CN111553021A - Design method of active suspension system based on cascade disturbance observer - Google Patents

Design method of active suspension system based on cascade disturbance observer Download PDF

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CN111553021A
CN111553021A CN202010340486.9A CN202010340486A CN111553021A CN 111553021 A CN111553021 A CN 111553021A CN 202010340486 A CN202010340486 A CN 202010340486A CN 111553021 A CN111553021 A CN 111553021A
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王刚
张文康
孙峥淏
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Guizhou Institute of Technology
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Abstract

The invention discloses a design method of an active suspension system based on a cascade disturbance observer, which comprises the following steps: the method comprises the following steps: establishing an active suspension system model, and obtaining a sprung mass dynamic model of the system as follows:
Figure DDA0002468354510000011
step two: designing an active suspension active disturbance rejection control scheme based on a cascade disturbance observer; aiming at an 1/4 vehicle active suspension system, the finite time stability of the system is satisfied by an active disturbance rejection control scheme based on a cascade disturbance observer and a supercoiling algorithm; using a cascaded disturbance observer instead of the conventional oneThe linear expansion state observer can obtain accurate observation precision of limited time; the active suspension controller designed by the method can remarkably improve the vibration reduction performance of an active suspension system, and the cascade disturbance observer structure does not need excessive model information and observation bandwidth, has better robustness and convergence precision, and can provide theoretical and experimental references for active disturbance rejection control research of the active suspension.

Description

Design method of active suspension system based on cascade disturbance observer
Technical Field
The invention relates to a control method of an automobile active suspension, in particular to a design method of an active suspension system based on a cascade disturbance observer.
Background
An active suspension system is an important vibration isolation element of an automobile and has gained a lot of attention, the design of a control algorithm is crucial in the active suspension control research, and the research of theory and experiment is an essential link in order to ensure the stability and comfort of the system;
in the design process of the existing active suspension system, the parameter activeness, unknown nonlinear dynamics and uncertainty of a model generally exist; the model parameters of the system need to be measured before design, more time and cost are spent, the measurement precision cannot reach the standard, part of nonlinear dynamics is difficult to measure, and the control precision, the vibration reduction effect, the comfort and the like of the designed active suspension system cannot well meet the design requirements; in addition, in the conventional active disturbance rejection control scheme, only a linear extended state observer is adopted, the limited time convergence performance cannot be obtained, and the observation bandwidth is limited by hardware equipment and cannot be increased randomly, so that the interference rejection performance is poor;
therefore, an effective robust observer design scheme is urgently needed in the design process of the active suspension system, and the centralized uncertainty of the system can be accurately compensated and eliminated without increasing the observation bandwidth, so that the model-free finite time control effect is achieved.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a design method of an active suspension system based on a cascade disturbance observer, aiming at 1/4 main active suspension system,
the finite time stability of the system is met by an active disturbance rejection control scheme based on a cascade disturbance observer and combining a supercoiling algorithm, a traditional linear expansion state observer is replaced by the cascade disturbance observer, the finite time zero error observation precision can be obtained, the effect of improving the vibration damping performance of the active suspension system is obviously achieved, excessive model information is not needed for a control structure, better robustness is achieved, and reference is provided for the research of the active suspension system.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
a design method of an active suspension system based on a cascade disturbance observer, the design method comprising the following steps:
the method comprises the following steps: building active suspension system model
Based on an 1/4 vehicle active suspension system, an active suspension system model is established, and the dynamic relation of the sprung mass of the system model is obtained as follows:
Figure BDA0002468354490000024
the built system model comprises a sprung mass layer, a motor drive active suspension layer, an unsprung mass layer and a tire layer;
step two: a cascade interference observer is added into an active suspension system model to design an active suspension system capable of realizing finite time convergence and active disturbance rejection performance, wherein the cascade interference observer consists of an inner loop observer and an outer loop observer, and the method comprises the following steps:
s1, selecting a state variable x of a system on the basis of an active suspension system model1＝zs，
Figure BDA0002468354490000021
x3P, dynamic model of sprung mass
Figure BDA0002468354490000022
Rewritten as the following state space equation:
Figure BDA0002468354490000023
wherein: x is the number of1Representing the vertical displacement of the sprung mass, x2Denotes x1First derivative of (a), x3Which represents the total uncertainty of the system,
Figure BDA0002468354490000031
representing the rate of change of the uncertainty, b representing the inverse of the nominal sprung mass, u representing the motor output force,
Figure BDA0002468354490000032
a derivative representing the uncertainty in the concentration;
s2, designing an inner loop observer of the cascading disturbance observer on the basis of an active suspension system model, wherein the inner loop observer actively estimates and inhibits external disturbance, unknown nonlinear dynamics and uncertainty of the active suspension system;
s3, after the inner loop observer is set, an outer loop observer of the cascading disturbance observer is further designed, and the outer loop observer can further reduce the residual observation error under the condition that the bandwidth of the inner loop observer is not increased;
s4, after the outer ring observer is arranged, a controller of the cascade disturbance observer is further designed through a supercoiling algorithm, and the supercoiling algorithm is designed at a control end to ensure the limited time stability of the active suspension system;
and S5, verifying the effectiveness of the active suspension system.
Further, the inner loop observer uses a topological state observer, and the outer loop observer uses a high-order sliding mode observer.
Further, the step one of the concrete steps of the active suspension system model building includes:
s1, arranging in an active suspension system model: mass of sprung mass layer is ms(ii) a The active control force u of the motor-driven active suspension layer is generated by a servo motor, and the spring force of the suspension is FsDamping force of suspension FdMass of unsprung mass layer is mu(ii) a Simplifying the tyre components of the tyre layer into a parallel distributed spring and damper with the stress of F respectivelytAnd Fb(ii) a Vertical displacement of sprung mass zsVertical displacement of unsprung mass zuThe vertical excitation displacement of the ground is zrThe vertical displacement of each part is measured by an encoder, the vertical acceleration of the sprung mass is measured by an accelerometer, and the vertical excitation of the ground is measured byA servo motor;
s2, the dynamic differential equation of the active suspension system model can be expressed as:
Figure BDA0002468354490000041
wherein:
Figure BDA0002468354490000042
Figure BDA0002468354490000043
is a time-varying unknown parameter that is,
Figure BDA0002468354490000044
a nominal portion of the sprung mass is shown,
Figure BDA0002468354490000045
is sprung mass acceleration;
s3, when the active suspension system is disturbed by the quality parameters, rewriting the formula (2) as follows:
Figure BDA0002468354490000046
the centralized uncertainty of the system is defined as:
Figure BDA0002468354490000047
wherein:
Figure BDA0002468354490000048
representing the inverse of the nominal sprung mass, p being the central uncertainty of the system, FΔIn order for the external interference to be unknown,
Figure BDA0002468354490000049
is the sprung mass vertical acceleration;
the sprung mass dynamics of the resulting system are:
Figure BDA00024683544900000410
wherein
Figure BDA00024683544900000411
For sprung mass acceleration, ρ is compensated with a cascaded observer and the controlled system equation (5) is guaranteed to satisfy the finite time stability, i.e. within a finite time
Figure BDA00024683544900000412
Further, the controlled system formula (5) has the following properties and theorem:
(1) attribute 1: the active suspension system is a bounded input and bounded state system, and the first derivative of the input is bounded;
(2) attribute 2: the collective uncertainty ρ of the system is unknown, but it is continuously derivable with respect to Lipschitz, i.e.
Figure BDA00024683544900000413
Wherein the parameter L can be determined experimentally;
(3) theorem 1: the following second order systems exist:
Figure BDA00024683544900000414
if c is1> 0 and c2> 0, the trajectory x of the system1、x2、
Figure BDA0002468354490000051
Convergence to zero point within a finite time, the convergence time t < 2V12(x0) Y, where x0Representing the initial state of the system, gamma being dependent on a parameter c1And c2V (x) is a strict Lyapunov function and satisfies
Figure BDA0002468354490000052
In the formula c1And c2Is two normalCounting;
(4) theorem 2: the following high-order systems exist:
Figure BDA0002468354490000053
wherein: x is the number ofiRepresenting the state of the system, wherein n is the order of the system, | omega | < L, and L is a bounded normal number;
designing a high-order sliding mode observer by using an equation (7) as follows:
Figure BDA0002468354490000054
wherein:
Figure BDA0002468354490000055
is xiThe estimated amount of (a) is,
Figure BDA0002468354490000056
sign represents a sign function; if the gain kiSatisfy the requirement of
Figure BDA0002468354490000057
k31.1L, the above-described high-order sliding-mode observer is time-limited accurate.
Further, the specific steps of designing the inner loop observer in step two S2 include:
(1) firstly, designing a centralized uncertainty rho of an inner loop observer estimation system, and defining a state observer as follows:
Figure BDA0002468354490000058
wherein:
Figure BDA00024683544900000514
is the bandwidth of the state observer,
Figure BDA0002468354490000059
is xiI is 1,2,3,
Figure BDA00024683544900000510
represents the inverse of the nominal sprung mass, u being the control input;
(2) subtracting equation (1) from equation (9) yields the following observed error dynamics:
Figure BDA00024683544900000511
wherein:
Figure BDA00024683544900000512
i＝1,2,3，eiwhich is indicative of an error in the observation,
Figure BDA00024683544900000513
a derivative representing the uncertainty in the concentration;
(3) order to
Figure BDA00024683544900000615
When i is 1,2,3, we can get:
Figure BDA0002468354490000061
wherein:
Figure BDA0002468354490000062
further, in the formula (11), a constant σ existsi> 0 and finite time T1> 0, for arbitrarily bounded
Figure BDA0002468354490000063
If T > T1And
Figure BDA00024683544900000616
when there is a currenti(t)|≤σiWherein i is 1,2,3,
Figure BDA00024683544900000617
k is not less than 3 and is an integer, the error isThe difference will be in a finite time T1Internally converge to
Figure BDA00024683544900000618
Wherein: o (-) represents a direct scale factor,
Figure BDA00024683544900000619
is the bandwidth of the state observer.
Further, the designing step of the outer loop observer in step two S3 includes:
(1) order to
Figure BDA0002468354490000064
un＝uc+usWherein
Figure BDA0002468354490000065
Figure BDA0002468354490000066
Measured by an inner loop observer, formula (1) was substituted to obtain:
Figure BDA0002468354490000067
wherein: u. ofsFor the finite time compensation control law to be designed,
Figure BDA0002468354490000068
is the observation error of the inner loop observer and satisfies the continuously-derivable Lipschitz condition, i.e.
Figure BDA0002468354490000069
M is an
Figure BDA00024683544900000610
A parameter that is positively correlated;
(2) order to
Figure BDA00024683544900000611
Can obtain the product
Figure BDA00024683544900000612
(3) Applying a high order sliding mode observer as in equation (14) to the residual
Figure BDA00024683544900001410
And (3) estimating:
Figure BDA00024683544900000614
wherein: z is a radical of1、z2、z3Is an estimator of the observer, k1、k2、k3To observer gain, x1Has an estimation error of
Figure BDA0002468354490000071
(4) Definition of
Figure BDA0002468354490000072
Then the observed error dynamics can be obtained:
Figure BDA0002468354490000073
wherein:
Figure BDA0002468354490000074
is an error variable, k, of a higher order sliding mode observer1、k2、k3Is the observer gain;
(5) according to theorem 2, if the observed gain is chosen to be
Figure BDA0002468354490000075
k31.1M, then
Figure BDA0002468354490000076
Will converge to zero within a finite time.
Further, the specific steps of the controller design in step two S4 include:
(1) let us＝ut-z3Alternatively, formula (12) may be:
Figure BDA0002468354490000077
wherein: u. oftIn order to be a superspiral control law,
Figure BDA0002468354490000078
estimating an error for a high-order sliding mode observer;
(2) according to theorem 2, there is a finite time
Figure BDA0002468354490000079
Equation (16) will become a second order integration chain as follows:
Figure BDA00024683544900000710
(3) applying theorem 1 to design control law u of integral chaintThe finite time stability of the system can be satisfied, and the following control law u is designedt：
Figure BDA00024683544900000711
Wherein: c. C1And c2Is any positive parameter, and upsilon is an integral part of a control law;
(4) substituting the control law (18) into the system (17) yields:
Figure BDA00024683544900000712
(5) according to theorem 1, x2、υ、
Figure BDA00024683544900000713
Will converge to zero in a limited time, i.e. satisfy
Figure BDA00024683544900000714
The limited time stability of the system can be guaranteed.
Further, the design method further includes a step S5 of verifying the effectiveness of the active suspension system, which includes the following specific steps:
s1, square wave signal excitation experiments prove that the control method obtains the minimum acceleration amplitude value, so that the vibration reduction performance of the system is improved;
s2, sine signal excitation, and experiments prove that the control method obtains the minimum acceleration amplitude under the same observer bandwidth, the vibration reduction effect is superior to the traditional ADRC and LQR control, and the dynamic stroke of a suspension and the dynamic stroke of a tire are smaller than the passive control, so the overall performance is improved;
s3, analyzing results, wherein the results show that the acceleration of the control method is reduced by 69% under square wave excitation relative to ADRC control; under sinusoidal excitation, the acceleration of the control method is reduced by 82% compared with ADRC control; the comfort performance and the vibration damping performance of the suspension are improved, and the experimental result is in accordance with the theoretical analysis, so that the sprung mass acceleration of the active suspension system is reduced to zero in a limited time theoretically under the active suspension active disturbance rejection control scheme based on the cascade disturbance observer.
The invention has the beneficial effects that: the invention provides a design method of an active suspension system based on a cascade disturbance observer, and compared with the prior art, the design method has the following improvement:
(1) aiming at an 1/4 vehicle active suspension system, an active suspension Active Disturbance Rejection (ADRC) control scheme based on a Cascade Disturbance Observer (CDO) is designed, and compared with the traditional ADRC control, the CDO active suspension ADRC scheme can accurately compensate the unknown dynamics of the active suspension system without increasing the observation bandwidth, so that higher control precision and limited time stability are obtained;
(2) experiments show that under different interference excitations, the acceleration root mean square value of the control scheme designed by the invention under square wave excitation is respectively reduced by 69% and 87%, and the acceleration root mean square value under sine excitation is respectively reduced by 82% and 89%, so that the control scheme designed by the invention is obviously superior to the traditional ADRC and LQR control;
(3) the 1/4 vehicle active suspension system designed by the control method provided by the invention has the advantages that the vehicle body vertical acceleration is remarkably reduced (as shown in fig. 6 and 10), and the suspension dynamic stroke and the tire dynamic stroke are also smaller than the maximum limit value of 10mm (as shown in fig. 7, 8, 11 and 12), so that the 1/4 vehicle active suspension system designed by the invention has the advantages of good comfort, strong robustness and limited time stability.
Drawings
Fig. 1 is a diagram of an active suspension system model according to the present invention.
Fig. 2 is a control flow chart of a conventional ADRC control scheme of embodiment 1 of the present invention.
Fig. 3 is a control flow chart of the ADRC control scheme based on CDO in embodiment 1 of the present invention.
Fig. 4 is a diagram of a square wave signal for road surface excitation in the square wave signal excitation experiment in embodiment 2 of the present invention.
Fig. 5 is a diagram of the sprung mass acceleration signal of the square wave signal excitation experiment in embodiment 2 of the invention.
Fig. 6 is a diagram of a test signal of a suspension dynamic stroke in a square wave signal excitation experiment in embodiment 2 of the invention.
Fig. 7 is a signal diagram of a tire dynamic stroke test in a square wave signal excitation experiment in embodiment 2 of the invention.
Fig. 8 is a motor control force diagram of a square wave signal excitation experiment in embodiment 2 of the present invention.
Fig. 9 is a diagram of sprung mass acceleration signals from a sinusoidal signal excitation experiment in embodiment 2 of the present invention.
Fig. 10 is a signal diagram of a suspension dynamic stroke test in a sine signal excitation experiment in embodiment 2 of the invention.
FIG. 11 is a signal diagram of a tire dynamic stroke test in a sinusoidal signal excitation experiment of example 2 of the present invention.
Fig. 12 is a motor control force diagram of a sine signal excitation experiment in embodiment 2 of the present 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. 1-12, a method for designing an active suspension system based on a cascaded disturbance observer, the method comprising the steps of:
the method comprises the following steps: building active suspension system model
Based on an 1/4 vehicle active suspension system, an active suspension system model is established, and the dynamic relation of the sprung mass of the system model is obtained as follows:
Figure BDA0002468354490000101
the built system model comprises a spring mass layer, a motor drive active suspension layer, an unsprung mass layer and a tire layer;
the specific process for building the active suspension system model comprises the following steps:
s1, setting in an active suspension system model (shown in figure 1): mass of sprung mass layer is ms(ii) a The active control force u of the motor-driven active suspension layer is generated by a servo motor, and the spring force of the suspension is FsDamping force of suspension FdThe spring mass of the unsprung mass layer is mu(ii) a Simplifying the tyre components of the tyre layer into a parallel distributed spring and damper with the stress of F respectivelytAnd Fb(ii) a Vertical displacement of sprung mass zsVertical displacement of unsprung mass zuThe vertical excitation displacement of the ground is zrThe vertical displacement of each part is measured by an encoder, the vertical acceleration of the sprung mass is measured by an accelerometer, and the vertical excitation of the ground is simulated by a servo motor;
s2, the dynamic differential equation of the active suspension system model can be expressed as:
Figure BDA0002468354490000111
in the present active suspension system model, the sprung mass is generally a function of load and number of passengersSo that it can be decomposed into
Figure BDA0002468354490000112
Wherein
Figure BDA0002468354490000113
Is a time-varying unknown parameter
Figure BDA0002468354490000114
Representing a nominal portion of sprung mass;
s3, when the active suspension system is disturbed by the mass parameter, the equation (2) is rewritten as follows:
Figure BDA0002468354490000115
the centralized uncertainty of the system is defined as:
Figure BDA0002468354490000116
wherein:
Figure BDA0002468354490000117
representing the inverse of the nominal sprung mass, p being the central uncertainty of the system, FΔIn order for the external interference to be unknown,
Figure BDA0002468354490000118
is the sprung mass vertical acceleration;
the sprung mass dynamics of the resulting system are:
Figure BDA0002468354490000119
wherein:
Figure BDA00024683544900001110
for sprung mass acceleration, ρ is compensated with a cascaded observer, ensuring that the controlled system equation (5) meets the finite time stability, i.e. within a finite time
Figure BDA00024683544900001111
The partial attributes and theorem existing in the controlled system formula (5) are as follows:
(1) attribute 1: the active suspension system is a bounded input and a bounded state, and the derivative of the input is bounded;
(2) attribute 2: the collective uncertainty ρ of the system is unknown, but it is continuously derivable with respect to Lipschitz, i.e.
Figure BDA00024683544900001112
The parameter L can be set through experiments;
(3) theorem 1: the controlled system formula (5) has the following second-order system:
Figure BDA0002468354490000121
if c is1> 0 and c2> 0, the trajectory x of the system1、x2、
Figure BDA0002468354490000122
Convergence to zero point within a finite time, the convergence time t < 2V1/2(x0) Y, where x0Representing the initial state of the system, gamma being dependent on a parameter c1And c2V (x) is a strict Lyapunov function and satisfies
Figure BDA0002468354490000123
In the formula c1And c2Are two normal numbers;
(4) theorem 2: the controlled system formula (5) has the following high-order system:
Figure BDA0002468354490000124
wherein: x is the number ofiAnd (3) representing the state of the system, wherein n is the order of the system, | omega | is less than or equal to L, and L is a bounded normal number.
Designing a high-order sliding mode observer (HOSMO) by using the formula (7) as follows:
Figure BDA0002468354490000125
wherein:
Figure BDA0002468354490000126
is xiThe estimated amount of (a) is,
Figure BDA0002468354490000127
sign represents a sign function; if the gain kiSatisfy the requirement of
Figure BDA0002468354490000128
k31.1L, the above-described high-order sliding-mode observer is time-limited accurate.
Step two: adding a cascade disturbance observer into an active suspension system model to design an active suspension system capable of realizing finite time convergence and active disturbance rejection control performance, wherein the cascade disturbance observer is composed of an inner ring observer and an outer ring observer, the inner ring observer uses a topological state observer, and the outer ring observer uses a high-order sliding mode observer, and the method comprises the following steps:
s1, selecting the state variable of the system as x1＝zs，
Figure BDA0002468354490000129
x3P, dynamic model of sprung mass
Figure BDA00024683544900001210
Rewritten as the following state space equation:
Figure BDA0002468354490000131
wherein: x is the number of1Representing the vertical displacement of the sprung mass, x2Denotes x1First derivative of (a), x3Which represents the total uncertainty of the system,
Figure BDA0002468354490000132
representing the rate of change of the uncertainty, b representing the derivative of the nominal sprung mass, u representing the motor output force,
Figure BDA0002468354490000133
the derivative of the uncertainty in the concentration is represented.
S2, designing relevant parameters of an inner ring observer of the cascade observer on the basis of an active suspension system model, wherein the specific process is as follows:
(1) first, an inner loop observer is designed to estimate the central uncertainty ρ of the system, defining the following Linear Extended State Observer (LESO):
Figure BDA0002468354490000134
wherein:
Figure BDA00024683544900001313
is the bandwidth of the state observer,
Figure BDA0002468354490000135
is xiI is 1,2,3,
Figure BDA0002468354490000136
represents the inverse of the nominal sprung mass, u being the control input;
(2) subtracting equation (1) from equation (9) yields the following observed error dynamics:
Figure BDA0002468354490000137
wherein:
Figure BDA0002468354490000138
i＝1,2,3，eiwhich is indicative of an error in the observation,
Figure BDA0002468354490000139
derivation representing uncertainty in concentrationCounting;
(3) order to
Figure BDA00024683544900001312
When i is 1,2,3, we can get:
Figure BDA00024683544900001310
wherein:
Figure BDA00024683544900001311
the following theorem exists in equation (11): exists with a constant σi> 0 and finite time T1> 0, for arbitrarily bounded
Figure BDA0002468354490000141
If T > T1And
Figure BDA00024683544900001412
when there is a currenti(t)|≤σiWherein i is 1,2,3,
Figure BDA00024683544900001411
k is an integer greater than or equal to 3, the error will be within the finite time T1Then converge to
Figure BDA00024683544900001413
O (-) represents a direct scale factor,
Figure BDA00024683544900001414
is the bandwidth of the state observer.
In the step, the centralized uncertain dynamics can be roughly estimated by adopting the LESO, so that the observation error is converged to a smaller boundary, and the unknown dynamics of the control system is compensated; in LESO, by increasing the observation bandwidth
Figure BDA00024683544900001415
The observation error can be reduced, but the observation bandwidth is limited by the noise of the sensor and the sampling frequency, so the observation bandwidth is not suitableAnd if the amplitude is too large, in order to further improve the observation precision and obtain better vibration reduction performance, a high-order sliding mode observer (HOSMO) is adopted to perform accurate nonlinear compensation.
S3, after designing the inner loop observer, further designing relevant parameters of the outer loop observer of the cascade observer, wherein the specific process is as follows:
(1) order to
Figure BDA0002468354490000142
un＝uc+usWherein
Figure BDA0002468354490000143
Figure BDA0002468354490000144
Measured by an inner loop observer, formula (1) was substituted to obtain:
Figure BDA0002468354490000145
wherein: u. ofsFor a finite time compensation control law to be designed, e3Is the observation error of the inner loop observer and satisfies the continuously-derivable Lipschitz condition, i.e.
Figure BDA0002468354490000146
M is an
Figure BDA0002468354490000147
A parameter that is positively correlated;
(2) order to
Figure BDA0002468354490000148
Can obtain the product
Figure BDA0002468354490000149
(3) Applying a high order sliding mode observer as in equation (14) to the residual
Figure BDA00024683544900001410
And (3) estimating:
Figure BDA0002468354490000151
wherein: z is a radical of1、z2、z3Is the state of the observer, k1、k2、k3To observer gain, x1Has an estimation error of
Figure BDA0002468354490000152
(4) Order to
Figure BDA0002468354490000153
Then the observed error dynamics can be obtained:
Figure BDA0002468354490000154
wherein:
Figure BDA0002468354490000155
is an error variable, k, of a higher order sliding mode observer1、k2、k3Is the observer gain;
(5) according to theorem 2, if the observed gain is chosen to be
Figure BDA0002468354490000156
k31.1M, then ei(i ═ 1,2,3) will converge to zero in a finite time;
the step of applying the observer of the outer ring can further compensate the estimation error caused by the observer of the inner ring, thereby accurately compensating the unknown nonlinear dynamics of the system, and because the observation error generated by the observer of the inner ring is smaller, the adoption of a high-order sliding mode observer (HOSMO) as the observer of the outer ring has the advantages that no overlarge observation gain is needed, and the generation of obvious sliding mode buffeting is avoided; further, the controller of the cascaded disturbance observer is designed by utilizing a supercoiled algorithm (STA) in the next step to meet the limited time stability of the system.
S4, designing parameters of the cascaded observer controller, wherein the specific process is as follows:
(1) let us＝ut-z3Alternatively, formula (12) may be:
Figure BDA0002468354490000157
wherein: u. oftIn order to be a superspiral control law,
Figure BDA0002468354490000158
estimating an error for a high-order sliding mode observer;
(2) according to theorem 2, there is a finite time
Figure BDA0002468354490000159
The system (16) therefore becomes a second order integration chain as follows:
Figure BDA0002468354490000161
(3) applying theorem 1 to design control law u of integral chaintThe finite time stability of the system can be satisfied, and the following control law u is selectedt：
Figure BDA0002468354490000162
Wherein: c. C1And c2For any positive parameter, v is the integral part of the control law.
(4) Substituting the controller (18) into the system (17) can result in:
Figure BDA0002468354490000163
(5) according to theorem 1, x2And
Figure BDA0002468354490000164
will converge to zero in a limited time, i.e. satisfy
Figure BDA0002468354490000165
The limited time stability of the system can be guaranteed. Thus, under the CDO-based ADRC scheme, the acceleration of the active suspension system will theoretically decrease to zero in a finite time.
Through the establishment and derivation processes of the control method, a cascaded interference observer is constructed in the proposed active disturbance rejection design scheme; the cascaded disturbance observer consists of an inner loop observer and an outer loop observer; the inner loop observer uses a linear expansion state observer, and the outer loop observer uses a high-order sliding mode observer; the inner loop observer actively estimates and suppresses concentrated external disturbances, unknown nonlinear dynamics and uncertainties of the active suspension system; the outer loop observer can further reduce the remaining observation error without increasing the bandwidth of the inner loop observer; and designing a supercoiling algorithm at a control end to ensure the limited time stability of the active suspension system.
S5, comparison of technical schemes (example 1):
the control scheme of the conventional ADRC and the control scheme of the CDO-based active suspension ADRC of the present invention:
(1) as shown in fig. 2, only one Linear Extended State Observer (LESO) is used to observe the unknown dynamics of the system, and the controller adopts a conventional Proportional Derivative (PD) controller, so the control accuracy and convergence accuracy of the system are not high;
(2) the control scheme of the active suspension ADRC based on the CDO is shown in figure 3, and the scheme is based on the traditional LESO, an observer of an outer ring can be applied to further compensate estimation errors caused by an inner ring observer LESO, so that unknown nonlinear dynamics of a system can be accurately compensated, and the errors are converged to zero; secondly, different from the traditional PD controller, the supercoiled controller can ensure the finite time convergence of the system state, and further improves the robustness and the steady-state performance; meanwhile, because the observation error generated by the inner loop observer is smaller, the adoption of the HOSMO as the outer loop observer has the advantages that excessive observation gain is not needed, and obvious sliding mode buffeting is avoided;
through comparison of the technical schemes, compared with the traditional technical scheme of the ADRC based on the LESO, the technical scheme provided by the invention has the advantage that the limited time convergence can be met under the condition that the observation bandwidth is not increased, and further illustrates the feasibility of the technical scheme provided by the invention.
Step three, experimental verification and result analysis (example 2):
in order to verify and research the effectiveness of the control scheme of the invention, a hardware loop experiment is carried out by applying a two-degree-of-freedom flexible active suspension prototype, wherein the sampling frequency is 1000Hz, and the bandwidth of an observer is taken
Figure BDA0002468354490000172
The test time was 15s, the state of each part was measured by the encoder, and the sprung mass velocity was obtained using a low pass filter. To illustrate the uniqueness of the control scheme of the present invention, it is compared to a conventional ADRC control scheme, taking the proportional, differential gain as kP＝401、kD40, limited by measurement noise and sampling frequency, the observation bandwidth is taken as
Figure BDA0002468354490000171
Since the observation bandwidth is sensitive to measurement noise, increasing the observation bandwidth does not improve the control performance.
In the experiment, the following four control schemes were compared, respectively: 1, passive control; 2 conventional LQR control; 3 conventional ADRC control; CDO-based ADRC control (CDO-ADRC), where the control gain of LQR is K ═ 24.6648.87-0.473.68.
S1. Square wave signal excitation experiment
After test setting according to experiments, taking L as 30 and M as 10;
(1) firstly, testing by using a square wave signal with the amplitude of 0.2cm, wherein the actually generated waveform is shown in figure 4;
(2) the impact resistance of the system can be verified by using the square wave signal, and the test results are shown in fig. 5-8:
in the evaluation of the control performance of the active suspension, the magnitude and root mean square value of the acceleration of the sprung mass (vehicle body) are closely related to the comfort of the vehicle, and as can be seen from fig. 5, the CDO-ADRC control scheme provided by the invention achieves the minimum acceleration amplitude value under the condition of not needing detailed information of a model and having the same observer bandwidth, so that the vibration damping performance of the system is greatly improved; furthermore, to ensure the safety performance of the system, the suspension dynamic stroke and tire dynamic stroke waveforms are shown in fig. 6 and 7, respectively, both of which are less than the maximum limit ± 1 cm; FIG. 8 is a graph of the active control forces generated by the various control schemes, and it can be seen that the controller proposed herein has a weak buffeting that meets the actuator requirements.
S2. sine signal excitation experiment
The sine wave is z for simulating the road unevennessr(t) ═ hsin (2 pi ft), where h is 0.2cm, the excitation frequency is taken to be the natural frequency of the sprung mass, i.e. f is 3 Hz;
the experimental test results are shown in fig. 9-12, and it can be seen from the graphs that CDO-ADRC obtains the minimum acceleration amplitude under the same observer bandwidth, so the vibration reduction effect is obviously better than that of the traditional ADRC and LQR control; the suspension and tire stroke is also smaller than in passive control, so the overall performance is improved, and fig. 12 shows the control force of the motor required by each control scheme.
S3, result analysis
To quantify the control effect of each control scheme, the root mean square value (RMS) of the acceleration is calculated using the following formula:
Figure BDA0002468354490000191
where the excitation time is T-15 s, table 1 is the acceleration rms:
TABLE 1 suspension Performance index comparison
Figure BDA0002468354490000192
As can be seen from table 1:
(1) under square wave excitation, acceleration of ADRC control based on CDO decreased by 69% relative to ADRC control;
(2) acceleration for CDO-based ADRC control drops by 82% relative to ADRC control under sinusoidal excitation;
therefore, the comfort performance and the vibration damping performance of the suspension are greatly improved, and the experimental result is in accordance with the theoretical analysis, so that the effectiveness of the control scheme is verified.
Through the technical scheme and the embodiment, the effectiveness of the 1/4 vehicle main-driven suspension system based on the CDO-ADRC is proved. The following conclusions can be drawn by comparing theoretical analysis with experiments:
(1) according to the control scheme provided by the invention, the model parameters of the system do not need to be measured in advance, and compared with the traditional ADRC control, the ADRC adopting the CDO can obtain higher control precision and limited time stability under the condition of not increasing observation bandwidth;
(2) under different interference excitations, the control scheme designed by the invention is obviously superior to the traditional ADRC and LQR control, the mean square root value of the acceleration under square wave excitation is respectively reduced by 69 percent and 87 percent, and the mean square root value of the acceleration under sine excitation is respectively reduced by 82 percent and 89 percent, so the comfort performance is greatly improved, and meanwhile, the dynamic stroke of the suspension and the dynamic stroke of the tire also meet the requirements.
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 active suspension system based on a cascade disturbance observer is characterized by comprising the following steps:
the method comprises the following steps: building active suspension system model
Based on an 1/4 vehicle active suspension system, an active suspension system model is established, and the dynamic relation of the sprung mass of the system model is obtained as follows:
Figure FDA0002468354480000011
the built system model comprises a sprung mass layer, a motor drive active suspension layer, an unsprung mass layer and a tire layer;
step two: a cascade interference observer is added into an active suspension system model to design an active suspension system capable of realizing finite time convergence and active disturbance rejection performance, wherein the cascade interference observer consists of an inner loop observer and an outer loop observer, and the method comprises the following steps:
s1, selecting a state variable x of a system on the basis of an active suspension system model1＝zs，
Figure FDA0002468354480000012
x3P, dynamic model of sprung mass
Figure FDA0002468354480000013
Rewritten as the following state space equation:
Figure FDA0002468354480000014
wherein: x is the number of1Representing the vertical displacement of the sprung mass, x2Denotes x1First derivative of (a), x3Which represents the total uncertainty of the system,
Figure FDA0002468354480000015
representing the rate of change of the uncertainty, b representing the inverse of the nominal sprung mass, u representing the motor output force,
Figure FDA0002468354480000016
a derivative representing the uncertainty in the concentration;
s2, designing an inner loop observer of the cascading disturbance observer on the basis of an active suspension system model, wherein the inner loop observer actively estimates and inhibits external disturbance, unknown nonlinear dynamics and uncertainty of the active suspension system;
s3, after the inner loop observer is set, an outer loop observer of the cascading disturbance observer is further designed, and the outer loop observer can further reduce the residual observation error under the condition that the bandwidth of the inner loop observer is not increased;
s4, after the outer ring observer is arranged, a controller of the cascade disturbance observer is further designed through a supercoiling algorithm, and the supercoiling algorithm is designed at a control end to ensure the limited time stability of the active suspension system;
and S5, verifying the effectiveness of the active suspension system.
2. The design method of the active suspension system based on the cascade disturbance observer is characterized in that the inner loop observer uses a topological state observer, and the outer loop observer uses a high-order sliding mode observer according to claim 1.
3. The design method of the active suspension system based on the cascade disturbance observer as claimed in claim 2, wherein the step one of building the active suspension system model specifically comprises the steps of:
s1, arranging in an active suspension system model: mass of sprung mass layer is ms(ii) a The active control force u of the motor-driven active suspension layer is generated by a servo motor, and the spring force of the suspension is FsDamping force of suspension FdMass of unsprung mass layer is mu(ii) a Simplifying the tyre components of the tyre layer into a parallel distributed spring and damper with the stress of F respectivelytAnd Fb(ii) a Vertical displacement of sprung mass zsVertical displacement of unsprung mass zuThe vertical excitation displacement of the ground is zrThe vertical displacement of each part is measured by an encoder, the vertical acceleration of the sprung mass is measured by an accelerometer, and the vertical excitation of the ground is generated by a servo motor;
s2, the dynamic differential equation of the active suspension system model can be expressed as:
Figure FDA0002468354480000021
wherein:
Figure FDA0002468354480000031
Figure FDA0002468354480000032
is a time-varying unknown parameter that is,
Figure FDA0002468354480000033
a nominal portion of the sprung mass is shown,
Figure FDA0002468354480000034
representing sprung mass acceleration;
s3, when the active suspension system is disturbed by the quality parameters, rewriting the formula (2) as follows:
Figure FDA0002468354480000035
the centralized uncertainty of the system is defined as:
Figure FDA0002468354480000036
wherein:
Figure FDA0002468354480000037
representing the inverse of the nominal sprung mass, p being the central uncertainty of the system, FΔIn order for the external interference to be unknown,
Figure FDA0002468354480000038
is the sprung mass vertical acceleration;
the sprung mass dynamics of the resulting system are:
Figure FDA0002468354480000039
wherein
Figure FDA00024683544800000310
For sprung mass acceleration, ρ is compensated with a cascaded observer and the controlled system equation (5) is guaranteed to satisfy the finite time stability, i.e. within a finite time
Figure FDA00024683544800000311
4. The design method of the active suspension system based on the cascade disturbance observer is characterized in that the following properties and theorems exist in the controlled system formula (5):
(1) attribute 1: the active suspension system is a bounded input and bounded state system, and the first derivative of the input is bounded;
(2) attribute 2: the collective uncertainty ρ of the system is unknown, but it is continuously derivable with respect to Lipschitz, i.e.
Figure FDA00024683544800000312
Wherein the parameter L can be determined experimentally;
(3) theorem 1: the following second order systems exist:
Figure FDA00024683544800000313
if c is1> 0 and c2> 0, the trajectory x of the system1、x2、
Figure FDA00024683544800000314
Convergence to zero point within a finite time, the convergence time t < 2V1/2(x0) Y, where x0Representing the initial state of the system, gamma being dependent on a parameter c1And c2V (x) is a strict Lyapunov function and satisfies
Figure FDA0002468354480000041
In the formula c1And c2Are two normal numbers;
(4) theorem 2: the following high-order systems exist:
Figure FDA0002468354480000042
wherein: x is the number ofiRepresenting the state of the system, wherein n is the order of the system, | omega | < L, and L is a bounded normal number;
designing a high-order sliding mode observer by using an equation (7) as follows:
Figure FDA0002468354480000043
wherein:
Figure FDA0002468354480000044
is xiThe estimated amount of (a) is,
Figure FDA0002468354480000045
sign represents a sign function; if the gain kiSatisfy the requirement of
Figure FDA0002468354480000046
k31.1L, the above-described high-order sliding-mode observer is time-limited accurate.
5. The design method of the active suspension system based on the cascaded disturbance observer according to claim 4, wherein the step two S2 includes the following specific steps:
(1) firstly, designing a centralized uncertainty rho of an inner loop observer estimation system, and defining a state observer as follows:
Figure FDA0002468354480000047
wherein: theta is the bandwidth of the state observer,
Figure FDA0002468354480000048
is xiI is 1,2,3,
Figure FDA0002468354480000049
represents the inverse of the nominal sprung mass, u being the control input;
(2) subtracting equation (1) from equation (9) yields the following observed error dynamics:
Figure FDA00024683544800000410
wherein:
Figure FDA00024683544800000411
i＝1,2,3，eiwhich is indicative of an error in the observation,
Figure FDA00024683544800000412
a derivative representing the uncertainty in the concentration;
(3) order toi＝ei/θi-1And i is 1,2,3, then:
Figure FDA0002468354480000051
wherein:
Figure FDA0002468354480000052
6. the design method of active suspension system based on cascaded disturbance observer as claimed in claim 5, wherein in equation (11), there is constant σi> 0 and finite time T1> 0, for renWith intention of being bounded
Figure FDA0002468354480000053
If T > T1And when theta is greater than 0, has-i(t)|≤σiWhere i is 1,2,3, σi＝O(1/θk) K is an integer greater than or equal to 3, the error will be within a finite time T1Inner convergence to ei＝O(1/θk-i+1)；
Wherein: o (-) represents a direct scaling factor and θ is the bandwidth of the state observer.
7. The design method of the active suspension system based on the cascade disturbance observer as claimed in claim 5, wherein the design step of the outer loop observer in step two S3 includes:
(1) order to
Figure FDA0002468354480000054
un＝uc+usWherein
Figure FDA0002468354480000055
Figure FDA0002468354480000056
Measured by an inner loop observer, formula (1) was substituted to obtain:
Figure FDA0002468354480000057
wherein: u. ofsFor the finite time compensation control law to be designed,
Figure FDA0002468354480000058
is the observation error of the inner loop observer and satisfies the continuously-derivable Lipschitz condition, i.e.
Figure FDA0002468354480000059
M is an
Figure FDA00024683544800000510
A parameter that is positively correlated;
(2) order to
Figure FDA00024683544800000511
Can obtain the product
Figure FDA00024683544800000512
(3) Applying a high order sliding mode observer as in equation (14) to the residual
Figure FDA00024683544800000513
And (3) estimating:
Figure FDA0002468354480000061
wherein: z is a radical of1、z2、z3Is an estimator of the observer, k1、k2、k3To observer gain, x1Has an estimation error of
Figure FDA0002468354480000062
(4) Definition of
Figure FDA0002468354480000063
Then the observed error dynamics can be obtained:
Figure FDA0002468354480000064
wherein:
Figure FDA0002468354480000065
is an error variable, k, of a higher order sliding mode observer1、k2、k3Is the observer gain;
(5) according to theorem 2, if the observed gain is chosen to be
Figure FDA0002468354480000066
k31.1M, then
Figure FDA0002468354480000067
Will converge to zero within a finite time.
8. The method for designing an active suspension system based on a cascaded disturbance observer according to claim 7, wherein the controller design in step two S4 comprises the following specific steps:
(1) let us＝ut-z3Alternatively, formula (12) may be:
Figure FDA0002468354480000068
wherein u istIn order to be a superspiral control law,
Figure FDA0002468354480000069
estimating an error for a high-order sliding mode observer;
(2) according to theorem 2, there is a finite time
Figure FDA00024683544800000610
Equation (16) will become a second order integration chain as follows:
Figure FDA00024683544800000611
(3) applying theorem 1 to design control law u of integral chaintThe finite time stability of the system can be satisfied, and the following control law u is designedt：
Figure FDA0002468354480000071
Wherein: c. C1And c2Is any one ofPositive parameter upsilon is an integral part of a control law;
(4) substituting the control law (18) into the system (17) yields:
Figure FDA0002468354480000072
(5) according to theorem 1, x2、υ、
Figure FDA0002468354480000073
Will converge to zero in a limited time, i.e. satisfy
Figure FDA0002468354480000074
The limited time stability of the system can be guaranteed.
9. The design method of an active suspension system based on a cascaded disturbance observer according to claim 1, further comprising the step of verifying the validity of the active suspension system at step S5, wherein the specific process is as follows:
s1, square wave signal excitation experiments prove that the control method obtains the minimum acceleration amplitude value, so that the vibration reduction performance of the system is improved;
s2, sine signal excitation, and experiments prove that the control method obtains the minimum acceleration amplitude under the same observer bandwidth, the vibration reduction effect is superior to the traditional ADRC and LQR control, and the dynamic stroke of a suspension and the dynamic stroke of a tire are smaller than the passive control, so the overall performance is improved;
s3, analyzing results, wherein the results show that the acceleration of the control method is reduced by 69% under square wave excitation relative to ADRC control; under sinusoidal excitation, the acceleration of the control method is reduced by 82% compared with ADRC control; the comfort performance and the vibration damping performance of the suspension are improved, and the experimental result is in accordance with the theoretical analysis, so that the sprung mass acceleration of the active suspension system is reduced to zero in a limited time theoretically under the active suspension active disturbance rejection control scheme based on the cascade disturbance observer.
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