CN110239500A - Time-varying slip rate inverting dynamic surface based on second-order slip-flow rate model constrains control algolithm - Google Patents
Time-varying slip rate inverting dynamic surface based on second-order slip-flow rate model constrains control algolithm Download PDFInfo
- Publication number
- CN110239500A CN110239500A CN201910421863.9A CN201910421863A CN110239500A CN 110239500 A CN110239500 A CN 110239500A CN 201910421863 A CN201910421863 A CN 201910421863A CN 110239500 A CN110239500 A CN 110239500A
- Authority
- CN
- China
- Prior art keywords
- time
- varying
- slip rate
- slip
- slip ratio
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 33
- 238000000034 method Methods 0.000 claims abstract description 14
- 238000013461 design Methods 0.000 claims abstract description 10
- 238000004880 explosion Methods 0.000 claims abstract description 7
- 230000004888 barrier function Effects 0.000 claims description 8
- 238000009795 derivation Methods 0.000 claims description 5
- 230000001133 acceleration Effects 0.000 claims description 3
- 230000037396 body weight Effects 0.000 claims description 3
- 230000005484 gravity Effects 0.000 claims description 3
- 230000006641 stabilisation Effects 0.000 claims description 3
- 238000011105 stabilization Methods 0.000 claims description 3
- 230000001419 dependent effect Effects 0.000 claims description 2
- 238000012938 design process Methods 0.000 claims description 2
- 239000011159 matrix material Substances 0.000 claims description 2
- 230000003044 adaptive effect Effects 0.000 description 2
- 238000013459 approach Methods 0.000 description 2
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 238000011217 control strategy Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000000087 stabilizing effect Effects 0.000 description 1
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
- B60T8/00—Arrangements for adjusting wheel-braking force to meet varying vehicular or ground-surface conditions, e.g. limiting or varying distribution of braking force
- B60T8/17—Using electrical or electronic regulation means to control braking
- B60T8/176—Brake regulation specially adapted to prevent excessive wheel slip during vehicle deceleration, e.g. ABS
- B60T8/1761—Brake regulation specially adapted to prevent excessive wheel slip during vehicle deceleration, e.g. ABS responsive to wheel or brake dynamics, e.g. wheel slip, wheel acceleration or rate of change of brake fluid pressure
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60T—VEHICLE BRAKE CONTROL SYSTEMS OR PARTS THEREOF; BRAKE CONTROL SYSTEMS OR PARTS THEREOF, IN GENERAL; ARRANGEMENT OF BRAKING ELEMENTS ON VEHICLES IN GENERAL; PORTABLE DEVICES FOR PREVENTING UNWANTED MOVEMENT OF VEHICLES; VEHICLE MODIFICATIONS TO FACILITATE COOLING OF BRAKES
- B60T2270/00—Further aspects of brake control systems not otherwise provided for
- B60T2270/10—ABS control systems
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Fluid Mechanics (AREA)
- Transportation (AREA)
- Mechanical Engineering (AREA)
- Regulating Braking Force (AREA)
Abstract
The invention discloses the time-varying slip rate inverting dynamic surfaces based on second-order slip-flow rate model to constrain control algolithm, change too fast situation for slip rate under the conditions of complex road surface, based on Burckhardt tire model, establish second-order slip-flow rate model, not only reflect slip rate situation of change, the case where can also reflecting the variation of slip rate derivative, the vehicle ABS system slip rate changing rule under complex working condition can more be described.The asymmetric obstacle liapunov function of time-varying is introduced into the design of slip-based controller device simultaneously, solves time-varying slip rate constraint control problem, fundamentally avoids slip rate work in unstable region.The present invention solves the differential explosion issues in back stepping control algorithm using dynamic surface control algorithm.Designed slip rate constraint controller can have faster braking time and shorter braking distance in the case where not violating constraint condition, and wheel speed and braking moment are not shaken in braking process, improve the comfort of vehicle.
Description
Technical Field
The invention relates to the field of intelligent automobiles, in particular to a time-varying slip ratio inversion dynamic surface constraint control algorithm based on a second-order slip ratio model.
Background
An anti-lock Braking System (ABS) is one of active safety devices, and is important to improve the stability and safety of a vehicle. The ABS is required not only to provide maximum braking force to achieve high braking performance, but also to avoid wheel slip to avoid locking during the entire braking process of the vehicle. The ABS control system usually adopts a slip rate control method, and the vehicle slip rate tracks the optimal slip rate through a control algorithm so as to obtain the maximum braking torque. With the continuous development of modern control theory, several ABS slip rate control algorithms, such as logic threshold value, PID control, fuzzy control, neural network control, extremum search control, sliding mode variable structure control, etc., have been proposed in the existing literature. According to the road surface adhesion coefficient curve, the working range of the tire slip ratio can be divided into a stable area and an unstable area. If the tire slip is in an unstable region due to the braking torque being greater than the ground braking torque, a drop in wheel speed occurs, the slip rate increases, and the ground braking force continues to drop until the tire is locked. However, the slip ratio control algorithm of the existing literature mainly tracks the optimal slip ratio, mainly focuses on how to obtain the optimal tracking effect, and does not consider how to fundamentally avoid the slip ratio from working in an unstable area. The document 'constraint inversion sliding mode control of slip rate of an all-electric brake system of an airplane' provides an inversion sliding mode control method of the all-electric brake system of the airplane based on an obstacle Lyapunov function, and boundary constraint of the slip rate is achieved. A thesis 'constraint control of a nonlinear system and application research thereof' provides a slip rate output constraint control strategy for an airplane electric brake system. However, both of the two documents are directed to an aircraft braking system, and because the operating condition of an aircraft landing system is relatively single, both of the two documents do not consider the condition that the slip rate constraint limit is time-varying, and meanwhile, both of the two documents are based on a first-order slip rate model to perform slip rate control. However, the conditions under which the vehicle brakes are much more complex than the landing of an aircraft, especially on abrupt and uneven roads. The second-order slip rate model can reflect the change condition of the slip rate and the change condition of the derivative of the slip rate, and can describe the change rule of the slip rate of the ABS system of the vehicle under the complex working condition. In the literature, "inverse adaptive sliding mode ABS control based on LuGre model" a second-order slip rate model is deduced based on the LuGre tire model, and an inverse adaptive sliding mode control algorithm is adopted to control the slip rate. However, the document does not consider the problem of slip rate constraint control, and cannot fundamentally avoid the slip rate from working in an unstable region. Meanwhile, in an inversion control algorithm, a large amount of derivative calculation needs to be carried out on the intermediate virtual controller, and particularly for a high-order system, "differential explosion" can be caused, so that the control law is highly complex and highly nonlinear.
Disclosure of Invention
Aiming at the problems, in order to fundamentally avoid the slip ratio from working in an unstable area under a complex working condition, the invention provides a time-varying slip ratio inversion dynamic surface constraint control algorithm based on a second-order slip ratio model, and fundamentally avoids the brake working point from working in the unstable area. Aiming at the condition that the slip rate changes too fast under the complex road surface condition, the invention establishes a second-order slip rate model based on the Burckhardt tire model, not only reflects the change condition of the slip rate, but also reflects the change condition of the derivative of the slip rate, and can describe the change rule of the slip rate of the ABS system of the vehicle under the complex working condition. Meanwhile, aiming at the characteristic that the slip rate constraint limit is time-varying under the working condition of a sudden change road surface or an uneven road surface, the time-varying asymmetric barrier Lyapunov function is introduced into the design of the slip rate controller, so that the problem of time-varying slip rate constraint control is solved, and the slip rate is fundamentally prevented from working in an unstable area. Meanwhile, the invention adopts a dynamic surface control algorithm to solve the problem of differential explosion in the inversion control algorithm. The slip rate constraint controller designed by the invention can have faster braking time and shorter braking distance without violating the constraint condition, and the wheel speed and the braking torque do not shake in the braking process, thereby improving the comfort of the vehicle.
The technical scheme of the invention is as follows: a time-varying slip ratio inversion dynamic surface constraint control algorithm based on a second-order slip ratio model is composed of a second-order slip ratio model modeling and a time-varying slip ratio inversion dynamic surface constraint control algorithm. The second-order slip rate model modeling is responsible for establishing a second-order slip rate model on the basis of the quarter vehicle model and reflecting the change condition of the slip rate derivative. The time-varying slip rate inversion dynamic surface constraint control algorithm is responsible for designing a time-varying barrier Lyapunov function and a constraint controller, and the slip rate is ensured not to violate a constraint boundary, so that the slip rate is fundamentally prevented from working in an unstable area.
The second-order slip rate model is modeled as follows:
the dynamic equation of the wheel during braking can be obtained according to the quarter vehicle model
Wherein: m is 1/4 vehicle body weight, v is vehicle traveling speedDegree, μ (λ) is the coefficient of adhesion, g is the acceleration of gravity, J is the moment of inertia of the wheel relative to the axis of rotation, ω is the wheel speed, r is the tire radius, T is the wheel speedbIs the braking torque.
The road surface adhesion coefficient mu (lambda) and the slip ratio lambda have strong nonlinearity, and the relationship between the road surface adhesion coefficient and the slip ratio is solved by adopting a Burckhardt tire model. The Burckhardt tire model is shown by the following formula:
wherein, c1,c2,c3Are all model constants, mu (lambda), which are dependent only on road adhesion conditionsk) Is the maximum adhesion coefficient.
Slip ratio is defined as follows
Derived from equation (5)
Substituting equations (1) and (2) into equation (6) yields a first order slip ratio model:
derived from equation (7)
Derived from equation (3)
Substituting equations (3) and (9) into equation (8) yields the second derivative of slip ratio:
is provided with Then equation (10) can be rewritten as:
let the desired slip ratio be λ*The present invention defines a state variable x when the desired slip rate is time varying1＝λ-λ*, Controller inputThe second order slip rate model is then:
wherein,
the time-varying slip ratio inversion dynamic surface constraint control algorithm comprises the following steps:
defining the desired time-varying slip ratio as λ*(t) a desired time-varying slip ratio constraint lower limit of kc(t) a desired time-varying slip ratio constraint upper limit ofThen a time varying slip rate tracking error constraint bound of
The first step is as follows: designing a barrier Lyapunov function to ensure a state variable x1The closed loop stabilizes without violating the constraints.
Defining slip rate tracking error as z1＝x1＝λ-λ*Virtual error z2＝x2-α1，α1Is a virtual controller. In order to avoid the differential explosion problem in the inversion control algorithm, a desired virtual controller is designedMake itVirtual controller α generated by a first order filter with time constant τ1I.e. by
Defining the output error of the filter asThus can obtain
Selecting a time-varying barrier Lyapunov function as
Wherein,
for convenience of the following description, q (z) is represented by q in the present invention1)。
To V1(z1) The derivation is as follows:
designing the desired virtual controller to
Wherein k is1In order to fix the gain of the signal,the gain is changed in a time-varying manner,and β is more than or equal to 0.
Is provided withThen
Substituting equation (17) into equation (16) may result:
the derivative for χ x is:
here, theIs continuous and bounded, i.e. | ξ2|≤M。
Substituting equation (20) into equation (19) yields:
from the Young's inequality:
substituting equations (22), (23) into equation (21) yields:
as can be seen from the formula (24), whenAnd isIn time, according to the Lyapunov stability theorem, the closed-loop system is gradually stabilized, and based on the Barbalt theorem, the slip rate tracking error z1Asymptotically approaches zero in finite time, and the filter error approaches zero in finite time. The convergence requirement is satisfied. Wherein the cross termsIs eliminated in the second step of the controller design process.
The second step is that: the Lyapunov function is designed such that the variable x2The closed loop asymptotically stabilizes, thus ensuring that z is within t → ∞2→ 0, and ensures the state variable x1The closed loop stabilizes without violating the constraints.
Selecting the Lyapunov function as
The derivation of V is:
the design controller is
Substituting equation (27) into equation (26) may result:
is provided with
Then equations (25) and (28) can be rewritten as:
for | z1|＜ka(t) and | z1|＜kb(t) is provided withAndthis is true.
The following inequality holds:
further, it is possible to obtain:
define the positive definite matrix as follows
Selecting c ═ min [2 lambda ]min(Q),2κ2]And satisfy Ki≥c，i＝1,2，κ2C is more than or equal to c. Thus, when-ka(t)≤z1≤kbThe following inequality holds in (t).
The following inequality can thus be found:
thus, the signal z1，z2，α1，Semi-global consistency is ultimately bounded. And (4) gradually stabilizing the closed-loop system according to the Lyapunov stabilization theorem. From the first step, when t → ∞ is reached, z1→ 0 and the tracking error is always at the tracking error constraint limit, ensuring that the slip ratio is always in the stable region.
The invention has the beneficial effects that:
aiming at the condition that the slip rate changes too fast under the complex road surface condition, the invention establishes a second-order slip rate model based on the Burckhardt tire model, and can accurately describe the change rule of the vehicle slip rate under the complex working condition. Meanwhile, aiming at the characteristic that the slip rate constraint limit is time-varying under the working condition of a sudden change road surface or an uneven road surface, the time-varying asymmetric barrier Lyapunov function is introduced into the design of the slip rate controller, so that the slip rate is fundamentally prevented from working in an unstable area. Meanwhile, the invention adopts a dynamic surface control algorithm to solve the problem of differential explosion in the inversion control algorithm. The slip rate constraint controller designed by the invention can have faster braking time and shorter braking distance without violating the constraint condition, and the wheel speed and the braking torque do not shake in the braking process, thereby improving the comfort of the vehicle.
Drawings
FIG. 1 is a quarter vehicle model.
Fig. 2 is a block diagram of the control process of the present invention.
Detailed Description
The concept and the specific working process of the invention will be described more clearly and completely with reference to the attached drawings and examples. It is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and those skilled in the art can obtain other embodiments without inventive efforts based on the embodiments of the present invention, and all embodiments are within the scope of the present invention.
Referring to fig. 2, the time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second-order slip ratio model is composed of a vehicle model, a second-order slip ratio model and a time-varying slip ratio inversion dynamic surface constraint controller.
Firstly, establishing a second-order slip rate model according to a quarter vehicle model; secondly, calculating a tracking error constraint limit of the time-varying slip ratio; and finally, designing a time-varying slip ratio inversion dynamic surface constraint controller.
The specific implementation steps are as follows:
(1) establishing a second order slip rate model
Establishing a second-order vehicle slip rate model based on the quarter vehicle model and the Burckhardt tire model as shown in FIG. 1
Wherein, the model slip rate model parameters are as follows:
wherein the vehicle parameters are as follows:
m is 1/4 car body weight, g is gravity acceleration, FzFor vertical loading, FxIs the longitudinal friction of the wheel, r is the radius of the tire, TbFor braking torque, v is vehicle travel speed and ω is wheel speed.
Wherein the Burckhardt tire model parameter c1,c2,c3Are all model constants that are related only to road adhesion conditions. The corresponding 3 parameter values for different road surface types are shown in table 1.
TABLE 1
(2) Computing time-varying slip rate tracking error constraint limits
Wherein λ is*(t) is the desired time-varying slip ratio,k c(t) is a desired time-varying slip ratio lower constraint limit,to the desired time-varying slip ratio constraint upper limit, ka(t) is the time-varying slip ratio lower constraint limit, kbAnd (t) is the time-varying slip ratio constraint upper limit.
(3) Design time-varying slip ratio inversion dynamic surface constraint controller
Defining slip rate tracking error as z1＝x1＝λ-λ*Virtual error z2＝x2-α1，α1In order to be a virtual control function,
in order to avoid the problem of differential explosion in the inversion control algorithm, the invention designs a desired virtual controllerMake itVirtual controller α generated by a first order filter with time constant τ1Having an order filter function of
The output error of the filter is expressed as
According to the time-varying slip rate tracking error constraint limit, designing a slip rate constraint controller as follows:
among them, the virtual controller α1The derivatives being obtained by first-order filters, i.e.Anticipating a virtual controllerTime varying controller gain parameterβ is more than or equal to 0, and the gain parameter k of the controller is fixed1> 0 and k2＞0。
The above-listed detailed description is only a specific description of a possible embodiment of the present invention, and they are not intended to limit the scope of the present invention, and equivalent embodiments or modifications made without departing from the technical spirit of the present invention should be included in the scope of the present invention.
Claims (8)
1. The time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second-order slip ratio model is characterized by comprising second-order slip ratio model modeling and time-varying slip ratio inversion dynamic surface constraint control algorithm design; the second-order slip rate model modeling is responsible for establishing a second-order slip rate model on the basis of the quarter vehicle model and reflecting the change condition of the slip rate derivative; the time-varying slip rate inversion dynamic surface constraint control algorithm is responsible for designing a time-varying barrier Lyapunov function and a constraint controller, and the slip rate is guaranteed not to violate a constraint boundary, so that the slip rate is fundamentally prevented from working in an unstable area.
2. The time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second-order slip ratio model according to claim 1, wherein the modeling method of the second-order slip ratio model comprises the following steps:
obtaining a dynamic equation of wheel braking according to the quarter vehicle model
Wherein: m is 1/4 vehicle body weight, v is vehicle traveling speed, μ (λ) is adhesion coefficient, g is gravity acceleration, J is rotational inertia of the wheel relative to the rotation axis, ω is wheel speed, r is tire radius, T is tire radiusbIs the braking torque.
3. The time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second-order slip ratio model according to claim 2, wherein the modeling method of the second-order slip ratio model further comprises: establishing a relation between the road adhesion coefficient mu (lambda) and the slip ratio lambda:
a Burckhardt tire model is adopted to establish the relationship between the road adhesion coefficient and the slip ratio, and the relationship is shown as the following formula:
wherein, c1,c2,c3Are all model constants, mu (lambda), which are dependent only on road adhesion conditionsk) Is the maximum adhesion coefficient.
4. The time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second order slip ratio model according to claim 3, wherein the modeling method of the second order slip ratio model further comprises:
definition of slip Rate
The formula of the slip rate is derived
5. The time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second-order slip ratio model according to claim 4, wherein the modeling method of the second-order slip ratio model further comprises: obtaining a second-order slip rate model according to the first-order slip rate model;
the modeling method of the first-order slip rate model is obtained according to a kinetic equation and a slip rate derivative equation during wheel braking, and the model expression is as follows:
derived from equation (7)
Derived from equation (3)
Substituting equations (3) and (9) into equation (8) yields the second derivative of slip ratio:
order to Then equation (10) can be rewritten as:
let the desired slip ratio be λ*Defining a state variable x when the desired slip rate is time varying1＝λ-λ*, Controller inputThe second order slip rate model is then:
wherein,
6. the second order slip rate model-based time-varying slip rate inversion dynamic surface constraint control algorithm of claim 1, wherein the time-varying slip rate inversion dynamic surface constraint control algorithm design comprises designing a time-varying slip rate tracking error constraint bound and designing a slip rate constraint controller.
7. The second-order slip rate model-based time-varying slip rate inversion dynamic surface constraint control algorithm of claim 6, wherein the design time-varying slip rate tracking error constraint bound is:
wherein λ is*(t) desired time-varying slip ratio, kc(t) is a desired time-varying slip ratio lower constraint limit,to the desired time-varying slip ratio constraint upper limit, ka(t) is the time-varying slip ratio lower constraint limit, kbAnd (t) is the time-varying slip ratio constraint upper limit.
8. The time-varying slip ratio inversion dynamic surface constraint control algorithm based on the second-order slip ratio model according to claim 7, wherein the method for designing the slip ratio constraint controller is as follows:
the first step is as follows: designing a barrier Lyapunov function to ensure a state variable x1Closed loop stabilization without violating constraints:
defining slip rate tracking error as z1＝x1＝λ-λ*Virtual error z2＝x2-α1，α1To be a virtual controller, in order to avoidInverting the differential explosion problem in the control algorithm and designing an expected virtual controllerMake itVirtual controller α generated by a first order filter with time constant τ1I.e. by
Defining the output error of the filter asCan obtain
Selecting a time-varying barrier Lyapunov function as
Wherein,
q (z) is represented by q1)；
To V1(z1) The derivation is as follows:
designing the desired virtual controller to
Wherein k is1In order to fix the gain of the signal,in order to obtain a time-varying gain, the gain is,β is more than or equal to 0;
is provided withThen
Substituting equation (17) into equation (16) may result:
pair chi2The derivation is as follows:
here ξ2(x1,x2,λ*,λ*) Is continuous and bounded, i.e. | ξ2|≤M；
Substituting equation (20) into equation (19) yields:
from the Young's inequality:
substituting equations (22), (23) into equation (21) yields:
as can be seen from the formula (24), whenAnd isIn time, according to the Lyapunov stability theorem, the closed-loop system is gradually stabilized, and based on the Barbalt theorem, the slip rate tracking error z1The filter error gradually tends to zero in the finite time, and the filter error tends to zero in the finite time, so that the convergence requirement is met; wherein the cross termsEliminated in the second step controller design process;
the second step is that: the Lyapunov function is designed such that the variable x2The closed loop asymptotically stabilizes, thus ensuring that z is within t → ∞2→ 0, and ensures the state variable x1Closed loop stability without violating constraints;
selecting the Lyapunov function as
The derivation of V is:
the design controller is
Substituting equation (27) into equation (26) may result:
is provided withK2＝k2，
Then equations (25) and (28) can be rewritten as:
for | z1|＜ka(t) and | z1|＜kb(t) is provided withAndif true;
the following inequality holds:
further, it is possible to obtain:
define the positive definite matrix as follows
Selecting c ═ min [2 lambda ]min(Q),2κ2]And satisfy Ki≥c，i＝1,2，κ2C is more than or equal to c; when is-ka(t)≤z1≤kb(t) the following inequality holds:
the following inequality holds:
signal z1，z2，α1，The semi-global consistency is finally bounded, the closed-loop system is gradually stabilized according to the Lyapunov stabilization theorem, and the first step can be used for realizingIt is known that when t → ∞ is reached, z1→ 0 and the tracking error is always at the tracking error constraint limit, ensuring that the slip ratio is always in the stable region.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910421863.9A CN110239500A (en) | 2019-05-21 | 2019-05-21 | Time-varying slip rate inverting dynamic surface based on second-order slip-flow rate model constrains control algolithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910421863.9A CN110239500A (en) | 2019-05-21 | 2019-05-21 | Time-varying slip rate inverting dynamic surface based on second-order slip-flow rate model constrains control algolithm |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110239500A true CN110239500A (en) | 2019-09-17 |
Family
ID=67884680
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910421863.9A Pending CN110239500A (en) | 2019-05-21 | 2019-05-21 | Time-varying slip rate inverting dynamic surface based on second-order slip-flow rate model constrains control algolithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110239500A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112363538A (en) * | 2020-11-09 | 2021-02-12 | 哈尔滨工程大学 | AUV (autonomous underwater vehicle) area tracking control method under incomplete speed information |
| CN118288807B (en) * | 2024-06-06 | 2024-07-30 | 成都赛力斯科技有限公司 | Staged torque control method and device based on slip rate and new energy automobile |
-
2019
- 2019-05-21 CN CN201910421863.9A patent/CN110239500A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112363538A (en) * | 2020-11-09 | 2021-02-12 | 哈尔滨工程大学 | AUV (autonomous underwater vehicle) area tracking control method under incomplete speed information |
| CN118288807B (en) * | 2024-06-06 | 2024-07-30 | 成都赛力斯科技有限公司 | Staged torque control method and device based on slip rate and new energy automobile |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110254408A (en) | A kind of adaptive time-varying slip rate constraint control algolithm of intelligent automobile anti-lock braking system | |
| CN110254407A (en) | Vehicle anti-lock brake system slip rate based on second-order slip-flow rate model constrains control algolithm | |
| CN108107731B (en) | Automobile stability control method based on tire nonlinear characteristics | |
| Nagai et al. | Integrated control of active rear wheel steering and direct yaw moment control | |
| US6804594B1 (en) | Active steering for handling/stability enhancement | |
| Gaspar et al. | The design of a combined control structure to prevent the rollover of heavy vehicles | |
| CN112606826B (en) | State variable full-constraint direct yaw moment control algorithm based on road adhesion coefficient | |
| Ding et al. | A comprehensive vehicle stability assessment system based on enabling tire force estimation | |
| CN110239500A (en) | Time-varying slip rate inverting dynamic surface based on second-order slip-flow rate model constrains control algolithm | |
| Boisvert et al. | Estimators of wheel slip for electric vehicles using torque and encoder measurements | |
| WO2024114037A1 (en) | Path tracking control method and apparatus for intelligent electric vehicle | |
| Polack et al. | Finite-time stabilization of longitudinal control for autonomous vehicles via a model-free approach | |
| CN114194202B (en) | Vehicle stable state judging method based on phase plane, chassis coordination control method and system | |
| Amdouni et al. | Optimal control approach developed to four-wheel active steering vehicles | |
| CN111027136A (en) | Nonlinear ABS control method based on fractional extreme value search | |
| KR102261527B1 (en) | Apparatus and method of controlling torque vectoring for vehicles with inwheel motor | |
| Yun et al. | Brake performance evaluation of ABS with sliding mode controller on a split road with driver model | |
| CN113830075B (en) | Vehicle stability control method, device, electronic device, and medium | |
| Palmieri et al. | A preliminary study to integrate LTV-MPC lateral vehicle dynamics control with a slip control | |
| Dabladji et al. | Toward a robust motorcycle braking | |
| CN113460055A (en) | Online vehicle driving control area division and area boundary estimation method | |
| CN113386767A (en) | Four-wheel steering rolling time domain control method based on Koopman operator | |
| Kocak et al. | Damping of the Shimmy Behavior in Nose Landing Gear System via PIR Controller | |
| CN113815600A (en) | Main loop-servo loop double closed loop controller of vehicle ESC system | |
| VAN ZANTEN et al. | Optimal control of the tractor-semitrailer truck |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20190917 |
|
| RJ01 | Rejection of invention patent application after publication |