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Suspension hybrid control for in-wheel motor driven electric vehicle with dynamic vibration absorbing structures
5th IFAC Conference on 5th IFAC Conference on Engine Powertrain Simulation and online Modeling 5th IFACand Conference onControl, Available at www.sciencedirect.com Engine Powertrain Simulation and Modeling 5th IFACand Conference onControl, Changchun, China, September 2018 and Modeling Engine and Powertrain Control,20-22, Simulation Changchun, China, September 20-22, 2018 Engine and Powertrain Control, Simulation and Modeling Changchun, China, September 20-22, 2018 Changchun, China, September 20-22, 2018
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IFAC PapersOnLine 51-31 (2018) 973–978
Suspension hybrid control for in-wheel Suspension Suspension hybrid hybrid control control for for in-wheel in-wheel motor driven electric vehicle with dynamic Suspension hybrid control for in-wheel motor driven electric vehicle with dynamic motor driven electric vehicle with absorbing structures motorvibration driven electric vehicle with dynamic dynamic vibration absorbing structures vibration absorbing structures vibration absorbing structures ∗ ∗ ∗ ∗ Yechen Yechen Yechen Yechen
Qin Qin ∗∗∗ Qin ∗ Qin
Chenchen ∗ Mingming Dong ∗ Chenchen He He ∗∗∗ Peng Peng Ding Ding ∗∗ ∗ ∗ Mingming Dong ∗ ∗ Chenchen He ∗ Peng Ding Yanjun Huang ∗∗ ∗ Mingming Dong ∗ Yanjun Huang ∗∗ Chenchen He Peng Ding Mingming Dong ∗∗ Yanjun Huang ∗∗ Yanjun Huang ∗ ∗ Beijing Institute of Technology, Beijing, 100081 P.R. China. ∗ Beijing Institute of Technology, Beijing, 100081 P.R. China. ∗∗ ∗ of Waterloo, ON 3G1 (e-mail: of Technology, P.R. China. ∗∗ University ∗ Beijing Institute of Waterloo, Waterloo, Waterloo,Beijing, ON N2L N2L100081 3G1 Canada Canada (e-mail: ∗∗ University Beijing Institute of Technology, P.R. China. ∗∗ University of Waterloo, Waterloo,Beijing, ON N2L100081 3G1 Canada (e-mail: [email protected])., Corresponding author ∗∗ [email protected])., Corresponding author(e-mail: University of Waterloo, Waterloo, ON N2L 3G1 Canada [email protected])., Corresponding author [email protected])., Corresponding author Abstract: This paper presents aa hybrid hybrid control control strategy strategy for for suspension suspension of of the the in-wheel in-wheel motor motor Abstract: This paper presents (IWM) driven driven electric vehicle (EV) to improve improve vehicle ride comfort comfort and reduce reduce IWM vibration. A Abstract: This papervehicle presents a hybrid control strategy for suspension of the in-wheel motor (IWM) electric (EV) to vehicle ride and IWM vibration. A Abstract: This paperwith presents a hybrid control strategy for suspension of the in-wheel motor quarter vehicle model the dynamic vibration absorbing structure (DVAS) is first developed. (IWM) driven electric vehicle (EV) to improve vehicle ride comfort and reduce IWM vibration. A quarter vehicleelectric model with the(EV) dynamic vibration absorbing structure (DVAS) is firstvibration. developed. (IWM) driven vehicle to improve vehicle ride comfort reduce IWM A Different from the the traditional suspension system, the DVAS uses anand extra spring-damper system quarter vehicle model with thesuspension dynamic vibration absorbing structure (DVAS) is first developed. Different from traditional system, the DVAS uses an extra spring-damper system quarter vehicle model with the dynamic vibration absorbing structure (DVAS) is first developed. Different from the traditional suspension system, the DVAS uses an extra spring-damper system to achieve achieve vibration vibration reduction. reduction. The The dynamics dynamics and and boundary boundary models models for for two two commercially commercially to Different from the traditional suspension system, the an extra spring-damper system available and controllable dampers are dynamics then presented. Bothuses dampers in the the suspension and the to achieveand vibration reduction. The andDVAS boundary models for two commercially available controllable dampers are then presented. Both dampers in suspension and the to achieve vibration reduction. The dynamics and boundary models for two commercially DVAS are used to allocate the hybrid control force synthesized depend on the system responses. available and controllable dampers are then presented. Both dampers in the suspension and the DVAS areand used to allocatedampers the hybrid control force synthesized dependinonthe thesuspension system responses. available controllable areboth thenrandom presented. and the Simulation results for excitations excitations of roadBoth anddampers bump input aresystem finally responses. analyzed, DVAS are used to allocate the hybrid control force synthesized depend on the Simulation results for of both random road and bump input are finally analyzed, DVAS are used to allocate the hybrid control force synthesized depend on the system responses. Simulation results for excitations of both random road and bump input are finally analyzed, and the the proposed proposed hybrid hybrid controller controller can can simultaneously simultaneously improve improve ride ride comfort comfort and and reduce reduce IWM IWM and Simulation results hybrid for ofcan both randomsystem. roadimprove and bump are and finally analyzed, vibration compared to excitations thecontroller traditional suspension and the proposed simultaneously rideinput comfort reduce IWM vibration compared to the traditional suspension system. and the proposed hybrid cansuspension simultaneously improve ride comfort and reduce IWM vibration compared to thecontroller traditional system. vibration compared to theFederation traditional system.Hosting by Elsevier Ltd. All rights reserved. © 2018, IFAC (International of suspension Automatic Control) Keywords: Electric Electric vehicle, vehicle, Semi-active Semi-active suspension, suspension, Hybrid Hybrid control, control, Dynamic Dynamic vibration vibration Keywords: absorbing structure, In-wheel motor Keywords: Electric vehicle, Semi-active suspension, Hybrid control, Dynamic vibration absorbing structure, In-wheel motor Keywords: Electric vehicle, Semi-active suspension, Hybrid control, Dynamic vibration absorbing structure, In-wheel motor absorbing structure, In-wheel motor 1. INTRODUCTION INTRODUCTION Shao 1. Shao et et al. al. [2017], [2017], Wang Wang et et al. al. [2015] [2015] used used an an actuator actuator 1. INTRODUCTION located the sprung mass syntheShao etbetween al. [2017], Wang etand al.unsprung [2015] used anto located between the sprung and unsprung mass toactuator synthe1. INTRODUCTION Shao et al. [2017], Wang et al. [2015] used an actuator size active control force, and dynamic performances were Optimization and dynamics control of electric vehicle (EV) located between the sprung and unsprung mass to syntheactive control force, and dynamic performances were Optimization and dynamics control of electric vehicle (EV) size between the sprung and unsprung mass to syntheOptimization and dynamics control of electricand vehicle (EV) located improved based on H-inf controllers. As for the DVAS, attracts much attention in both academia industry, size active control force, and dynamic performances were improved based on H-inf controllers. As for the DVAS, attracts much attention in both academia and industry, size active control and dynamic performances were Optimization and dynamics of electric vehicle (EV) improved based onforce, H-inf controllers. As for the DVAS, attracts much attention in control both academia and industry, Nagaya et al. [2003], Qin et al. [2018a] proposed a structure and many remarkable works had been done in the past Nagaya et al. [2003], et controllers. al. [2018a] proposed a structure and many remarkable works had academia been doneand in industry, the past improved based on Qin H-inf As for the DVAS, attracts much attention in [2017], both and many remarkable works had been done in[2017a,b]. the past Nagaya with the DVAS connected to the unsprung mass. Simuladecades, see Huang et al. Tang et al. et al. [2003], Qin et al. [2018a] proposed a structure with theetDVAS connected to unsprung mass. Simuladecades, Huang et works al. [2017], Tang done et al.in[2017a,b]. al.revealed [2003], Qin et such al. the [2018a] proposed a structure and manysee remarkable had been the decades, see Huang et al. [2017], Tang tion results that structure can remarkably Compared to the traditional traditional centrally driven EV, thepast in- Nagaya with the DVAS connected to the unsprung mass. Simulaet al.EV, [2017a,b]. tion results revealed that such structure can remarkably Compared to the centrally driven the inthe both DVAS connected toand thestructure unsprung mass. Simuladecades, see et al. [2017], Tang et al.EV, [2017a,b]. Compared to Huang the traditional centrally driven the in- with improve ride comfort road handling. As wheel motor (IWM) driven EV has numerous of merits, tion results revealed that such can remarkably improve both ride comfort and structure road handling. As noted noted wheel motor (IWM) driven EV has numerous of merits, tion results revealed that such can remarkably Compared to the traditional centrally driven EV, the inimprove both ride comfort and road handling. As noted wheel motor (IWM) driven EV has numerous of merits, the application of DVAS e.g. fast fast system system response, response, flexible flexible configuration, configuration, high high enen- by by the the papers, papers, thecomfort application of the thehandling. DVAS introduces introduces e.g. improve both ride and road As noted wheel motor (IWM) driven EV has numerous of merits, e.g. fast systemand response, flexible configuration, high en- by extra spring-damper components and forms a novel multiergy efficiency, space saving. the papers, the application of the DVAS introduces extra spring-damper componentsof and forms a novel multiergy efficiency, and space saving. by the papers, the application the DVAS introduces e.g. fast system response, flexible configuration, high energy efficiency, and space saving. input suspension which new for extra components and forms novel multiinput spring-damper suspension system, system, which brings brings new aachallenges challenges for However, major problem associated with with the the IWM IWM applispring-damper components and forms novel multiergy efficiency, andproblem space saving. appli- extra However, aa major associated vibration control of IWM driven EV. input suspension system, which brings new challenges vibration control of IWM which drivenbrings EV. new challenges for However, a major problem associated with the IWM cation is the increased unsprung mass. Previous research appliinput suspension system, for vibration control of IWM driven EV. cation is the increased unsprung mass. Previous research However, a major problem associated with the IWM application is the increased unsprung mass. Previous research This paper combines both semi-active control strategy has shown that the application of the IWMs will not vibration control of IWM driven EV. not This paper combines both semi-active control strategy has shown the application of thePrevious IWMs will cation is thethat increased unsprung mass. research has that the application of the will not This and DVAS to vertical dynamic peronly shown deteriorate vehicle ride comfort comfort andIWMs road handling handling paper combines both vehicle semi-active control strategy and the the DVAS to improve improve vehicle vertical dynamic peronly deteriorate vehicle ride and road This paper combines bothsystem semi-active control strategy has shown thatalso the influence application of the will not and the DVAS to improve vehicle vertical dynamic peronly deteriorate vehicle ride comfort andIWMs road handling formance. The suspension control issue is firstly capacities, but motor lifespan due to the formance. The suspension system control issue is firstly capacities, but also influence motor lifespan due to the and the DVAS to improve vehicle vertical dynamic peronly deteriorate vehicle ride comfort and road handling capacities, but also influence Tan motor lifespan due created to the formance. transformed into a multi-objective optimization problem harsh vibration environment. and Lu [2016] The suspension system control issue is firstly transformed intosuspension a multi-objective optimization problem created harsh vibration environment. Tan andlifespan Lu [2016] formance. The system control issue is firstly capacities, but also influence motor due to the harsh vibration environment. Tanand andinvestigated Lu [2016] created (MOOP). novel hybrid controller is PMSM-suspension system model, model, the inin- transformed optimization (MOOP). A A into novelaa multi-objective hybrid suspension suspension controller problem is then then PMSM-suspension system and the into multi-objective optimization problem harsh vibration environment. Tan andinvestigated Lu [2016] created (MOOP). Aand novel hybrid control suspension controller is then PMSM-suspension system model, and investigated theand in- transformed developed, the force is allocated and fluence of motor unbalance force on the vehicle vertical developed, and the hybrid control force is allocated and fluence of motor unbalance force on the vehicle vertical and (MOOP). A novel hybrid suspension controller is PMSM-suspension system model, the in- achieved developed, and the hybrid control force issuspension allocated then fluence of motor unbalance force onand the investigated vehicle vertical and by the two dampers locate in the and lateral responses. Sun et al. [2015] investigated the effects achieved byand the two damperscontrol locate force in theissuspension and lateral responses. Sun et al.force [2015] investigated the effects developed, the hybrid allocated and fluence of motor unbalance on the vehicle vertical and lateral Sun et al.vertical [2015] investigated effects achieved the DVAS. commercially available controllable of IWM IWMresponses. on the the suspension suspension response, and andthe designed by Two the two dampers locate in theand suspension and the DVAS. Two commercially available and controllable of on vertical response, designed achieved by the two dampers locate in the suspension and lateral responses. Sun et al. [2015] investigated the effects of IWM on current the suspension vertical response, and designed dampers are tested and models are a modified modified chopping controller to improve improve system the DVAS. commercially available and controllable dampers areTwo tested and their their dynamics dynamics models are used used for for aof chopping controller to system the DVAS. Two commercially available andexcitations controllable IWM performance on current the suspension vertical response, and designed are tested andSimulation their dynamics models are used for avertical modified current chopping controller toconstant improve system dampers numerical simulation. results for of in both starting and velocity numericalare simulation. Simulation results for excitations of vertical performance in both starting and constant velocity dampers tested and their dynamics models are used for a modified current chopping controller to improve system numerical simulation. Simulation results for excitations of vertical performance in both starting and constant velocity both random road and bump input are finally presented working condition. both random road and bump input are finally presented working condition. in both starting and constant velocity numerical simulation. Simulation results for excitations of vertical performance working condition. to show the superiority of the proposed method. both random road and bump input are finally presented show the superiority the proposed To reduce reducecondition. the vibration vibration caused caused by by the the increased increased unsprung unsprung to both random road and of bump input are method. finally presented working To the to show the superiority of the proposed method. To reduce the vibration caused by the increased unsprung The rest of this paper is organized as follows. Firstly, mass, two methodologies have been proposed, i.e. controlto show the superiority of the proposed method. The rest of this paper is organized as follows. Firstly, the the mass, two methodologies have been proposed, i.e.unsprung controlTo reduce the vibration caused by the increased mass, two methodologies havedynamic been proposed, i.e. control- The DVAS based quarter vehicle model and damper dynamic lable suspension system and vibration absorbing rest of this paper is organized as follows. Firstly, the DVAS based quarter vehicle model and damper dynamic lable suspension system and dynamic vibration absorbing The rest of this papervehicle isinorganized as follows. Firstly, the mass, two(DVAS). methodologies have been proposed, i.e. controllable suspension system and dynamic vibration absorbing models are introduced Section 2. Then, the proposed structure For the controllable suspension system, DVAS based quarter model and damper dynamic are introduced in Section 2.and Then, the proposed structure (DVAS). For the controllable suspension system, models DVAS based quarter vehicle model damper dynamic lable suspension system and dynamic vibration absorbing models are introduced in Section 2. Then, the proposed structure (DVAS). For the controllable suspension system, hybrid controller is in Section 3. The authors acknowledge the support of the National Natural hybrid suspension suspension controller is illustrated illustrated in 3. models aresimulations introduced in Section 2. Then, theSection proposed structure (DVAS). For thethe controllable The authors acknowledge support of suspension the National system, Natural Numerical are carried out in Section 4 for two hybrid suspension controller is illustrated in Section 3. Science Foundation of Chinathe(Grant No.ofU1564210), Innovative The authors acknowledge support the National Natural Numerical simulations are carried out in Section 4 for two hybrid suspension controller is illustrated in Section 3. Science Foundation of China (Grant No. U1564210), Innovative different road excitations. Conclusion and future work are Numerical simulations are carried out in Section 4 for two The authors acknowledge the support of the National Natural talent support program for Chinese post-doctorates (Grant No. Sciencesupport Foundation of China (Grant post-doctorates No. U1564210),(Grant Innovative different road excitations. Conclusion and future 4work are talent program for Chinese No. Numerical simulations are carried out in Section for two Science Foundation of China (Grant No.Natural U1564210), Innovative 2016M600934, BX201600017), and Beijing Science Foundadiscussed at different road excitations. Conclusion and future work are talent support program for Chinese post-doctorates (Grant No. 2016M600934, BX201600017), and Beijing Natural Science Foundadiscussed at last. last. different excitations. Conclusion and future work are talent support post-doctorates (Grant No. tion (Grant No. program 3184058).for Chinese discussedroad at last. 2016M600934, and Beijing Natural Science Foundation (Grant No.BX201600017), 3184058). 2016M600934, and Beijing Natural Science Foundadiscussed at last. tion (Grant No.BX201600017), 3184058).
tion (Grant©No. 3184058). 2405-8963 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 1017 Copyright © under 2018 IFAC 1017Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 1017 10.1016/j.ifacol.2018.10.054 Copyright © 2018 IFAC 1017
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2. SYSTEM MODELING This section presents the quarter vehicle models of IWM driven EV, and introduces the controllable damper models used in the DVAS. 2.1 Quarter vehicle model Despite its simplicity, quarter vehicle model is widely used in vertical dynamics analysis and controller design, see Cao et al. [2011], Wang et al. [2017b]. Figure 1 depicts the structure of the quarter vehicle model for IWM driven EV. The dynamics equations can be described according to Newton’s law of motion as follows.
2.2 Controllable damper model
Controllable damper force can be expressed as a function of control current and relative velocity. The damper force of both the suspension and the DVAS can be expressed as: Fcs = f1 (ics , x˙ b − x˙ s1 ) (3) Fcd = f2 (icd , x˙ s1 − x˙ s )
To accurate depict such relationship, many methods like Bouc-Wen and polynomial models can be used, see Dong et al. [2010], Spencer Jr et al. [1997], Zhang et al. [2017]. This paper adopts a nonparametric model proposed by Song et al. [2005]. A continuous damping control (CDC) damper from ZF Sachs is used to generate the suspension controllable damper force, and a smaller magnetorheological (MR) damper from Lord is utilized in the DVAS due to the limited space. The dynamics characteristics of both the CDC damper and the MR damper are tested with an MTS test rig, which is shown in Fig. 3(a).
Fig. 1. IWM driven EV quarter vehicle model ¨b + ks (xb − xsa ) + cs (x˙ b − x˙ sa ) = 0 mb x msa x ¨sa + kt (xsa − xz ) + ks (xsa − xb ) + cs (x˙ sa − x˙ b ) = 0 (1) where mb is the sprung mass/ msa is the unsprung mass, including tire, IWM, and braking system. ks , cs and kt denote suspension stiffness, damper and tire stiffness, respectively. The DVAS based quarter vehicle model is introduced by Qin et al. [2018a]. The structure and dynamics equations of this system are given below.
¨b + ks (xb − xs1 ) + cs (x˙ b − x˙ s1 ) = 0 mb x ¨r + kb (xr − xs ) = 0 mr x ¨s + kd (xs − xs1 ) + kb (xs − xr ) + cd (x˙ s − x˙ s1 ) = 0 ms x ms1 x ¨s1 + ks (xs1 − xb ) + cs (x˙ s1 − x˙ b ) + kd (xs1 − xs ) + cd (x˙ s1 − x˙ s ) = 0 (2) where ms1 , ms and mr are unsprung mass, stator mass and rotor mass, respectively. kd and cd are stiffness and damper of DVAS, and kb represents the bearing stiffness between the stator and the rotor. The main purpose of this paper is then to synthesize time-varying controllable damper force to replace both cs (x˙ b − x˙ s1 ) and cd (x˙ s − x˙ s1 ).
With the method proposed by Song et al. [2005], the controllable damper force can be expressed as: Fdamper = A (i) · Sb (vrelative ) , k (4) an in , A (i) = n=0
Sb (vrelative ) = tanh [(b1 i+b0 ) vrelative ] where n is the function order, and n = 2 is adopted in this paper. an and bn are coefficients to be determined, and i is the control current. All unknown coefficients in (4) can be estimated by optimization method, e.g. Particle swarm optimization (PSO). With the estimated parameters, the control current can then be expressed as i = f −1 (Fdamper , vrelative ) and calculated as per (4). For more details, readers can refer to Qin et al. [2017]. The velocity-force map of the MR damper can be depicted as Fig. 3(b) with the aforementioned methodology. Note that the damper dynamics depicted in (3) do not constraint the output force. The calculated force may be unrealizable and thus results in exaggerated or negative control current. A damper boundary model derived from 3(b) is also applied in this paper, as shown in Fig. 4.
3. HYBRID SUSPENSION CONTROLLER
Fig. 2. IWM driven EV quarter vehicle model with DVAS
This section formulates the hybrid controller, and discusses the allocation of the hybrid control force to the two controllable dampers.
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3.2 Hybrid control for DVAS based suspension system
The skyhook control is proposed by virtually linking the vehicle chassis to the sky to reduce vehicle chassis vertical vibration, while the groundhook performs in a dual way to the skyhook control to improve vehicle road handling capacity, see Savaresi et al. [2010]. Hybrid control is proposed to combine the merits of both the skyhook control and the groundhook control with single suspension controllable damper, see Qin et al. [2015]. For the proposed quarter vehicle model with DVAS, two fictitious dampers are applied as shown in Fig. 5.
Fig. 3. MR damper made by Lord: (a) damper in the test rig, (b) force map
Fig. 5. Skyhook and groundhook ideal principle illustration As the structure shown in Fig. 5 is theoretically impossible, both skyhook and groundhook control use damper force to reproduce the virtual dampers’ behaviour. Different from traditional suspension system, the extra controllable damper in the DVAS enables the proposed model use two individual dampers to mimic the virtual dampers.
Fig. 4. MR damper boundary model 3.1 Suspension system criterions Suspension system criteria are necessary for systems comparison. The sprung mass acceleration (SMA) x ¨b and stator acceleration (SA) x ¨s1 are taken as criteria to evaluate the ride comfort and motor vibration environment. This paper treats suspension control as a MOOP, which subject to several constraints. The MOOP can be expressed as follows: min
g1 (P) = σx¨b , g2 (P) = σx¨s1 , subject to 3 · |σRS | ≤ lim (RS) , (5) 3 · |σair | ≤ lim (air) , 3 · |σT D | ≤ lim (T D) where σ(·) represents signal RMS, and P = [ Fcs Fcd ] is the controllable force set. σRS is the RMS of the rattle space (RS) with lim(RS) = 0.1 m, σair is the RMS of the airgap between the stator and the rotor with lim(air) = 0.001 m, and σT D is the RMS of the tire deflection (TD) with lim(T D) = 0.018 m. For a linear suspension system excited by the road profile that can be modeled as Gaussian stochastic process, three times of RMS ensure the response within the range with possibility of 99.7 %.
The skyhook controller can be expressed as: csky (x˙ b ) , if x˙ b (x˙ b − x˙ w ) ≥ 0, Fcs = cmin (x˙ b − x˙ w ) , if x˙ b (x˙ b − x˙ w ) < 0
(6)
Similarly, the groundhook controller can be expressed as: cgrd (x˙ s ) , if x˙ s (x˙ s − x˙ s1 ) ≥ 0, Fcd = (7) cmin (x˙ s − x˙ s1 ) , if x˙ s (x˙ s − x˙ s1 ) < 0 Based on the damper model and the synthesized control force, the overall control structure of the proposed hybrid suspension controller is shown in Fig. 6. This structure includes two parts, named semi-active suspension and hybrid controller. The states obtained from the plant are taken as the controller input, and the controller generate ideal control force F . Then, both boundary and current model output realizable control force and current i. The damper model given in (4) finally synthesize the control force to improve suspension system dynamics responses. In the following section, simulation results for solely skyhook or groundhook and hybrid control are discussed. For the sake of the simplicity, all suspension system to be compared with are named as follows:
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• Passive: system modeled by (1);
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Fig. 6. Control structure for suspension hybrid controller • DVAS: system with the DVAS as shown in (2); • Skyhook: DVAS based system with the skyhook control in (6) and the passive DVAS damper force; • Groundhook: DVAS based system with the groundhook control in (7) and the passive suspension damper force; • Hybrid: DVAS based system with both the skyhook and the groundhook control.
DVAS structure can reduce 23.6% of SMA, and 63.6% of SA compared to the passive structure. For the three types of controllers, the conflict between ride comfort and motor vibration can be observed. The skyhook controller can achieve 31.8% improvement in SMA, while deterioration in the aspect of SA is unavoidable (8.2% w.r.t. the passive case). On the contrary, the groundhook controller can only reduce the SA (9.9% w.r.t. the passive case) with incasement of SMA compared to the DVAS. As for the hybrid controller, its SMA reduces to 0.5443 m/s2 (31.7% improvement compared to the passive one), and SA is smaller than the DVAS structure (3.1% improvement), which means the proposed hybrid controller simultaneously outperforms both the skyhook and the groundhook controllers.
4. NUMERICAL SIMULATION This section details the numerical simulation results for different excitation conditions. 4.1 Simulation settings The proposed hybrid control for IWM driven EV is evaluated for excitations of random road and bump input. The system parameters are tabulated in Table 1 as per Qin et al. [2018a]. Table 1. Quarter vehicle model parameters Parameters mb msa ks cs kt kb cgrd
Value 332 kg 70 kg 24000 N/m 2000 Ns/m 220000 Ns/m 7 × 106 N/m 600 N/m
Parameters ms ms1 mr kd cd csky cmin
Value 20 kg 25 kg 25 kg 53000 N/m 1900 Ns/m 3000 N/m 100 N/m
Fig. 7. PSD comparison for random road excitation
4.2 Simulation results and discussion The simulation is carried out under two different road excitations. For the random road excitation, the vehicle is traveling at a speed of 40 km/h under ISO road level C. For generation of random road profile, readers can refer to Qin et al. [2018b,c], Wang et al. [2017a]. The bump input is defined according to Zhao et al. [2016]:
xz =
0.025 [1 + sin(2πvt/2.5)] , 1 < t < 1 + 2.5/v 0 otherwise
(8)
Simulation results for random road excitation are tabulated in Table 2, and PSD comparison is depicted in Fig. 7. According to Table 2, it can be observed that all four suspension systems with the DVAS can improve both ride comfort and reduce motor vibration. Application of the
As for the PSD comparison shown in Fig. 7, it can be seen from the upper figure that all four systems with the DVAS can reduce SMA amplitude in both the sprung mass and the unsprung mass resonant frequencies. For the frequency range with which human beings are most sensitive, the proposed hybrid controller outperforms all other three systems, which means better ride comfort can be expected. In the case of the SA, the lower figure in Fig. 7 shows that all systems with the DVAS can remarkably reduce vibration amplitude around the unsprung mass resonant frequency. Among all these four systems, the groundhook controller performs better in the frequency range from 8 Hz to 12 Hz. Although the proposed hybrid controller is sightly worse than the groundhook controller within this range, much better vibration reduction effect can still be expected compared to both the DVAS and the skyhook controller. The system comparisons for a vehicle crosses over bumpy terrain are shown in Fig. 8. It can be seen from Fig. 8 that in the upper figure, both the proposed hybrid and the skyhook controllers outperforms the other three systems with smaller SMA
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Table 2. RMS Comparison for random road excitation 12345RMS SMA (m/s2 ) SA (m/s2 ) RS (m) Airgap (m)(1e-4) TD (m)
Passive 0.7975 11.67 0.0066 0.0026
DVAS 0.6092 4.24 0.0065 0.155 0.0019
Skyhook 0.5435 4.59 0.0075 0.168 0.0021
Groundhook 0.6114 3.82 0.0064 0.138 0.0019
Hybrid 0.5443 4.11 0.0075 0.148 0.0019
Fig. 8. System comparison for bumpy input amplitude and convergence time. As for the SA depicted in the lower figure, although all four systems with the DVAS have similar acceleration amplitude, both the hybrid and groundhook controllers converge faster than the DVAS and the skyhook controller. Thus, the proposed hybrid controller improves performance more obviously than the DVAS system and the DVAS based system with sole skyhook and groundhook controllers. To ensure system responses satisfy all the constraints defined in (5), system responses of TD, Airgap and RS are shown in Fig. 9. It can be seen for the sudden bumpy input, all three responses do not violate the constraints, which means the MOOP is settled by the proposed hybrid controller. 5. CONCLUSION In this paper, a hybrid controller was proposed for IWM driven EV with the DVAS. Different from previous hybrid controller, both the suspension and the DVAS dampers are used to allocate the synthesized hybrid control force. Two commercially available and controllable dampers, i.e. CDC and MR dampers, are used to reproduce the virtual dampers’ behaviour. Simulation results reveal that the proposed method can improve ride comfort for 31.7% and IWM lifespan vibration for 64.8% compared to the IWM driven EV without the DVAS. Further research will focus on more advanced control strategies and experimental validation.
Fig. 9. System constraints for bumpy input REFERENCES Cao, D., Song, X., and Ahmadian, M. (2011). Editorsąŕ perspectives: road vehicle suspension design, dynamics, and control. Vehicle system dynamics, 49(1-2), 3–28. Dong, X.m., Yu, M., Liao, C.r., and Chen, W.m. (2010). Comparative research on semi-active control strategies for magneto-rheological suspension. Nonlinear dynamics, 59(3), 433–453. Huang, Y., Khajepour, A., Zhu, T., and Ding, H. (2017). A supervisory energy-saving controller for a novel antiidling system of service vehicles. IEEE/ASME Transactions on Mechatronics, 22(2), 1037–1046. Nagaya, G., Wakao, Y., and Abe, A. (2003). Development of an in-wheel drive with advanced dynamic-damper mechanism. JSAE review, 24(4), 477–481. Qin, Y., Dong, M., Langari, R., Gu, L., and Guan, J. (2015). Adaptive hybrid control of vehicle semiactive suspension based on road profile estimation. Shock and Vibration, 2015. Qin, Y., He, C., Shao, X., Du, H., Xiang, C., and Dong, M. (2018a). Vibration mitigation for in-wheel switched reluctance motor driven electric vehicle with dynamic vibration absorbing structures. Journal of Sound and Vibration, 419, 249–267. Qin, Y., Wei, C., Tang, X., Zhang, N., Dong, M., and Hu, C. (2018b). A novel nonlinear road profile classification approach for controllable suspension system: Simulation and experimental validation. Mechanical Systems and Signal Processing, DOI:10.1016/j.ymssp.2018.07.015.
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Qin, Y., Xiang, C., Wang, Z., and Dong, M. (2018c). Road excitation classification for semi-active suspension system based on system response. Journal of Vibration and Control, 24(13), 2732–2748. Qin, Y., Zhao, F., Wang, Z., Gu, L., and Dong, M. (2017). Comprehensive analysis for influence of controllable damper time delay on semi-active suspension control strategies. Journal of Vibration and Acoustics, 139(3), 031006. Savaresi, S.M., Poussot-Vassal, C., Spelta, C., Sename, O., and Dugard, L. (2010). Semi-active suspension control design for vehicles. Elsevier. Shao, X., Naghdy, F., and Du, H. (2017). Reliable fuzzy hąÞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping. Mechanical Systems and Signal Processing, 87, 365–383. Song, X., Ahmadian, M., and Southward, S.C. (2005). Modeling magnetorheological dampers with application of nonparametric approach. Journal of intelligent material systems and structures, 16(5), 421–432. Spencer Jr, B., Dyke, S., Sain, M., and Carlson, J. (1997). Phenomenological model for magnetorheological dampers. Journal of engineering mechanics, 123(3), 230–238. Sun, W., Li, Y., Huang, J., and Zhang, N. (2015). Vibration effect and control of in-wheel switched reluctance motor for electric vehicle. Journal of Sound and Vibration, 338, 105–120. Tan, D. and Lu, C. (2016). The influence of the magnetic force generated by the in-wheel motor on the vertical and lateral coupling dynamics of electric vehicles. IEEE Transactions on Vehicular Technology, 65(6), 4655–4668. Tang, X., Hu, X., Yang, W., and Yu, H. (2017a). Novel torsional vibration modeling and assessment of a powersplit hybrid electric vehicle equipped with a dual mass flywheel. IEEE Transactions on Vehicular Technology. Tang, X., Yang, W., Hu, X., and Zhang, D. (2017b). A novel simplified model for torsional vibration analysis of a series-parallel hybrid electric vehicle. Mechanical Systems and Signal Processing, 85, 329–338. Wang, R., Jing, H., Yan, F., Karimi, H.R., and Chen, N. (2015). Optimization and finite-frequency hąÞ control of active suspensions in in-wheel motor driven electric ground vehicles. Journal of the Franklin Institute, 352(2), 468–484. Wang, Z.F., Dong, M.M., Gu, L., Rath, J.J., Qin, Y.C., and Bai, B. (2017a). Influence of road excitation and steering wheel input on vehicle system dynamic responses. Applied Sciences, 7(6), 570. Wang, Z., Dong, M., Qin, Y., Du, Y., Zhao, F., and Gu, L. (2017b). Suspension system state estimation using adaptive kalman filtering based on road classification. Vehicle System Dynamics, 55(3), 371–398. Zhang, X., Li, Z., Guo, K., Zheng, F., and Wang, Z. (2017). A novel pumping magnetorheological damper: Design, optimization, and evaluation. Journal of Intelligent Material Systems and Structures, 28(17), 2339–2348. Zhao, F., Ge, S.S., Tu, F., Qin, Y., and Dong, M. (2016). Adaptive neural network control for active suspension system with actuator saturation. IET Control Theory & Applications, 10(14), 1696–1705.
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IFAC PapersOnLine 51-31 (2018) 973–978
Suspension hybrid control for in-wheel Suspension Suspension hybrid hybrid control control for for in-wheel in-wheel motor driven electric vehicle with dynamic Suspension hybrid control for in-wheel motor driven electric vehicle with dynamic motor driven electric vehicle with absorbing structures motorvibration driven electric vehicle with dynamic dynamic vibration absorbing structures vibration absorbing structures vibration absorbing structures ∗ ∗ ∗ ∗ Yechen Yechen Yechen Yechen
Qin Qin ∗∗∗ Qin ∗ Qin
Chenchen ∗ Mingming Dong ∗ Chenchen He He ∗∗∗ Peng Peng Ding Ding ∗∗ ∗ ∗ Mingming Dong ∗ ∗ Chenchen He ∗ Peng Ding Yanjun Huang ∗∗ ∗ Mingming Dong ∗ Yanjun Huang ∗∗ Chenchen He Peng Ding Mingming Dong ∗∗ Yanjun Huang ∗∗ Yanjun Huang ∗ ∗ Beijing Institute of Technology, Beijing, 100081 P.R. China. ∗ Beijing Institute of Technology, Beijing, 100081 P.R. China. ∗∗ ∗ of Waterloo, ON 3G1 (e-mail: of Technology, P.R. China. ∗∗ University ∗ Beijing Institute of Waterloo, Waterloo, Waterloo,Beijing, ON N2L N2L100081 3G1 Canada Canada (e-mail: ∗∗ University Beijing Institute of Technology, P.R. China. ∗∗ University of Waterloo, Waterloo,Beijing, ON N2L100081 3G1 Canada (e-mail: [email protected])., Corresponding author ∗∗ [email protected])., Corresponding author(e-mail: University of Waterloo, Waterloo, ON N2L 3G1 Canada [email protected])., Corresponding author [email protected])., Corresponding author Abstract: This paper presents aa hybrid hybrid control control strategy strategy for for suspension suspension of of the the in-wheel in-wheel motor motor Abstract: This paper presents (IWM) driven driven electric vehicle (EV) to improve improve vehicle ride comfort comfort and reduce reduce IWM vibration. A Abstract: This papervehicle presents a hybrid control strategy for suspension of the in-wheel motor (IWM) electric (EV) to vehicle ride and IWM vibration. A Abstract: This paperwith presents a hybrid control strategy for suspension of the in-wheel motor quarter vehicle model the dynamic vibration absorbing structure (DVAS) is first developed. (IWM) driven electric vehicle (EV) to improve vehicle ride comfort and reduce IWM vibration. A quarter vehicleelectric model with the(EV) dynamic vibration absorbing structure (DVAS) is firstvibration. developed. (IWM) driven vehicle to improve vehicle ride comfort reduce IWM A Different from the the traditional suspension system, the DVAS uses anand extra spring-damper system quarter vehicle model with thesuspension dynamic vibration absorbing structure (DVAS) is first developed. Different from traditional system, the DVAS uses an extra spring-damper system quarter vehicle model with the dynamic vibration absorbing structure (DVAS) is first developed. Different from the traditional suspension system, the DVAS uses an extra spring-damper system to achieve achieve vibration vibration reduction. reduction. The The dynamics dynamics and and boundary boundary models models for for two two commercially commercially to Different from the traditional suspension system, the an extra spring-damper system available and controllable dampers are dynamics then presented. Bothuses dampers in the the suspension and the to achieveand vibration reduction. The andDVAS boundary models for two commercially available controllable dampers are then presented. Both dampers in suspension and the to achieve vibration reduction. The dynamics and boundary models for two commercially DVAS are used to allocate the hybrid control force synthesized depend on the system responses. available and controllable dampers are then presented. Both dampers in the suspension and the DVAS areand used to allocatedampers the hybrid control force synthesized dependinonthe thesuspension system responses. available controllable areboth thenrandom presented. and the Simulation results for excitations excitations of roadBoth anddampers bump input aresystem finally responses. analyzed, DVAS are used to allocate the hybrid control force synthesized depend on the Simulation results for of both random road and bump input are finally analyzed, DVAS are used to allocate the hybrid control force synthesized depend on the system responses. Simulation results for excitations of both random road and bump input are finally analyzed, and the the proposed proposed hybrid hybrid controller controller can can simultaneously simultaneously improve improve ride ride comfort comfort and and reduce reduce IWM IWM and Simulation results hybrid for ofcan both randomsystem. roadimprove and bump are and finally analyzed, vibration compared to excitations thecontroller traditional suspension and the proposed simultaneously rideinput comfort reduce IWM vibration compared to the traditional suspension system. and the proposed hybrid cansuspension simultaneously improve ride comfort and reduce IWM vibration compared to thecontroller traditional system. vibration compared to theFederation traditional system.Hosting by Elsevier Ltd. All rights reserved. © 2018, IFAC (International of suspension Automatic Control) Keywords: Electric Electric vehicle, vehicle, Semi-active Semi-active suspension, suspension, Hybrid Hybrid control, control, Dynamic Dynamic vibration vibration Keywords: absorbing structure, In-wheel motor Keywords: Electric vehicle, Semi-active suspension, Hybrid control, Dynamic vibration absorbing structure, In-wheel motor Keywords: Electric vehicle, Semi-active suspension, Hybrid control, Dynamic vibration absorbing structure, In-wheel motor absorbing structure, In-wheel motor 1. INTRODUCTION INTRODUCTION Shao 1. Shao et et al. al. [2017], [2017], Wang Wang et et al. al. [2015] [2015] used used an an actuator actuator 1. INTRODUCTION located the sprung mass syntheShao etbetween al. [2017], Wang etand al.unsprung [2015] used anto located between the sprung and unsprung mass toactuator synthe1. INTRODUCTION Shao et al. [2017], Wang et al. [2015] used an actuator size active control force, and dynamic performances were Optimization and dynamics control of electric vehicle (EV) located between the sprung and unsprung mass to syntheactive control force, and dynamic performances were Optimization and dynamics control of electric vehicle (EV) size between the sprung and unsprung mass to syntheOptimization and dynamics control of electricand vehicle (EV) located improved based on H-inf controllers. As for the DVAS, attracts much attention in both academia industry, size active control force, and dynamic performances were improved based on H-inf controllers. As for the DVAS, attracts much attention in both academia and industry, size active control and dynamic performances were Optimization and dynamics of electric vehicle (EV) improved based onforce, H-inf controllers. As for the DVAS, attracts much attention in control both academia and industry, Nagaya et al. [2003], Qin et al. [2018a] proposed a structure and many remarkable works had been done in the past Nagaya et al. [2003], et controllers. al. [2018a] proposed a structure and many remarkable works had academia been doneand in industry, the past improved based on Qin H-inf As for the DVAS, attracts much attention in [2017], both and many remarkable works had been done in[2017a,b]. the past Nagaya with the DVAS connected to the unsprung mass. Simuladecades, see Huang et al. Tang et al. et al. [2003], Qin et al. [2018a] proposed a structure with theetDVAS connected to unsprung mass. Simuladecades, Huang et works al. [2017], Tang done et al.in[2017a,b]. al.revealed [2003], Qin et such al. the [2018a] proposed a structure and manysee remarkable had been the decades, see Huang et al. [2017], Tang tion results that structure can remarkably Compared to the traditional traditional centrally driven EV, thepast in- Nagaya with the DVAS connected to the unsprung mass. Simulaet al.EV, [2017a,b]. tion results revealed that such structure can remarkably Compared to the centrally driven the inthe both DVAS connected toand thestructure unsprung mass. Simuladecades, see et al. [2017], Tang et al.EV, [2017a,b]. Compared to Huang the traditional centrally driven the in- with improve ride comfort road handling. As wheel motor (IWM) driven EV has numerous of merits, tion results revealed that such can remarkably improve both ride comfort and structure road handling. As noted noted wheel motor (IWM) driven EV has numerous of merits, tion results revealed that such can remarkably Compared to the traditional centrally driven EV, the inimprove both ride comfort and road handling. As noted wheel motor (IWM) driven EV has numerous of merits, the application of DVAS e.g. fast fast system system response, response, flexible flexible configuration, configuration, high high enen- by by the the papers, papers, thecomfort application of the thehandling. DVAS introduces introduces e.g. improve both ride and road As noted wheel motor (IWM) driven EV has numerous of merits, e.g. fast systemand response, flexible configuration, high en- by extra spring-damper components and forms a novel multiergy efficiency, space saving. the papers, the application of the DVAS introduces extra spring-damper componentsof and forms a novel multiergy efficiency, and space saving. by the papers, the application the DVAS introduces e.g. fast system response, flexible configuration, high energy efficiency, and space saving. input suspension which new for extra components and forms novel multiinput spring-damper suspension system, system, which brings brings new aachallenges challenges for However, major problem associated with with the the IWM IWM applispring-damper components and forms novel multiergy efficiency, andproblem space saving. appli- extra However, aa major associated vibration control of IWM driven EV. input suspension system, which brings new challenges vibration control of IWM which drivenbrings EV. new challenges for However, a major problem associated with the IWM cation is the increased unsprung mass. Previous research appliinput suspension system, for vibration control of IWM driven EV. cation is the increased unsprung mass. Previous research However, a major problem associated with the IWM application is the increased unsprung mass. Previous research This paper combines both semi-active control strategy has shown that the application of the IWMs will not vibration control of IWM driven EV. not This paper combines both semi-active control strategy has shown the application of thePrevious IWMs will cation is thethat increased unsprung mass. research has that the application of the will not This and DVAS to vertical dynamic peronly shown deteriorate vehicle ride comfort comfort andIWMs road handling handling paper combines both vehicle semi-active control strategy and the the DVAS to improve improve vehicle vertical dynamic peronly deteriorate vehicle ride and road This paper combines bothsystem semi-active control strategy has shown thatalso the influence application of the will not and the DVAS to improve vehicle vertical dynamic peronly deteriorate vehicle ride comfort andIWMs road handling formance. The suspension control issue is firstly capacities, but motor lifespan due to the formance. The suspension system control issue is firstly capacities, but also influence motor lifespan due to the and the DVAS to improve vehicle vertical dynamic peronly deteriorate vehicle ride comfort and road handling capacities, but also influence Tan motor lifespan due created to the formance. transformed into a multi-objective optimization problem harsh vibration environment. and Lu [2016] The suspension system control issue is firstly transformed intosuspension a multi-objective optimization problem created harsh vibration environment. Tan andlifespan Lu [2016] formance. The system control issue is firstly capacities, but also influence motor due to the harsh vibration environment. Tanand andinvestigated Lu [2016] created (MOOP). novel hybrid controller is PMSM-suspension system model, model, the inin- transformed optimization (MOOP). A A into novelaa multi-objective hybrid suspension suspension controller problem is then then PMSM-suspension system and the into multi-objective optimization problem harsh vibration environment. Tan andinvestigated Lu [2016] created (MOOP). Aand novel hybrid control suspension controller is then PMSM-suspension system model, and investigated theand in- transformed developed, the force is allocated and fluence of motor unbalance force on the vehicle vertical developed, and the hybrid control force is allocated and fluence of motor unbalance force on the vehicle vertical and (MOOP). A novel hybrid suspension controller is PMSM-suspension system model, the in- achieved developed, and the hybrid control force issuspension allocated then fluence of motor unbalance force onand the investigated vehicle vertical and by the two dampers locate in the and lateral responses. Sun et al. [2015] investigated the effects achieved byand the two damperscontrol locate force in theissuspension and lateral responses. Sun et al.force [2015] investigated the effects developed, the hybrid allocated and fluence of motor unbalance on the vehicle vertical and lateral Sun et al.vertical [2015] investigated effects achieved the DVAS. commercially available controllable of IWM IWMresponses. on the the suspension suspension response, and andthe designed by Two the two dampers locate in theand suspension and the DVAS. Two commercially available and controllable of on vertical response, designed achieved by the two dampers locate in the suspension and lateral responses. Sun et al. [2015] investigated the effects of IWM on current the suspension vertical response, and designed dampers are tested and models are a modified modified chopping controller to improve improve system the DVAS. commercially available and controllable dampers areTwo tested and their their dynamics dynamics models are used used for for aof chopping controller to system the DVAS. Two commercially available andexcitations controllable IWM performance on current the suspension vertical response, and designed are tested andSimulation their dynamics models are used for avertical modified current chopping controller toconstant improve system dampers numerical simulation. results for of in both starting and velocity numericalare simulation. Simulation results for excitations of vertical performance in both starting and constant velocity dampers tested and their dynamics models are used for a modified current chopping controller to improve system numerical simulation. Simulation results for excitations of vertical performance in both starting and constant velocity both random road and bump input are finally presented working condition. both random road and bump input are finally presented working condition. in both starting and constant velocity numerical simulation. Simulation results for excitations of vertical performance working condition. to show the superiority of the proposed method. both random road and bump input are finally presented show the superiority the proposed To reduce reducecondition. the vibration vibration caused caused by by the the increased increased unsprung unsprung to both random road and of bump input are method. finally presented working To the to show the superiority of the proposed method. To reduce the vibration caused by the increased unsprung The rest of this paper is organized as follows. Firstly, mass, two methodologies have been proposed, i.e. controlto show the superiority of the proposed method. The rest of this paper is organized as follows. Firstly, the the mass, two methodologies have been proposed, i.e.unsprung controlTo reduce the vibration caused by the increased mass, two methodologies havedynamic been proposed, i.e. control- The DVAS based quarter vehicle model and damper dynamic lable suspension system and vibration absorbing rest of this paper is organized as follows. Firstly, the DVAS based quarter vehicle model and damper dynamic lable suspension system and dynamic vibration absorbing The rest of this papervehicle isinorganized as follows. Firstly, the mass, two(DVAS). methodologies have been proposed, i.e. controllable suspension system and dynamic vibration absorbing models are introduced Section 2. Then, the proposed structure For the controllable suspension system, DVAS based quarter model and damper dynamic are introduced in Section 2.and Then, the proposed structure (DVAS). For the controllable suspension system, models DVAS based quarter vehicle model damper dynamic lable suspension system and dynamic vibration absorbing models are introduced in Section 2. Then, the proposed structure (DVAS). For the controllable suspension system, hybrid controller is in Section 3. The authors acknowledge the support of the National Natural hybrid suspension suspension controller is illustrated illustrated in 3. models aresimulations introduced in Section 2. Then, theSection proposed structure (DVAS). For thethe controllable The authors acknowledge support of suspension the National system, Natural Numerical are carried out in Section 4 for two hybrid suspension controller is illustrated in Section 3. Science Foundation of Chinathe(Grant No.ofU1564210), Innovative The authors acknowledge support the National Natural Numerical simulations are carried out in Section 4 for two hybrid suspension controller is illustrated in Section 3. Science Foundation of China (Grant No. U1564210), Innovative different road excitations. Conclusion and future work are Numerical simulations are carried out in Section 4 for two The authors acknowledge the support of the National Natural talent support program for Chinese post-doctorates (Grant No. Sciencesupport Foundation of China (Grant post-doctorates No. U1564210),(Grant Innovative different road excitations. Conclusion and future 4work are talent program for Chinese No. Numerical simulations are carried out in Section for two Science Foundation of China (Grant No.Natural U1564210), Innovative 2016M600934, BX201600017), and Beijing Science Foundadiscussed at different road excitations. Conclusion and future work are talent support program for Chinese post-doctorates (Grant No. 2016M600934, BX201600017), and Beijing Natural Science Foundadiscussed at last. last. different excitations. Conclusion and future work are talent support post-doctorates (Grant No. tion (Grant No. program 3184058).for Chinese discussedroad at last. 2016M600934, and Beijing Natural Science Foundation (Grant No.BX201600017), 3184058). 2016M600934, and Beijing Natural Science Foundadiscussed at last. tion (Grant No.BX201600017), 3184058).
tion (Grant©No. 3184058). 2405-8963 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 1017 Copyright © under 2018 IFAC 1017Control. Peer review responsibility of International Federation of Automatic Copyright © 2018 IFAC 1017 10.1016/j.ifacol.2018.10.054 Copyright © 2018 IFAC 1017
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2. SYSTEM MODELING This section presents the quarter vehicle models of IWM driven EV, and introduces the controllable damper models used in the DVAS. 2.1 Quarter vehicle model Despite its simplicity, quarter vehicle model is widely used in vertical dynamics analysis and controller design, see Cao et al. [2011], Wang et al. [2017b]. Figure 1 depicts the structure of the quarter vehicle model for IWM driven EV. The dynamics equations can be described according to Newton’s law of motion as follows.
2.2 Controllable damper model
Controllable damper force can be expressed as a function of control current and relative velocity. The damper force of both the suspension and the DVAS can be expressed as: Fcs = f1 (ics , x˙ b − x˙ s1 ) (3) Fcd = f2 (icd , x˙ s1 − x˙ s )
To accurate depict such relationship, many methods like Bouc-Wen and polynomial models can be used, see Dong et al. [2010], Spencer Jr et al. [1997], Zhang et al. [2017]. This paper adopts a nonparametric model proposed by Song et al. [2005]. A continuous damping control (CDC) damper from ZF Sachs is used to generate the suspension controllable damper force, and a smaller magnetorheological (MR) damper from Lord is utilized in the DVAS due to the limited space. The dynamics characteristics of both the CDC damper and the MR damper are tested with an MTS test rig, which is shown in Fig. 3(a).
Fig. 1. IWM driven EV quarter vehicle model ¨b + ks (xb − xsa ) + cs (x˙ b − x˙ sa ) = 0 mb x msa x ¨sa + kt (xsa − xz ) + ks (xsa − xb ) + cs (x˙ sa − x˙ b ) = 0 (1) where mb is the sprung mass/ msa is the unsprung mass, including tire, IWM, and braking system. ks , cs and kt denote suspension stiffness, damper and tire stiffness, respectively. The DVAS based quarter vehicle model is introduced by Qin et al. [2018a]. The structure and dynamics equations of this system are given below.
¨b + ks (xb − xs1 ) + cs (x˙ b − x˙ s1 ) = 0 mb x ¨r + kb (xr − xs ) = 0 mr x ¨s + kd (xs − xs1 ) + kb (xs − xr ) + cd (x˙ s − x˙ s1 ) = 0 ms x ms1 x ¨s1 + ks (xs1 − xb ) + cs (x˙ s1 − x˙ b ) + kd (xs1 − xs ) + cd (x˙ s1 − x˙ s ) = 0 (2) where ms1 , ms and mr are unsprung mass, stator mass and rotor mass, respectively. kd and cd are stiffness and damper of DVAS, and kb represents the bearing stiffness between the stator and the rotor. The main purpose of this paper is then to synthesize time-varying controllable damper force to replace both cs (x˙ b − x˙ s1 ) and cd (x˙ s − x˙ s1 ).
With the method proposed by Song et al. [2005], the controllable damper force can be expressed as: Fdamper = A (i) · Sb (vrelative ) , k (4) an in , A (i) = n=0
Sb (vrelative ) = tanh [(b1 i+b0 ) vrelative ] where n is the function order, and n = 2 is adopted in this paper. an and bn are coefficients to be determined, and i is the control current. All unknown coefficients in (4) can be estimated by optimization method, e.g. Particle swarm optimization (PSO). With the estimated parameters, the control current can then be expressed as i = f −1 (Fdamper , vrelative ) and calculated as per (4). For more details, readers can refer to Qin et al. [2017]. The velocity-force map of the MR damper can be depicted as Fig. 3(b) with the aforementioned methodology. Note that the damper dynamics depicted in (3) do not constraint the output force. The calculated force may be unrealizable and thus results in exaggerated or negative control current. A damper boundary model derived from 3(b) is also applied in this paper, as shown in Fig. 4.
3. HYBRID SUSPENSION CONTROLLER
Fig. 2. IWM driven EV quarter vehicle model with DVAS
This section formulates the hybrid controller, and discusses the allocation of the hybrid control force to the two controllable dampers.
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3.2 Hybrid control for DVAS based suspension system
The skyhook control is proposed by virtually linking the vehicle chassis to the sky to reduce vehicle chassis vertical vibration, while the groundhook performs in a dual way to the skyhook control to improve vehicle road handling capacity, see Savaresi et al. [2010]. Hybrid control is proposed to combine the merits of both the skyhook control and the groundhook control with single suspension controllable damper, see Qin et al. [2015]. For the proposed quarter vehicle model with DVAS, two fictitious dampers are applied as shown in Fig. 5.
Fig. 3. MR damper made by Lord: (a) damper in the test rig, (b) force map
Fig. 5. Skyhook and groundhook ideal principle illustration As the structure shown in Fig. 5 is theoretically impossible, both skyhook and groundhook control use damper force to reproduce the virtual dampers’ behaviour. Different from traditional suspension system, the extra controllable damper in the DVAS enables the proposed model use two individual dampers to mimic the virtual dampers.
Fig. 4. MR damper boundary model 3.1 Suspension system criterions Suspension system criteria are necessary for systems comparison. The sprung mass acceleration (SMA) x ¨b and stator acceleration (SA) x ¨s1 are taken as criteria to evaluate the ride comfort and motor vibration environment. This paper treats suspension control as a MOOP, which subject to several constraints. The MOOP can be expressed as follows: min
g1 (P) = σx¨b , g2 (P) = σx¨s1 , subject to 3 · |σRS | ≤ lim (RS) , (5) 3 · |σair | ≤ lim (air) , 3 · |σT D | ≤ lim (T D) where σ(·) represents signal RMS, and P = [ Fcs Fcd ] is the controllable force set. σRS is the RMS of the rattle space (RS) with lim(RS) = 0.1 m, σair is the RMS of the airgap between the stator and the rotor with lim(air) = 0.001 m, and σT D is the RMS of the tire deflection (TD) with lim(T D) = 0.018 m. For a linear suspension system excited by the road profile that can be modeled as Gaussian stochastic process, three times of RMS ensure the response within the range with possibility of 99.7 %.
The skyhook controller can be expressed as: csky (x˙ b ) , if x˙ b (x˙ b − x˙ w ) ≥ 0, Fcs = cmin (x˙ b − x˙ w ) , if x˙ b (x˙ b − x˙ w ) < 0
(6)
Similarly, the groundhook controller can be expressed as: cgrd (x˙ s ) , if x˙ s (x˙ s − x˙ s1 ) ≥ 0, Fcd = (7) cmin (x˙ s − x˙ s1 ) , if x˙ s (x˙ s − x˙ s1 ) < 0 Based on the damper model and the synthesized control force, the overall control structure of the proposed hybrid suspension controller is shown in Fig. 6. This structure includes two parts, named semi-active suspension and hybrid controller. The states obtained from the plant are taken as the controller input, and the controller generate ideal control force F . Then, both boundary and current model output realizable control force and current i. The damper model given in (4) finally synthesize the control force to improve suspension system dynamics responses. In the following section, simulation results for solely skyhook or groundhook and hybrid control are discussed. For the sake of the simplicity, all suspension system to be compared with are named as follows:
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• Passive: system modeled by (1);
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Fig. 6. Control structure for suspension hybrid controller • DVAS: system with the DVAS as shown in (2); • Skyhook: DVAS based system with the skyhook control in (6) and the passive DVAS damper force; • Groundhook: DVAS based system with the groundhook control in (7) and the passive suspension damper force; • Hybrid: DVAS based system with both the skyhook and the groundhook control.
DVAS structure can reduce 23.6% of SMA, and 63.6% of SA compared to the passive structure. For the three types of controllers, the conflict between ride comfort and motor vibration can be observed. The skyhook controller can achieve 31.8% improvement in SMA, while deterioration in the aspect of SA is unavoidable (8.2% w.r.t. the passive case). On the contrary, the groundhook controller can only reduce the SA (9.9% w.r.t. the passive case) with incasement of SMA compared to the DVAS. As for the hybrid controller, its SMA reduces to 0.5443 m/s2 (31.7% improvement compared to the passive one), and SA is smaller than the DVAS structure (3.1% improvement), which means the proposed hybrid controller simultaneously outperforms both the skyhook and the groundhook controllers.
4. NUMERICAL SIMULATION This section details the numerical simulation results for different excitation conditions. 4.1 Simulation settings The proposed hybrid control for IWM driven EV is evaluated for excitations of random road and bump input. The system parameters are tabulated in Table 1 as per Qin et al. [2018a]. Table 1. Quarter vehicle model parameters Parameters mb msa ks cs kt kb cgrd
Value 332 kg 70 kg 24000 N/m 2000 Ns/m 220000 Ns/m 7 × 106 N/m 600 N/m
Parameters ms ms1 mr kd cd csky cmin
Value 20 kg 25 kg 25 kg 53000 N/m 1900 Ns/m 3000 N/m 100 N/m
Fig. 7. PSD comparison for random road excitation
4.2 Simulation results and discussion The simulation is carried out under two different road excitations. For the random road excitation, the vehicle is traveling at a speed of 40 km/h under ISO road level C. For generation of random road profile, readers can refer to Qin et al. [2018b,c], Wang et al. [2017a]. The bump input is defined according to Zhao et al. [2016]:
xz =
0.025 [1 + sin(2πvt/2.5)] , 1 < t < 1 + 2.5/v 0 otherwise
(8)
Simulation results for random road excitation are tabulated in Table 2, and PSD comparison is depicted in Fig. 7. According to Table 2, it can be observed that all four suspension systems with the DVAS can improve both ride comfort and reduce motor vibration. Application of the
As for the PSD comparison shown in Fig. 7, it can be seen from the upper figure that all four systems with the DVAS can reduce SMA amplitude in both the sprung mass and the unsprung mass resonant frequencies. For the frequency range with which human beings are most sensitive, the proposed hybrid controller outperforms all other three systems, which means better ride comfort can be expected. In the case of the SA, the lower figure in Fig. 7 shows that all systems with the DVAS can remarkably reduce vibration amplitude around the unsprung mass resonant frequency. Among all these four systems, the groundhook controller performs better in the frequency range from 8 Hz to 12 Hz. Although the proposed hybrid controller is sightly worse than the groundhook controller within this range, much better vibration reduction effect can still be expected compared to both the DVAS and the skyhook controller. The system comparisons for a vehicle crosses over bumpy terrain are shown in Fig. 8. It can be seen from Fig. 8 that in the upper figure, both the proposed hybrid and the skyhook controllers outperforms the other three systems with smaller SMA
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Table 2. RMS Comparison for random road excitation 12345RMS SMA (m/s2 ) SA (m/s2 ) RS (m) Airgap (m)(1e-4) TD (m)
Passive 0.7975 11.67 0.0066 0.0026
DVAS 0.6092 4.24 0.0065 0.155 0.0019
Skyhook 0.5435 4.59 0.0075 0.168 0.0021
Groundhook 0.6114 3.82 0.0064 0.138 0.0019
Hybrid 0.5443 4.11 0.0075 0.148 0.0019
Fig. 8. System comparison for bumpy input amplitude and convergence time. As for the SA depicted in the lower figure, although all four systems with the DVAS have similar acceleration amplitude, both the hybrid and groundhook controllers converge faster than the DVAS and the skyhook controller. Thus, the proposed hybrid controller improves performance more obviously than the DVAS system and the DVAS based system with sole skyhook and groundhook controllers. To ensure system responses satisfy all the constraints defined in (5), system responses of TD, Airgap and RS are shown in Fig. 9. It can be seen for the sudden bumpy input, all three responses do not violate the constraints, which means the MOOP is settled by the proposed hybrid controller. 5. CONCLUSION In this paper, a hybrid controller was proposed for IWM driven EV with the DVAS. Different from previous hybrid controller, both the suspension and the DVAS dampers are used to allocate the synthesized hybrid control force. Two commercially available and controllable dampers, i.e. CDC and MR dampers, are used to reproduce the virtual dampers’ behaviour. Simulation results reveal that the proposed method can improve ride comfort for 31.7% and IWM lifespan vibration for 64.8% compared to the IWM driven EV without the DVAS. Further research will focus on more advanced control strategies and experimental validation.
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