CN111487870A - Design method of adaptive inversion controller in flexible active suspension system - Google Patents
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Abstract
The invention discloses a design method of a self-adaptive inversion controller in a flexible active suspension system, which comprises the steps of building an active suspension model, designing a self-adaptive inversion controller based on a neural network, aiming at the two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, constructing a control condition meeting the system stability by selecting a B L function in the control design of the automobile active suspension system, and realizing the compensation of asymmetric control saturation by introducing a second-order auxiliary system, designing the self-adaptive inversion controller based on the neural network by the method, wherein a hardware loop experiment shows that the method can better attenuate the vertical vibration of the sprung mass in the automobile active suspension system and improve the grounding performance of the automobile active suspension system under sine and impact excitation compared with the traditional PD and L QR control in the control design of the automobile active suspension system.
Description
Technical Field
The invention belongs to the field of automatic control of automobiles, and particularly relates to a design method of an adaptive inversion controller in a flexible active suspension system.
Background
The automobile suspension system is a key part of an automobile, the shimmy and the comfort of the automobile can be improved in the using process, the suspension system is used for attenuating the vibration transmitted to an automobile body by road interference, and also must ensure the dynamic stroke, the grounding property and other time domain constraint conditions of the suspension, the vibration control of the suspension system is realized by researching an advanced active control method, and in the research process of the automobile suspension system, certain research results are obtained at present: for example, network control of an active suspension of an automobile is developed, and communication burden is reduced through an event trigger mechanism; a self-organized fuzzy controller is provided to control the active suspension system, and the stability and the comfort of the automobile suspension system are improved to a certain extent;
when the automobile runs, the mass of the automobile body generally changes along with the weight and the load of a driver, and the perturbation of the automobile needs to be considered; sunwei et al propose a nonlinear suspension adaptive inversion control strategy, and estimate the change of the vehicle body mass by an adaptive method; on the basis, the saturation of the control force is compensated by adding the state constraint compensation module, a self-adaptive road control method of the active suspension is researched, and a relatively ideal effect is achieved;
although a control method of adaptive fuzzy and neural network is provided aiming at the uncertainty of the suspension system, most researches are mainly numerical simulation and only stay on the level of simulation, and related hardware loop experiments are rare;
therefore, in the design process of an automobile active suspension system, a control method which can not only consider unknown nonlinear dynamics, parameter perturbation and asymmetric control saturation effects of the system, but also can consider hard nonlinear characteristics such as friction force and clearance contained in the active suspension system and can meet the continuous and bounded condition of L ipschitz is urgently needed, so that the automobile active suspension system which can compensate the asymmetric saturation phenomenon of the control force, can better attenuate vertical vibration of sprung mass and can improve the grounding performance and stability is designed.
Disclosure of Invention
Aiming at the two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, the invention aims to provide a design method of an adaptive inversion controller in a flexible active suspension system, wherein a control condition meeting the system stability is constructed by selecting a Barrier-L yapunov (B L) function in the control design of the automobile active suspension system, the compensation of asymmetric control saturation is realized by introducing a second-order auxiliary system, and the weight and the body mass of a neural network are estimated by using an adaptive law based on error convergence.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
a design method of an adaptive inversion controller in a flexible active suspension system comprises the following steps:
the method comprises the following steps: building flexible active suspension model
In a two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, a flexible active suspension is built, and the dynamic relation of the model is as follows:
step two: designing adaptive inversion controller based on neural network
According to the flexible active suspension model established in the first step, a B L function is introduced to construct a control condition meeting the system stability, a second-order auxiliary system is introduced to compensate asymmetric control saturation in the flexible active suspension system, and a neural network-based adaptive inversion controller is designed through a saturation adaptive inversion control method to improve the control performance of the active suspension.
Preferably, the building process of the flexible active suspension model in the step one is as follows:
s1, arranging in a flexible active suspension model: m issIs a sprung mass; m isuIs an unsprung mass; z is a radical ofsIs the vertical displacement at the center of mass of the sprung mass, zuIs the vertical displacement at the unsprung mass centroid; z is a radical ofrExciting the unevenness of the road surface; fsForce generated for a non-linear spring of a suspension, FdA force generated for the damper; ftElastic force generated for tire rigidity, FbA damping force generated for damping; u is the active control force generated by the DC servo motor in the active suspension;
s2, the dynamic relation of the flexible active suspension model is as follows:
wherein: fΔIs an unknown disturbance force caused by friction and control errors, and FΔBounded but not continuously bounded with respect to L ipschitz, in the flexible active suspension model, the spring force FsAnd a damping force FdIs not measurable and belongs to unknown nonlinear dynamics, msIs a parameter perturbation term;
s3, setting the state variable of the system as x1＝zs，
x3＝zu，
Then the state space equation of the controlled system equation (1) is:
preferably, the step of designing the adaptive inversion controller based on the neural network in the second step includes:
s1, firstly, considering the saturation phenomenon of an active control force u, introducing a second-order auxiliary system to compensate a control error caused by saturation, and defining the saturation condition of the control force u;
s2, defining a tracking error e1＝x1-xr-λ1，e2＝x2α, and selecting a B L function to construct a control condition meeting the stability of the flexible active suspension system;
s3, designing a virtual control law f by utilizing a self-adaptive neural network algorithm to enable a variable e1、e2、
Asymptotically converges to the origin or near the origin,
is an estimator;
s4, designing an adaptive law based on error convergence to estimate the NN weight and the sprung mass;
and S5, analyzing the stability of the flexible active suspension system by using L yapunov functions and carrying out classification discussion on an error convergence set.
Preferably, the specific design process of step two S1 is as follows:
(1) according to the type of a flexible active suspension system, considering an asymmetric input saturated self-adaptive NN inversion control law of an active suspension model, and introducing a second-order auxiliary system to compensate a control error caused by saturation, wherein the second-order auxiliary system is as follows:
wherein: u-f, λ1And λ2Representing state variables of the auxiliary system, and zero initial state λ1(0)、λ2(0) Is zero; c. C1And c2Is a normal number, and is,
is the inverse number theta of the sprung mass equal to 1/msAn estimate of (a);
(2) according to the introduced second-order auxiliary system, the saturation phenomenon of the control force in the active suspension model is considered, and the saturation condition met by the control force u is defined as follows:
wherein: f is the virtual control law to be designed.
Preferably, the specific design process of step two S2 is as follows:
(1) defining a tracking error: e.g. of the type1＝x1-xr-λ1，e2＝x2-α；
Wherein: x is the number of1Is a state variable of the closed-loop system equation (2), xrIs the system state x1Reference track of (2), xrNormally zero, α is system state x2The virtual trajectory of (2);
(2) let initial tracking error | e1(0)|＜1Wherein1Is an arbitrarily small positive number;
(3) selecting a B L function, wherein the B L function is expressed as follows:
wherein: v1(e1) The function of B L is represented as,1is an arbitrarily small positive number, e1Represents a tracking error;
(4) by deriving equation (7), we can obtain:
wherein
k1＞0，e2Which is indicative of a tracking error,
equation (8) can be transformed into:
(5) as can be seen from equation (9): if the error e2→ 0, then
Therefore e1Asymptotically converge to zero and satisfy V1(e1)≤V1(e1(0) ); get xrZero, | x can be obtained from step (2)1(0)|＜1When t → ∞, there is | x1(t)|＜||λ1||∞；
(6) To study | | | λ1||∞Taking parameter c according to the change rule of delta u1＝50、c1＝60、
Performing numerical simulation on the formula (6) to obtain a simulation curve, and as can be seen from the simulation curve, when the control error Δ u is 10N, | λ1The | ∞ is still less than 3 mm; it is thus possible to adjust the control parameter c1And c2To adjust | λ1||∞Thus decreasing | x1(t)|。
Preferably, the specific design process of step two S3 is as follows:
(1) for tracking error e2The derivation is carried out to obtain:
wherein phi is-Fd-Fs-FΔ+u,
Can see-Fd-Fs-FΔFor unknown nonlinear dynamics, θ is 1/msIs a perturbation parameter;
(2) designing a self-adaptive neural network algorithm to approach the unknown nonlinear dynamics phi, wherein the neural network algorithm is as follows:
TNN＝W1 Tφ1+1＝θ(-Fd-Fs-FΔ) (11)
wherein: t isNNApproximate quantity, W, representing unknown nonlinear dynamics1Represents the ideal NN weight, phi1A vector of the activation function is represented,1representing bounded approximation error, i.e.1|＜1N，1N＞0；
(3) By substituting formula (11) into formula (10), it is possible to obtain:
wherein Θ is1＝[W1 Tθ]T，
(4) Definition of
Is composed of
Equation (12) may be rewritten as:
wherein
(5) In order to ensure asymptotic stability of closed-loop system formula (2) and to make the error variable e1、e2、
Asymptotically converging to the origin or the vicinity of the origin, and designing a virtual control law as follows:
wherein: k is a radical of2To control the gain, and k2＞0。
Preferably, the specific design process of step two S4 is as follows:
(1) defining virtual filter variables e2f、
The filter variable e2f、
The relationship of (A) is as follows:
wherein: k > 0 is a design parameter;
(2) defining a virtual filter matrix P1Sum vector Q1Satisfies the following relation:
wherein: l > 0 is a design parameter;
(3) the following adaptive law based on error convergence is designed:
wherein:1is a diagonal matrix, σ > 0 is a learning gain value, and
(4) according to the formula (16), H can be represented by1Further decomposing into:
wherein:
1fis that1Filter factor of, i.e.
(5) It can be seen from equation (18) that for all bounded active control forces u and state vectors x, there is | | | Δ1||＜1Nf，1NfIs a bounded constant; current regression vector
Upon continued excitation, the matrix P1More than 0 is a positive definite matrix, and the minimum eigenvalue satisfies the condition
I.e., complete the design of the active suspension control strategy.
Preferably, the specific design process of step two S5 is as follows:
(1) to analyze the stability and error convergence set of the flexible active suspension system, the following L yapunov function was chosen:
wherein: v1The function of B L is represented as,
and is1Is a diagonal matrix;
by substituting equation (14) into equation (13), the following can be obtained:
by combining equation (20) and equation (18) after derivation of equation (19), the following can be obtained:
wherein: k is a radical of1，k2To control the gain, and k1＞0，k2＞0；
(2) Equation (21) is discussed in two cases, the first case: if the neural network algorithm can ideally approximate the nonlinear dynamics of a flexible active suspension system, the approximation error is10, and Δ1When 0, then equation (21) satisfies:
according to the L yapunov stabilization theory, V (t) ≦ V (0), and the error variable e when time t → ∞1、e2、
Will converge to the origin and satisfy | e over the entire time domain1(t)|＜1；
(3) In the second case: when approaching error1When not equal to 0, the young can be obtained by applying the young inequality:
wherein η and η1Are all positive tuning parameters;
substituting equation (23) into equation (21) can yield:
wherein:
always present η1Guarantee
To represent
The maximum singular value of;
the L yapunov function thus satisfies:
from the L yapunov theory of stability, the error variable e can be known1、e2、
Is eventually consistently bounded and will converge to a set:
wherein:
to represent
The minimum singular value of;
as can be seen from the formula (26), | e1(t)|＜1The same can be satisfied in the formula (26), and the radius of the set depends on the approximation error1Is measured by the size of1On → 0, the same conclusion can be reached as in case 1, which is aggregated as follows:
preferably, the method for designing the adaptive inversion controller in the flexible active suspension system further comprises the third step of: testing the performance of the adaptive inversion controller by a hardware loop test experiment, wherein the specific process of the experiment comprises the following steps:
(1) sine wave excitation experiment
Under the excitation of sine action, the self-adaptive inversion control method can well control vibration, and meanwhile under the road excitation of resonance frequency, the comfort and the grounding stability of the self-adaptive inversion control method are superior to those of the traditional PD, L QR and passive control;
(2) square wave impact excitation experiment
Under impact excitation, compared with the traditional PD, L QR and passive control, the adaptive inversion control method has smaller overshoot displacement and acceleration, and has control force output of saturation effect, and the control effect of the method is obviously better than that of the traditional PD and L QR control.
The invention has the beneficial effects that: the invention discloses a design method of a self-adaptive inversion controller in a flexible active suspension system, and compared with the prior art, the improvement of the invention is as follows:
(1) aiming at a two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, a Barrier-L yapunov (B L) function is introduced to construct a control condition meeting the stability of the system, and a controller design method with small conservative property is obtained;
(2) meanwhile, through a hardware loop experiment, the adaptive inversion controller designed by the adaptive inversion control method is compared with the traditional classical PD control and L QR control, and a sine excitation experiment and a square wave impact excitation experiment prove that the active suspension of the adaptive inversion controller designed by the method can better attenuate the vertical vibration of the sprung mass and improve the grounding performance under sine and impact excitation, so that the effectiveness of the adaptive inversion controller designed by the adaptive inversion control method is further verified, and the superiority of the adaptive inversion control method is proved.
Drawings
Fig. 1 is a diagram of an active suspension model of the flexible active suspension system according to the present invention.
FIG. 2 shows the invention1||∞And (4) a change rule graph along with the delta u.
Fig. 3 is a diagram showing the vertical displacement of the sprung mass in a sine wave excitation experiment in embodiment 1 of the present invention.
Fig. 4 is a diagram of the sprung mass vertical acceleration of the sine wave excitation experiment in embodiment 1 of the present invention.
Fig. 5 is a suspension dynamic stroke diagram of a sine wave excitation experiment in embodiment 1 of the present invention.
Fig. 6 is a tire dynamic stroke chart of a sine wave excitation experiment in example 1 of the present invention.
Fig. 7 is a motor control force diagram of a sine wave excitation experiment in embodiment 1 of the present invention.
Fig. 8 is a diagram of the vertical displacement of the sprung mass for the square wave shock excitation experiment in embodiment 1 of the present invention.
Fig. 9 is a diagram of the sprung mass vertical acceleration of the square wave shock excitation experiment of embodiment 1 of the present invention.
Fig. 10 is a suspension dynamic stroke diagram of a square wave impact excitation experiment in embodiment 1 of the invention.
FIG. 11 is a graph of the tire stroke during square wave shock excitation experiments in example 1 of the present invention.
Fig. 12 is a motor control force diagram of the square wave impact excitation experiment in embodiment 1 of the present invention.
Wherein: pass stands for passive control and AB control stands for adaptive inversion control of the invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments;
referring to fig. 1 to 12, a method for designing an adaptive inversion controller in a flexible active suspension system includes:
the method comprises the following steps: building flexible active suspension model
In a two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, a flexible active suspension is built, and the dynamic relation of the model is as follows:
the construction process of the active suspension model comprises the steps of construction of the active suspension model and performance evaluation of the active suspension model:
the concrete process of building the active suspension model comprises the following steps:
s1, researching a two-degree-of-freedom active suspension model shown in the figure 1, wherein the two-degree-of-freedom active suspension model is arranged in the active suspension model: m issIs a sprung mass; m isuIs an unsprung mass; z is a radical ofsIs the vertical displacement at the center of mass of the sprung mass, zuIs the vertical displacement at the unsprung mass centroid; z is a radical ofrExciting the unevenness of the road surface; fsForce generated for a non-linear spring of a suspension, FdA force generated for the damper; ftElastic force generated for tire rigidity, FbA damping force generated for damping; u is the active control force generated by the DC servo motor in the active suspension;
s2, the dynamic relation of the flexible active suspension model is as follows:
wherein FΔIs an unknown disturbance force caused by friction and control errors, and FΔBounded but not continuously bounded with respect to L ipschitz, in the flexible active suspension model, the spring force FsAnd a damping force FdIs not measurable, belongs to unknown nonlinear dynamics, and has a parameter perturbation term m because the mass of the vehicle body changes along with the weight of a drivers，msIs a parameter perturbation term;
s3, setting the state variable of the system as x1＝zs，
x3＝zu，
Then the state space equation of the controlled system equation (1) is:
(II) evaluation of the Performance of the active suspension model (generally, when implementing the control strategy of the active suspension, the following four problems need to be considered)
1. Vibration attenuation: since the vertical motion of the vehicle body is closely related to the comfort of the suspension, the main objective of the controller is to suppress the vibration transmitted to the vehicle body by the road surface disturbance and make it approach the vicinity of the zero point;
2. suspension dynamic stroke: due to the limitation of the chassis structure, the suspension dynamic stroke must move within a specified range, namely, the time domain constraint condition | z is required to be mets-zu|≤zmaxWherein z ismaxA safety threshold allowed for the structure;
3. grounding property: in order to ensure the safety and maneuverability of the vehicle, the dynamic load of the tire is required to be less than the static load thereof, i.e. the time domain constraint condition | F is required to be satisfiedt+Fb|＜(ms+mu) g; it is noted that the dynamic load of the tire is proportional to the dynamic travel z of the tireu-zr||∞So that it is desirable that the smaller the amplitude is, the better;
4. asymmetric input saturation: limited by the output of the motor, in order to guarantee the stability of the closed loop system, the control force saturation must be considered, taking the following constraints: u. ofmin≤u≤umaxWherein u isminAnd umaxRespectively the upper and lower limit values of the control force;
in performance evaluation, the root mean square value and the maximum value of vibration can reflect the quality of vibration attenuation performance, so the root mean square value and the maximum value of design output need to be considered, and the design formula is as follows:
|χ(t)|max＝max{χ(t)|,t∈[0,T]} (4)
wherein χ (T) represents the vibration output and T represents the system response time;
and are marked in the present invention as follows:
||x||∞＝max(xi)，i＝1…n，
λmin/max(A) the minimum/large eigenvalue of matrix a is represented,
a > 0 indicates that it is a positive definite matrix.
Step two: designing adaptive inversion controller based on neural network
According to the flexible active suspension model established in the step one, a Barrier-L yapunov (B L) function is introduced to construct a control condition meeting the system stability, meanwhile, a second-order auxiliary system is introduced to realize the compensation of asymmetric control saturation in the flexible active suspension system, and a neural network-based adaptive inversion controller is designed through a saturation adaptive inversion control method to improve the control performance of the active suspension;
the design steps of the adaptive inversion controller based on the neural network comprise (the used method is an adaptive inversion control method):
s1, firstly considering the saturation phenomenon of an active control force u, introducing a second-order auxiliary system to compensate a control error caused by saturation, and defining the saturation condition of the control force u, wherein the specific design process comprises the following steps:
(1) according to the type of a flexible active suspension system, considering an asymmetric input saturated self-adaptive NN inversion control law of an active suspension model, and introducing a second-order auxiliary system to compensate a control error caused by saturation, wherein the second-order auxiliary system is as follows:
wherein u-f, λ1And λ2Represents a state variable of the auxiliary system, and the zero initial state is zero; c. C1And c2Is a normal number, and is,
is the inverse number theta of the sprung mass equal to 1/msAn estimate of (a);
(2) according to the introduced second-order auxiliary system, the saturation phenomenon of the control force in the active suspension model is considered, and the saturation condition met by the control force u is defined as follows:
where f is the virtual control law.
S2, defining a tracking error e1＝x1-xr-λ1，e2＝x2α, and selecting a B L function to construct a control condition meeting the stability of the flexible active suspension system, wherein the specific process is as follows:
(1) defining a tracking error: e.g. of the type1＝x1-xr-λ1，e2＝x2- α, where x1Is a state variable of a controlled system formula (2), xrIs the system state x1Reference track of (2), xrNormally zero, α is system state x2The virtual trajectory of (2);
(2) let initial tracking error | e1(0)|＜1Wherein1Is an arbitrarily small positive number (since in suspension systems, x1Is set to zero, and x is setrIs zero, state quantity lambda1Is also zero, so1Any small positive number can meet the requirement);
(3) selecting a B L function, wherein the B L function is expressed as follows:
wherein: v1(e1) The function of B L is represented as,1is an arbitrarily small positive number, e1Represents a tracking error;
(4) by deriving equation (7), we can obtain:
wherein
k1＞0，e2Which is indicative of a tracking error,
equation (8) can be transformed into:
(5) as can be seen from equation (9): if the error e2→ 0, then
Therefore e1Asymptotically converge to zero and satisfy V1(e1)≤V1(e1(0) ); get xrZero, | x can be obtained from step (2)1(0)|＜1When t → ∞, there is | x1(t)|＜||λ1||∞；
(6) To study | | | λ1||∞Taking parameter c according to the change rule of delta u1＝50、c1＝60、
The numerical simulation of the formula (6) is performed to obtain a simulation curve (as shown in fig. 2), and it can be seen from the simulation curve that | λ |, when the control error Δ u is 10N1||∞Still less than 3 mm; it is thus possible to adjust the control parameter c1And c2To adjust | λ1||∞Thus decreasing | x1(t)|。
S3, designing a virtual control law f by utilizing a self-adaptive neural network algorithm to enable a variable e1、e2、
Asymptotically converges to the origin or near the origin,
the specific process for designing the estimator is as follows:
(1) for tracking error e2The derivation is carried out to obtain:
wherein phi is-Fd-Fs-FΔ+u,
Can see-Fd-Fs-FΔFor unknown nonlinear dynamics, θ is 1/msIs a perturbation parameter;
(2) designing a self-adaptive neural network algorithm to approach the unknown nonlinear dynamics phi, wherein the neural network algorithm is as follows:
TNN＝W1 Tφ1+1＝θ(-Fd-Fs-FΔ) (11)
wherein: t isNNApproximate quantity, W, representing unknown nonlinear dynamics1Represents the ideal NN weight, phi1A vector of the activation function is represented,1representing bounded approximation error, i.e.1|＜1N，1N＞0；
(3) By substituting formula (11) into formula (10), it is possible to obtain:
wherein Θ is1＝[W1 Tθ]T，
(4) Definition of
Is theta1＝[W1 Tθ]TEquation (12) may be rewritten as:
wherein
(5) In order to ensure asymptotic stability of the closed-loop system (2) and to make the error variable e1、e2、
Asymptotically converging to the origin or the vicinity of the origin, and designing a virtual control law as follows:
wherein k is2To control the gain, and k20 (see S5 below for a detailed demonstration procedure).
S4, designing an adaptive law based on error convergence to estimate the NN weight and the sprung mass, wherein the specific design process comprises the following steps:
(1) defining virtual filter variables e2f、
The filter variable e2f、
The relationship of (A) is as follows:
wherein k > 0 is a design parameter;
(2) defining a virtual filter matrix P1Sum vector Q1Satisfies the following relation:
wherein l > 0 is a design parameter;
(3) the following adaptive law based on error convergence is designed:
wherein:1is a diagonal matrix, σ > 0 is a learning gain value, and
(4) according to the formula (16), H can be represented by1Further decomposing into:
wherein
1fIs that1Filter factor of, i.e.
(5) It can be seen from equation (18) that for all bounded active control forces u and state vectors x, there is | | | Δ1||＜1Nf，1NfIs a bounded constant; current regression vector
Upon continued excitation, the matrix P1More than 0 is a positive definite matrix, and the minimum eigenvalue satisfies the condition
Namely, the design of the active suspension control strategy is completed, and the stability of the active suspension is further discussed below;
s5, analyzing the stability of the flexible active suspension system by using an L yapunov function and carrying out classification discussion on an error convergence set, wherein the specific design process comprises the following steps:
(1) to analyze the stability and error convergence set of the flexible active suspension system, the following L yapunov function was chosen:
wherein: v1The function of B L is represented as,
and is1Is a diagonal matrix;
by substituting equation (14) into equation (13), the following can be obtained:
by combining equation (20) and equation (18) after derivation of equation (19), the following can be obtained:
wherein: k is a radical of1，k2To control the gain, and k1＞0，k2＞0；
(2) Equation (21) is discussed in two cases, the first case: if the neural network algorithm can ideally approximate the nonlinear dynamics of a flexible active suspension system, the approximation error is10, and Δ1When 0, then equation (21) satisfies:
according to the L yapunov stabilization theory, V (t) ≦ V (0), and the error variable e when time t → ∞1、e2、
Will converge to the origin and be overSatisfies | e in the time domain1(t)|＜1；
(3) In the second case: when approaching error1When not equal to 0, the young can be obtained by applying the young inequality:
η and η therein1Are all positive tuning parameters;
substituting equation (23) into equation (21) can yield:
wherein
Always present η1Guarantee
To represent
The maximum singular value of;
the L yapunov function thus satisfies:
from the L yapunov theory of stability, the error variable e can be known1、e2、
Is eventually consistently bounded and will converge to a set:
wherein:
to represent
The minimum singular value of;
as can be seen from the formula (26), | e1(t)|＜1The same can be satisfied in the formula (26), and the radius of the set depends on the approximation error1Is measured by the size of1On → 0, the same conclusion can be reached as in case 1, which is aggregated as follows:
according to the universal approximation principle of the neural network, the approximation error is very small, so that x is reduced1(t) convergence to a set of residuals near the origin; stability certification is complete and the system state can converge to an arbitrarily small set.
Step three: hardware Loop test experiment (example 1)
In order to test the performance of the adaptive inversion controller designed in the step two, a hardware loop experiment (HI L) is carried out on the adaptive inversion controller, a control program adopts C language to carry out S-function programming, a T L C file is connected in series to carry out hardware accelerated operation, and a reference track x is setrIs zero;
in the control parameter setting, the maximum suspension travel is taken as z according to the system's user manualmax0.02cm, maximum control force | u | less than or equal to 10N, zero initial parameter of self-adaptive law
In the experiment, the precise parameters of the system are not needed, and only the sprung mass displacement x needs to be fed back1The vertical displacement of each part is measured by an encoder, the acceleration of the sprung mass is measured by an accelerometer, and the vertical speed is obtained by a filter;
NN activation function vector phi1And adaptive gainThe vectors are:
φ1＝[x2-x4x1-x3(x1-x3)3]T
1＝diag([50 100 500 1×10-5])
wherein x1-x3For the suspension stroke, x2-x4Is its derivative; the parameters of the controller after setting are shown in table 1:
table 1: controller gain parameter
In the experiment, the road surface excitation is generated by a direct current servo motor at the bottom, two typical road surface excitations are considered, the first is sine wave excitation, and the second is square wave impact excitation; setting the gain of the PD controller to kP＝5，k Q6, L gain of QR controller is K-24.6648.87-0.473.68]；
Thus, vibration is most pronounced when the excitation frequency is close to the natural frequency of the flexible active suspension system, so the waveform of the sine wave is set to zr0.002 × sin (6 π t) m, the excitation frequency being the same as the natural frequency of the sprung mass;
(1) sine wave excitation experiment:
3-7 show the test result under sine excitation, the excitation time is 15s, 3 shows the sprung mass displacement response, 4 shows the sprung mass acceleration response, 5 shows the suspension moving stroke response, 6 shows the tire moving stroke, 7 shows the active control force generated by the controller, in the figure, Pass represents the passive control, and AB control represents the adaptive inversion control of the invention, and it can be seen from the figure that the adaptive inversion control provided by the invention achieves good vibration control effect without system precise parameters compared with typical PD control and L QR control;
further, the root mean square value of the sprung mass acceleration can be calculated by using the formula (3), wherein the root mean square value under the uncontrolled condition is 0.9813m/s2The root mean square value of PD is 0.8882m/s2L QR with a root mean square value of 0.3819m/s2The root mean square value of the adaptive inversion control is 0.0421m/s2Compared with PD control and L QR passive control, the acceleration root mean square value of the self-adaptive inversion control of the invention is reduced by 95 percent;
it can also be seen from fig. 5 that the maximum value of the suspension dynamic travel of the adaptive inversion control is less than 0.02cm and less than the passive control; the size of the tire dynamic stroke directly reflects the quality of the grounding stability, and the adaptive inversion control can obtain smaller tire dynamic stroke;
therefore, in summary, under the excitation of the road surface with the resonant frequency, the comfort and the grounding stability of the adaptive inversion control are better than those of the traditional PD, L QR and passive control.
(2) Square wave impact excitation experiment
In order to test the shock resistance of the active suspension system, a group of square waves are adopted to excite the active suspension system, and the excitation time is 15 s; FIGS. 8-12 show results of tests under impact excitation; in order to verify that the active suspension system has anti-saturation performance, an asymmetric saturation module is connected to a control input end, wherein the maximum value and the minimum value are respectively set as umax＝1N，umin＝-3N；
As can be seen from fig. 8 and 9, under the impact excitation, the adaptive inversion control method provided by the invention has smaller overshoot displacement and acceleration;
as can be seen from fig. 10 and 11, the suspension stroke and the tire stroke of the adaptive inversion control method proposed by the present invention are also less than given limit values;
FIG. 12 is the control force output with saturation effect, and it can be seen that the control effect of the adaptive inversion control method proposed by the present invention is obviously better than that of the conventional PD and L QR control;
as can be seen from fig. 2, when the control error is not large, | | λ1||∞The method is a very small value, so that the effectiveness of the adaptive inversion control method provided by the invention is further verified.
The adaptive inversion control method provided by the invention is designed for a flexible active suspension system with two degrees of freedom and unknown nonlinear dynamics and asymmetric control saturation, the adaptive inversion controller based on a neural network is designed, the adaptive inversion control method is different from the traditional Q L function, the control condition of B L function analysis closed-loop system stability is selected, the controller design method with less conservation is obtained, the asymmetric saturation phenomenon of control force is compensated by introducing a second-order auxiliary system, the effectiveness of the adaptive inversion controller based on the neural network designed by the adaptive inversion control method is further verified through a hardware loop experiment, and the adaptive inversion control method provided by the invention can better attenuate the vertical vibration of spring load mass and simultaneously improve the grounding performance under sine and impact excitation compared with the classical PD and L QR control.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (9)
1. A design method of an adaptive inversion controller in a flexible active suspension system is characterized by comprising the following steps:
the method comprises the following steps: building flexible active suspension model
In a two-degree-of-freedom flexible active suspension system containing unknown nonlinear dynamics, a flexible active suspension is built, and the dynamic relation of the model is as follows:
step two: designing adaptive inversion controller based on neural network
According to the flexible active suspension model established in the first step, a B L function is introduced to construct a control condition meeting the system stability, a second-order auxiliary system is introduced to compensate asymmetric control saturation in the flexible active suspension system, and a neural network-based adaptive inversion controller is designed through a saturation adaptive inversion control method to improve the control performance of the active suspension.
2. The method for designing the adaptive inversion controller in the flexible active suspension system according to claim 1, wherein the building process of the flexible active suspension model in the step one is as follows:
s1, arranging in a flexible active suspension model: m issIs a sprung mass; m isuIs an unsprung mass; z is a radical ofsIs the vertical displacement at the center of mass of the sprung mass, zuIs the vertical displacement at the unsprung mass centroid; z is a radical ofrExciting the unevenness of the road surface; fsForce generated for a non-linear spring of a suspension, FdA force generated for the damper; ftElastic force generated for tire rigidity, FbA damping force generated for damping; u is the active control force generated by the DC servo motor in the active suspension;
s2, the dynamic relation of the flexible active suspension model is as follows:
wherein: fΔIs an unknown disturbance force caused by friction and control errors, and FΔBounded but not continuously bounded with respect to L ipschitz, in the flexible active suspension model, the spring force FsAnd a damping force FdIs not measurable and belongs to unknown nonlinear dynamics, msIs a parameter perturbation term;
s3, setting the state variable of the system as x1＝zs，
x3＝zu，
Then the state space equation of the controlled system equation (1) is:
3. the method for designing the adaptive inversion controller in the flexible active suspension system according to claim 1, wherein the step two of designing the adaptive inversion controller based on the neural network comprises the steps of:
s1, firstly, considering the saturation phenomenon of an active control force u, introducing a second-order auxiliary system to compensate a control error caused by saturation, and defining the saturation condition of the control force u;
s2, defining a tracking error e1＝x1-xr-λ1，e2＝x2α, and selecting a B L function to construct a control condition meeting the stability of the flexible active suspension system;
s3, designing a virtual control law f by utilizing a self-adaptive neural network algorithm to enable a variable e1、e2、
Asymptotically converges to the origin or near the origin,
is an estimator;
s4, designing an adaptive law based on error convergence to estimate the NN weight and the sprung mass;
and S5, analyzing the stability of the flexible active suspension system by using L yapunov functions and carrying out classification discussion on an error convergence set.
4. The design method of the adaptive inversion controller in the flexible active suspension system according to claim 3, wherein the specific design process of step two S1 is as follows:
(1) according to the type of a flexible active suspension system, considering an asymmetric input saturated self-adaptive NN inversion control law of an active suspension model, and introducing a second-order auxiliary system to compensate a control error caused by saturation, wherein the second-order auxiliary system is as follows:
wherein: u-f, λ1And λ2Representing state variables of the auxiliary system, and zero initial state λ1(0)、λ2(0) Is zero; c. C1And c2Is a normal number, and is,
is the inverse number theta of the sprung mass equal to 1/msAn estimate of (a);
(2) according to the introduced second-order auxiliary system, the saturation phenomenon of the control force in the active suspension model is considered, and the saturation condition met by the control force u is defined as follows:
wherein: f is the virtual control law to be designed.
5. The design method of the adaptive inversion controller in the flexible active suspension system according to claim 4, wherein the specific design process of step two S2 is as follows:
(1) defining a tracking error: e.g. of the type1＝x1-xr-λ1，e2＝x2-α；
Wherein: x is the number of1Is a state variable of the closed-loop system equation (2), xrIs the system state x1Reference track of (2), xrNormally zero, α is system state x2The virtual trajectory of (2);
(2) let initial tracking error | e1(0)|＜1Wherein1Is an arbitrarily small positive number;
(3) selecting a B L function, wherein the B L function is expressed as follows:
wherein: v1(e1) The function of B L is represented as,1is an arbitrarily small positive number, e1Represents a tracking error;
(4) by deriving equation (7), we can obtain:
wherein
k1＞0，e2Which is indicative of a tracking error,
equation (8) can be transformed into:
(5) as can be seen from equation (9): if the error e2→ 0, then
Therefore e1Asymptotically converge to zero and satisfy V1(e1)≤V1(e1(0) ); get xrZero, | x can be obtained from step (2)1(0)|＜1When t → ∞, there is | x1(t)|＜||λ1||∞；
(6) To study | | | λ1||∞Taking parameter c according to the change rule of delta u1＝50、c1＝60、
Carrying out numerical simulation on the formula (6) to obtain a simulation curve, and obtaining the simulation curve from the simulation curveAs can be seen from the line, | | λ when the control error Δ u is 10N1||∞Still less than 3 mm; it is thus possible to adjust the control parameter c1And c2To adjust | λ1||∞Thus decreasing | x1(t)|。
6. The design method of the adaptive inversion controller in the flexible active suspension system according to claim 5, wherein the specific design process of step two S3 is as follows:
(1) for tracking error e2The derivation is carried out to obtain:
wherein phi is-Fd-Fs-FΔ+u,
Can see-Fd-Fs-FΔFor unknown nonlinear dynamics, θ is 1/msIs a perturbation parameter;
(2) designing a self-adaptive neural network algorithm to approach the unknown nonlinear dynamics phi, wherein the neural network algorithm is as follows:
wherein: t isNNApproximate quantity, W, representing unknown nonlinear dynamics1Represents the ideal NN weight, phi1A vector of the activation function is represented,1representing bounded approximation error, i.e.1|＜1N，1N＞0；
(3) By substituting formula (11) into formula (10), it is possible to obtain:
wherein
(4) Definition of
Is composed of
Equation (12) may be rewritten as:
wherein
(5) In order to ensure asymptotic stability of closed-loop system formula (2) and to make the error variable e1、e2、
Asymptotically converging to the origin or the vicinity of the origin, and designing a virtual control law as follows:
wherein: k is a radical of2To control the gain, and k2＞0。
7. The design method of the adaptive inversion controller in the flexible active suspension system according to claim 6, wherein the specific design process in step two S4 is as follows:
(1) defining virtual filter variables e2f、
The filter variable e2f、
The relationship of (A) is as follows:
wherein: k > 0 is a design parameter;
(2) defining a virtual filter matrix P1Sum vector Q1Satisfies the following relation:
wherein: l > 0 is a design parameter;
(3) the following adaptive law based on error convergence is designed:
wherein:1is a diagonal matrix, σ > 0 is a learning gain value, and
(4) according to the formula (16), H can be represented by1Further decomposing into:
wherein:
1fis that1Filter factor of, i.e.
(5) It can be seen from equation (18) that for all bounded active control forces u and state vectors x, there is | | | Δ1||＜1Nf，1NfIs a bounded constant; current regression vector
Upon continued excitation, the matrix P1More than 0 is a positive definite matrix, and the minimum eigenvalue satisfies the condition
I.e., complete the design of the active suspension control strategy.
8. The design method of the adaptive inversion controller in the flexible active suspension system according to claim 7, wherein the specific design process in step two S5 is as follows:
(1) to analyze the stability and error convergence set of the flexible active suspension system, the following L yapunov function was chosen:
wherein: v1The function of B L is represented as,
and is1Is a diagonal matrix;
by substituting equation (14) into equation (13), the following can be obtained:
by combining equation (20) and equation (18) after derivation of equation (19), the following can be obtained:
wherein: k is a radical of1，k2To control the gain, and k1＞0，k2＞0；
(2) Equation (21) is discussed in two cases, the first case: if the neural network algorithm can ideally approximate the nonlinear dynamics of a flexible active suspension system, the approximation error is10, and Δ1When 0, then equation (21) satisfies:
according to the L yapunov stabilization theory, V (t) ≦ V (0), and the error variable e when time t → ∞1、e2、
Will converge to the origin and satisfy | e over the entire time domain1(t)|＜1；
(3) In the second case: when approaching error1When not equal to 0, the young can be obtained by applying the young inequality:
wherein η and η1Are all positive tuning parameters;
substituting equation (23) into equation (21) can yield:
wherein:
always present η1Guarantee
To represent
The maximum singular value of;
the L yapunov function thus satisfies:
from the L yapunov theory of stability, the error variable e can be known1、e2、
Is eventually consistently bounded and will converge to a set:
wherein:
to represent
The minimum singular value of;
as can be seen from the formula (26), | e1(t)|＜1The same can be satisfied in the formula (26), and the radius of the set depends on the approximation error1Is measured by the size of1On → 0, the same conclusion can be reached as in case 1, which is aggregated as follows:
9. the method for designing the adaptive inversion controller in the flexible active suspension system according to claim 3, wherein the method for designing the adaptive inversion controller in the flexible active suspension system further comprises the following steps: testing the performance of the adaptive inversion controller by a hardware loop test experiment, wherein the specific process of the experiment comprises the following steps:
(1) sine wave excitation experiment
Under the excitation of sine action, the self-adaptive inversion control method can well control vibration, and meanwhile under the road excitation of resonance frequency, the comfort and the grounding stability of the self-adaptive inversion control method are superior to those of the traditional PD, L QR and passive control;
(2) square wave impact excitation experiment
Under impact excitation, compared with the traditional PD, L QR and passive control, the adaptive inversion control method has smaller overshoot displacement and acceleration, and has control force output of saturation effect, and the control effect of the method is obviously better than that of the traditional PD and L QR control.
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