Integration of Skyhook Control in a Quarter Car with Magnetorheological (MR) Damper

Semi-active suspension (SAS) systems attenuate vibrations with minimal power Consumption and is usually paired with magnetorheological (MR) dampers which are a type of variable damper that produces high damping forces with no mechanical movement. This paper presents the analysis of a Skyhook controller in a quarter car test rig equipped with MR damper to reduce vibration peaks when excited by a sinusoidal signal which simulates the unevenness of road surfaces. The viability of Skyhook control in mitigating vibration was examined from the experiments. The study discovered that there was an improvement of 12.72% by Skyhook control when compared to passive damping based on the sprung mass acceleration of both damping modes. The Skyhook controller surpassed passive damping and was deemed a success in vibration control.


Introduction
One's driving experience is heavily influenced by the suspension system which reduces the vibrations towards the chassis and then the passengers.A semi-active suspension consists of an actuator and controller which computes the necessary forces to cancel out the vibrations [1].Skyhook control is a virtual controller that, in theory, functions by hooking the chassis to a certain point in the sky to dampen the vibrations [2], [3].The theory can be made practical if the method was modified to adapt to a physical system while keeping the ruling of selecting damping coefficients.
Selecting the corresponding damping coefficients should relate to the computation of acceleration in the sprung and unsprung bodies.A minimum and maximum value of damping coefficients are calculated based on the preset damping constant achievable by the magnetorheological (MR) damper [4].Should accelerations not meet the threshold, the preset damping coefficient will be selected, as it acts as the mid-range coefficient.Simultaneously, the allowance of current flow to the MR damper will affect the intensity of forces for vibration attenuation.An automatically tuned current flow may fluctuate and cause the MR damper to act differently.The opposite is said for a manually tuned current controller as a steady current flow allows the actuator to deliver constant forces under the same power load [5].
The inputs of Skyhook controllers are undemanding as it mainly requires the acceleration of both sprung and unsprung bodies.An excitation signal in the form of a sinusoidal disturbance with a standard frequency of 2 Hz was selected for the tests.Experiments were validated by the per cent reduction in root mean square (RMS) of sprung mass acceleration (SMA).

Skyhook Controller System
Development of Skyhook controller was initially conducted in MATLAB to verify that the code was running successfully before deployed into LabVIEW.The code revolves around Equation (1) which will be the force that counteracts the vibrations [6].
Equation ( 2) is the ruling that determines the minimum or maximum damping coefficient for deployment [7].
The block diagrams in LabVIEW were separated into three while loops that were connected to each other which are: suspension model, disturbance signal and damper controller.All three loops are shown in Figure 1.The suspension model loop will replicate the quarter car suspension equation and includes data collection at the sprung and unsprung bodies.The disturbance signal loop contains the sinusoidal signal of 2 Hz at 5 mm amplitude to replicate road surfaces.Lastly, the damper controller loop has the MATLAB code integrated into the loop and an option for passive damping.

Quarter Car Test Rig
The quarter car test rig was setup as shown in Figure 2. A power supply unit and a data acquisition module (DAQ) which will power the shaker and collect data was located behind the test rig.The air compressor which supplies air to the shaker for vertical movement and computer for running LabVIEW as well as MATLAB were considered part of the entire setup.

FIGURE 2. Setup of the quarter car test rig
The actuator was a LORD RD-8040-1 MR damper which is a variable damper that produces damping forces based on the intensity of the magnetic field and received current.Two types of sensors were used to acquire data in terms of acceleration and velocity.An RP12 Analog Linear Displacement Sensor by Vishay was installed beside the MR damper to measure the sprung mass displacement, while Dytran Instruments, Inc's 3255A2 accelerometers will measure the acceleration of both the sprung and unsprung masses.

Selection of Damping Coefficient
The damping coefficient of the Skyhook controller that determines the minimum and maximum values of Skyhook force was conducted in two parts for Experiment 1.Each had five different damping coefficients but ran in automatic (Experiment 1a) and manual (Experiment 1b) tuning of the current controller respectively.As for the sprung mass, a 10 kg weight disk was placed on the test rig to act as an intrinsic weight.The parameters for the damping constant selection were listed in Table 1.The purpose of Experiment 1 was to identify the optimal operating parameter for the semi-active suspension system.Determining the appropriate damping coefficient will help to ensure an optimally damped system, while a manually tuned current flow will have a steady supply of current to the MR damper, vice versa.Figure 4 shows the electrical unit which houses the current controller, as well as the power supply unit and data acquisition module.

Skyhook Performance under Increased Mass
In Experiment 2, Skyhook controller performance will be first evaluated by increasing the sprung mass with weight disks from 20 kg to 60 kg, with 20 kg increments [8].The experimental parameters are shown in Table 2.The current tuning type and the damping coefficient retrieved from Experiment 1 will be used in Experiment 2. It proves that the two parameters can return optimal sprung mass acceleration values of the damped system.Experiment 2 will focus on the SMA values of the Skyhook controller under each sprung mass weight to determine if increased mass will affect the controller's performance either positively or negatively.The green (10 kg) and blue (20 kg) weight disks used in Experiment 2 are placed on top of the test rig as shown in Figure 5.

Results and Discussions
Prior to the testing, a benchmark of the sprung mass acceleration was set for both tuning types.The root mean square SMA for automatic tuning was 0.85128 m/s2 while manual tuning was 0.83942 m/s2.To determine the optimal damping constant, the SMA of the system with the utilized constant must be lower than the stated SMA for their respective tuning group.All results from Experiment 1 were recorded in Table 3.The results in Experiment 1a for automatic tuning of the current showed that damping coefficients 1334 Ns/m and 5781 Ns/m were the most optimal constants as the SMA for both are the lowest in the group.At the same time, their performance in the time domain was very stable and remained under the peaks which were set by passive damping, at 2 m/s2.Meanwhile in the frequency domain, the natural frequencies of the system were obtainable at 1.95 Hz onwards, and the data further justified the two coefficients as the optimal values under automatic tuning because both had the lowest power at that point.For Experiment 1b, different damping coefficients were retrieved which were 651 Ns/m and 3482 Ns/m.Similarly in Experiment 1a, the optimal damping coefficients have the most consistent acceleration in the group and remains under the benchmark acceleration.The powers of both damping coefficients in the frequency domain were not the lowest at 1.95 Hz, however in the frequencies prior to that point had low and consistent power after the noise region.The occurrence of heavy noise before the 1 Hz mark is mainly caused by the lack of weight on the sprung mass, as this situation improved in Experiment 2.
In Experiment 1b, the two damping coefficients from each tuning types were compared directly based on their SMA and power in the frequency domain.Coefficients in the manually tuned group were significantly lower in SMA at 0.5805 to 0.5808 m/s2 compared to the lowest SMA for automatic tuning at 0.7346 m/s2 (5781 Ns/m).Besides that, Manual 651 Ns/m had the lowest SMA and power in the frequency domain of 0.0623 (m/s2)2/Hz at 1.95 Hz.The damping constants under automatic tuning were in similar power regions however due to their high SMA difference, Manual 651 Ns/m was chosen.On the other hand, Manual 3482 Ns/m was excluded as it had the highest power at 1.95 Hz, despite having the lowest sprung mass acceleration overall.A high power in the natural frequency would lead to more discomfort and reduce ride quality.Figure 6 portrays the comparison of the damping coefficients from both tuning types.Manual 651 Ns/m shows more stable acceleration in the mid-region (5 -8 seconds) compared to the rest, and it has relatively lesser, as well as lower amplitudes in the time domain.As for the frequency domain, the noisy region depicts the startup of the excited system and approaching the 1 Hz mark, all damping constants have begun to act steadily.The chosen damping coefficient, Manual 651 Ns/m, was utilized in Experiment 2 where an increase in sprung mass was made to test the capability of the Skyhook controller with the optimal parameters.There was a trend in improvement of vibrations where the sprung mass acceleration reduces when the sprung mass increases.From this observation, it can be noted that the SMA is inversely proportional to the sprung mass whereby the SMA decreases when the chassis weight.Figure 7 shows the sprung mass acceleration in the (a) time and (b) frequency domains respectively.The 60 kg test produced more stable amplitudes in the time domain, and it has a reduction in power after every harmonic.It also managed to properly stay within 0.5 m/s 2 in the time domain and produced a desirable SMA of 0.2512 m/s 2 .In Figure 7b, the harmonic after every frequency is more noticeable, and the noise region has reduced significantly, making the first harmonic (1 Hz) much more observable compared to Experiment 1. Increasing the sprung mass has an additional effect on the natural frequencies as well.In the first harmonic, the 60 kg test was seen to have the highest power, but it eventually reduces and becomes the lowest.Other tests had the powers reduce by a small amount compared to the 60 kg test.8a are almost identical to each other.Skyhook control was able to reach peaks that are lesser than passive in the time domain.On the other hand, Figure 8b shows the frequency domain for the damping comparison and the noise region shows that the Skyhook controller has lesser noise but has a power of 0.2472 (m/s 2 ) 2 /Hz which is significantly higher than passive damping.However, Skyhook's power drastically decreases at the second and following harmonics, making it lesser than passive damping.For this reason, the currently tested Skyhook controller may not be suitable for passenger vehicles, but better in sports cars instead.This is because common cars' natural frequencies are in the ranges of 1 to 1.5 Hz while the latter is in the ranges of 2 to 2.5 Hz [6].

Conclusion
The Skyhook controller was successfully constructed and integrated onto the quarter car test rig equipped with MR damper.The sprung mass acceleration and natural frequencies of Skyhook and passive damping were acquired by experimenting on various damping coefficients and sprung masses with the same sinusoidal disturbances.Different damping constants in manual and automatic current tuning were tested to determine that the system would be in the proper damping conditions.A damping coefficient of 651 Ns/m under manual tuning was found appropriate as it reached lower SMA values than the benchmarked passive damping.The constant was used in the varied sprung mass experiment and there was a trend of vibration reduction from 20 kg to 60 kg which showed that the Skyhook controller accounts for weight in the damping force.The controller reduced vibrations on the quarter car test rig loaded with 60 kg weights by 12.72 per cent compared to the passive damping.

FIGURE 1 .
While loops of the LabVIEW code (a) suspension model (b) disturbance signal (c) damper controller

Figure 3 FIGURE 3 .
FIGURE 3. Setup of MR damper and sensors on the test rig (a) MR damper and LVDT, (b) accelerometers

FIGURE 7 .
Sprung mass acceleration of Experiment 2 in (a) time domain, (b) frequency domain By directly comparing the Skyhook controller to passive damping at 60 kg of sprung mass, the damping patterns in the time domain in Figure

FIGURE 8 .
FIGURE 8. Sprung mass acceleration of Skyhook and passive damping in (a) time domain, (b) frequency domain

TABLE 1 .
Parameters for selection of damping coefficient FIGURE 4. Current controller in the electrical unit 7th International Conference on Noise, Vibration and Comfort (NVC 2023)

TABLE 2 .
Parameters for evaluating Skyhook controller performance FIGURE 5. Placement of weight disks on the quarter car test rig

TABLE 3 .
Results from Experiment 1

FIGURE 6. Sprung
mass acceleration of Experiment 1b in (a) time domain, (b) frequency domain