Vehicle (QoV) with suspension using a controllable shock absorber which uses ... A fault detection in an automotive semi-active ... Advanced Fault Detection and.
13AC-0123
Fault Detection in Automotive Semi-active Suspension: Experimental Results Author, co-author (Do NOT enter this information. It will be pulled from participant tab in MyTechZone) Affiliation (Do NOT enter this information. It will be pulled from participant tab in MyTechZone) Copyright ยฉ 2013 SAE International
sensors and / or actuators. The study case is a Quarter of Vehicle (QoV) with a suspension using a configurable shock absorber. The experimental testbed uses Hardware-in-theLoop (HiL) to validate the fault detection approach. The HiL is an automotive Electronic Control Unit (ECU), and the QoV model is embedded in a Field-Programmable Gate Array (FPGA). The proposed scheme is performed for discrete time systems. The LPV approach is designed to detect a sensor fault on a vertical acceleration dynamic system. A control system for a semi-active suspension can take into account that detection and be online modified to assure the best performance in comfort, as well as messages to driver of a malfunction. The main technical contribution is the capability of fault sensor detection using a differences equation of second order which uses a measurement-based scheduling parameter.
ABSTRACT A proposal of fault detection using Linear Parameter Varying (LPV) systems is experimentally validated on embedded systems. The fault detection system is oriented to faulty sensors and / or actuators. The study case is a Quarter of Vehicle (QoV) with suspension using a controllable shock absorber which uses a SkyHook controller. The experimental testbed uses Hardware-in-the-Loop (HiL) to validate the approach. The HiL is an automotive Electronic Control Unit (ECU), and the QoV model is embedded in a FieldProgrammable Gate Array (FPGA). Results exhibit the effectiveness of the approach which is consistent with numerical simulation. These results open the application of LPV approaches to commercial vehicles since it is easy of implementation for several features such as, low computation load, lumped parameter model and available for nonlinear dynamic systems.
This paper is organized as follows. Section 2 shows a literature review. Section 3 describes the automotive suspension system. Section 4 presents the proposed solution where the Hardware-in-the-Loop including the semi-active suspension control system testbed using a Controller Area Network (CAN) is described. Section 5 discusses results. Section 6 concludes the paper.
1.-INTRODUCTION A controlled automotive suspension in actual vehicles claims to improve comfort and road holding using semi-active shock absorbers. This control system uses measurements from vertical acceleration in sprung mass, unsprung mass and suspension deflection. Hence, if a fault is presented in sensors, the suspension performance will be deteriorated. The fault detection of sensors allows to reconfigurate the system to nominal performance and/or advice driver of the system fault for maintenance. Since these control systems are implemented in computation constrained embedded systems, fault detection methods with light computation are mandatory.
2.-LITERATURE REVIEW Fast fault detection of automotive suspensions in extreme applications or situations, i.e. racing (car, bike), multiple uses of vehicles (off-road to highway changes) has opportunity areas. The detection of fault in sensors in racing application will allows to always keep an optimum damping, while in vehicles will decrease the risks of loss of stability at high speeds / maneouvres after off-road suspension operation. Consumers actually expect safety, security, reliability, comfort, etc. from their vehicles as they do from their other electronic products, [1]. Advanced Fault Detection and Isolation (FDI) methods are classified into two major groups, those which do not assume any form of model information
A fault detection in an automotive semi-active suspension using Linear Parameter Varying (LPV) systems, [9], is experimental validated on automotive embedded systems. The fault detection system is oriented to faulty 1
(process history-based methods) and those which use accurate dynamic process models (model-based methods), [10]. Basically, the FDI selection depends on the availability of a reliable model or process measurements under the considered faulty modes of operation. Faults in engineering processes belong to one of the following categories, [4]: faults in sensor and actuator called soft faults or, process faults where some plant parameters change because of physical/mechanical problems.
linear viscous friction (๐น๐ ), a spring force (๐น๐ ) and an electrically variable force (๐น๐ ) which is subject to saturations. It is herby proposed to model the effects of a damper failure as an arbitrary additive force, denoted by ๐น๐ . Thus, the resulting model for the damper force (๐น๐๐
) can be stated as:
๐น๐ = ๐ผ๐ ๐ tanh(๐1 ๐งฬ๐๐๐ + ๐2 ๐ง๐๐๐ ) + ๐ 1 ๐งฬ๐๐๐ + ๐ 2 ๐ง๐๐๐ + ๐น๐ (2) ๏ฟฝ๏ฟฝ๏ฟฝ ๏ฟฝ๏ฟฝ๏ฟฝ ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ ๐น๐
which can be rewritten:
FDI of automotive suspensions shows model based approaches have prohibitive computation [6, 12, 3, 2, 11]. In general, the approach methodology proposes the online register of data from the condition of the sensors / actuatos using mems, and then, through an online adapation of models and observers, the fault is detected. Fault detection that uses memory and online identification are prohibitive in automotive industry. Hence efficient computing and accurate methods to perform FDI in suspensions systems are an open issue.
โ๐น๐๐
โ ๐๐ ๐ง๐๐๐ ๐๐ ๐ง๐๐๐ + ๐น๐๐
โ ๐๐ก (๐ง๐ข๐ โ ๐ง๐ )
(3)
where ๐1 = tanh(๐1 ๐งฬ๐๐๐ + ๐2 ๐ง๐๐๐ ). Therefore a state-space representation of the QoV model is given by: ๐งฬ๐ ๐งฬ๐ ๏ฟฝ ๏ฟฝ ๐งฬ๐ข๐ ๏ฟฝ ๏ฟฝ๐งฬ๏ฟฝ ๐ข๐ ๐ฅฬ
๐1
=
๐งฬ๐ ๐งฬ ๏ฟฝ ๐ข๐ ๏ฟฝ ๐ง๐๐๐ ๏ฟฝ๏ฟฝ๏ฟฝ
(1)
where ๐๐ and ๐๐ข๐ are the sprung and unsprung mass, respectively; ๐ง๐๐๐ is the suspension deflection; ๐ง๐ represents the road profile; ๐๐ and ๐๐ก are respectively the stiffness of the suspension and the tire and ๐น๐๐
the semiactive damping force.
๐ฆ
๐1
๐๐
=
๐ฅฬ ๐ฆ
๐1
๐1
โกโ ๐๐ โ ๐๐ ๐๐ โค ๐งฬ๐ ๐๐ โข1 โฅ ๐ง๐ 0 0 0 โข ๐1 ๐1 ๐1 ๐1 +๐๐ก โฅ ๏ฟฝ๐งฬ ๏ฟฝ ๐ข๐ โ โ โข๐๐ข๐ ๐๐ข๐ ๐๐ข๐ ๐๐ข๐ โฅ ๐ง ๏ฟฝ๏ฟฝ ๏ฟฝ ๐ข๐ โฃ0 โฆ ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ 0 1 0
The dynamic behavior of a QoV with a semiactive suspension, Figure 1, is described by the following system of ordinary differential equations: = =
๐น๐
๐น๐ = ๐ผ๐๐ ๐1 + ๐1 ๐งฬ๐๐๐ + ๐2 ๐ง๐๐๐ + ๐น๐
3.-AUTOMOTIVE SUSPENSION SYSTEM
๐๐ ๐งฬ๐ ๐๐ข๐ ๐งฬ๐ข๐
๐น๐
๐1
๐ด
๐ 1 0โค โกโ ๐๐ 0 ๐ผ โข 0 0โฅ ๏ฟฝ๐ง ๏ฟฝ + โข๐0๐๐1 โฅ ๐ ๐๐ก 0โฅ ๏ฟฝ ๐น๐ โข ๐๐ข๐ ๐๐ข๐ โฃ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ โฆ 0 0 0 ๐ข
๐1
๐ต ๐1
๐ฅ
(4)
๐1
๐งฬ โกโ ๐๐ โ ๐๐ ๐๐ โค ๐ ๐๐ ๐ง โข ๐1 ๐1 ๐ ๐ +๐ โฅ ๐ โ 1 โ 1 ๐ก โฅ ๏ฟฝ๐งฬ๐ข๐ ๏ฟฝ โข๐๐ข๐ ๐๐ข๐ ๐๐ข๐ ๐๐ข๐ โฃ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ โฆ ๐ง๐ข๐ 0 1 0 โ1 ๐ถ ๐๐ ๐1
= =
1โค ๐ผ โกโ ๐๐ 0 โข โฅ ๐ง ๐ ๐ ๐ ๐ก + ๐ 1 0โฅ ๏ฟฝ ๐ ๏ฟฝ โข ๐๐ข๐ ๐๐ข๐ ๐น๐ โฃ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ๏ฟฝ 0 0 0โฆ
๐ด๐ฅ + ๐ต๐ข ๐ถ๐ฅ + ๐ท๐ข
๐ท
(5)
with ๐1 = ๐๐ + ๐2 .
In this application, it is proposed to implement fault detection and control algorithms for a quarter of vehicle system. The QoV model is implemented in an FPGA, National Instruments Compact RIO. The fault detection and control functionalities are implemented in a MPC5517 microcontroller. Both modules communicated via a CAN network. Figure 2 illustrates the components under consideration.
Figure 1. QoV model of a semi-active suspension
The semiactive suspension is represented by an MR damper, which can be modeled as the sum of various forces: a
The QoV model is implemented in the NI-FPGA inside the real-time module of the Compact RIO โcRIO-9004โ. The 2
chassis includes a CAN module NI-9852 composed of two low-speed CAN.
Both fault detection and control algorithms are computed inside the Freescale microcontroller. The microcontroller runs at 18 ๐โ๐ง. It is equipped with a CAN controller in order to achieve transmission with the cRIO FPGA. Thanks to the low computational load of the algorithms, real time computations are available at the constant rate specified by the system: ๐น๐ = 100 ๐ป๐ง. Computations are made in 32 bits floating point precision.
(a)
Once all data has been received, fault detection and control algorithms are computed. Then, those data are sent to cRIO. The CAN network ensures the communication between both modules. It has been chosen to use this type of network due to its great utilization in automotive industry. The CAN network is programmed in both components to work at a constant bit rate of 100 ๐๐๐๐ก๐ /๐ . The National Instrument FPGA sends the 3 sensors data coded as 32 bits fixed point data. As the way of coding data is different between cRIO and Freescale, is has been chosen to multiply the decimal data to be sent by a constant ๐ผ = 10242 and transmit directly an integer. Then, division by ๐ผ is made in the receiving module. Each integer ๐ผ are split in 4 bytes ๐ผ = [๐ผ1 ๐ผ2 ๐ผ3 ๐ผ4 ] as CAN network work with bytes.
(b)
After experiments, it has been shown that the transmission delay was roughly 1 ms for 1 integer. Transmitting the 3 data from cRIO to Freescale took 3 ms. Figure 3 illustrates the communication.
Figure 2. Experimental implementation (a) Photo, (b) Block diagram The model runs at the sampling frequency ๐น๐ = 100๐ป๐ง in order to achieve real-time computations. The state space model is implemented as : ๏ฟฝ
๐๐+1 ๐ด ๏ฟฝ=๏ฟฝ ๐๐ ๐ถ
๐ต ๐๐ ๏ฟฝ๏ฟฝ ๏ฟฝ ๐ท ๐๐
Figure 3. Communication between modules
(6)
4.-FAULT DETECTION APPROACH
where the numerical values are shown in the Appendix. It results as output the vectors of the next state ๐๐+1 and the outputs ๐๐ of the system. The inputs of the matrix are the states ๐๐ and the control input ๐๐ composed by the input current ๐ผ๐ and the road profile ๐ง๐๐ .
This section presents the fault detection approach which is used to detect a fault on the sprung mass acceleration sensor. The aim is by making use of the system inputs and outputs, recover if the actuator is faulty or healthy. The approach is facing several difficulties such as :
Once all the outputs are computed, they are sent to the fault detector and controller in order to detect a fault and compute the input current in the system.
1. The non linearity of the inputs 2. The road profile which is unmeasured The approach presented in [8] is adapted for the system under consideration as it proposes a fault detector for LPV systems with uncertainties. Nevertheless, a simpler
All decimal numbers inside the FPGA are coded in fixed point since floating point computation is not available. 3
synthesis can considerations.
be
handled
according
to
the
The parity matrix ๐ฒ๐ exists if and only if the rank of [โ | ๐ข๐ข ] is degenerated. However, it is known that the rank of the concatenation is given by :
further
The fault detection scheme is based on the parityspace approach. Since the nonlinearity of the system is only in the input matrices ๐ต and ๐ท, it is proposed to consider the nonlinearity outside the matrices, directly inside the control input. For this purpose, it is considered the system : ๐๐+1 ๐๐
= =
๐ด๐๐ + ๐ต๐ผ ๐ ๏ฟฝ ๐ ๐ผ๐ + ๐ต๐ ๐ง๐ ๐ผ๐๐
๐ด๐ถ๐ + ๐ท๐ผ ๐ ๏ฟฝ ๐ ๐ผ๐ + ๐ท๐ ๐ง๐ + ๐ท๐ ๐น๐
rank([โ
(7)
๐ = ๐ฒ โ
(๐๐ โ ๐ข๐ผ ๐๐ผ๐ )
The parity space approach aims to express the output of the system ๐๐ along a horizon ๐ . It leads to the following system :
๐ท๐ฅ โก๐ถ๐ต โข ๐ฅ ๐ถ๐ด๐ต โข 2๐ฅ where ๐ข๐ฅ = โข๐ถ๐ด ๐ต๐ฅ โข โฎ๐ฅ โข๐ถ๐ด๐ โ2 ๐ต๐ฅ โฃ and
๐ถ โก๐ถ๐ด โค โข โฅ โ = โข๐ถ๐ด2 โฅ โขโฎ โฅ โฃ๐ถ๐ด๐ โ1 โฆ
0 ๐ท๐ฅ ๐ถ๐ต๐ฅ ๐ถ๐ด๐ต๐ฅ โฑ ๐ถ๐ด๐ โ3 ๐ต๐ฅ
โฏ 0 โฑ โฑ โฑ โฏ
โฏ โฏ โฑ โฑ โฑ ๐ถ๐ด๐ต๐ฅ
[5] proposed a controller to minimize the vertical motion of the sprung mass by connecting a virtual damper between the body and the sky, named Sky Hook (SH). It is a practical and feasible solution to improve comfort on primary ride driving. In practice, the adjustable damper is approximated to mimic the virtual damper. The needed damping force is:
(8)
โฏ โฏ โฑ โฑ โฑ ๐ถ๐ต๐ฅ
0 0 โค โฅ โฎ โฅ โฎ โฅ 0 โฅ ๐ท๐ฅ โฅ โฆ
๐ ๐งฬ ๐น๐๐ป = ๏ฟฝ ๐๐ป ๐ ๐๐๐๐ (๐งฬ๐ โ ๐งฬ๐ข๐ )
๐งฬ๐ (๐งฬ๐ โ ๐งฬ๐ข๐ ) โฅ 0 (12) ๐งฬ๐ (๐งฬ๐ โ ๐งฬ๐ข๐ ) < 0
The SH force was converted from Newtons to Amperes using a proportional relation of 5 A / 3000 N that is the maximum force that the identified model of the MR damper can achive in the span of 0 to 5 A, [7]. The electric current was saturated in the aforementioned span.
5.-EXPERIMENTAL RESULTS The road profile is composed of a sine wave. Table 1 presents the frequencies and corresponding normalized amplitudes. The real amplitudes has been multiplied by ๐ด๐ = 15 ๐๐. First, the vehicle is in uncontrolled system, meaning the control input is ๐ผ = 0๐ด. Then, the SH controller is integrated. Several experiments corresponding to different excitation frequencies has been performed. The sprung mass
To fulfill the requirements of sensitivity to the fault and insensitivity to disturbances like the road profile, it can be synthesized a parity-matrix ๐ฒ๐ as : | ๐ข๐ข ] = 0
๐๐ ๐๐
where ๐น๐๐ป is the SH force, ๐๐๐ป is the damping coefficient to achieve the comfort, ๐๐๐๐ is the minimum damping coefficient, ๐งฬ๐ , and ๐งฬ๐ข๐ are the vertical velocity of sprung and unsprung masses. This technique certainly improves the ride comfort. This controller is the reference in comfort oriented suspensions due to its practical implementation and design.
In order to detect the fault ๐น๐ , a residual has to be synthesized. Two approaches has been carried out. First, an exact decoupling face to the state and the road profile has been handled. Then a sub-optimal optimization process face to road profile is presented, making use of lower computation time.
๐ฒ๐ โ
[โ
(11)
This application allows to reduce the horizon ๐ , and so computations and computation time, [8].
๐
๐๐ผ๐
(10)
The parity matrix is synthesized considering ๐ = ๐ + 1, where ๐ is the number of states of the system. It results a residual given by :
Now, the system under consideration is an LTI system. The aim is to synthesize a residual sensitive to the fault ๐น๐ , and insensitive to the road profile ๐ง๐ .
๐๐
๐ข๐ข ]) โค rank([โ]) + rank([๐ข๐ข ])
Finally, the condition of existence of the parity matrix leads to a long horizon time ๐ , so large computations. The next part makes use of an optimization approach in order to guarantee the orthogonality (decoupling face) to the states combines with an optimization approach in order to minimize the effect of the road profile.
๐ผ๐๐
๐น๐ ๐ง๐ ๐ฆ ๐ผ โก ฬ โค โก๐งฬ๐ โค โก๐ฆฬ โค โก๐ผ ฬ โค ๐น โข ๐ โฅ โข๐งฬ โฅ โข๐ฆฬ โฅ โข โฅ โข โฅ โ ๐ข๐ผ โข๐ผ ฬ โฅ = โ๐ฅ + ๐ข๐น โข๐น๐ฬ โฅ + ๐ข๐ข โข ๐ โฅ โขโฎ โฅ โขโฎ โฅ โขร โฎ โฅ โขโฎ โฅ (๐ ) โฃ๏ฟฝ โฃ๐ฆ (๐ ) โฆ โฃ๐ง๐ (๐ ) โฆ ๏ฟฝ๏ฟฝ๏ฟฝ ๐ผ (๐ ) โฆ โฃ๐น โฆ
|
(9)
4
accelerometer is considered as faulty and its fault has to be estimated. Table 1.Frequencies and relative amplitude for each sine wave tested. F(Hz) A(mm) F(Hz) A(mm)
0.5 1
0.57 1
0.65 1
0.76 1
0.85 1
0.97 1
1.10 0.98
1.26 0.95
1.44 0.91
1.64 0.87
1.87 0.83
2.14 0.79
F(Hz) A(mm)
2.44 0.76
2.78 0.72
3.17 0.67
3.62 0.57
4.13 0.47
4.72 0.36
F(Hz) A(mm)
5.38 0.29
6.14 0.26
7.01 0.23
8.00 0.20
9.13 0.14
10.42 0.10
F(Hz) A(mm)
11.89 0.09
13.53 0.08
15.48 0.07
17.66 0.06
20.16 0.05
23.00 0.04 Figure 5. Faulty outputs: left plots are for uncontrolled systems and right plots are for SH control system
Figure 4 compares the uncontrolled system and the SH control system. The SH controller has been implemented. Several experiments for different frequencies between ๐๐ = 0.5 ๐ป๐ง to ๐๐ = 23 ๐ป๐ง has been carried out. A pseudoBode diagram shows the benefits of a SH control system against uncontrolled system for the resonance frequenct. At this frequency the sprung mass has a high peak when the suspension is soft (I = 0A), and low peak for the SH control system.
The fault estimation procedures estimate presented fault in Figure 6. This figure shows the effectiveness of the approach. The road profile effect is well attenuated, even in the suboptimal approach. The proposal approach is robust since the fault estimation is good no matter the changes in the road profile and the SH control compensation. This shows the exact decoupling face to the road profile and the manipulation of the semi-active damper.
The residual as proposed in (11) is implemented. However, only the most significant resonating frequency ๐๐ โ 1.88 ๐ป๐ง is presented.
The proposed approach has been proved to be feasible for commercial implementation given its light computing time and high efficiency.
6.-CONCLUSIONS This paper presents an applicative fault detection combined with a Sky Hook Controller for a class of semiactive controllers. The proposed test-bed aims to highlight the performances of a fault detector and a controller for practical industrial applications. Two theoretical approaches has been presented for fault detection. For industrial implementation reasons, a simpler form based on the combination of a parityspace approach and optimization face to road profile is taken for study. The performances of the methodology highlight the interest of this approach. On the other hand, a SkyHook controller has been implemented. The combination of those low computational load algorithms allows for real time implementation, even for industrial applications.
Figure 4. Comparison of sprung mass acceleration for uncontrolled and SH control systems
Acknoledgement.
A fault of ๐น๐ = +1๐. ๐ โ2 is present on the output all the time, except between ๐ก๐ = 2.4๐ and ๐ก๐ = 6.6๐ in uncontrolled system and between ๐ก๐ = 6.2๐ and ๐ก๐ = 12.1 in SH control system. The outputs are presented in Figure 5.
This work is partially supported by the PCP 03/10 CONACYT Mรฉxico and the Rรฉseau Universitaire pour l'Innovation Industrielle from CNRS France, the Autotronics 5
Research chair at Tecnolรณgico de Monterrey, and the French National Project INOVE / ANR 2010 BLAN 0308.
6.
Kim, J., Lee, H., 2011. โSensor Fault Detection and Isolation Algorithm for a Continuous Damping Control Systemโ. J. of Automobile Eng 225, 1347โ1364 . 7. Lozoya-Santos, J., Tudรณn-Martรญnez, J.C., MoralesMenendez, R., Ramirez-Mendoza, R., Sename, O., Dugard, L., 2011. โControl Strategies for an Automotive Suspension with a MR Damperโ . 18 ๐กโ IFAC World Congress, Italy , pp:1820โ1825. 8. Varrier, S., D.Koenig, Martinez, J., 2012. โRobust Fault Detection for Vehicle Lateral Dynamicsโ, 51st IEEE Conf on Decision and Control, USA. 9. Varrier, S., Koenig, D., Martinez, J., 2012. โA parity Space-Based Fault Detection On LPV Systems: Approach For Vehicle Lateral Dynamics Control Systemโ, 8 ๐กโ IFAC-SAFEPROCESS, pp:1191-1196. 10. Venkatasubramanian, V., Rengaswamy, R., Kavuri, S., Yin, K., 2003. โA Review of Process Fault Detection and Diagnosis Part I Quantitative Model-Based Methodsโ. Computers and Chemical Eng 27, 293โ311 . 11. Vidal, Y., Acho, L., Pozo, F., Rodellar, J., 2010. โFault Detection in Base-Isolation Systems Via a Restoring Force Observerโ, Conf. on Control and Fault Tolerant Systems, France , pp. 94โ99 . 12. Wang, H., Song, G., 2011. โFault Detection and Fault Tolerant Control of a Smart Base Isolation System with Magneto-Rheological Damperโ. Smart Mater. Struct. 20, 1โ9 .
Figure 6. Fault estimation: upper plot shows the uncontrolled response, and lower plot, the SH control system.
Appendix ๐ง ๐งฬ ๐งฬ ๐๐ ๐๐ ๐๐๐
๐ผ
REFERENCES 1.
2.
3.
4. 5.
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Variable
๐ ๐๐ ๐๐ข๐ ๐๐ ๐๐ก ๐๐ ๐1 ๐2 ๐1 ๐2
6
deflection in meters deflection velocity in meters/sec deflection acceleration in meters/secยฒ passive stiffness constant in ๐/๐, passive damping constant in ๐๐ /๐, MR damping constant in (๐ โ
๐ด)/๐, applied current in A Value 9.81 500 100 118,000 170,000 600.95 37.85 22.15 2831 -7897
Unit ๐. ๐ โ2 ๐๐ ๐๐ ๐. ๐โ1 ๐. ๐โ1 ๐ ๐. ๐ . ๐โ1 ๐. ๐โ1 ๐. ๐ . ๐โ1 ๐. ๐โ1
Description gravity acceleration constant sprung mass unsprung mass spring rigidity constant tire rigidity constant Damper non-linear force Suspension non-linear damping Damper non-linear stifness Suspension passive damping Suspension passive stiffness