degrade ride comfort by increasing roll rate of the vehicle. However, at higher speed, all controllers manage to improve roll rate response in comparison with passive. PI-PD type FLC worsens the roll rate response up to –10.16 % for 40 km/h slalom test due to obvious spikes at roll rate magnitude, as can be seen in Fig. 11. STFPI-PD controller remains as the best among the tested controllers.

4.2. Step steer test

In order to evaluate steady state performance, step steer test has been carried out at 60 km/h speed by using steering input signal similar to that used in [4]. Similar input were chosen because the result will better reflect the actual difference between simulation output (as discussed by Xinpeng and Duan [4]) and the experimental output obtained in this research. Furthermore, to evaluate steady state performance, it is required to have noise free input to allow the system output settles to a constant value within the margin of error. For this test, the steering wheel is turned suddenly to the left 90° and keeping the steering wheel position fixed until the end of the test. The steering wheel takes about one second to turn from 0° to 90° left. The vehicle moves at a constant speed of 60 km/h throughout the test. Fig. 16 shows the roll angle response for this test.

The STF PID controller continues to fluctuate for 5 seconds, where the other two tested controller settles down within the given period. Overshoot cannot be avoided due to the actual hardware inertia. However, for STF PI-PD controller small overshoot occurs, reaching not higher than 0.5°, which will not be felt by most of the passengers. STF PI-PD controller also has quick settling time, which is within 1 second after the input given. The overshoot for PI-PD type FLC is more evident, reaching approximately 2°, however manage to settle down near zero position within the margin of error similar to STF PI-PD controller. PI-PD type FLC takes approximately 2 seconds to settle down. The steady state error for both PI-PD Type FLC and STF PI-PD controller is too small for a passenger to feel in real driving environment. Next, Fig. 17 shows the roll rate response for the step steer test.

Fig. 16Roll angle response for 60 km/h step steer test

Fig. 17Roll rate response for 60 km/h step steer test

It is expected that STF PID controller will continue to fluctuate and increases the roll rate with time. As mentioned earlier, STF PID controller is not suitable for a system with high noise. For this test, the noise is from the sensors since there is no noise from the steering angle input itself. Once the model given constant input for considerable amount of time, the sensor’s signal drift causes the controller lose control and starts to fluctuates, as can be seen after the 3.5th seconds. A typical load cell will has its signal to drift if it is given constant load for longer period of time. This is due to the nature of quartz crystal in the sensor itself. However, both PI-PD Type FLC and STF PI-PD controller manages to overcome this problem and settles down to almost zero position within 5 seconds frame. STF PI-PD performs the best in improving ride comfort in this test. PI-PD type FLC clocks highest roll rate magnitude due to its overshoot characteristics. Again, this is affected by the limited sensitivity of the controller due to small number of Fuzzy membership functions. Fig. 18 shows the force response for the mentioned test.

Fig. 18 shows that STF PI-PD controller requires the largest amount of force in order to reduce steady state error. It can be seen that all controllers seem to have their output force reducing with time. This is because the whole HIL setup is running on battery power. A battery could not provide high ampere output (higher than the value intended by the manufacturer) in a constant manner for a long period. Due to internal chemical reaction, high ampere output will cause the battery to drop voltage, hence reducing its output power. This is the reason why that step steer test was not carried out at higher speed, as more power is required and the battery will lose its power before the controller can achieve steady state. Other than that, test speed is limited to avoid possible risk of damage on other mechanical parts in the HIL setup. Furthermore, the reason of fluctuations of roll rate by the output of STF PID controller is not caused by limited power supply by the battery, because Fig. 18 clearly shows that STF PID controller uses the least amount of energy compared to STF PI-PD. STF PI-PD controller on the other hand, uses significantly higher force, up to 1600 N in order to suppress roll angle while drawing the energy from the same power supply as STF PID controller did. Table 3 shows the percentage of improvement made by the presented controllers in step steer test.

Fig. 18Active force response for 60 km/h step steer test

Again, STF PI-PD controller performs well in this test and reduce roll angle up to 98.35 % in comparison with passive system. The roll rate is also improved up to 81.47 %, hence ride comfort is significantly improved in steady state condition. PI-PD type FLC is also able to improve roll angle and roll rate response in comparison with passive system. However, if compared with STF PID controller, PI-PD Type FLC seems to perform lower in terms of roll rate reduction. These results shows that the proposed controller, STF PI-PD has a smoother response in the steady state region, with minor overshoot and fluctuations in the transient region. The steady state error is also negligible for both PI-PD Type FLC and STF PI-PD controllers.

4.3. Stability analysis

Fig. 19 shows the change of body roll angle in response to lateral acceleration. The effective lateral acceleration at the vehicle CG throughout the tests are from approximately –6 to 6 m/s² (–0.61 to 0.61G), as can be seen in Fig. 19. The lateral acceleration acting on the passive vehicle body is equal to the vehicle fitted with active system. According to [4], when the vehicle experience high lateral acceleration (at 0.6G) while having large roll angle, the vehicle will loss control. From Fig. 19, it can be seen that the vehicle fitted with STFPI-PD control system will retain its control due to roll angle value closer to zero. In fact, the STFPI-PD controller is able to retain negligible roll angle throughout the entire range of tested lateral acceleration. STFPID does improve roll angle compared to passive system, but the magnitude is still noticeable at 4° on 5.8 m/s². PI-PD type FLC fails to retain the vehicle stability at higher than 4.5 m/s² lateral acceleration value and produces high roll angle similar to STFPID controller. It can be said that the controller’s optimum working range is limited and tend to be out of control when high amount of lateral acceleration being applied. This is a dangerous since the driver will experience sudden roll change without prior warning until the vehicle is about to lose control. In contrast to that, STFPI-PD controller is able to hold the roll angle closer to zero at any given lateral acceleration value and ensures driver safety. The minor error caused by STFPI-PD is related to stroke length limitation as discussed earlier, as the data plots are mostly focused about zero point.

Fig. 19Relation between lateral acceleration and vehicle roll angle

The effective lateral acceleration at the vehicle CG throughout the tests are from approximately –6 to 6 m/s² (–0.61 to 0.61G), as can be seen in Fig. 19. The lateral acceleration acting on the passive vehicle body is equal to the vehicle fitted with active system. According to [4], when the vehicle experience high lateral acceleration (at 0.6G) while having large roll angle, the vehicle will loss control. From Fig. 19, it can be seen that the vehicle fitted with STFPI-PD control system will retain its control due to roll angle value closer to zero. In fact, the STFPI-PD controller is able to retain negligible roll angle throughout the entire range of tested lateral acceleration. STFPID does improve roll angle compared to passive system, but the magnitude is still noticeable at 4° on 5.8 m/s². PI-PD type FLC fails to retain the vehicle stability at higher than 4.5 m/s² lateral acceleration value and produces high roll angle similar to STFPID controller. It can be said that the controller’s optimum working range is limited and tend to be out of control when high amount of lateral acceleration being applied. This is a dangerous since the driver will experience sudden roll change without prior warning until the vehicle is about to lose control. In contrast to that, STFPI-PD controller is able to hold the roll angle closer to zero at any given lateral acceleration value and ensures driver safety. The minor error caused by STFPI-PD is related to stroke length limitation as discussed earlier, as the data plots are mostly focused about zero point.