CN118770258A - Robust coordination control method for vehicle under unknown driver state - Google Patents
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Abstract
The invention discloses a robust coordination control method of a vehicle under the condition of unknown driver state, which comprises the steps of establishing a nonlinear bicycle model comprising a vehicle sideslip angle and a yaw rate, discretizing the model by a piecewise linear perturbation method, and introducing polyhedral constraint to define an operation mode and input constraint of a system; designing a robust control strategy based on set theory and multi-model adaptive control to handle uncertainty of driver input and road friction coefficient; by solving the optimization problem, control commands are distributed to each wheel, and stability and operability of the vehicle under various complex driving conditions are ensured. The invention can effectively improve the dynamic performance and safety of the vehicle under the condition of unknown driver states and various road conditions, and is suitable for the distributed driving electric vehicle which needs high stability and accurate control.
Description
Technical Field
The invention relates to the technical field of vehicle control systems, in particular to a robust coordination control method for a vehicle under the condition of unknown driver state.
Background
With the rapid development of the automotive industry and increasing importance of driving safety, modern vehicles are commonly equipped with a variety of active safety systems, such as ESC (Electronic Stability Control ) and AFS (Active Front Steering, active front steering) systems. The ESC system improves the stability of the vehicle under the conditions of turning and emergency obstacle avoidance through controlling the braking moment of wheels; and the AFS system improves the steering performance and response speed of the vehicle by adjusting the steering angle of the front wheels.
While existing ESC and AFS systems have achieved significant success in improving vehicle stability and drivability, they still have certain limitations in facing complex driving environments and uncertain driver behavior. Conventional control strategies generally assume that the driver's input is known and that the road friction coefficient and vehicle dynamics parameters can be accurately predicted. However, during actual driving, the driver's intention and input often have great uncertainty, and road conditions and vehicle conditions may also be abrupt, which factors affect the dynamic performance and control effects of the vehicle.
Disclosure of Invention
The purpose of the invention is that: the vehicle robust coordination control method under the condition of unknown driver state is provided, and the uncertainty of driver input and vehicle state is brought into control design by constructing a control framework based on multi-model self-adaptive control and set theory, so that the accurate control of the yaw rate and the centroid side deflection angle of the vehicle is realized, and the stability and the operability of the vehicle under various driving conditions are ensured.
In order to solve the technical problems, the technical scheme of the invention is as follows: a robust coordination control method for a vehicle under the condition of unknown driver state comprises the following steps:
s1, constructing a vehicle model under the condition that the state of a driver is unknown.
S2, designing a robust coordination control strategy by utilizing the model in the step S1, and completing control of the vehicle.
Further, in step S1, constructing a vehicle model under the condition that the driver state is unknown includes the following sub-steps:
s101, constructing a classical nonlinear bicycle model, wherein the specific expression is as follows:
wherein m represents the mass of the whole vehicle, Indicating the lateral acceleration of the vehicle,Which is indicative of the longitudinal velocity,Representing yaw rate, F cf、Fcr represents the front and rear axle tire sidewall forces, respectively, I represents the moment of inertia of the vehicle about the z-axis,The yaw rate acceleration is represented by a, the distance from the center of gravity of the vehicle to the front axle is represented by b, the distance from the center of gravity of the vehicle to the rear axle is represented by M, and the external yaw moment is represented by M.
Tire side force F c· is obtained based on Pacejka model, and the specific expression is:
Fc·＝fc,·(α·,σ·,Fz·,μ·) (19)
Where F c,· represents a nominal tire side force, α·represents a tire slip angle, σ·represents a slip ratio, μ·represents a coefficient of friction between the tire and the road surface, and F z· represents a normal force.
S102, supposing:
(1) The coefficient of friction and normal force of all tires are known data and are constant and equal;
(2) The longitudinal speed is a known data and constant, and assumed σ.zero;
then F c· is a function of α·only, expressed as a linear function of state and input using a small angle approximation and assuming no steering of the rear wheels, expressed as:
Wherein alpha f represents the front wheel slip angle, alpha r represents the rear wheel slip angle, Represents lateral speed, delta f represents front wheel steering angle relative to the longitudinal axis of the vehicle.
S103, linearizing the nonlinear tire by using a piecewise linear perturbation method, wherein the piecewise linear perturbation of the nonlinear function in the formula (19) is shown as the formula (21):
Wherein, Representing a nonlinear function, c s representing the angular stiffness of the tire in the saturation region, c l representing the angular stiffness of the tire in the linear region,Indicating the slip angle at which the lateral force is greatest.
S104, combining formulas (18), (20) and (21) to obtain a piecewise linear perturbation bicycle model, wherein the specific expression is as follows:
Where a i represents the state transition matrix, B i represents the control matrix, and f i represents the residual term.
S105, nine modes of the piecewise linear perturbation bicycle model are formed by combining all possible modes of a front wheel and a rear wheel; in a vehicle equipped with a front-wheel steering system, δ f is composed of the sum of two independent inputs, specifically expressed as:
δf＝δd+δAFS(23)
Where δ d denotes the driver input on the steering wheel, and δ AFS denotes the front wheel steering input.
S106, introducing additional uncertainty w u into the input, and representing the piecewise linear perturbation bicycle model as follows by using a discrete time state space form:
wherein z represents the output variable, U represents a control variable, u= [ delta AFS,M]T;Qi ] represents a set of polyhedral areas of the input constraint and states corresponding to the ith mode of the vehicle; w u (u) represents the set value map of the upper limit.
S107, obtaining a delta d boundary by assuming a worst case according to the constraint of delta d∈Wz (z) obtained in the step S106, wherein W z (-) represents a set value mapping of z; based on the steady-state cornering analysis of the linear bicycle model, the maximum boundary of delta d is deduced, under steady-state conditions,The relationship with δ f is expressed as:
Wherein, Representing steady-state yaw rate; δ f,ss represents the front wheel steady state rotation angle; g ψ,ss denotes a steady-state yaw rate gain,K ψ,ss represents the reciprocal of the yaw-rate gain.
Setting the condition of no control in steady state conditions, i.e. δ AFS,ss =0, yields:
Using δ d,ss obtained in equation (26) as a linear state estimate of the driver steering input, the actual value of δ d,ss is set to lie within the interval centered on δ d,ss, thus yielding a perturbation range, expressed in detail as:
Where e represents a non-negative parameter and δ d,max represents the maximum value of δ d.
Constraint delta d∈Wz (z) is expressed asThe specific expression of the polyhedral constraint in (a) is as follows:
wherein W d represents the perturbation set of the front wheel corner.
Further, in step S2, the completion of the control of the vehicle includes the following sub-steps:
S201, setting a linear mode of the front and rear tires in a linear region under the input values delta d and the additional uncertainty values w u of all allowed drivers on the steering wheel as a mode 1; when the vehicle exceeds the mode 1, obtaining steering input by the controller, and returning the vehicle to the mode 1 in a time step; when the vehicle is in the mode 1, the controller is utilized to enable the vehicle in the next time step to be in the mode 1, and the specific contents are as follows:
In the state space, a single step robust backward reachable set of a given target set Z is defined as:
Wherein z + represents the predicted state of the next time step, obtained by formula (24); q represents a set of polyhedral regions of states and input constraints corresponding to nine modes of the vehicle, Pre (Z) represents a single step robust backward reachable set.
Set P 1＝Projz(Q1), whereinFor the state and input constraints of mode 1, the robust control invariant set, the maximum robust control invariant set, and the corresponding control map are represented as:
If for each And each delta d∈Wz (z), there is a control u such that (z, u, delta d)∈Q1 andAnd is true for all w u∈Wu (u), then the setIs a robust control invariant set for mode 1, wherein the maximum robust control invariant set for mode 1Is included in all modes 1A robust control invariant set of (2) corresponding toControl mapping of (a)The definition is as follows:
The N-step backward reachable set Z N of the target set Z is expressed as:
Zk＝Pre(Zk-1),(k＝1,...,N),Z0＝Z(31)。
If the vehicle state is in Z N, then the state of the vehicle is guaranteed to be controlled within the target set Z in N steps by a series of control inputs u (k) k=0 N-1.
The control map U k (·) corresponding to Z k is expressed as:
When the vehicle state exceeds the robust control invariant set, generating a control sequence by equation (15) such that the predicted state of the vehicle after N steps is within the target set, the controller driving the state back
S202, a specific formula of optimal control input is as follows:
Where u * represents the optimal control input, u *＝[δAFS,M]T; q and R represent positive definite matrices, u pre represents the control input of the previous time step command; r denotes the reference signal and,
If it isThenWhereas U *(z,δd)＝Uk(z,δd) where k represents the smallest positive integer where Z e Z k.
Equation (33) applies only when the vehicle is in mode 1 or the front tire is not saturated; when the front tire is saturated, penalty terms are applied to the front wheel slip angle, and the AFS controls only the front wheel slip angle, so the optimization control problem translates into:
Wherein P is more than 0, Linear approximation representing the wheel slip angle before the next time step
U * comprises two parts: u * (1) represents the front wheel steering angle, and δ AFS＝u*(1),u* (2) represents a yaw moment command; the two are sent to the executor through the CAN bus to complete the whole control process.
Compared with the prior art, the technical scheme provided by the invention has the following technical effects:
The method provided by the invention can effectively improve the dynamic performance and safety of the vehicle under the condition of unknown driver states and various roads, and is suitable for the distributed driving electric vehicle which needs high stability and accurate control.
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FIG. 1 is a flow chart of an overall implementation of the present invention.
FIG. 2 is a two-degree-of-freedom bicycle model diagram of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
In order to achieve the above objective, the present invention provides a robust coordination control method for a vehicle under the condition of unknown driver status, as shown in fig. 1, comprising the following specific steps:
S1, constructing a vehicle model under the condition that the state of a driver is unknown: a non-linear bicycle model is built that takes into account the centroid slip angle and yaw rate of the vehicle to simulate and predict vehicle behavior under different driving conditions. The model is then discretized by piecewise linear perturbation methods and polyhedral constraints are introduced to define the operating modes and input constraints of the system. Finally, taking into account the unpredictability of the driver input, the driver's steering input is introduced into the model as a bounded disturbance, adding possible dynamics and errors to the model. The specific contents are as follows:
s101, constructing a classical nonlinear bicycle model, wherein the specific expression is as shown in fig. 2:
wherein m represents the mass of the whole vehicle, Indicating the lateral acceleration of the vehicle,Which is indicative of the longitudinal velocity,Representing yaw rate, F cf、Fcr represents the front and rear axle tire sidewall forces, respectively, I represents the moment of inertia of the vehicle about the z-axis,The yaw rate acceleration is represented by a, the distance from the center of gravity of the vehicle to the front axle is represented by b, the distance from the center of gravity of the vehicle to the rear axle is represented by M, and the external yaw moment is represented by M.
Tire side force F c· is obtained based on Pacejka model, and the specific expression is:
Fc·＝fc,·(α·,σ·,Fz·,μ·) (36)
Where F c,· represents a nominal tire side force, α·represents a tire slip angle, σ·represents a slip ratio, μ·represents a coefficient of friction between the tire and the road surface, and F z· represents a normal force.
S102, supposing:
(1) The coefficient of friction and normal force are known, constant and the same for both wheels;
(2) The longitudinal speed is known and constant. Longitudinal vehicle dynamics are ignored and σ is assumed to be zero (pure roll);
then F c· is a function of α·only, expressed as a linear function of state and input using a small angle approximation and assuming no steering of the rear wheels, expressed as:
Wherein alpha f represents the front wheel slip angle, alpha r represents the rear wheel slip angle, Represents lateral speed, delta f represents front wheel steering angle relative to the longitudinal axis of the vehicle.
S103, linearizing the nonlinear tire by using a piecewise linear perturbation method, wherein the piecewise linear perturbation of the nonlinear function in the formula (36) is shown in the formula (38):
Wherein, Representing a nonlinear function, c s representing the angular stiffness of the tire in the saturation region, c l representing the angular stiffness of the tire in the linear region,Indicating the slip angle at which the lateral force is greatest.
S104, combining formulas (35), (37) and (38) to obtain a piecewise linear perturbation bicycle model, wherein the specific expression is as follows:
Where a i represents the state transition matrix, B i represents the control matrix, and f i represents the residual term.
S105, nine modes of the piecewise linear perturbation bicycle model are formed by combining all possible modes of a front wheel and a rear wheel; note that in a vehicle equipped with a front-wheel steering system, δ f is composed of the sum of two independent inputs, namely:
δf＝δd+δAFS(40)
Where δ d denotes the driver input on the steering wheel, and δ AFS denotes the front wheel steering input.
S106, introducing an additional uncertainty w u in the input to account for unmodeled actuator dynamics and input delays, the piecewise linear perturbation bicycle model can be expressed in terms of a discrete time state space:
wherein z represents the output variable, U represents a control variable, u= [ delta AFS,M]T;Qi ] represents a set of polyhedral areas of the input constraint and states corresponding to the ith mode of the vehicle; w u (u) represents the set value map of the upper limit.
It is noted that W u (·) is defined as a collective value function, since the uncertainty in the inputs may depend on their value, where the uncertainty in each control input is 10%.
S107, obtaining a constraint of delta d∈Wz (z) according to the step S106, wherein W z (·) is a set value mapping of the state z, and a conservative delta d boundary can be obtained by assuming a worst case; based on steady state turn analysis of the linear bicycle model, the maximum boundary of δ d can be derived. In the case of a steady-state condition,The relationship with δ f is expressed as:
Wherein, Representing steady-state yaw rate; l=a+b; v ch denotes the characteristic speed of the vehicle; δ f,ss represents the front wheel steady state rotation angle; k ψ,ss represents the reciprocal of the yaw-rate gain; g ψ,ss denotes a steady-state yaw rate gain,
Setting the condition of no control in steady state conditions, i.e. δ AFS,ss =0, gives:
Using the δ d,ss value obtained in equation (43) as a linear state estimate of the driver steering input, the actual value of δ d,ss is set to lie within the interval centered on δ d,ss, thus yielding a perturbation range, expressed in detail as:
Where e represents a non-negative parameter, typically set to 1; δ d,max represents the maximum value of δ d.
Constraint delta d∈Wz (z) is expressed asThe specific expression of the polyhedral constraint in (a) is as follows:
wherein W d represents the perturbation set of the front wheel corner.
S2, designing a robust coordination control strategy by utilizing the model in the step S1, and completing control of the vehicle: by establishing a robust control invariant set, it is ensured that the state of the vehicle is still within safe limits in the presence of disturbances and uncertainties. The driver input is then treated as a measured disturbance using a predictive control strategy, while the active front wheel steering is treated as a constrained control input. With this strategy, each time step can provide robust control over the uncertainty of the driver input. And finally, designing a control law, and generating optimal control input by solving a secondary optimization problem so as to ensure that the vehicle is kept stable under various complex driving conditions. The specific contents are as follows:
S201, designing a control framework based on robust reachability: setting the linear mode of the front and rear tires in the linear region at all allowable driver input values δ d and additional uncertainty values w u on the steering wheel to mode 1; when the vehicle exceeds the mode 1, a feasible steering input is obtained by the controller, and the vehicle is ensured to return to the mode 1 in a time step; when the vehicle is in the mode 1, the controller is utilized to enable the vehicle in the next time step to be in the mode 1, and the specific contents are as follows:
In the state space, a single step robust backward reachable set of a given target set Z is defined as:
Wherein z + represents the predicted state for the next time step, obtainable by equation (41); q represents a set of polyhedral regions of states and input constraints corresponding to nine modes of the vehicle, Pre (Z) represents a single step robust backward reachable set.
The map Pre (·) gives a set of states with at least one possible input that can ensure that the predicted state lies within the target set Z at all allowed delta d and w u values. In addition to the single step controllable set, the concept of a robust control invariant set and corresponding control map associated with mode 1 is introduced. Hypothetical P 1＝Projz(Q1), whereIs a state and input constraint for mode 1. The robust control invariant set, the maximum robust control invariant set, and the corresponding control map are as follows:
Definition 1: if for each And each delta d∈Wz (z), there is one control u such that (z, u, delta d)∈Q1 andAnd is true for all w u∈Wu (u), then the setIs a robust control invariant set for mode 1, wherein the maximum robust control invariant set for mode 1Is comprised of all modes 1Is a robust control invariant set. And corresponds toControl mapping of (a)The definition is as follows:
if the vehicle state z is located Then for each rotation angle delta d∈Wz (z), fromAny input u is selected to keep the predicted state of the next time step atAnd (3) inner part. However, due to uncertain factors in the model (e.g., sudden disturbances, changes in surface friction coefficients, etc.), the vehicle condition may exceedIn the event of such uncertainty of the presence parameter, it is still desirable to control the vehicle state back to the mode 1 robust control invariant set within a time step of N steps. For ease of illustration, this brings the concept of an N-step backward reachable set.
Definition 2: the N-step backward reachable set Z N of the target set Z can be defined by a recursive iterative method, as shown in formula (48):
Zk＝Pre(Zk-1),(k＝1,...,N),Z0＝Z(48)。
If the vehicle state is in Z N, then the vehicle state can be guaranteed to be controlled into the target set Z in N steps through a series of control inputs u (k) k=0 N-1. Z N is generally non-convex in that it is a union of multiple convex sets. Second, a control map corresponding to the k-step backward reachable set may be defined.
Definition 3: the control map U k (·) corresponding to Z k is defined as:
When the vehicle state exceeds the robust control invariant set, a control sequence may be generated by equation (49) to ensure that the predicted state of the vehicle after N steps is within the target set, to ensure that the controller will eventually drive the state back in a limited time step
(2) Robust control design with reference tracking
The stability control system provides front wheel steering correction commands and yaw moment control to track a given reference signal in the state space. Reference signalIs a function of the current state and the driver steering input, the calculation formula of the optimal control input u * is:
Where Q and R are appropriately selected positive definite matrices, u pre is the control input for the previous time step command, u *＝[δAFS,M]T.
The set of allowed control inputs U *(z,δd) is defined by either equation (47) or (49) depending on the value of the current z. If it isThenOtherwise U *(z,δd)＝Uk(z,δd), where k is the smallest positive integer at Z ε Z k.
Equation (50) is only used when the vehicle is in mode 1 or the front tires are not saturated. If the front tire is saturated, a penalty term is applied to the front wheel slip angle to drive it to a value that maximizes lateral force. In this case, AFS provides control only over the front wheel slip angle, ignoring the effect of the rear wheel slip angle in the cost function. Thus, the optimization control problem translates into:
Wherein P is more than 0, Is a linear approximation of the wheel slip angle before the next time step,Is the value of the front wheel slip angle at which lateral forces are maximized.
Control input u * includes two parts: u * (1) is the front wheel steering angle, and δ AFS＝u*(1),u* (2) is the yaw moment command. The two are sent to the executor through the CAN bus to complete the whole control process.
The foregoing is merely a preferred embodiment of the present invention, and it should be noted that modifications and variations could be made by those skilled in the art without departing from the technical principles of the present invention, and such modifications and variations should also be regarded as being within the scope of the invention.
Claims (3)
1. A robust coordination control method for a vehicle with an unknown driver state, comprising:
s1, constructing a vehicle model under the condition that the state of a driver is unknown;
S2, designing a robust coordination control strategy by utilizing the model in the step S1, and completing control of the vehicle.
2. The robust coordination control method for a vehicle under an unknown driver state according to claim 1, wherein in step S1, constructing a vehicle model under an unknown driver state includes the sub-steps of:
s101, constructing a classical nonlinear bicycle model, wherein the specific expression is as follows:
wherein m represents the mass of the whole vehicle, Indicating the lateral acceleration of the vehicle,Which is indicative of the longitudinal velocity,Representing yaw rate, F cf、Fcr represents the front and rear axle tire sidewall forces, respectively, I represents the moment of inertia of the vehicle about the z-axis,A represents yaw rate acceleration, a represents a distance from the center of gravity of the vehicle to the front axle, b represents a distance from the center of gravity of the vehicle to the rear axle, and M represents an external yaw moment;
Tire side force F c· is obtained based on Pacejka model, and the specific expression is:
Fc·＝fc,·(α·,σ·,Fz·,μ·)(2)
Wherein F c,· represents a nominal tire side force, α·represents a tire slip angle, σ·represents a slip ratio, μ·represents a coefficient of friction between the tire and the road surface, and F z· represents a normal force;
s102, supposing:
(1) The coefficient of friction and normal force of all tires are known data and are constant and equal;
(2) The longitudinal speed is a known data and constant, and assumed σ.zero;
then F c· is a function of α·only, expressed as a linear function of state and input using a small angle approximation and assuming no steering of the rear wheels, expressed as:
Wherein alpha f represents the front wheel slip angle, alpha r represents the rear wheel slip angle, Representing lateral speed, δ f represents the front wheel steering angle relative to the longitudinal axis of the vehicle;
S103, linearizing the nonlinear tire by using a piecewise linear perturbation method, wherein the piecewise linear perturbation of the nonlinear function in the formula (2) is shown as the formula (4):
Wherein, Representing a nonlinear function, c s representing the angular stiffness of the tire in the saturation region, c l representing the angular stiffness of the tire in the linear region,Representing the slip angle at which the lateral force is greatest;
S104, combining the formulas (1), (3) and (4) to obtain a piecewise linear perturbation bicycle model, wherein the specific expression is as follows:
Wherein a i represents a state transition matrix, B i represents a control matrix, and f i represents a residual term;
S105, nine modes of the piecewise linear perturbation bicycle model are formed by combining all possible modes of a front wheel and a rear wheel; in a vehicle equipped with a front-wheel steering system, δ f is composed of the sum of two independent inputs, specifically expressed as:
δf＝δd+δAFS(6)
Wherein δ d represents the driver input on the steering wheel, δ AFS represents the front wheel steering input;
s106, introducing additional uncertainty w u into the input, and representing the piecewise linear perturbation bicycle model as follows by using a discrete time state space form:
wherein z represents the output variable, U represents a control variable, u= [ delta AFS,M]T;Qi ] represents a set of polyhedral areas of the input constraint and states corresponding to the ith mode of the vehicle; w u (u) represents the set value mapping of the upper limit;
S107, obtaining a delta d boundary by assuming a worst case according to the constraint of delta d∈Wz (z) obtained in the step S106, wherein W z (-) represents a set value mapping of z; based on the steady-state cornering analysis of the linear bicycle model, the maximum boundary of delta d is deduced, under steady-state conditions, The relationship with δ f is expressed as:
Wherein, Representing steady-state yaw rate; δ f,ss represents the front wheel steady state rotation angle; g ψ,ss denotes a steady-state yaw rate gain,K ψ,ss represents the reciprocal of the yaw-rate gain;
setting the condition of no control in steady state conditions, i.e. δ AFS,ss =0, yields:
Using δ d,ss obtained in equation (9) as a linear state estimate of the driver steering input, the actual value of δ d,ss is set to lie within the interval centered on δ d,ss, thus yielding a perturbation range, expressed in detail as:
where e represents a non-negative parameter, δ d,max represents the maximum value of δ d;
Constraint delta d∈Wz (z) is expressed as The specific expression of the polyhedral constraint in (a) is as follows:
wherein W d represents the perturbation set of the front wheel corner.
3. The robust coordination control method for a vehicle under unknown driver status according to claim 2, wherein in step S2, the completion of the control of the vehicle includes the sub-steps of:
S201, setting a linear mode of the front and rear tires in a linear region under the input values delta d and the additional uncertainty values w u of all allowed drivers on the steering wheel as a mode 1; when the vehicle exceeds the mode 1, obtaining steering input by the controller, and returning the vehicle to the mode 1 in a time step; when the vehicle is in the mode 1, the controller is utilized to enable the vehicle in the next time step to be in the mode 1, and the specific contents are as follows:
In the state space, a single step robust backward reachable set of a given target set Z is defined as:
Wherein z + represents the predicted state of the next time step, obtained by formula (7); q represents a set of polyhedral regions of states and input constraints corresponding to nine modes of the vehicle, Pre (Z) represents a single step robust backward reachable set;
set P 1＝Projz(Q1), wherein For the state and input constraints of mode 1, the robust control invariant set, the maximum robust control invariant set, and the corresponding control map are represented as:
If for each And each delta d∈Wz (z), there is a control u such that (z, u, delta d)∈Q1 andAnd is true for all w u∈Wu (u), then the setIs a robust control invariant set for mode 1, wherein the maximum robust control invariant set for mode 1Is included in all modes 1A robust control invariant set of (2) corresponding toControl mapping of (a)The definition is as follows:
The N-step backward reachable set Z N of the target set Z is expressed as:
Zk＝Pre(Zk-1),(k＝1,...,N),Z0＝Z(14)；
If the vehicle state is in Z N, then the state of the vehicle is guaranteed to be controlled into the target set Z in N steps through a series of control inputs u (k) k=0 N-1;
The control map U k (·) corresponding to Z k is expressed as:
When the vehicle state exceeds the robust control invariant set, generating a control sequence by equation (15) such that the predicted state of the vehicle after N steps is within the target set, the controller driving the state back
S202, a specific formula of optimal control input is as follows:
Where u * represents the optimal control input, u *＝[δAFS,M]T; q and R represent positive definite matrices, u pre represents the control input of the previous time step command; r denotes the reference signal and,
If it isThenWhereas U *(z,δd)＝Uk(z,δd) where k represents the smallest positive integer where Z ε Z k;
Equation (16) applies only when the vehicle is in mode 1 or the front tires are not saturated; when the front tire is saturated, penalty terms are applied to the front wheel slip angle, and the AFS controls only the front wheel slip angle, so the optimization control problem translates into:
Wherein P is more than 0, A linear approximation representing the wheel slip angle before the next time step;
u * comprises two parts: u * (1) represents the front wheel steering angle, and δ AFS＝u*(1),u* (2) represents a yaw moment command;
The two are sent to the executor through the CAN bus to complete the whole control process.
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