CN108681257B - Design method of controller of active anti-roll system - Google Patents

Design method of controller of active anti-roll system Download PDF

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CN108681257B
CN108681257B CN201810648774.3A CN201810648774A CN108681257B CN 108681257 B CN108681257 B CN 108681257B CN 201810648774 A CN201810648774 A CN 201810648774A CN 108681257 B CN108681257 B CN 108681257B
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CN108681257A (en
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孙浩
李晨鸣
赵韩
黄康
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Hefei University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60G—VEHICLE SUSPENSION ARRANGEMENTS
    • B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
    • B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
    • B60G17/016—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by their responsiveness, when the vehicle is travelling, to specific motion, a specific condition, or driver input
    • B60G17/0162—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by their responsiveness, when the vehicle is travelling, to specific motion, a specific condition, or driver input mainly during a motion involving steering operation, e.g. cornering, overtaking
    • B60G17/0163—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by their responsiveness, when the vehicle is travelling, to specific motion, a specific condition, or driver input mainly during a motion involving steering operation, e.g. cornering, overtaking the control involving steering geometry, e.g. four-wheel steering

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Abstract

The invention provides a design method of a controller of an active anti-roll system, which comprises the following steps: constructing a dynamic model of the active anti-roll system with parameter uncertainty; taking a target roll angle of the active roll preventing system as a performance constraint, and constructing a second-order constraint form of the target roll angle; designing a leakage type self-adaptive robust controller based on the constructed dynamic model and the second-order constraint form; performing stability analysis on the constructed adaptive robust controller; and adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect. The design method of the controller of the active anti-roll system can effectively process the influence of uncertainty of system parameters and external interference, simultaneously enables the system to quickly and stably control moment output accurately, and has better anti-roll characteristic and riding comfort.

Description

Design method of controller of active anti-roll system
Technical Field
The invention relates to the field of automobile active safety control, in particular to a design method of a controller of an active anti-roll system.
Background
When the automobile turns, under the action of centrifugal force, the automobile body can roll under lateral acceleration, accidents such as overturning are easily caused, the comfort of personnel in the automobile and the maneuverability of the automobile are reduced, and the safety factor is indirectly reduced. In order to reduce the side inclination of the automobile during turning, the passenger car is generally provided with a passive stabilizer bar at the bottom of the automobile body or the automobile frame, and two ends of the passive stabilizer bar are connected with a lower swing arm of a suspension or an upright post of a shock absorber. When the automobile rolls, the twisted stabilizer bar applies an anti-rolling moment to the automobile body, so that the possibility of rolling and overturning is reduced.
The passive stabilizer bar reduces roll to some extent, but cannot actively adjust the anti-roll moment and cannot completely eliminate roll. The active stabilizer bar system can adjust the exciter according to the signal data of lateral acceleration, roll angle, vehicle speed and the like obtained by feedback or calculation of the sensor by adopting a proper control method to output anti-roll moment with corresponding magnitude, has good anti-roll effect, and can improve the safety and the controllability of the vehicle and the riding comfort of people in the vehicle.
In order to solve the problem, researchers at home and abroad develop various control methods in turn, and have certain effects, such as PID control, linear feedback control, LQR (linear quadratic regulator) control, robust control and the like. The system is easy to vibrate under nonlinear disturbance by PID control and linear feedback control, the robustness of LQR control is not strong, and overshoot and unnecessary control consumption are easy to generate by robust control.
Therefore, it is highly desirable to provide a control scheme with high stability and robustness.
Disclosure of Invention
In view of the above technical problems, the present invention provides a method for designing a controller of an active anti-roll system, which can effectively handle the uncertainty of system parameters and the influence of external interference, and at the same time, make the system quickly and stably control the torque output accurately.
The technical scheme adopted by the invention is as follows:
the embodiment of the invention provides a design method of a controller of an active anti-roll system, which comprises the following steps:
constructing a dynamic model of the active anti-roll system with parameter uncertainty;
taking a target roll angle of the active roll preventing system as a performance constraint, and constructing a second-order constraint form of the target roll angle;
designing a leakage type self-adaptive robust controller based on the constructed dynamic model and the second-order constraint form;
performing stability analysis on the constructed adaptive robust controller;
and adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect.
Optionally, the constructing a dynamic model of the active anti-roll system with parameter uncertainty comprises:
constructing a dynamic model of the active anti-roll system shown in the following equation (1):
Figure BDA0001704155090000021
wherein the content of the first and second substances,
Figure BDA0001704155090000022
the moment of inertia of the sprung mass about the roll axis,
Figure BDA0001704155090000023
in order to damp the roll,
Figure BDA0001704155090000024
roll stiffness, MafFor anti-roll moment of the front wheel, MarFor the rear wheel anti-roll moment, msIs the center of mass of the vehicle body, hsIs the vertical distance of the center of mass from the roll axis, ayIn order to be the lateral acceleration,
Figure BDA0001704155090000025
the inclination angle of the vehicle body is the inclination angle,
Figure BDA0001704155090000026
in order to obtain the damping coefficient of the front suspension,
Figure BDA0001704155090000027
for the damping coefficient of the rear suspension,
Figure BDA0001704155090000028
the front and rear suspension stiffness respectively,
Figure BDA0001704155090000029
respectively the rigidity of the front and rear stabilizer bars;
based on the constructed kinetic model, constructing a standard kinetic model containing uncertain parameters shown in the following equation (2):
Figure BDA00017041550900000210
wherein t is a time variable, q is a generalized coordinate,
Figure BDA00017041550900000211
in the case of a speed in a broad sense,
Figure BDA00017041550900000212
in the case of a generalized acceleration,
Figure BDA00017041550900000213
sigma is an uncertainty parameter, and M is an inertia matrix of the active anti-roll system
Figure BDA00017041550900000214
C is the coriolis force/centrifugal force matrix of the active anti-roll system,
Figure BDA00017041550900000215
g is the gravity matrix of the active anti-roll system,
Figure BDA00017041550900000216
Figure BDA0001704155090000031
τ is control of the system, τ ═ Maf+Mar)；
The matrix of uncertainties of the constructed standard kinetic model is decomposed according to the following equations (3) to (5):
Figure BDA0001704155090000032
Figure BDA0001704155090000033
Figure BDA0001704155090000034
wherein the content of the first and second substances,
Figure BDA0001704155090000035
the uncertainty part of the inertia matrix, the Coriolis force/centrifugal force matrix and the gravity matrix of the active anti-roll system is Δ M (q, σ, t), Δ C (q, σ, t) and Δ G (q, σ, t).
Optionally, regarding a target roll angle of the active anti-roll system as a performance constraint, constructing a second-order constraint form of the target roll angle includes:
target roll angle of active roll prevention system
Figure BDA0001704155090000036
Is considered as a performance constraint and is written in the form shown in equation (6) below:
f(q，t)＝0 (6)
the first and second derivatives of equation (6) are derived to obtain the following equations (7) and (8):
Figure BDA0001704155090000037
Figure BDA0001704155090000038
wherein A is a constraint matrix; c is a first order constraint vector; b is a second order constraint vector.
Optionally, the designing a leakage-type adaptive robust controller based on the constructed dynamic model and the second-order constraint form specifically includes:
constructing a controller shown in the following equation (9) based on the constructed dynamic model and the second-order constraint form:
Figure BDA0001704155090000039
wherein the content of the first and second substances,
Figure BDA0001704155090000041
P1is the nominal control of the system, in equation (10)
Figure BDA0001704155090000042
The deterministic portions of the inertia matrix, the Coriolis force/centrifugal force matrix and the gravity matrix of the active anti-roll system in equations (3) to (5) respectively, and A, b is a constraint matrix and a second-order constraint vector obtained by derivation in equations (7) and (8);
Figure BDA0001704155090000043
P2is used for solving the condition that the initial condition of the system can not meet the performance constraint, kappa is an initial condition incompatible compensation parameter and is any positive number, P is any positive definite matrix, beta is the constraint tracking error of the system,
Figure BDA0001704155090000044
c is a first order constraint vector obtained by derivation in equation (7);
Figure BDA0001704155090000045
wherein the content of the first and second substances,
Figure BDA0001704155090000046
Figure BDA0001704155090000047
P3is used for solving the problem that the system has uncertainty, the pi function is the upper bound of the uncertainty of the system,
Figure BDA0001704155090000048
including as adaptive parameters
Figure BDA0001704155090000049
And xi is a control precision adjusting parameter.
Optionally, the adaptive parameter
Figure BDA00017041550900000410
The adaptation law determination is shown by the following equation (13):
Figure BDA00017041550900000411
wherein k is1，k2Parameters are adjusted for the adaptive law.
Optionally, the performing the stability analysis on the constructed adaptive robust controller includes:
the final stable bound of the constructed adaptive lyru controller was analyzed using the lyapunov function as shown in equation (14) below:
Figure BDA0001704155090000051
where P is a positive definite matrix, ρEAlpha is an upper bound parameter for uncertainty of the active anti-roll system, being any constant greater than-1.
Optionally, the analyzing the final stable boundary of the constructed adaptive law robust controller by using the lyapunov function shown in equation (14) specifically includes:
calculation of equation (14) yields the following formula (15):
Figure BDA0001704155090000052
wherein the content of the first and second substances,
Figure BDA0001704155090000053
Figure BDA0001704155090000054
k3＝1+ρE2；
the final stable limit of the active anti-roll system is obtained based on equation (15), and the trade-off parameter R is shown in equation (16) below:
Figure BDA0001704155090000055
the final consistent stable limit of the active anti-roll system is obtained based on equation (14), as shown in equation (17):
Figure BDA0001704155090000056
wherein the content of the first and second substances,
Figure BDA0001704155090000057
a lower limit value representing the size of the final uniform stability limit of the active anti-roll system,
Figure BDA0001704155090000058
λmin(P) represents the minimum eigenvalue, λ, of the positive definite matrix Pmax(P) represents the maximum eigenvalue of the positive definite matrix P;
according to the lyapunov theory of stability, the time for the active anti-roll system to reach the final stable limit can be obtained, as shown in the following formula (18):
Figure BDA0001704155090000061
where T denotes the time for the active anti-roll system to reach the final uniform stable limit, r denotes the initial state of the system,
Figure BDA0001704155090000062
is arbitrarily greater than
Figure BDA0001704155090000063
Positive number of (c).
Optionally, the adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect includes:
adjusting initial condition incompatible compensation parameters, adaptive law adjustment parameters and control precision adjustment parameters in the constructed adaptive law robust controller;
and analyzing whether the error between the actual roll angle and the target roll angle meets the preset error requirement or not based on the adjusted parameters.
The design method of the controller of the active anti-roll system provided by the embodiment of the invention comprises the steps of firstly, constructing a dynamic model of the active anti-roll system with uncertain parameters; secondly, taking a target roll angle of the active anti-roll system as a performance constraint, and constructing a second-order constraint form of the target roll angle; designing a leakage type adaptive robust controller based on the constructed dynamic model and the second-order constraint form; finally, performing stability analysis on the constructed adaptive robust controller; the main parameters in the constructed adaptive robust controller are adjusted, and the control effect is analyzed, so that the influence of uncertainty of system parameters and external interference can be effectively processed, the system can quickly and stably control moment output accurately, and the adaptive robust controller has good anti-roll characteristic and riding comfort.
Drawings
Fig. 1 is a schematic flow chart illustrating a method for designing a controller of an active anti-roll system according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of an anti-roll system according to an embodiment of the present invention;
fig. 3 is a schematic overall structure diagram of a controller according to an embodiment of the present invention;
fig. 4 is a schematic diagram illustrating a stability simulation of the anti-roll system according to the embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
Fig. 1 is a schematic flow chart of a method for designing a controller of an active anti-roll system according to an embodiment of the present invention. As shown in fig. 1, a method for designing a controller of an active anti-roll system according to an embodiment of the present invention includes the following steps:
s101, constructing a dynamic model of the active anti-roll system with parameter uncertainty;
s102, taking a target roll angle of the active roll preventing system as a performance constraint, and constructing a second-order constraint form of the target roll angle;
s103, designing a leakage type self-adaptive robust controller based on the constructed dynamic model and the second-order constraint form;
s104, performing stability analysis on the constructed adaptive robust controller;
and S105, adjusting main parameters in the constructed adaptive robust controller, and analyzing the control effect.
In the present invention, the dynamic model constructed in step S101 is the basis for the model-based adaptive robust controller design in step S103; the second-order form of the performance constraint constructed in step S102 is a final control target for the model-based adaptive robust controller design in step S103; step S104 is to analyze the stability of the adaptive robust controller designed in step S103 to ensure that the controller can realize the final stability of the active anti-roll system; step S105 is to analyze the influence of the main parameters in the adaptive robust controller designed in step S103 on the control effect.
Specifically, the step S101 of constructing a dynamic model of the active anti-roll system with parameter uncertainty includes:
constructing a dynamic model of the active anti-roll system shown in the following equation (1):
Figure BDA0001704155090000071
wherein the content of the first and second substances,
Figure BDA0001704155090000072
the moment of inertia of the sprung mass about the roll axis,
Figure BDA0001704155090000073
in order to damp the roll,
Figure BDA0001704155090000074
roll stiffness, MafFor anti-roll moment of the front wheel, MarFor the rear wheel anti-roll moment, msIs the center of mass of the vehicle body, hsIs the vertical distance of the center of mass from the roll axis, ayIn order to be the lateral acceleration,
Figure BDA0001704155090000081
the inclination angle of the vehicle body is the inclination angle,
Figure BDA0001704155090000082
in order to obtain the damping coefficient of the front suspension,
Figure BDA0001704155090000083
for the damping coefficient of the rear suspension,
Figure BDA0001704155090000084
the front and rear suspension stiffness respectively,
Figure BDA0001704155090000085
respectively the rigidity of the front and rear stabilizer bars;
based on the constructed kinetic model, constructing a standard kinetic model containing uncertain parameters shown in the following equation (2):
Figure BDA0001704155090000086
equation (2) above is performed in consideration of the uncertainty of the system, where t is a time variable, q is a generalized coordinate,
Figure BDA0001704155090000087
in the case of a speed in a broad sense,
Figure BDA0001704155090000088
in the case of a generalized acceleration,
Figure BDA0001704155090000089
sigma is an uncertainty parameter, and M is an inertia matrix of the active anti-roll system
Figure BDA00017041550900000810
C is the coriolis force/centrifugal force matrix of the active anti-roll system,
Figure BDA00017041550900000811
g is the gravity matrix of the active anti-roll system,
Figure BDA00017041550900000812
τ is control of the system, τ ═ Maf+Mar)；
The matrix of uncertainties of the constructed standard kinetic model is decomposed according to the following equations (3) to (5):
Figure BDA00017041550900000813
Figure BDA00017041550900000814
Figure BDA00017041550900000815
the above equations (3) to (5) are obtained by decomposing the matrix of uncertainties in the active roll prevention system due to the existence of parameter uncertainties, the purpose of the decomposition being to design corresponding control terms for the deterministic portion and the indeterminate portion of the active roll prevention system, respectively. Wherein the content of the first and second substances,
Figure BDA00017041550900000816
Figure BDA00017041550900000817
the uncertainty part of the inertia matrix, the Coriolis force/centrifugal force matrix and the gravity matrix of the active anti-roll system is Δ M (q, σ, t), Δ C (q, σ, t) and Δ G (q, σ, t).
Further, regarding the target roll angle of the active anti-roll system as a performance constraint in step S102, constructing a second-order constraint form of the target roll angle includes:
to target the control of an active anti-roll system (i.e. target roll angle)
Figure BDA00017041550900000818
Is considered as a performance constraint and is written in the form shown in equation (6) below:
f(q，t)＝0 (6)
the first and second derivatives of equation (6) are derived to obtain the following equations (7) and (8):
Figure BDA0001704155090000091
Figure BDA0001704155090000092
wherein A is a constraint matrix; c is a first order constraint vector; b is a second-order constraint vector, and equation (8) is the form of the second-order constraint matrix of the embodiment of the present invention.
Here, the lateral acceleration a to which the vehicle body is subjected is taken into accountyIs 6sin0.5tm/s2Target roll angle of the vehicle body
Figure BDA0001704155090000093
Then by derivation one can obtain:
Figure BDA0001704155090000094
Figure BDA0001704155090000095
thus, there are
Figure BDA0001704155090000096
These values are substituted into the controller design in step S103 to calculate the required control inputs.
Further, designing a leakage type adaptive law robust controller based on the constructed dynamic model and the second order constraint form in step S104 specifically includes:
constructing a controller shown in the following equation (9) based on the constructed dynamic model and the second-order constraint form:
Figure BDA0001704155090000101
wherein the content of the first and second substances,
Figure BDA0001704155090000102
P1is the nominal control of the system, the superscript "+" sign indicating the M-P of the matrixGeneralized inverse, of equation (10)
Figure BDA0001704155090000103
The deterministic portions of the inertia matrix, the Coriolis force/centrifugal force matrix and the gravity matrix of the active anti-roll system in equations (3) to (5) respectively, and A, b is a constraint matrix and a second-order constraint vector obtained by derivation in equations (7) and (8);
Figure BDA0001704155090000104
P2is used for solving the condition that the initial condition of the system can not meet the performance constraint, kappa is an initial condition incompatible compensation parameter and is any positive number, P is any positive definite matrix, beta is the constraint tracking error of the system,
Figure BDA0001704155090000105
c is a first order constraint vector obtained by derivation in equation (7);
Figure BDA0001704155090000106
wherein the content of the first and second substances,
Figure BDA0001704155090000107
(arbitrary positive real number)
Figure BDA0001704155090000108
P3Is used for solving the problem that the system has uncertainty, the pi function is the upper bound of the uncertainty of the system,
Figure BDA0001704155090000109
for adaptive parameters, adaptive parameters are designed
Figure BDA00017041550900001010
Is used to estimate the upper bound of the system uncertaintyAnd the parameters alpha and xi are control precision adjusting parameters.
In the embodiment of the invention, the adaptive parameters
Figure BDA0001704155090000111
The adaptation law determination is shown by the following equation (13):
Figure BDA0001704155090000112
the adaptation law shown in equation (13) is of the leaky type. When the initial error is large, the error is large,
Figure BDA0001704155090000113
then
Figure BDA0001704155090000114
Will continue to increase to compensate for system uncertainties; when the tracking error of the system becomes smaller and smaller
Figure BDA0001704155090000115
When the temperature of the water is higher than the set temperature,
Figure BDA0001704155090000116
it is continually reduced to avoid excessive control overhead of the system. Wherein k is1，k2Parameters are adjusted for the adaptive law.
Further, the stability analysis of the constructed adaptive robust controller in step S104 includes:
the final stable bound of the constructed adaptive lyru controller was analyzed using the lyapunov function as shown in equation (14) below:
Figure BDA0001704155090000117
where P is a positive definite matrix, ρEAlpha is an upper bound parameter for uncertainty of the active anti-roll system, being any constant greater than-1.
Specifically, the analyzing the consistent stable bound and the final consistent stable bound of the constructed adaptive law robust controller by using the lyapunov function shown in equation (14) specifically includes:
calculation of equation (14) yields the following formula (15):
Figure BDA0001704155090000118
wherein the content of the first and second substances,
Figure BDA0001704155090000119
Figure BDA00017041550900001110
k3＝1+ρE2；
obtaining a balance parameter R of the final consistent stable limit of the active anti-roll system based on the formula (15), and specifically, analyzing the formula (15) as follows:
by
Figure BDA00017041550900001111
The following can be obtained:
Figure BDA00017041550900001112
Figure BDA0001704155090000121
Figure BDA0001704155090000122
it follows that the active anti-roll system eventually conforms to a well-defined trade-off parameter R, as shown in equation (16) below:
Figure BDA0001704155090000123
and (3) obtaining the final consistent stable limit size of the active anti-roll system based on the formula (14), and specifically, analyzing the formula (14) as follows:
Figure BDA0001704155090000124
wherein λ ismin(P) represents the minimum eigenvalue, λ, of the positive definite matrix Pmax(P) represents the maximum eigenvalue of the positive definite matrix P.
Due to the fact that
Figure BDA0001704155090000125
Figure BDA0001704155090000126
Therefore, there are:
Figure BDA0001704155090000127
this gives:
Figure BDA0001704155090000128
Figure BDA0001704155090000131
according to the Lyapunov stability theory, the final consistent stable limit of the active anti-roll system can be obtained, as shown in the following formula (17):
Figure BDA0001704155090000132
according to the lyapunov theory of stability, the time for the active anti-roll system to reach the final stable limit can be obtained, as shown in the following formula (18):
Figure BDA0001704155090000133
where T denotes the time for the active anti-roll system to reach the final uniform stable limit, r denotes the initial state of the system,
Figure BDA0001704155090000134
is arbitrarily greater than
Figure BDA0001704155090000135
Positive number of (c). Further, the step S105 adjusts main parameters in the constructed adaptive robust controller, and analyzing the control effect includes:
an initial condition incompatibility compensation parameter kappa and an adaptive law adjustment parameter k in the constructed adaptive law robust controller1，2Adjusting the control precision adjusting parameter xi; and analyzing whether the error between the actual roll angle and the target roll angle meets the preset error requirement or not based on the adjusted parameters. Specifically, Matlab software can be used for performing performance simulation of the control system, whether the error between the actual roll angle and the target roll angle meets the preset error requirement is analyzed, if the preset error requirement is met, the process is ended, and if the preset error requirement is not met, the control parameters are continuously adjusted until the preset error requirement is met.
In the embodiment of the invention, the parameter kappa is related to the incompatibility problem of the compensation initial conditions, and the larger the value of kappa is, the better the effect is and the larger the corresponding control cost is; parameter k1，2Associated with the compensation uncertainty, which directly affects the size of the stability region, k, of the active anti-roll system1，2The larger the control performance is, the more accurate the control performance is, but the corresponding control cost is also larger; and xi prevents the situation that the control cost is too large when the error precision is very high, the larger the xi value is, the smaller the calculated amount of the controller is, the closer the xi value is to 0, the smaller the calculated amount of the controller is, and the better the control effect is. That is, the larger the value of the initial condition incompatible compensation parameter is, the better the control effect is, and the corresponding control isThe larger the manufacturing cost is; the larger the control precision adjusting parameter is, the more accurate the control performance is, but the larger the corresponding control cost is; the larger the value of the adaptive law adjusting parameter is, the smaller the calculated amount of the controller is, the closer the value is to 0, the smaller the calculated amount of the controller is, and the better the control effect is. The specific values of the parameters can be determined by a designer according to the actual control precision of the system. In an exemplary embodiment, the better control parameter values may be: k is 1, k1＝4，k2＝0.2，ξ＝0.0001。
The active anti-roll system shown in fig. 2 is the subject of control of the present invention. As shown in fig. 2, the system includes two stabilizer bars, a front stabilizer bar and a rear stabilizer bar, and a driving actuator, wherein the front driving actuator is integrated in the middle of the front stabilizer bar, and the rear driving actuator is integrated in the middle of the rear stabilizer bar. When the automobile turns and rolls, the active actuator outputs the rotating torque in the opposite direction, and the anti-rolling control target is realized.
Fig. 3 shows the overall structure of the controller of the present invention. As shown in FIG. 3, first, the nominal controller P of the system is written from the kinetic equation and the target trajectory1Then, a controller P for compensating the initial condition incompatibility problem is provided according to the error of the system2And then, providing a controller P for compensating the uncertainty of the system according to each function and parameter in the adaptive law3。
FIG. 4 shows a view at P1、P2And P3Under the cooperative control of the system, the roll angle of the vehicle body follows the simulation structure schematic diagram of the expected required track. The figure shows that the roll angle of the vehicle body can accurately, quickly and stably follow the expected track through the torque output by the controller under the condition that the system has uncertainty. Meanwhile, compared with the control mode of the LQR in the simulation, the method disclosed by the invention can be found to be more accurate and smooth, and the effectiveness and the superiority of the design method disclosed by the invention are proved.
The above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (3)

1. A design method of a controller of an active anti-roll system is characterized by comprising the following steps:
constructing a dynamic model of the active anti-roll system with parameter uncertainty;
taking a target roll angle of the active roll preventing system as a performance constraint, and constructing a second-order constraint form of the target roll angle;
designing a leakage type self-adaptive robust controller based on the constructed dynamic model and the second-order constraint form;
performing stability analysis on the constructed adaptive robust controller;
adjusting main parameters in the constructed adaptive robust controller, and analyzing a control effect;
the dynamic model for constructing the active anti-roll system with parameter uncertainty comprises the following steps:
constructing a dynamic model of the active anti-roll system shown in the following equation (1):
Figure FDA0002752230480000011
wherein the content of the first and second substances,
Figure FDA0002752230480000012
the moment of inertia of the sprung mass about the roll axis,
Figure FDA0002752230480000013
roll damping.
Figure FDA0002752230480000014
Roll stiffness, MafFor anti-roll moment of the front wheel, MarFor the rear wheel anti-roll moment, msIs the center of mass of the vehicle body, hsIs the vertical distance of the center of mass from the roll axis, ayIn order to be the lateral acceleration,
Figure FDA0002752230480000015
the inclination angle of the vehicle body is the inclination angle,
Figure FDA0002752230480000016
in order to obtain the damping coefficient of the front suspension,
Figure FDA0002752230480000017
for the damping coefficient of the rear suspension,
Figure FDA0002752230480000018
the front and rear suspension stiffness respectively,
Figure FDA0002752230480000019
respectively the rigidity of the front and rear stabilizer bars;
based on the constructed kinetic model, constructing a standard kinetic model containing uncertain parameters shown in the following equation (2):
Figure FDA00027522304800000110
wherein t is a time variable, q is a generalized coordinate,
Figure FDA00027522304800000111
Figure FDA00027522304800000112
in the case of a speed in a broad sense,
Figure FDA00027522304800000113
Figure FDA00027522304800000114
in the case of a generalized acceleration,
Figure FDA00027522304800000115
sigma is an uncertainty parameter, and M is an inertia matrix of the active anti-roll system
Figure FDA00027522304800000116
Figure FDA00027522304800000117
C is the coriolis force/centrifugal force matrix of the active anti-roll system,
Figure FDA00027522304800000118
g is the gravity matrix of the active anti-roll system,
Figure FDA00027522304800000119
Figure FDA00027522304800000120
τ is control of the system, τ ═ Maf+Mar)；
The matrix of uncertainties of the constructed standard kinetic model is decomposed according to the following equations (3) to (5):
Figure FDA0002752230480000021
Figure FDA0002752230480000022
Figure FDA0002752230480000023
wherein the content of the first and second substances,
Figure FDA0002752230480000024
determining parts of an inertia matrix, a Coriolis force/centrifugal force matrix and a gravity matrix of the active anti-roll system, wherein Δ M (q, sigma, t), Δ C (q, sigma, t) and Δ G (q, sigma, t) are uncertainty parts of the inertia matrix, the Coriolis force/centrifugal force matrix and the gravity matrix of the active anti-roll system;
the target roll angle of the active roll prevention system is regarded as performance constraint, and the construction of the second-order constraint form of the target roll angle comprises the following steps:
target roll angle of active roll prevention system
Figure FDA0002752230480000025
Is considered as a performance constraint and is written in the form shown in equation (6) below:
f(q，t)＝0 (6)
the first and second derivatives of equation (6) are derived to obtain the following equations (7) and (8):
Figure FDA0002752230480000026
Figure FDA0002752230480000027
wherein A is a constraint matrix; c is a first order constraint vector; b is a second order constraint vector;
the designing of the leakage type adaptive robust controller based on the constructed dynamic model and the second order constraint form specifically comprises the following steps:
constructing a controller shown in the following equation (9) based on the constructed dynamic model and the second-order constraint form:
Figure FDA0002752230480000028
wherein the content of the first and second substances,
Figure FDA0002752230480000031
P1is the nominal control of the system, in equation (10)
Figure FDA0002752230480000032
The deterministic portions of the inertia matrix, the Coriolis force/centrifugal force matrix and the gravity matrix of the active anti-roll system in equations (3) to (5) respectively, and A, b is a constraint matrix and a second-order constraint vector obtained by derivation in equations (7) and (8);
Figure FDA0002752230480000033
P2is used for solving the condition that the initial condition of the system can not meet the performance constraint, kappa is an initial condition incompatible compensation parameter and is any positive number, P is any positive definite matrix, beta is the constraint tracking error of the system,
Figure FDA0002752230480000034
Figure FDA0002752230480000035
c is a first order constraint vector obtained by derivation in equation (7);
Figure FDA0002752230480000036
wherein the content of the first and second substances,
Figure FDA0002752230480000037
Figure FDA0002752230480000038
P3is used for solving the problem that the system has uncertainty, the pi function is the upper bound of the uncertainty of the system,
Figure FDA0002752230480000039
including as adaptive parameters
Figure FDA00027522304800000310
Xi is a control precision adjusting parameter;
the adaptive parameter
Figure FDA00027522304800000312
The adaptation law determination is shown by the following equation (13):
Figure FDA00027522304800000311
wherein k is1，k2Adjusting parameters for an adaptive law;
the stability analysis of the constructed adaptive robust controller comprises the following steps:
the final stable bound of the constructed adaptive lyru controller was analyzed using the lyapunov function as shown in equation (14) below:
Figure FDA0002752230480000041
where P is a positive definite matrix, ρEAlpha is an upper bound parameter for uncertainty of the active anti-roll system, being any constant greater than-1.
2. The method for designing a controller of an active anti-roll system according to claim 1, wherein the analyzing the final stable bound of the constructed adaptive law robust controller by using the lyapunov function shown in equation (14) specifically comprises:
calculation of equation (14) yields the following formula (15):
Figure FDA0002752230480000042
wherein the content of the first and second substances,
Figure FDA0002752230480000043
Figure FDA0002752230480000044
the final stable limit of the active anti-roll system is obtained based on equation (15), and the trade-off parameter R is shown in equation (16) below:
Figure FDA0002752230480000045
the final consistent stable limit of the active anti-roll system is obtained based on equation (14), as shown in equation (17):
Figure FDA0002752230480000046
wherein the content of the first and second substances,da lower limit value representing the size of the final uniform stability limit of the active anti-roll system,
Figure FDA0002752230480000047
Figure FDA0002752230480000048
λmin(P) represents the minimum eigenvalue, λ, of the positive definite matrix Pmax(P) represents the maximum eigenvalue of the positive definite matrix P;
according to the lyapunov theory of stability, the time for the active anti-roll system to reach the final stable limit can be obtained, as shown in the following formula (18):
Figure FDA0002752230480000051
where T denotes the time for the active anti-roll system to reach the final uniform stable limit, r denotes the initial state of the system,
Figure FDA0002752230480000052
is arbitrarily greater thandPositive number of (c).
3. The method of claim 1, wherein the adjusting of the main parameters in the adaptive law robust controller is constructed, and the analyzing the control effect comprises:
adjusting initial condition incompatible compensation parameters, adaptive law adjustment parameters and control precision adjustment parameters in the constructed adaptive law robust controller;
and analyzing whether the error between the actual roll angle and the target roll angle meets the preset error requirement or not based on the adjusted parameters.
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