CN114435058B - Method for controlling limited frequency domain robustness of active suspension system of electric automobile driven by hub motor - Google Patents
Method for controlling limited frequency domain robustness of active suspension system of electric automobile driven by hub motor Download PDFInfo
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- B60—VEHICLES IN GENERAL
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- B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
- B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
- B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
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Abstract
The invention relates to a limited frequency domain robust control method of an active suspension system of an electric automobile driven by a hub motor, which comprises the steps of firstly, establishing a dynamic uncertainty model of the suspension system of the electric automobile driven by the hub motor and a state equation of the system; secondly, designing multiple control targets of an electric vehicle active suspension system driven by a hub motor, wherein the multiple control targets comprise limiting unsprung mass dynamic displacement of an electric vehicle active suspension, dynamic load of a hub motor wheel contacted with the ground, control force of an electric vehicle active suspension actuator and disturbance attenuation in a limited frequency domain of human sensitivity; then, in order to enable the hub motor driven active suspension system of the electric automobile to meet the performance control requirements of multiple targets, the existence condition, the design result and the main process of the limited frequency domain robust control controller of the active suspension system of the electric automobile are given out in a theorem deducing mode; the invention not only improves the service life of the active suspension, but also effectively improves the comfort and the operation stability of the electric automobile.
Description
Technical Field
The invention relates to a limited frequency domain robust control method for an active suspension system of an electric automobile driven by a hub motor, and belongs to the field of active safety control of electric automobiles.
Background
In order to cope with the problems of environmental pollution, insufficient supply of traditional energy sources and the like, the government of China is out of the way for promoting and popularizing new energy automobiles by various policies. With the gradual maturity of new energy automobile technology, people's acceptance degree to new energy electric automobile is also higher. According to different arrangement modes of automobile power systems, electric automobiles can be divided into the following two types: centralized driving electric automobile and distributed electric automobile. The hub motor driven electric automobile is widely focused and studied in recent years as a most promising vehicle frame in a distributed electric automobile due to the characteristics of small environmental pollution, simple chassis structure, excellent vehicle dynamics control performance and the like.
The advanced frame of the electric automobile driven by the hub motor provides a plurality of advantages for a longitudinal and transverse control system of the chassis of the automobile, and simultaneously makes the vertical dynamics active safety of the electric automobile face new challenges. Firstly, because the hub motor is directly arranged on the hub of the automobile, unsprung mass of the automobile is increased, dynamic load of the wheel is increased, the grounding performance of the tire is deteriorated, and the safety of the automobile is further affected. Secondly, since the dynamic displacement of the unsprung mass is increased, the impact on the hub motor itself is also greater, which accelerates the process of fatigue failure of the motor, affecting the service life of the hub motor, which can seriously affect the comfort and steering stability of the vehicle. Further, according to the international standard of ISO2631, vibration in the frequency range of 4-8Hz can cause resonance of human viscera, so that human body is uncomfortable and even hurt, especially for an in-wheel motor driven electric automobile, the human body becomes extremely sensitive to vibration in the frequency range due to removal of large noise sources of the traditional vehicle such as an engine, and most of the existing active suspension control systems are designed aiming at disturbance attenuation in the full frequency range of the traditional automobile.
Therefore, how to cope with the new characteristics of the wheel hub motor driven electric automobile suspension, design of the wheel hub motor driven active suspension robust control system with disturbance attenuation in a limited frequency domain becomes a problem to be solved urgently for dynamic safety control of the electric automobile.
Disclosure of Invention
The invention provides a limited frequency domain robust control method of an active suspension system of an electric automobile driven by a hub motor, which not only improves the service life of the active suspension of the electric automobile, the grounding property of wheels and the safety of the automobile, but also effectively improves the comfort and the operation stability of the electric automobile.
The technical scheme adopted for solving the technical problems is as follows:
a limited frequency domain robust control method for an active suspension system of an electric automobile driven by an in-wheel motor specifically comprises the following steps:
step S1: according to the vertical dynamics characteristics of the active suspension system of the electric automobile driven by the hub motor, combining the uncertainty of the dynamic model of the active suspension system of the electric automobile, and establishing a dynamic uncertainty model of the active suspension system of the electric automobile driven by the hub motor and a state equation thereof;
step S2: based on the established dynamic uncertainty model and state equation of the active suspension system of the electric automobile driven by the hub motor, designing a multi-control target for the active suspension system of the electric automobile driven by the hub motor, wherein the multi-control target comprises the limit of unsprung mass dynamic displacement of the active suspension of the electric automobile, the dynamic load of the wheel of the hub motor contacting the ground, the control force of an actuator of the active suspension of the electric automobile and disturbance attenuation in a limited frequency domain of human body sensitivity;
step S3: in order to enable the active suspension system of the electric automobile driven by the hub motor to meet the multiple control targets in the step S2, deducing and obtaining the existence condition and the design result of the robust control controller of the limited frequency domain of the active suspension of the electric automobile;
as a further preferred feature of the invention,
in step S1, a dynamics uncertainty model of a quarter wheel hub motor driven electric automobile active suspension system is established based on vertical dynamics characteristics of the wheel hub motor driven electric automobile active suspension system
In the formula (1), m s 、m u And m h Sprung mass, wheel mass and hub motor mass of dynamic uncertainty model of driving suspension system of electric automobile driven by quarter hub motor respectively, K s Rigidity of active suspension of electric automobile, C s Damping coefficient K of active suspension of electric automobile h C, rigidity of vibration reduction system between hub motor and wheel h K is the damping coefficient of the vibration reduction system between the hub motor and the wheel t Representing the rigidity of the wheel, F a Indicating the active control force generated by the actuator, Z s 、Z u 、Z h And Z r The displacement of the vehicle body, the wheels, the hub motor and the ground is respectively;
as a further preferred feature of the invention,
in step S1, the state equation determining process of the active suspension system of the electric vehicle driven by the in-wheel motor specifically includes selecting a state vector at first
X(t)＝[x 1 (t) x 2 (t) x 3 (t) x 4 (t) x 5 (t) x 6 (t)] T
In the formula (2), x 1 (t)＝Z s (t)-Z u (t)，x 3 (t)＝Z u (t)-Z r (t)，x 5 (t)＝Z h (t)-Z u (t)，Wherein the vertical speed of the road surface selects the disturbance input, i.e +.>The state equation of the active suspension system of the electric automobile is that
In formula (2), a=a 0 +HδE 1 Wherein, the method comprises the steps of, wherein,H＝[0 1 0 0 0 0] T ，E 1 ＝[-αK s M s0 -αC s M s0 0 αC s M s0 0 0]；B 1 ＝[0 0 -1 0 0 0] T ；B 2 ＝B 20 +HδE 2 wherein B is 20 ＝[0 M s0 0 -1/m u 0 0] T ，E 2 ＝[αM s0 ]；
The sprung mass in the active suspension system of the electric automobile is uncertain, so
Wherein m is s0 Representing the nominal sprung mass, α representing the variation range of the sprung mass, δ being the position parameter, satisfying [ delta (t) ] II<1, thus E 1 And E is connected with 2 In,
as a further preferred feature of the invention,
in step S2, the multiple control targets include limiting the unsprung mass displacement of the active suspension of the electric vehicle, the dynamic load of the wheel hub motor wheel contacting the ground, and the control force of the active suspension actuator of the electric vehicle;
therefore, aiming at the increase of the dynamic displacement of the unsprung mass of the electric automobile, the impact on the hub motor accelerates the fatigue damage process of the motor, influences the service life of the hub motor and seriously influences the comfort and the operating stability of the vehicle, and the range of the working stroke limit for limiting the dynamic displacement of the unsprung mass of the active suspension of the electric automobile is satisfied
Z s -Z u ＜＜S max
Wherein S is max Z is the maximum working stroke of the active suspension of the electric automobile s For displacement of the body of the vehicle, Z u Is the displacement of the wheel;
in order to overcome the safety problem that a hub motor is directly arranged on a hub of an automobile, the unsprung mass of the automobile is increased, the dynamic load of a wheel is increased, the grounding property of a tire is reduced, and the safety of the automobile is further influenced, and the dynamic load of the wheel of the hub motor in contact with the ground meets the following conditions
K t (Z u -Z r )<(m s +m u +m h )g
Wherein m is s 、m u And m h Sprung mass, wheel mass and hub motor mass of dynamic uncertainty model of driving suspension system of electric automobile driven by quarter hub motor respectively, K t Representing the rigidity of the wheelDegree, Z u For displacement of the wheels, Z r Is the displacement of the ground;
the control force of the active suspension actuator of the electric automobile meets the requirement of
|F a |＜＜F amax
Wherein F is a Representing the active control force generated by the actuator;
after meeting the performance requirements of limiting the unsprung mass displacement of the active suspension of the electric automobile, the dynamic load of the hub motor wheel contacting the ground and the control force of the active suspension actuator of the electric automobile, selecting control output, particularly
Wherein z is p Representing performance output, z c Representing constraint output; the output equation is
In the above formula, C p ＝C p0 +δE 1 Wherein C p0 ＝[-K s M s0 -C s M s0 0 C s M s0 0 0]；D p ＝D p0 +δE 2 Wherein D is p0 ＝[M s0 ]；
Assuming that the state feedback controller is u (t) =kx (t), and K is a state feedback gain matrix, finally obtaining a state equation, a performance output equation and a constraint output equation of the hub motor driven electric vehicle active suspension system based on multiple control targets, specifically
In the formula (3),and | { z c (t)} i |≤1,i＝1,2,3；
As a further preferred embodiment of the present invention, in step S2, the multiple control targets further include setting of disturbance attenuation in a limited frequency domain of human body sensitivity, especially for an in-wheel motor driven electric vehicle, since the human body becomes abnormally sensitive to vibrations in a vibration frequency band within 4-8Hz due to removal of a large noise source of a conventional vehicle such as an engine, the state feedback gain matrix K makes the active suspension system of the electric vehicle asymptotically stable, and satisfiesWherein II G (j omega) II ∞ Representing the disturbance input w (t) to the performance output z p H of closed loop transfer function of (t) ∞ Norm, ω is the frequency band of interest, ω 1 =4hz is the upper bound of the frequency band of interest, ω 2 =8hz is the lower bound of the frequency band of interest, γ is a pre-specified positive scalar, and γ>0；
As a further preferred aspect of the present invention, in step S3, in order for the in-wheel motor driven electric vehicle active suspension system to meet the multiple control targets in step S2, the finite frequency domain robust control controller of the electric vehicle active suspension design satisfies the following theorem 1, for the electric vehicle active suspension system, given positive scalar values γ, η and ρ, if and only if there is a symmetric matrix P>0，P 1 >0，Q>Matrices F and K of 0 and appropriate dimensions and positive scalar epsilon 1 、ε 2 The following inequality is satisfied
In the formula (4), E g ＝E 1 +E 2 K, in the formula (5),
R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 i }, where Θ = sym (F T A 0 +F T B 20 K) The method comprises the steps of carrying out a first treatment on the surface of the There is a state feedback controller u (t) =kx (t) such that the active suspension system of the electric vehicle asymptotically stabilizes without disturbance and has less disturbance energy on the road surfaceWhen meeting the related constraint conditions;
as a further preferred aspect of the invention, in theorem 1, the unknown matrices F and K are coupled, non-convex, solved for their passing through theorem 2, in particular for an electric vehicle active suspension system, given positive scalar values γ, η and ρ, if and only if a symmetric matrix is present And matrix of appropriate dimension->And->Positive scalar epsilon 1 、ε 2 The following inequality is satisfied
In the formula (7) of the present invention,in the formula (8), ∈> R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 I }, wherein,in the formula (9), ∈>
Thus, there is a state feedback controller u (t) =kx (t), whereThe active suspension system of the electric automobile enables asymptotically to be stable under the condition of no disturbance, and the disturbance energy of the road surface is smaller than +.>When meeting the related constraint conditions;
as a further preferred aspect of the present invention, the theorem 2 defines the following full order matrix at the time of design:
Γ 1 ＝diag{F -1 ,F -1 ,F -1 ,I,I,I}
Γ 2 ＝diag{F -1 ,F -1 ,I,I,I,I,I,I}
Γ 3 ＝diag{I,F -1 }；
as a further preferred aspect of the present invention, the design objective of the limited frequency domain robust control controller for electric vehicle active suspension design is transformed into a convex optimization problem, specifically theorem 3
Finally, the convex optimization problem can be solved by utilizing an LMI tool box of MATLAB, so that a limited frequency domain robust controller designed by an active suspension system of the electric automobile driven by the hub motor can be obtained;
as a further preferred aspect of the present invention, the theorem 3 is obtained based on the formula (8),the left matrix contains complex elements which are converted into equivalent linear matrix inequality
In the method, in the process of the invention,wherein,
through the technical scheme, compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, a dynamic model of the active suspension system of the hub motor driven electric automobile taking the uncertainty of suspension model parameters into consideration is established, and the multi-control target of the active suspension robust system of the hub motor driven electric automobile is designed, so that the unsprung mass dynamic displacement of the hub driven suspension is limited, the impact of the hub motor and the fatigue damage of the motor are reduced, the service life of the active suspension of the electric automobile is prolonged, and the grounding property of a tire and the safety of a vehicle are improved;
2. aiming at the electric automobile driven by the hub motor, the invention considers the removal of large noise sources of the traditional automobile such as an engine and the like, the human body becomes extremely sensitive to vertical vibration in the 4-8Hz frequency band, designs the active suspension robust control system driven by the hub motor with disturbance attenuation in the limited frequency domain, suppresses disturbance input in the frequency band to the greatest extent, and effectively improves the comfort and the operation stability of the electric automobile.
Drawings
The invention will be further described with reference to the drawings and examples.
FIG. 1 is a wheel hub motor driven electric vehicle active suspension model designed in a preferred embodiment provided by the present invention;
FIG. 2 is a flow chart of a limited frequency domain robust control method of an active suspension system of an electric automobile driven by an in-wheel motor;
FIG. 3 is a graph showing the acceleration response of a vehicle body with an active suspension, a passive suspension and a full-frequency-domain active suspension on a bump road surface in a limited frequency domain;
fig. 4 is a graph comparing vehicle acceleration power spectral density of the active suspension, the passive suspension and the full-frequency domain active suspension in the limited frequency domain under the input of a B-stage random road surface.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings. In the description of the present application, it should be understood that the terms "left," "right," "upper," "lower," and the like indicate orientations or positional relationships based on the orientation or positional relationships shown in the drawings, and are merely for convenience in describing the present invention and simplifying the description, rather than indicating or implying that the apparatus or element being referred to must have a specific orientation, be configured and operated in a specific orientation, and that "first," "second," etc. do not represent the importance of the components and therefore should not be construed as limiting the present invention. The specific dimensions adopted in the present embodiment are only for illustrating the technical solution, and do not limit the protection scope of the present invention.
As set forth in the background art, a major problem with in-wheel motor driven electric vehicles is that the in-wheel motor is directly mounted on the hub of the vehicle, so that the unsprung mass of the vehicle increases and the dynamic displacement of the unsprung mass increases, the dynamic load of the wheel becomes large due to the increase of the unsprung mass, the grounding property of the wheel becomes poor, the safety of the vehicle is affected, and the degree of fatigue damage of the motor is accelerated due to the dynamic displacement of the unsprung mass, which directly affects the service life of the in-wheel motor; secondly, when a large noise source in a traditional vehicle is removed, a human body becomes very sensitive to vertical vibration in a 4-8Hz frequency band generated by directly mounting a hub motor on a hub, so that in order to solve the problems, the application provides a limited frequency domain robust control method of an active suspension system of an electric automobile driven by the hub motor, which is mainly based on two principles, firstly, the multi-control target of the active suspension robust system of the electric automobile driven by the hub motor is designed, so that unsprung mass dynamic displacement of the suspension driven by the hub is limited; secondly, a hub motor driving active suspension robust control system with disturbance attenuation in a limited frequency domain is designed in the multi-control target, and disturbance input of the frequency band is restrained to the greatest extent.
Next, a detailed explanation is made on the control method shown in fig. 2 provided in the present application, firstly, a dynamic uncertainty model of an active suspension system of an electric vehicle driven by an in-wheel motor is established, the present application is based on a quarter model of the electric vehicle driven by an in-wheel motor as shown in fig. 1, according to newton's second law, that is, the vertical dynamic characteristics of the active suspension system of the electric vehicle,
dynamic uncertainty model of active suspension system of quarter-hub motor driven electric automobile
In the formula (1), m s 、m u And m h Sprung mass, wheel mass and hub motor mass of dynamic uncertainty model of driving suspension system of electric automobile driven by quarter hub motor respectively, K s Rigidity of active suspension of electric automobile, C s Damping coefficient K of active suspension of electric automobile h C, rigidity of vibration reduction system between hub motor and wheel h K is the damping coefficient of the vibration reduction system between the hub motor and the wheel t Representing the rigidity of the wheel, F a Indicating the active control force generated by the actuator, Z s 、Z u 、Z h And Z r The displacement of the vehicle body, the wheels, the hub motor and the ground is respectively.
Here, the uncertainty of the sprung mass in the active suspension system of the electric automobile is considered, so that
Wherein m is s0 Representing the nominal sprung mass, α representing the variation range of the sprung mass, δ being the position parameter, satisfying [ delta (t) ] II<1, that is,
next, the state equation determining process of the active suspension system of the electric automobile driven by the hub motor is specifically that firstly, a state vector is selected
X(t)＝[x 1 (t) x 2 (t) x 3 (t) x 4 (t) x 5 (t) x 6 (t)] T
In the formula (2), x 1 (t)＝Z s (t)-Z u (t)，x 3 (t)＝Z u (t)-Z r (t)，x 5 (t)＝Z h (t)-Z u (t)，Wherein the vertical speed of the road surface selects the disturbance input, i.e +.>The state equation of the active suspension system of the electric automobile is that
In formula (2), a=a 0 +HδE 1 Wherein, the method comprises the steps of, wherein,H＝[0 1 0 0 0 0] T ，E 1 ＝[-αK s M s0 -αC s M s0 0 αC s M s0 0 0]；B 1 ＝[0 0 -1 0 0 0] T ；B 2 ＝B 20 +HδE 2 wherein B is 20 ＝[0 M s0 0 -1/m u 0 0] T ，E 2 ＝[αM s0 ]The method comprises the steps of carrying out a first treatment on the surface of the As already described above, E is based on the uncertainty of sprung mass in the active suspension system of the electric vehicle 1 And E is connected with 2 In (I)>
After the model and the state equation are established, in order to achieve the most important part of the application, namely, the unsprung mass dynamic displacement of the hub driving suspension needs to be limited and disturbance input in a certain frequency band needs to be restrained, the final purpose of designing the active suspension is to improve riding comfort and steering stability of a vehicle, and proper performance indexes need to be selected, so that a plurality of multi-control targets for the hub motor driving electric vehicle active suspension system are designed.
The method solves the first two problems in the background art, namely, the dynamic load of the wheel is increased, the grounding performance of the tire is poor, the fatigue damage process of the motor is accelerated, the service life of the hub motor is influenced, and the method is realized by designing the unsprung mass dynamic displacement of the active suspension of the electric automobile, the dynamic load of the wheel of the hub motor, which is contacted with the ground, and the control force of the active suspension actuator of the electric automobile in multiple control targets;
specifically, in order to prevent collision between mechanical structures of the active suspension of the hub electric vehicle, the range of the working stroke limitation for limiting the unsprung mass displacement of the active suspension of the electric vehicle is satisfied
Z s -Z u ＜＜S max
Wherein S is max Z is the maximum working stroke of the active suspension of the electric automobile s For displacement of the body of the vehicle, Z u Is the displacement of the wheel;
in order to ensure the safety of the electric automobile during running and protect the hub motor, the contact between the automobile wheel and the bottom surface must be ensured, so that the dynamic load of the contact between the wheel of the hub motor and the ground meets the requirement
K t (Z u -Z r )<(m s +m u +m h )g
Wherein m is s 、m u And m h Sprung mass, wheel mass and hub motor mass of dynamic uncertainty model of driving suspension system of electric automobile driven by quarter hub motor respectively, K t Representing the rigidity of the wheel, Z u For displacement of the wheels, Z r Is the displacement of the ground;
in addition, because the control force generated by the active suspension actuator of the hub electric automobile is not infinite, the control force of the active suspension actuator of the electric automobile meets the requirement
|F a |＜＜F amax
Wherein F is a Representing the active control force generated by the actuator;
to sum up, in order to meet the performance requirements of the active suspension system of the hub electric vehicle, the following control outputs are selected, in particular
Wherein z is p Representing performance output, z c Representing constraint output; the output equation is
In the above formula, C p ＝C p0 +δE 1 Wherein C p0 ＝[-K s M s0 -C s M s0 0 C s M s0 0 0]；D p ＝D p0 +δE 2 Wherein D is p0 ＝[M s0 ]；
Assuming that the state feedback controller is u (t) =kx (t), and K is a state feedback gain matrix, finally obtaining a state equation, a performance output equation and a constraint output equation of the hub motor driven electric vehicle active suspension system based on multiple control targets, specifically
In the formula (3),and | { z c (t)} i |≤1,i＝1,2,3。
Vehicle body vertical acceleration of active suspension of hub electric vehicle according to ISO2631 international standardThe constraint is concentrated in the 4-8Hz frequency band of high sensitivity of the human body, so that the human body becomes extremely sensitive to vertical vibration in the 4-8Hz frequency band after the large noise source of the traditional vehicle such as an engine is removed, and the effect of disturbance attenuation in the limited frequency domain of the human body sensitivity can be met by the hub motor driving active suspension robust control system of disturbance attenuation in the limited frequency domain designed in the multi-control target;
specifically, a state feedback gain matrix K is designed to enable an active suspension system of the electric automobile to be asymptotically stable and meet the requirements ofWherein II G (j omega) II ∞ Representing the disturbance input w (t) to the performance output z p H of closed loop transfer function of (t) ∞ Norm, ω is the frequency band of interest, ω 1 =4hz is the upper bound of the frequency band of interest, ω 2 =8hz is the lower bound of the frequency band of interest, γ is a pre-specified positive scalar, and γ>0。
In order for the in-wheel motor driven electric vehicle active suspension system to meet the aforementioned multi-control objectives, it is necessary to derive the conditions of the in-wheel motor driven electric vehicle active suspension system limited frequency domain robust controller, and the design process and the results of the limited frequency domain robust controller are given in the form of theorem below.
Theorem 1, for an electric vehicle active suspension system, gives positive scalar values γ, η and ρ if and only if there is a symmetric matrix P>0，P 1 >0，Q>Matrices F and K of 0 and appropriate dimensions and positive scalar epsilon 1 、ε 2 The following inequality is satisfied
In the formula (4), E g ＝E 1 +E 2 K, in the formula (5), R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 i }, where Θ = sym (F T A 0 +F T B 20 K) The method comprises the steps of carrying out a first treatment on the surface of the There is a state feedback controller u (t) =kx (t) such that the active suspension system of the electric vehicle is asymptotically stable without disturbance and the disturbance energy is less than +_ on the road surface>The relevant constraint is satisfied.
For ease of understanding, a detailed design process of theorem 1 is given here:
firstly, according to the lyapunov theory, when an active suspension closed-loop control system of an electric automobile is asymptotically stable, the following inequality is satisfied:
according to the reflection theorem, there are
Wherein sym (W) =w+w T ；
Let w=f --1 And (3) performing congruence transformation to obtain:
wherein,further comprises the following steps:Wherein,J 1 ＝[H T F 0 0 0] T ，L 1 ＝[0 E 1 +E 2 K 0 0]；
the inequality is further equivalent toWherein ε is 1 Is a positive scalar, further converted into formula (4)
Order theThen the performance requirement of the suspension control system of the electric automobile is equivalent to
According to the generalized Kalman-Yakubovich-Popov theorem, there are
Wherein,further rewritten as +.>Wherein,
according to the projection theorem, there are
Wherein,Λ＝[0 I 0]，
further simplifying the inequality to obtain
The performance requirement of the active suspension system of the electric automobile can be met
Wherein,
continuing to simplify the inequality to get formula (5)
In the formula (5) of the present invention,R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 I}；
next, the constraint conditions of the active suspension system of the electric automobile are further designed:
first, a semi-positive lyapunov function V (t) =x is defined T (t)P 1 x (t), can be obtained by deriving both sides thereof
Then it can be obtainedThen further getIntegrating the inequality to obtainWherein w is max Representing the maximum disturbance energy.
From the above, V (t) =x T (t)P 1 x(t)≤V(0)+ηw max ＝ρ
The constraint conditions of the active suspension system of the electric automobile can be expressed as follows
Wherein the vector is definedThere is further->Thus there are constraints
Wherein lambda is max (. Cndot.) is the most significant of the matrixLarge eigenvalues, as can be readily seen, if the inequality isIf so, the corresponding constraint condition is satisfied; finally, inequality (6)In summary, the condition of theorem 1 can be obtained.
In theorem 1, the unknown matrices F and K are coupled, non-convex, solving them through theorem 2, in particular for an electric vehicle active suspension system, given positive scalar quantities γ, η and ρ, if and only if there is a symmetric matrixAnd matrix of appropriate dimension->And->Positive scalar epsilon 1 、ε 2 The following inequality is satisfied
In the formula (7) of the present invention,in the formula (8), ∈> R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 I }, wherein,in the formula (9), ∈>
Thus, there is a state feedback controller u (t) =kx (t), whereThe active suspension system of the electric automobile enables asymptotically to be stable under the condition of no disturbance, and the disturbance energy of the road surface is smaller than +.>The relevant constraint is satisfied. />
Similarly, given the key design process in theorem 2, the following full-order matrix is defined
Γ 1 ＝diag{F -1 ,F -1 ,F -1 ,I,I,I}
Γ 2 ＝diag{F -1 ,F -1 ,I,I,I,I,I,I}
Γ 3 ＝diag{I,F -1 }
Carrying out corresponding collaborative transformation on the formula (4), the formula (5) and the formula (6) in the theorem 1 to obtain the formula (7), the formula (8) and the formula (9) in the theorem 2
The design objective of a limited frequency domain robust control controller for the design of an active suspension of an electric automobile is converted into a convex optimization problem, specifically theorem 3
The main design process for theorem 3 is based onIn the equation (8) of the theorem 2,the left matrix contains complex elements which are further converted into equivalent linear matrix inequality
In the method, in the process of the invention,wherein,
finally, the convex optimization problem can be solved by using an LMI tool kit of MATLAB, and a limited frequency domain robust controller designed by an active suspension system of the electric automobile driven by the hub motor can be obtained.
Examples:
in order to verify that the control method provided by the application has obvious superiority, the active suspension, the passive suspension and the full-frequency-domain active suspension in the limited frequency domain provided by the application are carried out in a simulation mode in a Simulink, so that the vehicle body acceleration response on a bump road surface as shown in fig. 3 is obtained, and as can be obviously seen from fig. 3, the electric vehicle H in the limited frequency domain ∞ The performance of the active suspension system is superior to that of the traditional electric automobile H in the full frequency domain ∞ The active suspension can prolong the service life of the active suspension;
FIG. 4 is a graph showing the results of analysis of the power spectral density of the acceleration of the vehicle body under B-stage random road surface input, as can be seen from the graph, in the 4-8Hz band of interest, the electric vehicle H in the limited frequency domain ∞ The amplitude of the active suspension is minimum in the active suspension, the passive suspension and the full-frequency-domain active suspension in the limited frequency domain, so that the active suspension in the limited frequency domain provided by the application can be obtained to be very excellent in suppressing disturbance in the sensitive frequency band of human bodyThe effect can better improve the comfort of the vehicle.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The meaning of "and/or" as referred to in this application means that each exists alone or both.
As used herein, "connected" means either a direct connection between elements or an indirect connection between elements via other elements.
With the above-described preferred embodiments according to the present invention as an illustration, the above-described descriptions can be used by persons skilled in the relevant art to make various changes and modifications without departing from the scope of the technical idea of the present invention. The technical scope of the present invention is not limited to the description, but must be determined according to the scope of claims.
Claims (3)
1. A limited frequency domain robust control method for an active suspension system of an electric automobile driven by an in-wheel motor is characterized by comprising the following steps of: the method specifically comprises the following steps:
step S1: according to the vertical dynamics characteristics of the active suspension system of the electric automobile driven by the hub motor, combining the uncertainty of the dynamic model of the active suspension system of the electric automobile, and establishing a dynamic uncertainty model of the active suspension system of the electric automobile driven by the hub motor and a state equation thereof;
step S2: based on the established dynamic uncertainty model and state equation of the active suspension system of the electric automobile driven by the hub motor, designing a multi-control target for the active suspension system of the electric automobile driven by the hub motor, wherein the multi-control target comprises the limit of unsprung mass dynamic displacement of the active suspension of the electric automobile, the dynamic load of the wheel of the hub motor contacting the ground, the control force of an actuator of the active suspension of the electric automobile and disturbance attenuation in a limited frequency domain of human body sensitivity;
step S3: in order to enable the active suspension system of the electric automobile driven by the hub motor to meet the multiple control targets in the step S2, deducing and obtaining the existence condition and the design result of the robust control controller of the limited frequency domain of the active suspension of the electric automobile;
in step S1, a dynamics uncertainty model of a quarter wheel hub motor driven electric automobile active suspension system is established based on vertical dynamics characteristics of the wheel hub motor driven electric automobile active suspension system
In the formula (1), m s 、m u And m h Sprung mass, wheel mass and hub motor mass of dynamic uncertainty model of driving suspension system of electric automobile driven by quarter hub motor respectively, K s Rigidity of active suspension of electric automobile, C s Damping coefficient K of active suspension of electric automobile h C, rigidity of vibration reduction system between hub motor and wheel h K is the damping coefficient of the vibration reduction system between the hub motor and the wheel t Representing the rigidity of the wheel, F a Indicating the active control force generated by the actuator, Z s 、Z u 、Z h And Z r The displacement of the vehicle body, the wheels, the hub motor and the ground is respectively;
in step S1, the state equation determining process of the active suspension system of the electric vehicle driven by the in-wheel motor specifically includes selecting a state vector at first
X(t)＝[x 1 (t) x 2 (t) x 3 (t) x 4 (t) x 5 (t) x 6 (t)] T
In the formula (2), x 1 (t)＝Z s (t)-Z u (t)，x 3 (t)＝Z u (t)-Z r (t)，x 5 (t)＝Z h (t)-Z u (t)，Wherein the vertical speed of the road surface selects the disturbance input, i.e +.>The state equation of the active suspension system of the electric automobile is that
In formula (2), a=a 0 +HδE 1 Wherein, the method comprises the steps of, wherein,H＝[0 1 0 0 0 0] T ，E 1 ＝[-αK s M s0 -αC s M s0 0 αC s M s0 00]；B 1 ＝[0 0 -1 0 0 0] T ；B 2 ＝B 20 +HδE 2 wherein B is 20 ＝[0 M s0 0 -1/m u 0 0] T ，E 2 ＝[αM s0 ]；
The sprung mass in the active suspension system of the electric automobile is uncertain, so
Wherein m is s0 Representing the nominal sprung mass, α representing the variation range of the sprung mass, δ being the position parameter, satisfying [ delta (t) ] II<1，
In step S2, the multiple control targets include limiting the unsprung mass displacement of the active suspension of the electric vehicle, the dynamic load of the wheel hub motor wheel contacting the ground, and the control force of the active suspension actuator of the electric vehicle;
therefore, aiming at the increase of the dynamic displacement of the unsprung mass of the electric automobile, the impact on the hub motor accelerates the fatigue damage process of the motor, influences the service life of the hub motor and seriously influences the comfort and the operating stability of the vehicle, and the range of the working stroke limit for limiting the dynamic displacement of the unsprung mass of the active suspension of the electric automobile is satisfied
Z s -Z u ＜S max
Wherein S is max Z is the maximum working stroke of the active suspension of the electric automobile s For displacement of the body of the vehicle, Z u Is the displacement of the wheel;
in order to overcome the safety problem that a hub motor is directly arranged on a hub of an automobile, the unsprung mass of the automobile is increased, the dynamic load of a wheel is increased, the grounding property of a tire is reduced, and the safety of the automobile is further influenced, and the dynamic load of the wheel of the hub motor in contact with the ground meets the following conditions
K t (Z u -Z r )＜(m s +m u +m h )g
Wherein m is s 、m u And m h Sprung mass, wheel mass and hub motor mass of dynamic uncertainty model of driving suspension system of electric automobile driven by quarter hub motor respectively, K t Representing the rigidity of the wheel, Z u For displacement of the wheels, Z r Is the displacement of the ground;
the control force of the active suspension actuator of the electric automobile meets the requirement of
|F a |＜F amax
Wherein F is a Representing the active control force generated by the actuator;
after meeting the performance requirements of limiting the unsprung mass displacement of the active suspension of the electric automobile, the dynamic load of the hub motor wheel contacting the ground and the control force of the active suspension actuator of the electric automobile, selecting control output, particularly
Wherein z is p Representing performance output, z c Representing constraint output; the output equation is
In the above formula, C p ＝C p0 +δE 1 Wherein C p0 ＝[-K s M s0 -C s M s0 0 C s M s0 0 0]；D p ＝D p0 +δE 2 Wherein D is p0 ＝[M s0 ]；
Assuming that the state feedback controller is u (t) =kx (t), and K is a state feedback gain matrix, finally obtaining a state equation, a performance output equation and a constraint output equation of the hub motor driven electric vehicle active suspension system based on multiple control targets, specifically
In the formula (3),and | { z c (t)} i |≤1,i＝1,2,3；
Step S2In the method, the multi-control target further comprises setting of disturbance attenuation in a limited human body sensitivity frequency domain, and for the electric automobile driven by the hub motor, the human body becomes extremely sensitive to vibration in a 4-8Hz frequency band due to removal of a large noise source of a traditional automobile, so that the state feedback gain matrix K enables an active suspension system of the electric automobile to be asymptotically stable and meets the requirements ofWherein II G (j omega) II ∞ Representing the disturbance input w (t) to the performance output z p H of closed loop transfer function of (t) ∞ Norm, ω is the frequency band of interest, ω 1 =4hz is the upper bound of the frequency band of interest, ω 2 =8hz is the lower bound of the frequency band of interest, γ is a pre-specified positive scalar, and γ>0；
In step S3, in order for the in-wheel motor driven electric vehicle active suspension system to meet the multiple control targets in step S2, the finite frequency domain robust control controller of the electric vehicle active suspension design meets the following theorem 1, for the electric vehicle active suspension system, given positive scalar values γ, η and ρ, if and only if there is a symmetric matrix P>0，P 1 >0，Q>Matrices F and K of 0 and appropriate dimensions and positive scalar epsilon 1 、ε 2 The following inequality is satisfied
In the formula (4), E g ＝E 1 +E 2 K, in the formula (5), R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 i }, where Θ = sym (F T A 0 +F T B 20 K) The method comprises the steps of carrying out a first treatment on the surface of the There is a state feedback controller u (t) =kx (t) such that the active suspension system of the electric vehicle is asymptotically stable without disturbance and the disturbance energy is less than +_ on the road surface>When meeting the related constraint conditions; in theorem 1, the unknown matrices F and K are coupled, non-convex, solving them through theorem 2, in particular for an electric vehicle active suspension system, given positive scalar quantities γ, η and ρ, if and only if there is a symmetric matrix ∈>And matrix of appropriate dimension->And->Positive scalar epsilon 1 、ε 2 The following inequality is satisfied
In the formula (7) of the present invention,in the formula (8), ∈> R 22 ＝-diag{ε 2 I,ε 2 I,ε 2 I,ε 2 I }, wherein,in the formula (9), ∈>
Thus, there is a state feedback controller u (t) =kx (t), whereThe active suspension system of the electric automobile enables asymptotically to be stable under the condition of no disturbance, and the disturbance energy of the road surface is smaller than +.>When meeting the related constraint conditions;
the design objective of a limited frequency domain robust control controller for the design of an active suspension of an electric automobile is converted into a convex optimization problem, specifically theorem 3
And finally solving the convex optimization problem by using an LMI tool kit of MATLAB, so that the finite frequency domain robust control controller designed by the active suspension system of the electric automobile driven by the hub motor can be obtained.
2. The method for controlling the finite frequency domain robustness of the active suspension system of the hub motor driven electric automobile according to claim 1, wherein the method comprises the following steps of: the theorem 2 defines the following full order matrix at the time of design:
Γ 1 ＝diag{F -1 ,F -1 ,F -1 ,I,I,I}
Γ 2 ＝diag{F -1 ,F -1 ,I,I,I,I,I,I}
Γ 3 ＝diag{I,F -1 }。
3. the method for controlling the finite frequency domain robustness of the active suspension system of the hub motor driven electric automobile according to claim 2, wherein the method comprises the following steps of: the theorem 3 is obtained based on the equation (8),the left matrix contains complex elements which are converted into equivalent linear matrix inequality
In the method, in the process of the invention,wherein,
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