CN113183710A - Fuzzy control method for active suspension system based on frequency domain characteristic improvement comfort - Google Patents

Fuzzy control method for active suspension system based on frequency domain characteristic improvement comfort Download PDF

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CN113183710A
CN113183710A CN202110577739.9A CN202110577739A CN113183710A CN 113183710 A CN113183710 A CN 113183710A CN 202110577739 A CN202110577739 A CN 202110577739A CN 113183710 A CN113183710 A CN 113183710A
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active suspension
automobile
frequency domain
suspension system
fuzzy
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CN113183710B (en
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王孟
严怀成
李郅辰
田永笑
贺敬
纪文强
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East China University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60G—VEHICLE SUSPENSION ARRANGEMENTS
    • 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

An active suspension system fuzzy control method for improving comfortableness based on frequency domain characteristics belongs to the technical field of automobile suspension control, and relates to the problem of how to enable an automobile active suspension closed-loop control system to be gradually stable and have an optimal limited frequency domain disturbance suppression performance index so as to improve the riding comfortableness of an automobile; firstly, establishing a dynamic equation of an automobile active suspension system, considering the change condition of automobile load bearing, and establishing a Takagi-Sugeno (T-S) fuzzy model of the automobile active suspension system; then designing a distributed compensation fuzzy controller to obtain a closed-loop suspension control system; giving out a limited frequency domain disturbance suppression performance index for depicting human body comfort; the stability and the limited frequency domain disturbance suppression performance of a closed-loop active suspension system are proved based on a Lyapunov stability theory and a linear matrix inequality technology; the method solves the problem that the disturbance suppression performance of the suspension control system is effectively enhanced according to the human body sensitive frequency domain characteristic information under the complex situation of automobile bearing change, thereby improving the riding comfort of the automobile.

Description

Fuzzy control method for active suspension system based on frequency domain characteristic improvement comfort
Technical Field
The invention belongs to the technical field of automobile suspension control, and relates to an active suspension system fuzzy control method for improving comfort based on frequency domain characteristics.
Background
As is known, the field of automobile manufacturing, which is centered on technologies such as unmanned driving and clean energy, is an angular force field of strong national competition in the world, and attracts more and more investment. As the main part of the automobile, the performance of a suspension system, namely a connection damping system between the wheels and the automobile body of the automobile directly influences the comfort of the automobile, so that the research on the automobile suspension system has extremely important practical significance. Currently, automobiles typically employ the most advanced active suspension systems. The active suspension system is provided with an actuating mechanism on the basis of a fixed spring and a damping structure, and the actuating mechanism is driven to assist the suspension system to move by designing a control rate, so that the expected system performance is achieved. By designing the active suspension controller, the active suspension system can better adapt to a complex road surface, a better vibration suppression effect is achieved, and the riding comfort of the automobile is realized, so that the active suspension controller is called as an important research hotspot.
In practice, the load of an active suspension system of an automobile is often changed, and unknown external disturbance and the like exist along with the change of a road surface, and the factors can influence the riding comfort of the automobile and even cause the instability of the suspension system. In order to eliminate the influence of external disturbance and the like, some control methods describe uncertainty in a system in a linear parameterization mode, and on the premise, the control method is designed to achieve the control problem of an automobile active suspension system. The linear parameterization method described above, however, cannot handle more general uncertainties such as load bearing variations. In addition, international standard ISO2631 indicates that human beings are most sensitive to vertical vibration of 4-8Hz, and vibration in this frequency domain section can cause resonance of internal organs of the human body, so that the human body can feel uncomfortable and even be injured. The existing disturbance suppression control method for the automobile active suspension system does not fully consider the fact that a human body is more sensitive to vertical vibration within the range of 4-8Hz, so that the disturbance suppression performance index cannot be guaranteed to be optimal.
In the prior art, the invention patent application of Chinese patent application 'fuzzy control method of automobile nonlinear active suspension system' with publication number CN104626914A, published on the date of 2015, 5 and 20, discloses a fuzzy control method for automobile active suspension system control, which only optimizes and selects order parameters of fractional order differential operation of fuzzy controller input quantity, can avoid the difficulties of mutual restriction and large calculation quantity of scale factors and quantization factors in the prior art, and has the characteristics of accurate control and calculation efficiency. However, the technical solution has the following disadvantages: 1) the controller design does not fully consider the human sensitive frequency domain characteristics, so that the comfort of the automobile is not fully optimized; 2) no consideration is given to the possible variation in vehicle weight bearing. The Chinese patent application 'a control method of an automobile active suspension system', with the publication number of CN110077191A and the publication date of 8 and 2 in 2019, discloses a control method of an automobile active suspension system, which comprises the steps of establishing an active suspension system model, establishing a dynamic differential equation of the automobile active suspension system according to the model, solving a state space equation of the automobile active suspension system, considering the uncertainty of the system, and designing an active suspension system controller under disturbance interference. The invention considers the output feedback H infinite controller under the condition of four factors, such as system parameter uncertainty, actuator delay, road surface unevenness disturbance, sensor measurement output disturbance and the like, realizes the control of the active suspension system, and has wider adaptability. However, the technical solution has the following disadvantages: 1) the automobile active suspension system adopts a linear model, and the method has great limitation in practical application; 2) the controller design does not fully consider the human sensitive frequency domain characteristics, so that the comfort of the automobile is not fully optimized. The technical scheme of Chinese patent application 'a control method of an automobile active seat suspension system with time-varying displacement constraint', which has publication date of 11/1/2019 and publication number of CN109188906A, provides a control method of an automobile active seat suspension system with time-varying displacement constraint, and designs the technical field of automobile seat safety. Firstly, establishing a time-varying displacement constraint mathematical model of a nonlinear uncertain active seat suspension system, and then designing a self-adaptive backstepping and pushing controller according to the model; verifying the active seat suspension system with the introduced time-varying displacement constraint by adopting an obstacle avoidance Lyapunov function; and finally, adjusting the control gain parameter of the self-adaptive backstepping and pushing controller to realize the time-varying displacement constraint control target of the active seat suspension system. The method improves driving comfort, ensures that the system can still achieve stable and controllable effect under the condition of uncertain parameters, and solves the problem of vertical displacement constraint of the nonlinear uncertain active seat suspension system. However, the technical solution has the following disadvantages: 1) in the design of the backstepping controller, excessive middle virtual controller design links exist, and the design method of the controller is complex; 2) the designed controller can only ensure that the state of the closed-loop active suspension system converges to the neighborhood of zero, but cannot ensure that the state converges to zero. According to a document 'study on fuzzy control-based automobile active suspension system' (university of Hebei industries, Yangzhu) published in 2012, aiming at a state space model of a two-degree-of-freedom quarter automobile active suspension system, a traditional Mamdani type fuzzy controller is designed, so that the suspension system is stable and has a certain vibration damping effect. However, the technical solution has the following disadvantages: 1) the gain of the traditional Mamdani fuzzy controller is obtained according to the experience of a designer, and has no complete and normalized design flow and great subjectivity. The whole fuzzy controller design process lacks rigorous mathematical demonstration to ensure that the controller can enable a closed-loop suspension system to be stable and has optimized control indexes. 2) The fuzzy control method proposed in this article, although generally also having a certain damping effect, cannot obtain a quantitative representation of the damping effect.
Disclosure of Invention
The invention aims to design an active suspension system fuzzy control method for improving the comfort based on frequency domain characteristics, so that an automobile active suspension closed-loop control system is gradually stable and has an optimal limited frequency domain disturbance suppression performance index, and the riding comfort of an automobile is further improved.
The invention solves the technical problems through the following technical scheme:
the active suspension system fuzzy control method for improving the comfort based on the frequency domain characteristics comprises the following steps:
s1, establishing an automobile active suspension system model according to the mechanical characteristics of each element; establishing a dynamic equation of an automobile active suspension system according to the change characteristics of automobile load bearing; further constructing a global T-S fuzzy model of the automobile active suspension system;
s2, designing a parallel compensation fuzzy controller aiming at a global T-S fuzzy model of the automobile active suspension system to obtain an automobile active suspension closed-loop control system; based on the human body sensitive frequency domain characteristic information, providing a limited frequency domain disturbance suppression performance index for depicting the riding comfort of the automobile;
s3, selecting a proper Lyapunov function V (t), and providing a design constraint condition that the closed-loop control system of the automobile active suspension meets the requirement of progressive stability and a design constraint condition that the closed-loop control system of the automobile active suspension meets the performance index gamma of the limited frequency domain disturbance suppression; proved that the given design constraint condition can ensure the gradual stability of the whole closed-loop active suspension control system, and has a disturbance suppression performance index gamma in a human sensitive frequency domain [4Hz 8Hz ];
s4, according to the human body sensitive frequency domain characteristic information, omega belongs to omega1,ω2],ω1＝4,ω2And (8) providing an optimization algorithm according to the design constraint conditions in the step S3 to obtain the optimal disturbance suppression performance gamma of the automobile active suspension systemminAnd a corresponding controller gain matrix.
Establishing a Takagi-Sugeno (T-S) fuzzy model of the automobile active suspension system by establishing a dynamic equation of the automobile active suspension system and considering the change condition of the automobile load; then designing a distributed compensation fuzzy controller to obtain a closed-loop suspension control system; giving out a limited frequency domain disturbance suppression performance index for depicting human body comfort; the stability and the limited frequency domain disturbance suppression performance of a closed-loop active suspension system are proved based on a Lyapunov stability theory and a linear matrix inequality technology; the method solves the problem that the disturbance suppression performance of the suspension control system is effectively enhanced according to the human body sensitive frequency domain characteristic information under the complex situation of automobile bearing change, thereby improving the riding comfort of the automobile.
As a further improvement of the technical solution of the present invention, the formula of the automobile active suspension system model in step S1 is:
Figure BDA0003084941920000031
wherein m issMass on the finger spring; m isuAn unsprung mass; u (t) is the control input to the suspension system; c. Cs,ks,ctAnd ktRespectively representing a suspension damping coefficient, a spring stiffness coefficient, a tire damping coefficient and a tire rigidity coefficient; z is a radical ofsIndicating the body distance, zuRepresenting the unsprung mass velocity.
As a further improvement of the technical solution of the present invention, the method for establishing the dynamic equation of the active suspension system of the vehicle according to the variation characteristic of the vehicle load-bearing as described in step S1 is as follows:
the sprung mass m is set in consideration of the variation in the weight of the occupant and the weight of the vehicle bodysUnsprung mass muThe variation intervals of (A) are respectively: m iss∈[msmin,msmax]，mu∈[mumin,mumax](ii) a Definition of x1(t)＝zs(t)-zu(t) suspension system displacement; x is the number of2(t)＝zu(t)-zr(t) is tire displacement;
Figure BDA0003084941920000041
representing the vehicle body speed;
Figure BDA0003084941920000042
represents unsprung mass velocity; selecting road speed as disturbance input, i.e.
Figure BDA0003084941920000043
Defining a state vector:
x(t)＝[x1(t) x2(t) x3(t) x4(t)]T (2)
obtaining a space state equation of the automobile active suspension system:
Figure BDA0003084941920000044
in order to measure the riding comfort, the vertical acceleration of the vehicle body is selected as the control output of the system, namely:
Figure BDA0003084941920000045
finally, the dynamic equation of the automobile active suspension system is described in the form of the following state space:
Figure BDA0003084941920000046
wherein, the matrixes A (t), B (t), G (t), C (t), D (t) are defined as follows:
Figure BDA0003084941920000047
Figure BDA0003084941920000048
Figure BDA0003084941920000049
as a further improvement of the technical solution of the present invention, the method for constructing the global T-S fuzzy model of the active suspension system of the automobile described in step S1 comprises:
in the dynamic equations of active suspension systems of motor vehicles
Figure BDA0003084941920000051
The two terms can be expressed as:
Figure BDA0003084941920000052
wherein,
Figure BDA0003084941920000053
respectively represent the front piece variables of the fuzzy system, and satisfy:
M1(ξ1(t))+M2(ξ1(t))＝1,N1(ξ2(t))+N2(ξ2(t))＝1. (7)
the membership function is selected as follows:
Figure BDA0003084941920000054
in summary, the active suspension system of the automobile is expressed by the following IF-THEN fuzzy rule:
fuzzy rule pi，IF(ξ1(t),ξ2(t))isΞi，THEN
Figure BDA0003084941920000055
Wherein i ∈ {1,2,3,4},
Figure BDA0003084941920000056
Figure BDA0003084941920000061
after the fuzzification, fuzzy reasoning and defuzzification steps, the IF-THEN fuzzy rule is converted into the following global T-S fuzzy system model:
Figure BDA0003084941920000062
wherein:
Figure BDA0003084941920000063
wherein the normalized membership function satisfies:
Figure BDA0003084941920000064
as a further improvement of the technical solution of the present invention, in step S2, a parallel compensation fuzzy controller is designed for the global T-S fuzzy model of the active suspension system of the vehicle, and the method for obtaining the closed-loop control system of the active suspension system of the vehicle comprises:
fuzzy rule Ki，IF(ξ1(t),ξ2(t))isΞi，THEN
u(t)＝Kix(t) (13)
Through the steps of fuzzification, fuzzy reasoning and defuzzification, the formula (13) of the fuzzy control rule is converted into the following form:
Figure BDA0003084941920000071
substituting the control signal u (T) in the formula (14) into a formula (11) of a global T-S fuzzy model of the automobile active suspension system to obtain a state equation of the automobile active suspension closed-loop control system:
Figure BDA0003084941920000072
wherein, the control output z (t) of the automobile active suspension closed-loop control system represents the vertical acceleration of the automobile body.
As a further improvement of the technical solution of the present invention, the step S2, which is based on the human body sensitive frequency domain characteristic information, provides a method for characterizing the limited frequency domain disturbance suppression performance index of the riding comfort of the vehicle, specifically comprising:
the frequency domain range of the human body sensitive frequency domain characteristic information is omega-epsilon [ omega ]1,ω2],ω1＝4,ω2＝8.；
The riding comfort of the automobile is characterized by the following formula, namely under the influence of disturbance w (t) input, the output of an automobile active suspension closed-loop control system is satisfied:
Figure BDA0003084941920000073
wherein, gamma is more than 0, which represents the limited frequency domain disturbance suppression performance index, and is a positive parameter to be optimized, and the smaller the numerical value is, the stronger the disturbance attenuation capability of the automobile active suspension closed-loop control system is.
As a further improvement of the technical solution of the present invention, the design constraint condition that the closed-loop control system of the active suspension of the vehicle satisfies the requirement of the progressive stability in step S3 is as follows:
Figure BDA0003084941920000074
the design constraint condition that the closed-loop control system of the automobile active suspension meets the limited frequency domain disturbance suppression performance index gamma is as follows:
Figure BDA0003084941920000081
wherein, positive definite matrix
Figure BDA0003084941920000082
And the parameter gamma > 0.
As a further improvement of the technical solution of the present invention, the method for proving that given controller design constraints can ensure the gradual stability of the entire closed-loop active suspension control system described in step S3 is:
the Lyapunov function was designed as follows:
V(t)＝xT(t)P-1x(t) (19)
wherein the matrix P is a positive definite matrix, i.e. P ═ PT＞0.；
Derivation of v (x) over time yields:
Figure BDA0003084941920000083
according to the normalized membership function property hi(xi (t)) > 0, and if the following inequality (21) is satisfied, the closed-loop control system of the automobile active suspension is gradually stabilized:
(Ai+BiKj)TP-1+P-1(Ai+BiKj)＜0. (21)
in order to solve the problem, a projection theorem is applied, and an inequality (22) is obtained and can be used for deducing the inequality (21);
Figure BDA0003084941920000084
defining new variables
Figure BDA0003084941920000085
The nonlinear inequality (22) is expressed as a linear inequality as follows:
Figure BDA0003084941920000086
can be guaranteed under the design constraint condition of the given inequality (17)
Figure BDA0003084941920000087
Namely, the closed-loop control system of the active suspension of the automobile is gradually stable.
As a further improvement of the technical solution of the present invention, the method for having the limited frequency domain disturbance rejection performance index γ in the human sensitive frequency domain [4Hz 8Hz ] interval described in step S3 is as follows:
the following inequalities are designed:
Figure BDA0003084941920000091
wherein,
Figure BDA0003084941920000092
making congruent transformation on inequality (24) to left-multiply vector [ x (t) w (t)]Right-hand multiplication of its conjugate transpose vector [ x (t) w (t)]*The following can be obtained:
Figure BDA0003084941920000093
wherein
Figure BDA0003084941920000094
By developing equation (25), the following can be obtained:
Figure BDA0003084941920000095
integration from t-0 to t- + ∞, which can be derived from equation (26):
Figure BDA0003084941920000096
wherein,
Figure BDA0003084941920000097
it should be noted that, since the closed-loop control system of the active suspension of the automobile is gradually stable, in the zero initial state, the following formula (27) can be obtained:
Figure BDA0003084941920000098
wherein,
Figure BDA0003084941920000099
tr(He(Sd) Q) represents a matrix He (S)d) Trace of Q;
let tr (He (S)d) Q) < 0, then there are
Figure BDA00030849419200000910
That is, the closed-loop control system of the active suspension of the automobile has disturbanceAn inhibition index γ;
defining the system state x (t) as x (j omega) through Fourier transform, and then SdRewritten as the following frequency domain expression:
Figure BDA0003084941920000101
thus, there are:
Figure BDA0003084941920000102
wherein, ω is1＝4,ω2＝8,ω∈[ω1,ω2]Thereby obtaining
Figure BDA0003084941920000103
Thus, the inequality (24) can ensure that the closed-loop suspension system has the disturbance suppression index γ.
As a further improvement of the technical scheme of the invention, step S4 shows that omega belongs to omega according to the frequency domain characteristic information of human body sensitivity1,ω2],ω1＝4,ω2An optimization algorithm is proposed to obtain the optimal disturbance suppression performance gamma of the automobile active suspension system under the design constraint conditions of 8 and the step S3minAnd a corresponding controller gain matrix, as follows: the inequality (24) is a nonlinear matrix inequality, the gain of the controller cannot be solved by solving the inequality (24) directly, and the inequality (24) needs to be converted into a linear matrix inequality; applying the projection theorem, obtaining the inequality (31) ensures that (24) holds:
Figure BDA0003084941920000104
then a matrix is defined:
Figure BDA0003084941920000105
since the matrix P is PTThus, J is equal to JT(ii) a The full rank symmetric matrix J is used to multiply left and right by equation (32) and the variables are redefined as follows:
Figure BDA0003084941920000106
using Schur's complement theorem while considering the normalized membership function property hi(xi (t)) > 0, the following inequality is obtained:
Figure BDA0003084941920000111
in conclusion, the finite frequency domain disturbance suppression performance index gamma of the suspension system and the corresponding fuzzy controller gain matrix are optimized through the following algorithm:
Figure BDA0003084941920000112
the minimum limited frequency domain disturbance suppression performance index gamma can be obtained by the algorithm, so that the riding comfort of the automobile is improved to the maximum extent;
meanwhile, the matrix P, K can be obtained through the algorithmjThen, the controller gain matrix K is obtained by using the following formulaj
Figure BDA0003084941920000113
The invention has the advantages that:
(1) the fuzzy control method of the automobile active suspension system based on the human body sensitive frequency domain characteristic information fully considers the weight change factors caused by the factors such as the change of the automobile along with passengers and the like, thereby widening the application range of the algorithm. In addition, the human body vertical sensitive frequency domain characteristic information is effectively utilized, and the riding comfort of the automobile is improved. The designed automobile active suspension controller fully considers human body sensitive frequency domain characteristic information, and human beings are most sensitive to vertical vibration of 4-8Hz (international standard ISO 2631). Has stronger disturbance inhibition performance, thereby improving the riding comfort of the automobile.
(2) A distributed fuzzy controller based on a compensator is constructed by utilizing characteristics of a fuzzy system approaching to bearing change and the like in an automobile active suspension system. Under the condition that the load bearing changes in real time, the designed controller can still ensure the gradual stability and the limited frequency domain disturbance suppression performance of the automobile active suspension system, and the method has strong robustness.
Drawings
FIG. 1 is a flow chart of a control algorithm of an embodiment of the present invention;
FIG. 2 is a diagram of analysis of vehicle body motion forces in accordance with an embodiment of the present invention;
FIG. 3 is a graph of the output response of the closed-loop control system for the active suspension of the vehicle according to the embodiment of the invention;
FIG. 4 is a corresponding curve of the disturbance suppression performance of the closed-loop control system of the active suspension of the automobile according to the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme of the invention is further described by combining the drawings and the specific embodiments in the specification:
example one
As shown in fig. 1, an active suspension system fuzzy control method for improving the riding comfort of a vehicle comprises the following steps:
1) establishing dynamic equation of automobile active suspension system
As shown in fig. 2, the model of the active suspension system of the automobile is established as follows:
Figure BDA0003084941920000121
wherein m issMass on the finger spring; m isuAn unsprung mass; u (t) is the control input to the suspension system; c. Cs,ks,ctAnd ktThe suspension damping coefficient, the spring rate coefficient, the tire damping coefficient, and the tire stiffness coefficient are respectively expressed. z is a radical ofsIndicating the body distance, zuRepresenting the unsprung mass velocity.
The sprung mass m is set in consideration of the factor that the weight of the occupant and the weight of the vehicle body may varysUnsprung mass muThe variation intervals of (A) are respectively: m iss∈[msmin,msmax]，mu∈[mumin,mumax]。
To establish the system state space equation, x is defined1(t)＝zs(t)-zu(t) suspension system displacement; x is the number of2(t)＝zu(t)-zr(t) is tire displacement;
Figure BDA0003084941920000122
representing the vehicle body speed;
Figure BDA0003084941920000126
represents unsprung mass velocity; selecting road speed as disturbance input, i.e.
Figure BDA0003084941920000124
Defining a state vector:
x(t)＝[x1(t) x2(t) x3(t) x4(t)]T (2)
obtaining a spatial state equation of the suspension system:
Figure BDA0003084941920000125
in order to measure the riding comfort, the vertical acceleration of the vehicle body is selected as the control output of the system, namely:
Figure BDA0003084941920000131
finally, an automotive suspension control system can be described in the form of a state space as follows:
Figure BDA0003084941920000132
wherein the matrices A (t), B (t), G (t), C (t), D (t) are defined as:
Figure BDA0003084941920000133
Figure BDA0003084941920000134
Figure BDA0003084941920000135
2) T-S fuzzy model for constructing automobile suspension system
Two items in the matrix of the automobile active suspension system
Figure BDA0003084941920000136
Can be expressed in the following forms, respectively:
Figure BDA0003084941920000137
wherein
Figure BDA0003084941920000138
Represents a front-part variable of the fuzzy system and satisfies
M1(ξ1(t))+M2(ξ1(t))＝1,N1(ξ2(t))+N2(ξ2(t))＝1. (7)
The membership function is selected as follows:
Figure BDA0003084941920000139
in summary, an automotive active suspension system can be represented by the following IF-THEN fuzzy rule:
fuzzy rule pi，IF(ξ1(t),ξ2(t))isΞi，THEN：
Figure BDA0003084941920000141
Wherein i ∈ {1,2,3,4},
Figure BDA0003084941920000142
Figure BDA0003084941920000143
through the steps of fuzzification, fuzzy reasoning, defuzzification and the like, the IF-THEN fuzzy rule can be converted into the following global T-S fuzzy system:
Figure BDA0003084941920000144
wherein:
Figure BDA0003084941920000151
it is noted that the normalized membership function satisfies
Figure BDA0003084941920000152
3) Fuzzy controller and design requirements thereof
1) Designing a distributed fuzzy controller (parallel compensation fuzzy controller) based on a compensator
Fuzzy rule Ki，IF(ξ1(t),ξ2(t))isΞi，THEN
u(t)＝Kix(t) (13)
Through the steps of fuzzification, fuzzy reasoning and defuzzification, the formula (13) of the fuzzy control rule is converted into the following form:
Figure BDA0003084941920000153
substituting the control signal u (T) in the formula (14) into a formula (11) of a global T-S fuzzy model of the automobile active suspension system to obtain a state equation of the automobile active suspension closed-loop control system:
Figure BDA0003084941920000154
the designed controller needs to ensure the gradual stability of a closed-loop control system and improve the riding comfort of the system. It is noted that the control output z (t) of the closed loop system represents the vertical acceleration of the vehicle body. The ride comfort of a vehicle can be characterized by the following equation, i.e., the closed-loop suspension system output is satisfied under the influence of the disturbance w (t) input:
Figure BDA0003084941920000155
wherein, gamma is more than 0, which represents disturbance attenuation index, and is a positive parameter to be optimized, and the smaller the numerical value is, the stronger the disturbance attenuation capability of the closed-loop suspension system is. It should be noted that international standard ISO2631 indicates that human beings are most sensitive to vertical vibration of 4-8Hz, and vibration in this frequency domain section can cause resonance of internal organs of the human body, so that the human body is uncomfortable and even injured. Assuming that the human sensitive frequency domain characteristics are not considered in the controller design, the disturbance attenuation index gamma will not be fully optimized. In order to fully improve the riding comfort of the automobile, the design considers that the frequency domain range is omega-epsilon [ omega ∈ ]1,ω2],ω1＝4,ω2＝8.
2) The system controller is designed as follows: given the formula (1) of the automotive suspension system, if a positive definite matrix exists
Figure BDA0003084941920000161
Figure BDA0003084941920000162
And the parameter gamma is larger than 0, the fuzzy controller (14) can enable the closed-loop system (15) to be gradually stable and meet the finite frequency domain disturbance suppression performance gamma, namely the following linear matrix inequality is satisfied:
Figure BDA0003084941920000163
wherein the controller gain matrix may be of the formula
Figure BDA0003084941920000164
And (6) obtaining.
And (3) proving that: first, a proof of the progressive stability of a closed-loop active suspension system is given.
The Lyapunov function is designed as follows
V(t)＝xT(t)P-1x(t) (19)
Wherein the matrix P is a positive definite matrix, i.e. P ═ PT＞0.。
Derivation of v (x) over time yields:
Figure BDA0003084941920000165
according to the normalized membership function property hi(xi (t)) > 0, the closed loop system becomes progressively stable if the following inequality holds:
(Ai+BiKj)TP-1+P-1(Ai+BiKj)＜0. (21)
in order to solve the problem, a projection theorem is applied, and an inequality (22) is obtained and can be used for deducing the inequality (21);
Figure BDA0003084941920000166
defining new variables
Figure BDA0003084941920000167
The nonlinear inequality (22) is expressed as a linear inequality as follows:
Figure BDA0003084941920000168
assuming that inequality (17) holds in the controller design, it can be guaranteed that
Figure BDA0003084941920000169
I.e. the closed-loop active suspension control system is progressively stabilized.
The following proves that the inequality (18) in the design of the controller is established, so that the closed-loop active suspension control system can be ensured to have the limited frequency domain disturbance suppression performance index gamma, and the optimal riding comfort is ensured. Consider the following inequality:
Figure BDA0003084941920000171
wherein
Figure BDA0003084941920000172
Making congruent transformation on inequality (24) to left-multiply vector [ x (t) w (t)]Right-hand multiplication of its conjugate transpose vector [ x (t) w (t)]*The following can be obtained:
Figure BDA0003084941920000173
wherein
Figure BDA0003084941920000174
Expansion (25) typeThe following can be obtained:
Figure BDA0003084941920000175
integration from t-0 to t- + ∞, which can be derived from equation (26):
Figure BDA0003084941920000176
wherein
Figure BDA0003084941920000177
It is noted that the closed loop system is asymptotically stable,
thus, in the zero initial state, from equation (27):
Figure BDA0003084941920000178
wherein
Figure BDA0003084941920000179
tr(He(Sd) Q) represents a matrix He (S)d) Trace of Q. Suppose that
Figure BDA00030849419200001710
Then there is
Figure BDA00030849419200001711
I.e. the closed loop system has a disturbance suppression indicator gamma. Defining the system state x (t) as x (j omega) through Fourier transform, and then SdRewritten as the following frequency domain expression:
Figure BDA0003084941920000181
thus, there are:
Figure BDA0003084941920000182
wherein, ω is1＝4,ω2＝8,ω∈[ω1,ω2]Thereby obtaining
Figure BDA0003084941920000183
Thus, the inequality (24) can ensure that the closed-loop suspension system has the disturbance suppression index γ.
It is noted that the inequality (24) is a non-linear matrix inequality and that the controller gain cannot be solved directly by solving the inequality (24). The inequality (24) is converted into a linear matrix inequality. Applying the projection theorem, the following inequality ensures that (24) holds:
Figure BDA0003084941920000184
then a matrix is defined:
Figure BDA0003084941920000185
since the matrix P is PTThus, J is equal to JT. The full rank symmetric matrix J is used to multiply left and right by equation (31) and the variables are redefined as follows:
Figure BDA0003084941920000186
using Schur's complement theorem while considering the normalized membership function property hi(xi (t)). gtoreq.0, the following inequality can be obtained:
Figure BDA0003084941920000187
in summary, the finite frequency domain disturbance rejection performance index γ of the suspension system and the corresponding fuzzy controller gain matrix can be optimized by the following algorithm:
Figure BDA0003084941920000191
the minimum limited frequency domain disturbance suppression performance index gamma can be obtained by the algorithm, so that the riding comfort of the automobile is improved to the maximum extent. Meanwhile, the matrix P, K can be obtained through the algorithmjThen, the controller gain matrix K is obtained by using the following formulaj
Figure BDA0003084941920000192
After the syndrome is confirmed.
Selecting a parameter ks＝42720N/，kt＝101115N/m，cs＝1095Ns/m，ct＝14.6Ns/m，ms(t)∈[950kg,996kg]，mu(t)∈[110kg,118kg]W (t) ═ 1-u (t-0.4)) sin (5t), where u (×) represents a step function. Pass through settings to be noted
Figure BDA0003084941920000193
The proposed finite frequency domain disturbance suppression optimization algorithm is degenerated into a traditional optimization algorithm. However, set up
Figure BDA0003084941920000194
The conventional disturbance rejection optimization algorithm obtains the disturbance rejection performance γ min 1.0584.
Different from the traditional algorithm, the design of the automobile active suspension controller based on the human body sensitive frequency domain characteristic information provided by the invention fully considers the human body sensitive frequency domain range omega E [ omega ]1,ω2],ω1＝4,ω2The finite frequency domain disturbance suppression optimization algorithm of the automobile active suspension system can find a feasible solution, so that a gain matrix of the fuzzy controller and the corresponding finite frequency domain disturbance suppression performance gamma are obtainedmin＝0.3654。
Fuzzy control method adopting traditional non-utilized human body sensitive frequency domain characteristics and human body sensitive frequency-based method provided by the inventionThe fuzzy control method of domain feature information can obtain control output z (t) and disturbance rejection ratio as shown in FIG. 3 and FIG. 4
Figure BDA0003084941920000195
As can be seen from FIG. 3, the fuzzy controller designed by the invention can stabilize the closed-loop control system of the automobile active suspension, and has smaller control output, namely smaller vertical vibration amplitude of the suspension system, compared with the traditional control method which does not utilize the human body sensitive frequency domain characteristics, and the controller designed by the method has better riding comfort.
It can be seen from fig. 4 that the fuzzy controller designed by the invention can effectively suppress the disturbance of disturbance on the closed-loop control system of the active suspension of the automobile, and has better disturbance suppression performance and better vibration reduction effect than the traditional control method which does not utilize the human body sensitive frequency domain characteristics.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. The active suspension system fuzzy control method for improving the comfort based on the frequency domain characteristics is characterized by comprising the following steps of:
s1, establishing an automobile active suspension system model according to the mechanical characteristics of each element; establishing a dynamic equation of an automobile active suspension system according to the change characteristics of automobile load bearing; further constructing a global T-S fuzzy model of the automobile active suspension system;
s2, designing a parallel compensation fuzzy controller aiming at a global T-S fuzzy model of the automobile active suspension system to obtain an automobile active suspension closed-loop control system; based on the human body sensitive frequency domain characteristic information, providing a limited frequency domain disturbance suppression performance index for depicting the riding comfort of the automobile;
s3, selecting a proper Lyapunov function V (t), and providing a design constraint condition that the closed-loop control system of the automobile active suspension meets the requirement of progressive stability and a design constraint condition that the closed-loop control system of the automobile active suspension meets the performance index gamma of the limited frequency domain disturbance suppression; proved that the given design constraint condition can ensure the gradual stability of the whole closed-loop active suspension control system, and has a disturbance suppression performance index gamma in a human sensitive frequency domain [4Hz 8Hz ];
s4, according to the human body sensitive frequency domain characteristic information, omega belongs to omega1,ω2],ω1＝4,ω2And (8) providing an optimization algorithm according to the design constraint conditions in the step S3 to obtain the optimal disturbance suppression performance gamma of the automobile active suspension systemminAnd a corresponding controller gain matrix.
2. The fuzzy control method for the active suspension system for improving comfort based on the frequency domain features of claim 1, wherein the formula of the automobile active suspension system model in the step S1 is as follows:
Figure FDA0003084941910000011
wherein m issMass on the finger spring; m isuAn unsprung mass; u (t) is the control input to the suspension system; c. Cs,ks,ctAnd ktRespectively representing a suspension damping coefficient, a spring stiffness coefficient, a tire damping coefficient and a tire rigidity coefficient; z is a radical ofsIndicating the body distance, zuRepresenting the unsprung mass velocity.
3. The fuzzy control method for the active suspension system based on the frequency domain characteristic for improving the comfort as claimed in claim 2, wherein the method for establishing the dynamic equation of the active suspension system of the automobile according to the variation characteristic of the automobile load bearing in step S1 is as follows:
considering the change of the weight of the passengers and the weight of the vehicle bodyTaking this factor into account, the sprung mass m is setsUnsprung mass muThe variation intervals of (A) are respectively: m iss∈[msmin,msmax]，mu∈[mumin,mumax](ii) a Definition of x1(t)＝zs(t)-zu(t) suspension system displacement; x is the number of2(t)＝zu(t)-zr(t) is tire displacement;
Figure FDA0003084941910000021
representing the vehicle body speed;
Figure FDA00030849419100000212
represents unsprung mass velocity; selecting road speed as disturbance input, i.e.
Figure FDA0003084941910000023
Defining a state vector:
x(t)＝[x1(t) x2(t) x3(t) x4(t)]T (2)
obtaining a space state equation of the automobile active suspension system:
Figure FDA0003084941910000024
in order to measure the riding comfort, the vertical acceleration of the vehicle body is selected as the control output of the system, namely:
Figure FDA0003084941910000025
finally, the dynamic equation of the automobile active suspension system is described in the form of the following state space:
Figure FDA0003084941910000026
wherein, the matrixes A (t), B (t), G (t), C (t), D (t) are defined as follows:
Figure FDA0003084941910000027
Figure FDA0003084941910000028
Figure FDA0003084941910000029
4. the fuzzy control method for the active suspension system for improving the comfort based on the frequency domain features of claim 3, wherein the method for constructing the global T-S fuzzy model of the active suspension system of the automobile in the step S1 comprises the following steps:
in the dynamic equations of active suspension systems of motor vehicles
Figure FDA00030849419100000210
The two terms can be expressed as:
Figure FDA00030849419100000211
wherein,
Figure FDA0003084941910000031
respectively represent the front piece variables of the fuzzy system, and satisfy:
M1(ξ1(t))+M2(ξ1(t))＝1,N1(ξ2(t))+N2(ξ2(t))＝1. (7)
the membership function is selected as follows:
Figure FDA0003084941910000032
in summary, the active suspension system of the automobile is expressed by the following IF-THEN fuzzy rule:
fuzzy rule pi，IF(ξ1(t),ξ2(t))isΞi，THEN
Figure FDA0003084941910000033
Wherein i ∈ {1,2,3,4},
Figure FDA0003084941910000034
Figure FDA0003084941910000041
after the fuzzification, fuzzy reasoning and defuzzification steps, the IF-THEN fuzzy rule is converted into the following global T-S fuzzy system model:
Figure FDA0003084941910000042
wherein:
Figure FDA0003084941910000043
wherein the normalized membership function satisfies: h isi(ξ(t))≥0,
Figure FDA0003084941910000044
5. The fuzzy control method for the active suspension system based on the frequency domain characteristic for improving the comfort of the claim 4, wherein the step S2 is to design a parallel compensation fuzzy controller for the global T-S fuzzy model of the active suspension system of the vehicle, and the method for obtaining the closed-loop control system for the active suspension system of the vehicle is as follows:
fuzzy rule Ki，IF(ξ1(t),ξ2(t))isΞi，THEN
u(t)＝Kix(t) (13)
Through the steps of fuzzification, fuzzy reasoning and defuzzification, the formula (13) of the fuzzy control rule is converted into the following form:
Figure FDA0003084941910000051
substituting the control signal u (T) in the formula (14) into a formula (11) of a global T-S fuzzy model of the automobile active suspension system to obtain a state equation of the automobile active suspension closed-loop control system:
Figure FDA0003084941910000052
wherein, the control output z (t) of the automobile active suspension closed-loop control system represents the vertical acceleration of the automobile body.
6. The fuzzy control method for the active suspension system based on the frequency domain characteristic for improving the comfort according to claim 5, wherein the method for providing the limited frequency domain disturbance suppression performance index characterizing the riding comfort of the automobile based on the human sensitive frequency domain characteristic information in the step S2 specifically comprises the following steps:
the frequency domain range of the human body sensitive frequency domain characteristic information is omega-epsilon [ omega ]1,ω2],ω1＝4,ω2＝8.；
The riding comfort of the automobile is characterized by the following formula, namely under the influence of disturbance w (t) input, the output of an automobile active suspension closed-loop control system is satisfied:
Figure FDA0003084941910000053
wherein, gamma is more than 0, which represents the limited frequency domain disturbance suppression performance index, and is a positive parameter to be optimized, and the smaller the numerical value is, the stronger the disturbance attenuation capability of the automobile active suspension closed-loop control system is.
7. The fuzzy control method for the active suspension system based on the frequency domain feature for improving the comfort of claim 6, wherein the design constraint condition that the closed-loop control system for the active suspension of the automobile satisfies the requirement of the gradual stability in the step S3 is as follows:
Figure FDA0003084941910000054
the design constraint condition that the closed-loop control system of the automobile active suspension meets the limited frequency domain disturbance suppression performance index gamma is as follows:
Figure FDA0003084941910000061
wherein, positive definite matrix
Figure FDA0003084941910000062
Figure FDA0003084941910000063
And the parameter gamma > 0.
8. The method for fuzzy control of active suspension system based on frequency domain feature improvement of comfort as claimed in claim 7, wherein said step S3 is performed by confirming that the given controller design constraint can ensure the gradual stability of the whole closed-loop active suspension control system as follows:
the Lyapunov function was designed as follows:
V(t)＝xT(t)P-1x(t) (19)
whereinThe matrix P is a positive definite matrix, i.e. P ═ PT＞0.；
Derivation of v (x) over time yields:
Figure FDA0003084941910000064
according to the normalized membership function property hi(xi (t)) > 0, and if the following inequality (21) is satisfied, the closed-loop control system of the automobile active suspension is gradually stabilized:
(Ai+BiKj)TP-1+P-1(Ai+BiKj)＜0. (21)
in order to solve the problem, a projection theorem is applied, and an inequality (22) is obtained and can be used for deducing the inequality (21);
Figure FDA0003084941910000065
defining new variables
Figure FDA0003084941910000066
The nonlinear inequality (22) is expressed as a linear inequality as follows:
Figure FDA0003084941910000067
can be guaranteed under the design constraint condition of the given inequality (17)
Figure FDA0003084941910000068
Namely, the closed-loop control system of the active suspension of the automobile is gradually stable.
9. The fuzzy control method for the active suspension system based on the frequency domain characteristic for improving the comfort according to claim 8, wherein the method with the limited frequency domain disturbance rejection performance index γ in the human sensitive frequency domain [4Hz 8Hz ] interval in step S3 is as follows:
the following inequalities are designed:
Figure FDA0003084941910000071
wherein,
Figure FDA0003084941910000072
making congruent transformation on inequality (24) to left-multiply vector [ x (t) w (t)]Right-hand multiplication of its conjugate transpose vector [ x (t) w (t)]*The following can be obtained:
Figure FDA0003084941910000073
wherein
Figure FDA0003084941910000074
By developing equation (25), the following can be obtained:
Figure FDA0003084941910000075
integration from t-0 to t- + ∞, which can be derived from equation (26):
Figure FDA0003084941910000076
wherein,
Figure FDA0003084941910000077
it should be noted that, since the closed-loop control system of the active suspension of the automobile is gradually stable, in the zero initial state, the following formula (27) can be obtained:
Figure FDA0003084941910000078
wherein,
Figure FDA0003084941910000079
tr(He(Sd) Q) represents a matrix He (S)d) Trace of Q;
let tr (He (S)d) Q) < 0, then there are
Figure FDA00030849419100000710
Namely, the automobile active suspension closed-loop control system has a disturbance suppression index gamma;
defining the system state x (t) as x (j omega) through Fourier transform, and then SdRewritten as the following frequency domain expression:
Figure FDA0003084941910000081
thus, there are:
Figure FDA0003084941910000082
wherein, ω is1＝4,ω2＝8,ω∈[ω1,ω2]Thereby obtaining
Figure FDA0003084941910000083
Thus, the inequality (24) can ensure that the closed-loop suspension system has the disturbance suppression index γ.
10. The fuzzy control method for active suspension system based on frequency domain characteristic improvement of comfort as claimed in claim 9, wherein in step S4, ω e [ ω ] is determined according to the human body sensitive frequency domain characteristic information1,ω2],ω1＝4,ω2An optimization algorithm is proposed to obtain the optimal disturbance suppression performance gamma of the automobile active suspension system under the design constraint conditions of 8 and the step S3minAnd corresponding controller gain matrix, as follows: the inequality (24) is a nonlinear matrix inequality, the gain of the controller cannot be solved by solving the inequality (24) directly, and the inequality (24) needs to be converted into a linear matrix inequality; applying the projection theorem, obtaining the inequality (31) ensures that (24) holds:
Figure FDA0003084941910000084
then a matrix is defined:
Figure FDA0003084941910000085
since the matrix P is PTThus, J is equal to JT(ii) a The full rank symmetric matrix J is used to multiply left and right by equation (32) and the variables are redefined as follows:
Figure FDA0003084941910000086
using Schur's complement theorem while considering the normalized membership function property hi(xi (t)) > 0, the following inequality is obtained:
Figure FDA0003084941910000091
in conclusion, the finite frequency domain disturbance suppression performance index gamma of the suspension system and the corresponding fuzzy controller gain matrix are optimized through the following algorithm:
Figure FDA0003084941910000092
the minimum limited frequency domain disturbance suppression performance index gamma can be obtained by the algorithm, so that the riding comfort of the automobile is improved to the maximum extent;
at the same time, the matrix P can be obtained by the above algorithm,Kjthen, the controller gain matrix K is obtained by using the following formulaj
Figure FDA0003084941910000093
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