CN111158264A - Model prediction control rapid solving method for vehicle-mounted application - Google Patents
Model prediction control rapid solving method for vehicle-mounted application Download PDFInfo
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Abstract
The invention discloses a model predictive control rapid solving method for vehicle-mounted application, which comprises the following steps: building a high-fidelity vehicle model; building a vehicle model describing the yaw motion and the lateral motion of the vehicle; establishing a reference model, and generating reference values of a yaw velocity and a centroid slip angle according to the current vehicle speed and the front wheel steering angle of the vehicle; describing the model predictive control problem as a typical nonlinear optimization problem according to the established vehicle model and control requirements; aiming at the nonlinear optimization problem, the nonlinear optimization problem is rapidly solved based on the Pontryagin minimum value principle and the Nelder-Mead algorithm; and respectively calculating additional torques of the four tires according to the optimal control input calculated by the model predictive controller, and distributing the additional torques to the four hub motors. The invention can greatly improve the solving speed and improve the real-time property of the controller on the premise of ensuring the solving precision.
Description
Technical Field
The invention relates to a method for quickly solving a nonlinear optimization problem in model predictive control for vehicle-mounted application, in particular to a method for quickly solving the nonlinear optimization problem by utilizing vehicle dynamics, a Pontryagin minimum value principle (PMP), a Nelder-Mead algorithm and the like, which is called NM-PMP for short.
Background
Model predictive control is a control method for on-line calculation rolling optimization based on a model of a controlled object. The model predictive control carries out optimization control on the system based on the current feedback information and the model of the system object, and because the model of the system is considered, the corresponding constraint of the system can be considered in the model predictive control, and meanwhile, the multi-objective optimization aiming at the system can be realized. Because the model predictive control has the characteristics and advantages, the technology based on the model predictive control framework system can well solve the problems in the field of vehicle control, such as vehicle stability control, vehicle automatic driving control, predictive cruise control and the like. With the continuous development of the technology, the performance requirements of the vehicle on the controller are higher and higher, but the computing power of the vehicle-mounted controller is quite limited. The vehicle is a typical fast-changing system, and particularly in certain typical applications, such as stability control of the vehicle, the calculation speed of a controller must be increased so as to obtain better performance. Therefore, the current model predictive control for vehicles has the following problems:
1. since the vehicle is a complex nonlinear system, and as the performance requirement of the controller is continuously improved, the traditional method for performing linear approximation near the working point cannot meet the precision requirement, so that a nonlinear model with higher precision needs to be adopted, and the complexity of the optimization problem is greatly increased due to the introduction of the nonlinear model.
2. Due to the fact that the complexity of the nonlinear optimization problem is greatly increased, the time required by corresponding solving is also greatly increased, and meanwhile, the vehicle is a quick-change system. Therefore, by applying the existing vehicle-mounted controller and the traditional solving algorithm (such as the sequence quadratic programming-SQP which is widely applied), the requirement of the vehicle on the real-time property of the controller is probably not met.
3. Although the problem of complex nonlinear optimization can be solved by installing a better-performance vehicle-mounted controller, the cost and the energy consumption of the whole vehicle are inevitably increased. Therefore, if the solving algorithm can be improved and the solving speed is increased, the performance of the controller can be improved on the basis of the existing vehicle-mounted controller, and meanwhile, the hardware cost is greatly saved and the energy consumption of the whole vehicle is not increased.
Disclosure of Invention
The method mainly aims at solving the problem that in model predictive control for vehicle-mounted application, because a vehicle system is a nonlinear system, when the system prediction time domain is long, the described nonlinear optimization problem is more complex, so that the solving time is increased, and a vehicle-mounted controller can not meet the requirement of vehicle real-time property; and the vehicle-mounted controller has limited computing capability due to the aspects of cost control, power consumption reduction and the like. Thus, when the described non-linear optimization problem is complex, the computational time required by the onboard controllers may not be sufficient to meet the real-time requirements of the vehicle system. Aiming at the problems, the invention provides a method for quickly solving a nonlinear optimization problem in model predictive control for vehicle-mounted application, and particularly relates to a method for quickly solving an optimal control nonlinear optimization problem based on the Pontryagin minimum value principle and a Nelder-Mead algorithm. The method can greatly improve the solving speed and improve the real-time performance of the controller on the premise of ensuring the solving precision.
In order to solve the technical problems, the invention is realized by adopting the following technical scheme:
a model predictive control rapid solving method for vehicle-mounted application comprises the following steps:
step one, building a high-fidelity vehicle model: selecting a vehicle model in CarSim software, reading the motion state parameters of the vehicle into Simulink, constructing a simulation working condition of running under a low-adhesion road surface based on the selected vehicle model, and simulating the yaw motion and the lateral motion characteristics of the actual vehicle;
step two, designing a model prediction controller based on a fast solving algorithm:
1) building a vehicle model describing the yaw motion and the lateral motion of the vehicle;
2) establishing a reference model, and generating reference values of a yaw velocity and a centroid slip angle according to the current vehicle speed and the front wheel steering angle of the vehicle;
3) describing the model predictive control problem as a typical nonlinear optimization problem according to the established vehicle model and control requirements;
4) aiming at the nonlinear optimization problem, the nonlinear optimization problem is rapidly solved based on the Pontryagin minimum value principle and the Nelder-Mead algorithm;
and step three, respectively calculating the additional torques of the four tires according to the optimal control input calculated by the model predictive controller, and distributing the additional torques to the four hub motors.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention provides an indirect solving mode of a nonlinear optimization problem in vehicle stability model predictive control for vehicle-mounted application according to the Pontryagin minimum value principle and vehicle dynamics, and provides a rapid solving algorithm of an optimal control problem based on the principle. Compared with the traditional optimization algorithm, the algorithm provided by the invention can effectively reduce the solving time and improve the algorithm instantaneity.
2. The method converts the original nonlinear optimization problem according to the Pontryagin minimum principle, and uses the Nelder-Mead algorithm to search and solve, and the method does not need to calculate derivatives, so that the method has wider applicability, and can adopt various vehicle dynamics models.
Drawings
These and/or other aspects of the present invention will become apparent from the following further description of embodiments of the invention, when taken in conjunction with the accompanying drawings. Wherein:
FIG. 1 is a block diagram of a controller in a simulation experiment;
FIG. 2 is a two degree of freedom model of a vehicle;
FIG. 3 is a schematic diagram of an optimal control input analytic solution iterative relationship;
FIG. 4 is a calculation time based on a conventional SQP solution method in a simulation process;
FIG. 5 is a calculation time of NM-PMP solution method according to the present invention during simulation;
FIG. 6 is the average computation time of two different solution methods in different prediction time domains during the simulation;
FIG. 7 is a plot of yaw rate of a vehicle and corresponding reference values when the controller is turned on and off as designed based on the solving algorithm described in the present invention during a simulation;
FIG. 8 is a plot of the centroid slip angle of the vehicle and corresponding reference values for the controller on and off as designed based on the solution algorithm described in the present invention during the simulation;
FIG. 9 is a plot of objective function values as solved during simulation based on the conventional SQP method and the NM-PMP method of the present invention, and in different prediction time domains;
FIG. 10 is a yaw-rate curve and its corresponding reference values when based on the conventional SQP method and the NM-PMP method according to the present invention in a simulation process;
FIG. 11 is a graph of centroid slip angle during simulation based on the conventional SQP method and the NM-PMP method of the present invention.
Detailed Description
The present invention will be fully explained with reference to the accompanying drawings for illustrating technical contents, construction features, and objects of the invention in detail.
A block diagram of a controller designed based on the fast solving algorithm of the present invention is shown in FIG. 1, wherein the driver is a driver model carried by CarSim, and is used in the simulation to maintain a specific vehicle speed and follow a given desired path. The reference model is used for generating reference values of the yaw rate and the centroid slip angle according to the current vehicle speed and the front wheel rotation angle given by the driver, and sending the generated reference values to the controller. The controller is used for calculating control quantity according to the reference value given by the reference model and the current state information of the vehicle so that the vehicle can track the reference value of the upper transverse swing angular speed and the centroid sideslip angle. The torque distribution is used for distributing required torque to the four hub motors according to the expected torque of the driver and the additional yaw moment calculated by the controller. In the simulation experiment, a vehicle model and a simulation working condition are both constructed in CarSim, and a controller is constructed in Simulink.
The rapid solving algorithm and the corresponding controller thereof are realized and verified by the joint simulation of a software system.
1. Software selection
The rapid solving algorithm, the corresponding controller of the rapid solving algorithm and the simulation model of the controlled object controlled by the controller are respectively built through Matlab/Simulink software and high-fidelity vehicle dynamics simulation software CarSim, the software versions are Matlab R2019b and CarSim2016.1 respectively, and the solver is ODE 1. The simulation step size is 0.001 s. The CarSim software is a commercial high-fidelity vehicle dynamics simulation platform, the main function of the system is to provide a high-fidelity vehicle dynamics model and corresponding simulation working conditions, and the model replaces a real vehicle in a simulation experiment to be used as an implementation object of a designed rapid solution algorithm; MATLAB/Simulink software is used for building a simulation model of the controller, namely the operation of the controller in the method is completed through Simulink programming.
2. Joint simulation setup
To realize the joint simulation of the two, firstly, a path of CarSim needs to be added in the path setting of Matlab; secondly, adding an output interface module in the CarSim interface; then the model information in the CarSim is compiled by the system and then is kept in the Simulink in the form of CarSimS-function, and finally the parameter setting of the CarSim module in the Simulink is carried out. When the Simulink simulation model is run, the CarSim model is also calculated and solved at the same time. And data exchange is continuously carried out between the two in the simulation process. If the model structure or parameter settings in the CarSim are modified, recompilation is required, and then the new CarSim module containing the latest setting information is sent back to Simulink.
3. The invention relates to a model prediction control rapid solving method for vehicle-mounted application, which comprises the steps of firstly, deducing a mathematical model capable of correctly describing yaw motion and lateral motion of a vehicle; secondly, selecting a proper vehicle model from high-fidelity vehicle dynamics simulation software CarSim and acquiring corresponding parameters; then, establishing a simulation working condition under a low-adhesion road surface based on the selected vehicle model; the controller for vehicle stability control is then derived based on the fast solution algorithm described in the present invention. Finally, the method provided by the invention is verified in a joint simulation experiment, and is compared with the traditional SQP solving algorithm to illustrate the beneficial effects of the method.
The invention provides a model predictive control rapid solving method for vehicle-mounted application, which specifically comprises the following steps:
step one, building a high-fidelity vehicle model: selecting a vehicle model from CarSim software, reading the motion state parameters of the vehicle into Simulink, constructing a simulation working condition of running under a low-adhesion road surface based on the selected vehicle model, and simulating the yaw motion and the lateral motion characteristics of the actual vehicle.
The high-fidelity vehicle model simulates a real controlled object and has the main function of accurately simulating the characteristics of the yaw motion and the lateral motion of an actual vehicle. In the invention, because the joint simulation is used, in CarSim, the vehicle model selection and the construction of the simulation working condition are mainly used.
Firstly, a typical passenger car model is selected, then relevant parameters of the model are modified and obtained, and vehicle model parameters are added into a Simulink simulation model. The main model parameters of the vehicle are vehicle mass, wheelbase tire cornering stiffness, and the like. After selecting the corresponding vehicle model and parameters, corresponding simulation conditions need to be constructed, and the driving route, the driving environment, the driver model and the like of the vehicle can be selected in the simulation conditions. In the invention, the stability of the vehicle is controlled only by adding the yaw moment, so that a driver model carried in CarSim is selected, the motion state parameters of the vehicle are read into Simulink, and the simulation working condition under the low-adhesion road surface is constructed based on the selected vehicle model.
Step two, designing a controller based on a fast solving algorithm: the required control problem is described based on a model prediction control principle, the control problem is described as a nonlinear optimization problem, and the design of the controller is carried out based on the rapid solution algorithm.
Since the controlled object of the present invention is a vehicle traveling on a low-adhesion road surface, the control target is to calculate the required additional yaw moment from the current state information of the vehicle and the current reference value, thereby improving the stability of the vehicle. The main design process is described below.
1) Mathematical models are created that describe the yaw motion and the lateral motion of the vehicle.
1.1) two-degree-of-freedom model building of vehicle
The invention uses a two-degree-of-freedom model of the vehicle in which only the lateral and yaw movements of the vehicle are taken into account. As shown in fig. 2, the front axle tire and the rear axle tire (gray tire in fig. 2) are compressed into one tire (black tire in fig. 2), respectively. The driver can only turn the front wheels and the turning angles of the two front wheels are equal. The vehicle model can be simplified into a vehicle two-degree-of-freedom model. Meanwhile, according to the theory of vehicle dynamics, the simplified two-degree-of-freedom model of the vehicle can be described by the following equation:
wherein the content of the first and second substances,
and
respectively representing the derivative of the centroid slip angle of the vehicle and the derivative of the yaw rate of the vehicle, V representing the longitudinal speed of the vehicle, FyfAnd FyrThen represents the tire lateral force of the front and rear tires, respectively, LfAnd LrRespectively, the distance from the front and rear axes to the center of mass of the vehicle, m being the mass of the vehicle, IzIs the moment of inertia, Δ M, of the vehicle about the center of masszAn additional yaw moment.
1.2) non-Linear tire model building
In the present invention, to improve the accuracy of the model, the lateral force of the tire is described by a non-linear model, using the Fiala tire model in which the tire slip angle is used as an internal variable, when the tire slip angle α is small, there is tan (α) ≈ α, after which the tire model can be approximated as:
wherein, FyIs the tire lateral force, mu is the road adhesion coefficient, FzCornering stiffness C of the tyre for vertical loadsαDividable into front wheel cornering stiffness CfAnd rear wheel cornering stiffness Crα is tire slip angle, which can be divided into front wheel slip angle αfAnd rear wheel side slip angle αrThey can be calculated from the following formula:
wherein, deltafIs the front wheel angle of the vehicle.
2) Vehicle reference model building
In the present invention, the yaw-rate reference value of the vehicle is determined by the current front wheel steering angle, and in general, it is first assumed that
And β is 0, then a first order linear reference model can be obtained, but in fact, when the vehicle is turning, the center of mass slip angle β of the vehicle is not equal to zerozWhen applied to a vehicle, the above assumption is not reasonable because the additional yaw moment causes a change in the yaw angle of the center of mass of the vehicle. However, when the vehicle is operating in the linear region, the vehicle must be stable, and then the reference centroid slip angle can be calculated based on the stable region of the vehicle. First, the non-linear term of the tire lateral force and the additional yaw moment are omitted, and then a two-degree-of-freedom linear model about the yaw rate and the mass center slip angle can be obtained:
on the basis of the equation (4), the response of the vehicle with respect to the front wheel steering angle can be obtained, and then the front wheel steering angle δ can be obtainedfReference yaw rate gamma to vehiclerefAnd a reference centroid slip angle βrefThe transfer function of (a) is:
at this time, we define the stability factor of the vehicle as
Wherein L ═ Lf+LrIs the wheelbase of the vehicle. The oscillation frequency of the system is
The damping coefficient of the system is
Yaw rate steady state gain of
Centroid slip angle steady state gain of
Wherein the differential coefficients are respectively defined as
And
it is also noted that when the road surface has a low traction coefficient, the maximum amount of tire force that can be generated by the tire is not sufficient to support the large yaw rate required. In this case, the reference value of the yaw rate needs to be appropriately limited to adapt to the friction coefficient of the road surface. To achieveTo achieve satisfactory performance, the upper limit value of the yaw rate is defined as
Reference value gamma of yaw raterefShould be constrained to | γref|≤γup. Similarly, we define the upper limit of the centroid slip angle as
Reference value β for yaw raterefShould be constrained to | βref|≤βup。
3) Non-linear controller design
In order to improve the stability of the vehicle, the main control requirement is to make the vehicle follow the reference value of the yaw rate under the action of the controller. A block diagram of the controller is shown in fig. 1. The additional yaw moment calculated by the controller is realized by the additional torques of the four hub motors.
Firstly, defining the state vector of the system as x ═ x1,x2]T＝[β/βup,γ/γup]T. The controlled variable is defined as u ═ Δ Mz/ΔMmax. At each sampling point kT by discretizing equation (1)sThe discretized state space equation can be obtained as follows:
in which the lateral force FyfAnd FyrCalculated from the non-linear tire model in equation (2), βupAnd gammaupUpper limit values, Δ M, of the centroid yaw angle and yaw rate, respectivelymaxFor maximum value of additional yaw moment, TsFor the sampling time,. DELTA.MzAn additional yaw moment.
Since the main objective of the controller is to track the reference value of the yaw rate while taking into account the reference value of the centroid slip angle, k +1 ≦ k at each instantiK + N +1 defines a cost function as:
wherein L is1(ki)、L'2(ki) And L3(ki) Respectively used for tracking a yaw angular velocity reference value, tracking a centroid slip angle reference value and inhibiting the actuating energy. The state constraint is | x1(ki) Less than or equal to 1, and the controlled quantity is limited to | u (k)i-1) less than or equal to 1. At this time, the objective function of the nonlinear model predictive control can be obtained as follows:
the constraint satisfied is | u (k)i-1) | is less than or equal to 1 and | x1(ki) L is less than or equal to 1, wherein gamma isβAnd ΓuRespectively are the weight coefficients of the centroid slip angle and the controlled variable, and N is a prediction time domain.
4) Fast solving algorithm
From the Pontryagin minimum principle, for a given integral performance index, the control is constrained to the optimal control problem:
if u*(t) and
an optimal solution that minimizes the performance index, and x under the action of the optimal solution*(t) the optimal trajectory formed, then the following requirements can be derived:
① x (t) and λ (t) satisfy the regular equation:
wherein H (x, λ, u) ═ L (x, u) + λT(t) f (x, u) is a Hamiltonian.
② x (t) and λ (t) satisfy the boundary condition:
the ③ Hamiltonian takes absolute minimum values under the action of the optimal control solution:
④ while the Hamiltonian satisfies at the ends of the trace:
H[x*(t),λ(t),u*(t)]＝H[x*(tf),λ(tf),u*(tf)]＝constant (13)
it can be seen from the above requirements that the state constraint of the system cannot be taken into account, so that the state constraint | x of the two-degree-of-freedom model of the vehicle needs to be constrained according to the vehicle dynamics equation1(ki) And (5) carrying out certain treatment with the | less than or equal to 1. The invention introduces a relaxation function to carry out conversion processing on the state constraint:
where κ represents the degree of relaxation of the function and ν is a large number to ensure that the optimal state trajectory is within the constraints. After the relaxation function is introduced, if the solved state is close to the constraint value, the penalty term of the function will increase rapidly, and when the state is within the constraint range, the penalty term of the function will be approximately equal to zero. Final cost function L2(ki) Can be expressed as:
L2(ki)＝L′2(ki)+ζ(ki) (15)
the optimization problem represented by equation (8) is redefined here as:
while satisfying the state constraint | x of the system1(ki)|≤1。
And discretizing the optimal necessity condition according to the Pontryagin minimum principle. Then according to the discretized two-degree-of-freedom model of the vehicle, defining that k is more than or equal to k at the moment k +1iThe Hamiltonian of ≦ k + N +1 is:
wherein F1(x(ki) And F) and2(x(ki) Respectively) are defined as:
in the above equation, λ1(k) And λ2(k) Respectively representing Lagrange multipliers, and obtaining the optimal necessity conditions according to the Pontryagin minimum value principle as follows:
the terminal conditions are as follows:
at each moment there is an optimum control law u*(ki) Minimizing the hamiltonian:
based on the requirement condition, we can give a mapping relationship from the initial state to the terminal state, as shown in fig. 3.
At a certain moment kiAt a known state λ (k)i) And x (k)i) Under the condition, an analytical solution of the optimization problem is given based on the Pontryagin minimum value principle. For the sake of simplicity, the present inventionThe Hamiltonian is rewritten with respect to the control quantity u (k)i) In the form of a quadratic function:
H(x(ki),u(ki))＝p1u(ki)2+p2(ki)u(ki)+g(x(ki)) (22)
wherein p is1＝Γu，p2(ki)＝λ2(ki)ΔMmax/(γupIz) And has the following components:
the optimal control law that minimizes the hamiltonian can then be given:
at this time, the original optimization problem is converted to find the optimal initial state lambda*(k) So that the terminal state satisfies the terminal condition. In other words, the original optimization problem is transformed into a two-point edge value problem:
the two-point boundary value problem is solved by a Nelder-Mead algorithm in the invention, and the optimal control law can be finally obtained as follows:
obtaining the optimal control law u*(k) Then, the additional torques of the four tires can be calculated according to the calculated control law:
wherein Δ Tcfl(k),ΔTcrl(k),ΔTcfr(k),ΔTcrr(k) Respectively, the additional torques of the left front wheel, the left rear wheel, the right front wheel and the right rear wheel, ReIndicating the rolling radius of the tire and d the width of the vehicle body.
4. Verifying and comparing by a simulation experiment:
in order to verify the effectiveness of the rapid solving algorithm of the model predictive control optimization problem provided by the invention, and meanwhile, in order to compare with the traditional solving algorithm, a simulation experiment needs to be designed for verification and comparison. The stability control of the vehicle is a typical vehicle control problem, and the control problem also has a high requirement on the real-time performance of the controller, so that the simulation experiment designed by the invention is a vehicle stability control problem on a low-adhesion road surface. In contrast, the traditional solution algorithm selects the Sequence Quadratic Programming (SQP) which is widely applied.
The invention designs a controller based on the algorithm to control the stability of the vehicle running on the low-adhesion road surface. Meanwhile, the solving speed and the solving effect of the traditional solving algorithm are compared. The above verification and comparison were performed by simulation experiments. The parameters of the vehicle model used in the simulation are mass m 1430kg and vehicle front axle base Lf1.05m, rear axle base L of vehicler1.61m, moment of inertia of vehicle about centre of mass Iz＝2059.2kg·m2Front wheel equivalent cornering stiffness Cf90700N/rad, rear wheel equivalent cornering stiffness Cr109000N/rad, wheel radius Re0.325m, 1.55m for the vehicle body width d, and 0.35 for the road surface adhesion coefficient μ. The state constraints are respectively gammaup0.2058rad/s and βup0.0376rad, vehicle longitudinal speed V60 km/h, sampling time Ts0.012s, predicted time domain N is 20, maximum additional yaw moment Δ Mmax800 Nm. The weight coefficients in the objective function are each Γβ0.2 and Γu＝0.125。
(1) Example (b): double-shift line working condition experiment
In a simulation experiment, a double-lane-shifting working condition is selected, the vehicle speed is 60km/h and is kept unchanged in the whole working condition, and the driver model is a pre-aiming driver model. In order to verify the effectiveness of the rapid solving algorithm provided by the invention and compare the algorithm with the traditional SQP algorithm, the two algorithms are respectively used for solving the optimization problem in model predictive control, and then the solving precision and the solving speed are compared.
Fig. 4 and 5 show the solving time of the SQP-based solving algorithm and the NM-PMP solving algorithm according to the present invention, respectively. As can be seen from the figure, both SQP-based and NM-PMP-based solution algorithms have increased computation time as the prediction horizon increases. However, under the same prediction time domain, the solution time of NM-PMP algorithm is much shorter than that of SQP algorithm. When the optimization problem is more complex, such as during seconds 4 through 11, the solution time for NM-PMP algorithm may be about ten times faster than the solution time for SQP algorithm. Fig. 6 shows the average calculation time of two solution algorithms in different prediction time domains, and it can be seen that as the prediction time domain increases, the average calculation time of the NM-PMP algorithm and the prediction time domain are in a substantially linear relationship and increase more slowly, while the average calculation time of the SQP algorithm and the prediction time domain are in an exponential relationship and increase more quickly, and the average calculation time is also greater than the calculation time of the NM-PMP algorithm. The two points fully show the benefits of the rapid solving algorithm.
Fig. 7 and 8 show the control effect of the vehicle under the action of the controller designed based on the NM-PMP algorithm of the present invention, and it can be seen from fig. 7 that under the action of the controller, the vehicle can better track the reference value of the yaw rate, effectively improving the maneuverability of the vehicle. As can be seen from fig. 8, under the action of the controller, the centroid slip angle of the vehicle can be suppressed within a small range, and the stability of the vehicle is greatly improved compared with the situation without the action of the controller. The NM-PMP algorithm of the invention has the advantages of high solving speed and good control effect.
The simulation experiment also compares the control effects of the two solving algorithms. Fig. 9 shows the convergence of the objective function values of the two solving algorithms in different prediction time domains, and it can be seen from fig. 9 that, when both algorithms can solve the optimization problem, the objective function value calculated by the NM-PMP algorithm of the present invention is only slightly smaller than the objective function value calculated by the SQP algorithm in the same prediction time domain. The NM-PMP algorithm of the invention can also keep higher solving precision under the condition of greatly accelerating the calculating speed. On the other hand, when the optimization problem is more complex and the SQP algorithm cannot be solved, the divergence of the objective function value of the SQP algorithm is increased rapidly, and the NM-PMP algorithm can find a suboptimal solution, so that the objective function is kept in a smaller range.
Fig. 10 and 11 show the control effect under the controller of the two algorithms, and it can be seen from fig. 10 that the vehicle can better track the reference value of the yaw rate and have better maneuverability under the controller of the NM-PMP algorithm. As can be seen from fig. 11, the centroid slip angle can be suppressed to a smaller range by the NM-PMP algorithm controller, thereby providing better stability to the vehicle.
As can be seen from the simulation example, the NM-PMP algorithm of the invention can ensure higher solving precision under the condition of greatly improving the calculating speed. In addition, when the traditional SQP algorithm cannot solve, the NM-PMP algorithm of the invention can solve a suboptimal solution, thereby realizing better overall performance.
Claims (6)
1. A model predictive control rapid solving method for vehicle-mounted application is characterized by comprising the following steps:
step one, building a high-fidelity vehicle model: selecting a vehicle model in CarSim software, reading the motion state parameters of the vehicle into Simulink, constructing a simulation working condition of running under a low-adhesion road surface based on the selected vehicle model, and simulating the yaw motion and the lateral motion characteristics of the actual vehicle;
step two, designing a model prediction controller based on a fast solving algorithm:
1) establishing a vehicle model describing the yaw motion and the lateral motion of the vehicle, wherein the vehicle model comprises a two-degree-of-freedom model and a non-linear tire model;
2) establishing a reference model, and generating reference values of a yaw velocity and a centroid slip angle according to the current vehicle speed and the front wheel steering angle of the vehicle;
3) describing the model predictive control problem as a typical nonlinear optimization problem according to the established vehicle model and control requirements;
4) aiming at the nonlinear optimization problem, the nonlinear optimization problem is rapidly solved based on the Pontryagin minimum value principle and the Nelder-Mead algorithm;
and step three, respectively calculating the additional torques of the four tires according to the optimal control law calculated by the model predictive controller, and distributing the additional torques to the four hub motors.
2. The method for rapidly solving the model predictive control oriented to the vehicle-mounted application as claimed in claim 1, wherein in the second step, the vehicle model established in the step 1) comprises:
vehicle two-degree-of-freedom model:
wherein the content of the first and second substances,
and
the derivative of the centroid slip angle of the vehicle and the derivative of the yaw rate of the vehicle are represented, V represents the longitudinal speed of the vehicle, FyfAnd FyrThen represents the tire lateral force of the front and rear tires, respectively, LfAnd LrRespectively, the distance from the front and rear axes to the center of mass of the vehicle, m being the mass of the vehicle, IzIs the moment of inertia, Δ M, of the vehicle about the center of masszAn additional yaw moment;
the tire model can be approximated as:
wherein, FyIs the tire lateral force, mu is the road adhesion coefficient, FzCornering stiffness C of the tyre for vertical loadsαDividable into front wheel cornering stiffness CfAnd rear wheel cornering stiffness Crα is the slip angle of tyre.
3. The method for rapidly solving the model predictive control oriented to the vehicle-mounted application as claimed in claim 1, wherein in the second step, the reference model established in the step 2) comprises:
two-degree-of-freedom linear models for centroid yaw angle and yaw rate:
in the formula (I), the compound is shown in the specification,
and
representing a derivative of a centroid slip angle of the vehicle and a derivative of a yaw rate of the vehicle, respectively; cfFront wheel cornering stiffness; crIs rear wheel cornering stiffness; v represents the longitudinal speed of the vehicle; l isfAnd LrRespectively representing the distance of the front and rear axes to the center of mass of the vehicle; m is the mass of the vehicle; i iszIs the moment of inertia of the vehicle about the center of mass.
4. The method for rapidly solving the model predictive control oriented to the vehicle-mounted application as claimed in claim 1, wherein in the second step, step 3) describes the model predictive control problem as a typical nonlinear optimization problem, and the objective function of the nonlinear model predictive control is as follows:
the constraint satisfied is | u (k)i-1) | is less than or equal to 1 and | x1(ki) L is less than or equal to 1, wherein gamma isβAnd ΓuRespectively are the weight coefficients of the centroid slip angle and the controlled variable, and N is a prediction time domain.
5. The vehicle-mounted application-oriented model predictive control rapid solving method as claimed in claim 1, wherein in the second step, the step 4) of rapidly solving the nonlinear optimization problem based on the Pontryagin minimum principle and the Nelder-Mead algorithm comprises the following processes:
rewriting the Hamiltonian as related to the control quantity u (k)i) In the form of a quadratic function:
H(x(ki),u(ki))＝p1u(ki)2+p2(ki)u(ki)+g(x(ki))
wherein p is1＝Γu，p2(ki)＝λ2(ki)ΔMmax/(γupIz) And has:
the optimal control law that minimizes the hamiltonian is given:
the original optimization problem is transformed into a two-point boundary value problem:
the two-point boundary value problem is solved through a Nelder-Mead algorithm, and finally the optimal control law is obtained as follows:
6. the on-vehicle application-oriented model predictive control fast solving method of claim 5, wherein in the third step, the additional torque calculation processes of four tires are as follows:
obtaining the optimal control law u through the step two*(k) Thereafter, the additional torques of the four tires were calculated, respectively:
wherein, Delta Tcfl(k),ΔTcrl(k),ΔTcfr(k),ΔTcrr(k) Respectively, the additional torques of the left front wheel, the left rear wheel, the right front wheel and the right rear wheel, ReIndicating the rolling radius of the tire and d the width of the vehicle body.
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