CN115113526A - Nonlinear error feedback torque control method, system and constraint method - Google Patents
Nonlinear error feedback torque control method, system and constraint method Download PDFInfo
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Abstract
The invention relates to a nonlinear error feedback torque control method, a nonlinear error feedback torque control system and a constraint method. The nonlinear error feedback torque control method comprises the following steps: taking one wheel of the automobile as a control object, acquiring a slip rate value and a slip rate threshold value of the wheel, and calculating a difference value between the slip rate value and the slip rate threshold value to obtain a slip rate deviation; acquiring a driving torque actual value of a wheel, and calculating a difference value between the driving torque actual value and a preset driving torque expected value to obtain a driving torque deviation; calculating a driving torque adjustment value of the wheel by nonlinear combination of the slip ratio deviation and the driving torque deviation; and adjusting the actual driving torque value of the wheel through the driving torque adjusting value until the actual driving torque value of the wheel is the same as the expected driving torque value. The invention adopts a nonlinear error mode to obtain the driving torque adjustment value, can reduce the error rate and improve the accuracy of the automobile torque adjustment, thereby effectively preventing the wheel from slipping.
Description
Technical Field
The invention relates to the technical field of electric automobiles, in particular to a nonlinear error feedback torque control method, a nonlinear error feedback torque control system and a particle swarm extension-based torque constraint control method.
Background
The distributed hub motor driven automobile has the advantages that the space in the hub is small, the motor is prone to generating faults, accordingly, the driving performance of the distributed hub motor driven automobile is affected, and the driving stability of the distributed hub motor driven automobile is affected in severe cases. Because the road surface condition of the automobile is changed all the time in the driving process, the wheel of the automobile is easy to slip when the automobile is driven on a low-attachment road surface, the driving torque of the wheel needs to be adjusted in order to prevent the wheel from slipping, and the accuracy of the adjustment of the automobile is limited due to large errors in the actual adjustment process, so that the wheel cannot be effectively prevented from slipping.
Disclosure of Invention
Accordingly, it is necessary to provide a nonlinear error feedback torque control method, a nonlinear error feedback torque control system, and a particle swarm extension-based control torque constraint method, for solving the problem of a large torque adjustment error for preventing wheel slip.
In order to realize the purpose, the invention adopts the following technical scheme:
the nonlinear error feedback torque control method is applied to an automobile and used for adjusting a driving torque parameter of an automobile model of the automobile, the automobile is provided with a plurality of wheels, the automobile model is provided with one driving torque parameter for each wheel, the automobile model obtains a driving torque actual value of a corresponding wheel according to different driving torque parameters so as to prevent the corresponding wheel from slipping, and the nonlinear error feedback torque control method comprises the following steps:
taking one wheel of an automobile as a control object, acquiring a slip rate value and a slip rate threshold value of the wheel, and calculating a difference value between the slip rate value and the slip rate threshold value to obtain a slip rate deviation;
acquiring a driving torque actual value of the wheel, and calculating a difference value between the driving torque actual value and a preset driving torque expected value to obtain a driving torque deviation;
and carrying out nonlinear combination on the slip rate deviation and the driving torque deviation to obtain a nonlinear control law, wherein the nonlinear control law u 0 ＝k 0 e 0 +fst(e 1 ，c 0 e 2 ，r 0 ，h 0 )，e 0 ＝∫e 1 ，k 0 Is a gain coefficient, c 0 As damping coefficient, h 0 For the sampling time, the coefficient r is adjusted 0 ＝0.05/h 0 Fst (-) is the steepest control synthesis function, e 1 As slip ratio deviation, e 2 Is the torque deviation;
calculating a driving torque adjustment value of the wheel through the nonlinear control rate, wherein the driving torque adjustment value
Wherein, b 0 Is a compensation factor;
and taking the driving torque adjustment value as the driving torque parameter to adjust the actual driving torque value of the wheel until the actual driving torque value of the wheel is the same as the expected driving torque value so as to prevent the wheel from skidding.
Further, the method for calculating the slip rate threshold value includes the following steps:
acquiring yaw rate deviation and the slip rate value of the wheels;
and obtaining the threshold value of the slip rate by the yaw rate deviation and the slip rate value through a fuzzy threshold value algorithm.
Further, the method for calculating the yaw-rate deviation includes the steps of:
acquiring an actual yaw rate value of the wheels;
and calculating the difference value between the actual yaw rate value and the reference yaw rate value of the wheels to obtain the yaw rate deviation.
Further, the design method of the steepest control synthesis function includes the following steps:
calculating an intermediate variable d according to the sampling time h required by the nonlinear error feedback control and a third input variable r corresponding to the sampling time h: d ═ rh;
calculating an intermediate variable d from the intermediate variable d 0 ：d 0 ＝hd；
According to a first input variable x 1 And a second input variable x 2 Calculating an intermediate variable y: y is x 1 +hx 2 ；
Calculating the intermediate variable a 0 ：
Calculating an intermediate variable a:
calculating the steepest control synthesis function fst (x) 1 ,x 2 ,r,h 0 )：
Further, the method for calculating the slip value comprises the following steps:
obtaining the wheel rotation linear velocity V of the automobile ω And the speed v of the vehicle x ；
Calculating the slip rate value:
the present invention also provides a nonlinear error feedback torque control system, which implements the steps of the above nonlinear error feedback torque control method when the system is in operation, and the nonlinear error feedback torque control system comprises:
the slip rate deviation calculation module is used for taking one wheel of an automobile as a control object, acquiring a slip rate value and a slip rate threshold value of the wheel, and calculating a difference value between the slip rate value and the slip rate threshold value to obtain a slip rate deviation;
the driving torque deviation calculation module is used for acquiring a driving torque actual value of the wheel and calculating a difference value between the driving torque actual value and a preset driving torque expected value to obtain a driving torque deviation;
a nonlinear control rate calculation module for obtaining a nonlinear control law by nonlinear combination of the slip rate deviation and the driving torque deviation, wherein the nonlinear control rate u is 0 ＝k 0 e 0 +fst(e 1 ，c 0 e 2 ，r 0 ，h 0 )，e 0 ＝∫e 1 ，k 0 Is a gain coefficient, c 0 Is a damping coefficient, h 0 For the sampling time, the coefficient r is adjusted 0 ＝0.05/h 0 Fst (-) is the steepest control integral function, e 1 As slip rate deviation, e 2 Is the torque deviation;
a driving torque adjustment value calculation module for calculating a driving torque adjustment value of the wheel by the nonlinear control rate, the driving torque adjustment value
Wherein, b 0 Is a compensation factor;
and the driving torque actual value adjusting module is used for taking the driving torque adjusting value as the driving torque parameter so as to adjust the driving torque actual value of the wheel until the driving torque actual value of the wheel is the same as the driving torque expected value, so as to prevent the wheel from skidding.
The invention also comprises a particle swarm extension-based control torque constraint method which is applied to the nonlinear error feedback torque control method, and the particle swarm extension-based control torque constraint method comprises the following steps:
s1, obtaining a slip rate value s of the wheel and an actual centroid slip angle beta of the vehicle as characteristic quantities to form Q (s, beta), and establishing a coordinate system of an extensible control domain by taking the slip rate value s as a horizontal coordinate and the actual centroid slip angle beta as a vertical coordinate;
s2, carrying out regional division on the extension control domain:
the classical domain: ((-s) 1 ,s 1 )，(-β 1 ,β 1 ))；
And (3) extension domain: ((-s) 1 1 ,s 1 1 )，(-β 1 1 ,β 1 1 ) In which-s) 1 1 ∈(-s 2 ,-s 1 )，s 1 1 ∈(s 1 ,s 2 )，-β 1 1 ∈(-β 2 ,-β 1 )，β 1 1 ∈(β 1 ,β 2 )；
Non-domain: ((-s) 2 1 ,s 2 1 )，(-β 2 1 ,β 2 1 ) In which-s) 2 1 ∈(-∞,-s 2 )，s 2 1 ∈(s 2 ,∞)，-β 2 1 ∈(-∞,-β 2 )，β 2 1 ∈(β 2 , ∞)；
S3, acquiring a linear region boundary of the actual mass center slip angle gain of the vehicle, and taking the linear region boundary as a boundary beta of a vertical coordinate of the classical domain 1 Obtaining a slip threshold s of the wheel max As the abscissa boundary s of the classical domain 1 I.e. s 1 ＝s max ；
S4, calculating the slip rate optimal value s of the wheel by the particle group algorithm according to the slip rate value s of the current state of the wheel and the actual mass center slip angle beta of the current state of the vehicle 2 And the slip ratio optimum s 2 Corresponding optimal centroid side slip angle beta 2 ；
S5, judging whether the characteristic quantity is in a classical domain, if so, implementing torque constraint of the classical domain on the wheels of the vehicle;
s6, when the characteristic quantity is not in the classical domain, judging whether the characteristic quantity is in an extension domain, if so, implementing torque constraint of the extension domain on wheels of the vehicle;
and S7, when the characteristic quantity is not in an extension domain, the characteristic quantity is in a non-domain, and the non-domain torque constraint is implemented on the wheels of the vehicle.
Further, the slip ratio optimum s 2 And its corresponding optimum centroid slip angle beta 2 Is calculated by the method ofThe following:
(1) obtaining an actual value ω of yaw rate of the wheels z According to the actual value omega of the yaw angular velocity z And setting a fitness function according to the actual centroid slip angle beta
Wherein v is x Is the vehicle speed of the wheel, μ is the road adhesion coefficient, g is the gravitational acceleration;
(2) taking one wheel of the vehicle as a target individual and all wheels of the vehicle as a group, and taking the actual value omega of the yaw rate of each wheel z And the corresponding actual centroid slip angle beta are used as particle parameters to form particles, and all the particles are grouped into particle groups;
(3) acquiring particle parameters of the population in the historical optimal state under the actual road adhesion coefficient to serve as the historical population optimal solution, and acquiring particle parameters of the target individual in the historical optimal state under the actual road adhesion coefficient to serve as the historical individual optimal solution;
(4) calculating an adaptive value of the target particle by using the target particle through the fitness function by taking the actual particle parameter of the target individual as the target particle;
(5) comparing the adaptive value of the target particle with the adaptive value of the historical individual optimal solution, if the adaptive value of the target particle is greater than the adaptive value of the historical individual optimal solution, replacing the particle parameter of the target particle with the particle parameter of the historical individual optimal solution, updating the individual optimal solution, and if the adaptive value of the target particle is less than the adaptive value of the historical individual optimal solution, keeping the particle parameter of the historical individual optimal solution inconvenient;
(6) comparing the adaptive value of the target particle with the adaptive value of the optimal solution of the historical population, if the adaptive value of the target particle is greater than the adaptive value of the optimal solution of the historical population, replacing the particle parameter of the target particle with the particle parameter of the optimal solution of the historical population, updating the optimal solution of the population, and if the adaptive value of the target particle is less than the adaptive value of the optimal solution of the historical population, keeping the particle parameter of the optimal solution of the historical population inconvenient;
(7) iteratively updating the particle parameters of the target particles according to the individual optimal solution and the new population optimal solution, judging whether the iteration times reach a preset maximum iteration number, if not, returning the updated target particles to the step (3), if so, stopping iteration, and calculating the optimal value s of the slip rate from the actual value of the yaw velocity after the iteration of the target particles through a slip rate calculation formula 2 Taking the actual centroid slip angle after the target particle iteration is finished as the optimal centroid slip angle beta 2 。
Further, the iterative update method of the target particle comprises the following steps:
obtaining a maximum yaw rate of the target particles
The inertia weight tau of the target particle, the random number rand () of the target particle, which is more than 0 and less than 1, and the population optimal solution p of the kth generation of the target particle g Individual optimal solution p of kth generation of the target particle i Acceleration constant c of the target particle 1 And an acceleration constant c of the target particle 2 ；
Actual value of yaw rate according to k generation of target particle
And centroid slip angle of kth generation of the target particle
Calculating the k +1 th generation actual value of the yaw rate of the target particle
Calculating the centroid slip angle of the k +1 th generation of the target particle
Calculating the k-th generation yaw rate actual value of the target particle
And centroid slip angle of kth generation of the target particle
Updating to the k +1 th generation actual value of the yaw rate of the target particle
And centroid slip angle of the k +1 th generation of the target particle
Further, the inertia weight τ of the target particle is updated with the change of the iteration number, and the calculation method of the inertia weight includes the following steps:
obtaining a maximum weight τ of the target particle max Minimum weight τ of the target particle min ；
According to the iteration times t of the target particles gen Calculating an inertial weight τ of the target particle:
the technical scheme provided by the invention has the following beneficial effects:
the driving torque adjusting value is obtained by adopting a nonlinear error mode, the error rate can be reduced, and the accuracy of automobile torque adjustment is improved, so that wheels are effectively prevented from slipping, meanwhile, torque constraint is set, the automobile is further stabilized, the safe driving of the automobile is guaranteed, the situation that the automobile enters dangerous working conditions is reduced, and the adjustment of the torque is in a stable range.
Drawings
FIG. 1 is a logic diagram of a nonlinear error feedback torque control method of the present invention;
FIG. 2 is a schematic diagram of a torque coordinated distribution system based on FIG. 1;
FIG. 3 is a three-dimensional simulation of the fuzzy rule of FIG. 1;
FIG. 4 is a schematic diagram of the structure of an extensible control domain based on the extensible control torque constraint of FIG. 2;
fig. 5 is a schematic structural diagram of a stable region of the yaw moment control system based on fig. 2;
FIG. 6 is a simulation of the torque distribution system based on FIG. 2 taking into account torque losses;
FIG. 7 is a simulation diagram of the single-wheel torque loss system based on FIG. 2;
FIG. 8 is a simulation diagram of the two-wheel torque loss system based on FIG. 2;
FIG. 9 is a logic diagram based on the torque coordinated distribution system of FIG. 2.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The nonlinear error feedback torque control method solves the technical problem of large torque adjustment error for preventing wheel slip in the prior art, and the method adopts a nonlinear error mode to obtain the drive torque adjustment value, so that the error rate can be reduced, and the accuracy of automobile torque adjustment is improved, so that the wheel slip is effectively prevented, meanwhile, torque constraint is set, the automobile is further stabilized, the safe driving of the automobile is ensured, the condition that the automobile enters dangerous working conditions is reduced, and the torque adjustment is in a stable range.
As shown in fig. 1, the present embodiment provides a nonlinear error feedback torque control method, including the steps of:
one wheel of an automobile is taken as a control object, and a slip rate value s and a slip rate threshold value s of the wheel are obtained max Calculating the difference value to obtain the slip rate deviation e 1 I.e. e 1 ＝s max -s，
V ω Is the rotational linear velocity of the wheel, v x Is the speed of the vehicle;
will drive the actual value of torque T m And a preset desired value T for the drive torque h Calculating the difference to obtain the deviation e of the driving torque 2 I.e. e 2 ＝T m -T h ；
By slip rate deviation e 1 And a driving torque deviation e 2 Carrying out nonlinear combination to obtain a nonlinear control law, wherein the nonlinear control rate u 0 ＝k 0 e 0 +fSt(e 1 ，c 0 e 2 ，r 0 ，h 0 )，e 0 ＝∫e 1 ，k 0 Is a gain coefficient, c 0 Is a damping coefficient, h 0 For the sampling time, the coefficient r is adjusted 0 ＝0.05/h 0 Fat (·) is the steepest control synthesis function;
calculating a drive torque adjustment value
Wherein, b 0 To compensate for the factor, b 0 ＝1/Jω，J ω Is the wheel rotational inertia of 0.9 kg.m 2;
and adjusting the actual driving torque value of the wheel by the driving torque adjusting value until the actual driving torque value of the wheel is the same as the expected driving torque value so as to prevent the wheel from skidding.
The embodiment also provides a nonlinear error feedback torque control system, which realizes the nonlinear error feedback torque control method during working, and the nonlinear error feedback torque control system comprises a slip rate deviation calculation module, a slip rate deviation calculation module and a slip rate deviation calculation module, wherein the slip rate deviation calculation module is used for taking one wheel of an automobile as a control object, obtaining a slip rate value and a slip rate threshold value of the wheel, and carrying out difference calculation on the slip rate value and the slip rate threshold value to obtain a slip rate deviation; the driving torque deviation calculation module is used for acquiring a driving torque actual value of a wheel, and calculating a difference value between the driving torque actual value and a preset driving torque expected value to obtain a driving torque deviation; the nonlinear control rate calculation module is used for carrying out nonlinear combination through the slip rate deviation and the driving torque deviation to obtain a nonlinear control law; the driving torque adjusting value calculating module is used for calculating a driving torque adjusting value of the wheel through the nonlinear control rate; and the driving torque actual value adjusting module is used for taking the driving torque adjusting value as a driving torque parameter to adjust the driving torque actual value of the wheel until the driving torque actual value of the wheel is the same as the driving torque expected value so as to prevent the wheel from skidding.
The embodiment further includes a particle swarm extension-based control torque constraint method, the particle swarm extension-based control torque constraint system is implemented when working, the particle swarm extension-based control torque constraint system is included in the torque coordination distribution system, and the torque coordination distribution system is specifically described below.
As shown in fig. 2, a torque coordination distribution system is designed aiming at the condition that the torque loss of a hub motor of a distributed drive automobile under a low-adhesion road surface seriously affects the operation stability and the driving safety of the automobile, and mainly comprises a nonlinear error feedback torque control system, a particle swarm extension control-based torque constraint system, an automobile stability-based yaw moment control system and a torque distribution system based on torque loss. When the nonlinear error feedback torque control system works, the nonlinear error feedback torque control method is adopted.
The following is a detailed description of the nonlinear error feedback torque control system:
as the road condition may change all the time, in order to prevent the tires of the automobile from skidding and increase the applicable working condition range of the stability control strategy, a fuzzy control algorithm is adopted to adaptively adjust the wheel slip rate threshold value.
By the deviation delta omega of the actual value of the yaw rate of the vehicle from a reference value z (Δω z ＝ω z -ω z ') and a slip rate value s for the current wheel, a slip rate threshold value s max As the output, fuzzy rule setting of the slip rate threshold value is carried out, for example, when the wheel slip rate value s and the yaw rate are larger, the vehicle is in urgent need of reducing the wheel slip to ensure the stability of the vehicle, and at the moment, the wheel slip rate threshold value output by fuzzy control is smaller. The fuzzy logic rule table established according to a plurality of simulation tests is shown in the following table.
Fuzzy rule table for slip rate threshold value
The fuzzy rule three-dimensional effect graph obtained by the fuzzy rule and the corresponding input and output membership function can judge and output the slip rate threshold value adaptive to the current working condition according to the parameter estimation condition as shown in fig. 3, and further carry out wheel anti-slip control to restrict the wheel driving torque.
Based on the slip threshold value of the fuzzy control, a non-linear error feedback torque control system is designed to obtain a desired torque to prevent the wheels from slipping. The nonlinear error feedback control principle is to make nonlinear combination of errors and then output the torque control demand, as shown in fig. 1, wherein the input of the nonlinear negative feedback control is the deviation e between the wheel slip ratio estimated value and the slip ratio threshold value 1 Deviation e between actual value of wheel drive torque and expected value of torque 2 Passing through a non-lineThe error of the two is combined to calculate the driving torque adjusting value T e To prevent the wheel from slipping. Beta is a centroid slip angle, and the designed nonlinear error feedback control mathematical expression is as follows:
wherein u is 0 For the nonlinear control law, k 0 Is a gain coefficient, c 0 Is a damping coefficient, h 0 For the sampling time, a factor b is compensated 0 ＝1/J ω (inertia of wheel 0.9kg · m2), coefficient of regulation r 0 ＝0.05/h 0 ，r 0 The function of (a) is to adjust the control force of the nonlinear feedback control system, for which the value can be determined empirically or through multiple experiments, fst (·) is a resultant function of the steepest control, and
the following describes a torque constraint system based on particle swarm extension control specifically:
designing torque constraint control by considering wheel slip prevention, wherein the wheel torque output constraint requirements under different working conditions are different, so that extension control domains are respectively divided by adopting an extension control theory, and an adaptive vehicle wheel torque constraint mode along with the change of the road working conditions is realized; the extension control domain is divided as shown in fig. 4, and the intersection points of the connecting line of the original point and the feature quantity in the extension set and the boundary of the extension domain and the classical domain from left to right are Q 1 、Q 2 、Q 3 、Q 4 And the slip rate of the automobile wheels in the classical domain is small, the mass center slip angle of the automobile is small, the automobile is in a working condition with good road adhesion condition, and the torque restriction of wheel slip is not needed at the moment. The slip rate and the centroid slip angle of the automobile wheel in the extension domain tend to increase, at the moment, constraint limitation needs to be applied to torque distribution, the state is kept to be the best in the extension domain, and the torque is prevented from continuously increasing to enter the non-domain. The wheel slip rate and the mass center slip angle in the non-central region are large, so that the automobile is about to be unstable or enters an unstable stateThe wheel torque is strictly restricted, and the safety and stability of the automobile are ensured as much as possible.
The method comprises the following steps that an extension set is divided in an extension control domain, the boundary of each region is determined, and then a wheel torque restriction mode of each control region is determined, wherein the design steps are as follows:
(1) selecting characteristic quantities
The characteristic quantities are used to indicate a wheel slip condition and a vehicle steady state. Therefore, in order to distinguish the wheel slip and driving stability boundaries and regions in the classical domain, the extension domain and the non-domain, the slip value s of the wheel and the actual centroid slip angle β of the vehicle are selected as characteristic quantities, and the two values form Q (s, β).
(2) Partitioning of scalable sets
The method comprises the following steps of firstly dividing a classical domain boundary, wherein the classical domain boundary is relatively easy to divide, and a linear region boundary of a yaw velocity gain is used as an actual centroid yaw angle classical domain boundary. Calculating the maximum value of the actual centroid slip angle of the linear region through a fitting relation, wherein the value of the actual centroid slip angle is the classical domain boundary beta 1 . The empirical formula of the front wheel steering angle limit value and the vehicle speed is as follows:
wherein, a 10 ，b 10 ，c 10 And d 10 The fitting parameters are respectively 0.05, 0.07, 0.6 and 13.3, and the values can be obtained by experiments or multiple experiments; the maximum value delta of the front wheel steering angle in the linear area is calculated max Substituting the two-degree-of-freedom model of the vehicle to calculate the classical domain boundary beta 1 。
Classical domain boundary s of wheel slip 1 Bounded by a slip threshold value of the fuzzy control output, i.e. s 1 ＝s max . And when the wheel slip rate is smaller than the slip rate threshold value, the wheel slip state is considered to be stable and is in the classical domain.
And secondly, dividing the extension domain boundary. Particle swarm optimization is independent of strict mathematics of optimization problem and accurate objective function and constraint conditionMathematical description, only a corresponding evaluation function needs to be designed, the extension domain boundary is a two-dimensional boundary, and the dimensionality is small, so that the extension domain boundary is divided by adopting a particle swarm algorithm, and the optimal boundary is iteratively searched. In each iteration of the algorithm, the particles continuously solve the optimal solution p according to the individual i And the population optimal solution p so far g Both extrema update themselves. The particle velocity and position are then updated according to the following formula:
wherein the content of the first and second substances,
is the velocity and position of the particle in the k-th generation,
is the maximum velocity of the particle, whose value is too large to fly through the optimal solution, rand () is a random number larger than 0 and smaller than 1, and the learning factor is c 1 ＝c 2 τ is an inertial weight that balances the local and global optima, and is designed as follows:
wherein the maximum weight τ max 1.4, minimum weight τ min ＝0.4，t gen Is the number of iterations.
The fitness function is set as:
therefore, the particle swarm algorithm determines the boundary of the extension domainThe process comprises the following steps:
step 4, calculating the adaptive value of the target particle by the target particle through a fitness function by taking the actual particle parameter of the target individual as the target particle;
step 6, comparing the adaptive value of the target particle with the adaptive value of the historical population optimal solution, if the adaptive value of the target particle is greater than the adaptive value of the historical population optimal solution, replacing the particle parameter of the historical population optimal solution with the particle parameter of the target particle, updating the population optimal solution, and if the adaptive value of the target particle is less than the adaptive value of the historical population optimal solution, keeping the particle parameter of the historical population optimal solution inconvenient;
step (ii) of7. Iteratively updating the particle parameters of the target particles according to the individual optimal solution and the new population optimal solution, judging whether the iteration number reaches a preset maximum iteration number, if not, returning the updated target particles to the step 3, if so, stopping iteration, and calculating the optimal value s of the slip rate according to the actual value of the yaw angular velocity after the iteration of the target particles is finished through a slip rate calculation formula 2 Taking the actual centroid slip angle after the iteration of the target particles is finished as the optimal centroid slip angle beta 2 。
(3) Design of relevance function
Designing a correlation function according to the position and the distance of the characteristic quantity in the control domain, wherein the extension distance from the characteristic point to the extension domain is as follows:
wherein X k If the extension range is, the correlation function k(s) is:
wherein, X j The domain is a classical domain interval, so that the domain where the characteristic quantity is located can be judged more conveniently through the calculation result of the correlation function K (S).
(4) Measure pattern partitioning
The measure mode of the characteristic quantity, namely the measure mode M, can be judged by the correlation function K (S) 1 When { S | k (S) > 1} the feature is in the classical domain; measure mode M 2 When the feature quantity is in an extension domain, the { S |0 is less than K (S) is less than or equal to 1 }; measure mode M 3 When { S | k (S) < 0}, the feature quantity is in the non-domain.
Thus at M 1 Under the measure mode, the torque constraint limitation of wheel slip does not need to be considered, and the torque is only constrained by the peak torque of the hub motor, namely
P max The rated power of the hub motor is obtained, and n is the rotating speed of the motor.
At M 2 Measure moduleIn the equation, a certain degree of wheel slip needs to be considered. Driving torque regulating value T output by non-linear error feedback torque control system e Design torque maximum constraint T max Comprises the following steps: t is max ＝[K(S)+1]T e 。
At M 3 In a measure mode, the wheel slip condition is serious, the centroid slip angle also enters a destabilization state, and the maximum value of the design torque is restrained T max Comprises the following steps: t is max ＝T e 。
The constraint mode of the wheel output torque is judged through the extension domain division of the slip rate value and the actual centroid slip angle of the wheel, and the optimal extension domain boundary is searched for the road surfaces under different attachment conditions through the particle swarm optimization.
The following is a detailed description of a yaw moment control system based on vehicle stability:
the loss of the output torque of the hub motor can cause sudden change of the yaw moment of the automobile. In the process, an overlarge yaw moment is generated, so that the automobile can possibly change a course angle and a running track rapidly and enter an unstable working condition, and further the running risk is increased. Therefore, the yaw moment constraint which is adapted to the yaw moment constraint is required to optimize the control of the yaw motion of the automobile and the control strategy of the distribution of the driving torque, so that the running stability of the automobile is ensured.
Firstly, a control boundary is determined according to the automobile state, namely a stability control criterion is determined, the automobile stability criterion determines whether a yaw moment control system is started or not, and an actual mass center slip angle-an actual mass center slip angular velocity (beta-v) is adopted β ) The phase plane is used as the criterion of the stability of the automobile.
Dividing the automobile stable region by using a bilinear method and a limit cycle method, namely adding an ellipse tangent to two straight lines in the region divided by the bilinear method, taking the ellipse as the stable region, wherein the schematic diagram is shown in FIG. 5, and the straight line l 1 And l 2 Phase plane stability bounds determined for bilinear methods, while ellipses and/ 1 And l 2 Tangent and a stable region finally determined in the interior of the ellipse, so that two tangent points are obtained by combining two straight lines and an ellipse equation, and the major and minor semiaxes a and a of the ellipse are finally calculatedb：
Wherein, c 11 And c 22 According to the actual phase diagram, the automobile stability criterion is obtained by the method, namely if the automobile state is outside an elliptical stable area, the yaw moment control system is required to act to output an additional yaw moment for recovering the stability, so that the torque distribution layer distributes the torque to enable the automobile to recover the stability. The lengths of the semiaxes of the stable area ellipses under different road adhesion coefficients obtained by the method are shown in the following table:
stable boundary parameter table
The fitting formula for obtaining the change of the stable boundary ellipse semi-axis along with the road adhesion coefficient according to the parameters in the table is as follows:
and (3) calculating the additional yaw moment required by the stability of the automobile by adopting a sliding mode control algorithm, wherein the sliding mode control law and the sliding mode surface can be changed according to the characteristic requirements of the controlled system and are unrelated to the disturbance and other parameters of the system.
Firstly, calculating a reference yaw moment of the automobile, wherein the road adhesion coefficient of the automobile is changed continuously due to various road conditions, so that the automobile theory can know that the yaw velocity and the centroid slip angle of the automobile are constrained by the adhesion conditions, and the two are constrained as follows according to the adhesion conditions:
then the ideal centroid slip angle beta of the automobile d And yaw angular velocity ω d Respectively as follows:
wherein
Is the coefficient of stability, v, of the vehicle x Is vehicle speed, delta is front wheel angle, l r Is the centroid to rear axle distance,/ f Is the distance from the center of mass to the front axle of the automobile, L is the wheel base of the wheels of the automobile, k 2 Is the rear wheel side yaw stiffness k of the automobile 2 ，k 1 Is the front wheel side deflection rigidity of the automobile, and m is the whole automobile mass
The designed sliding mode function is as follows: u ═ ω (ω) z -ω d )+h 2 (β-β d )，
And (3) carrying out derivation on the sliding mode control rate u, wherein the derivation formula is as follows:
the approach law of the sliding mode controller is as follows:
wherein beta is the actual barycenter slip angle of the automobile, epsilon is the torque loss coefficient of the automobile, and h 1 Is a weighting factor, h, of the sliding mode control rate calculation 2 Is a weighting coefficient h calculated by a sliding mode control approach rate 2 。
Because the sliding mode control has the buffeting problem, a filtering method can be adopted, a low-pass filter is used for a switching function of the sliding mode control, a smooth signal is obtained, and the buffeting of the system is reduced. And finally obtaining an additional yaw moment for maintaining the stable running requirement of the automobile by a simultaneous three-degree-of-freedom model of the automobile body as follows:
wherein, F yfr Is the front right tire lateral force, F yrr Is the rear right tire lateral force, F yfl Is the front left tire lateral force, F yrl Is the rear left tire lateral force.
The torque distribution system based on torque loss is described in detail below:
in order to ensure the yaw stability of the automobile, the torque distribution is carried out on the four-wheel drive torque of the distributed drive automobile according to the additional yaw moment required by the stability of the automobile, which is obtained by a yaw moment control system based on the stability of the automobile. The four-wheel torque distribution adopts a quadratic programming method. According to the theory of wheel dynamics, the wheel tire force is limited by the adhesion ellipse, the larger the wheel longitudinal force is, the less the margin is left for the lateral force, and the lateral stability of the automobile is influenced when the automobile is turned. Therefore, the tire load rate is adopted to restrain the wheel torque, so that the lateral stability of the automobile is ensured, and the automobile is provided with four wheels as an example.
Firstly, an optimization objective function is confirmed, and tire force is calculated according to a Dugoff tire model, wherein the relationship between the tire force and the tire adhesion force is as follows:
wherein, F xij Is the longitudinal force of the tire, F yij Is the tire lateral force, F zij Is the vertical load of the tyre
The tire load rate is set as follows:
where i ∈ { f, r } denotes front and back, and j ∈ { l, r } denotes left and right.
The driving torque of the hub motor can be directly controlled, the longitudinal force and the lateral force of the tire are provided by the adhesive force, the transverse force is ensured to reduce the longitudinal force, and therefore, the longitudinal force is mainly used for setting a quadratic objective function as follows:
wherein E (rho) represents the average mean value of the tire load rates, the E (rho) is added to enable each tire load rate to be close, the utilization rate of each tire can be improved, and eta is a weighting coefficient used for coordinating the two-part optimization target ratio.
Constraints for optimal allocation are then determined, mainly equality constraints for the additional yaw moment and the longitudinal driver model output driving force and inequality constraints for maximum torque constraints taking into account wheel slip, as shown in the following equation:
wherein F x For total driving force for vehicle running, P max Is the rated power of the hub motor, n is the motor speed, s is the wheel slip ratio, T m Actual value of drive torque, F xfr Is the front right tire longitudinal force, F xrr Is the rear right tire longitudinal force, F xfl Is the front left tire longitudinal force, F xrl Is the rear left tire longitudinal force.
And finally, determining an optimal distribution algorithm, optimally distributing the upper-layer yaw moment by using a quadratic programming theory, converting the target function into a standard quadratic form, wherein the quadratic programming function is as follows:
wherein x ═ F xfl ，F xfr ，F xrl ，F xrr ] T Expressing matrix transposition, and deducing a quadratic programming H matrix and a quadratic programming c matrix as follows by inequality constraint and a quadratic programming function:
F zfl is the vertical load of the front left tire of the automobile, F zfr Is the vertical load of the front right tire of the automobile, F zrl Is the rear left tire vertical load of the automobile, F zrr The vertical load of the rear right tire of the automobile is obtained by an inequality constraint function, wherein A and b are respectively as follows:
where r radius of the wheel, T flmax Is the maximum value of the driving torque, T, of the front left wheel of the automobile frmax Is the maximum value of the front right wheel driving torque, T, of the automobile rlmax Is the maximum value of the driving torque, T, of the rear left wheel of the automobile rrmax Is the maximum value of the driving torque of the rear right wheel of the automobile, therefore, the constraint of the inequality Ax is less than or equal to b is an affine function, A eq x＝b eq The equality constraint is also an affine function, which is consistent with the characteristics of the convex quadratic programming problem, which is thus a convex quadratic programming problem.
In addition, since the four-wheel hub motor has torque loss, it is necessary to reconstruct torque distribution according to the degree of torque loss, where ∈ ═ epsilon fl ，ε fr ，ε rl ，ε rr ]For quadratic programming function, constraint function is carried out according to inequality and epsilon is integrated to constraint coefficient matrix A eq And b eq To get
b eq ＝[ΔM F x ]
After the quadratic programming function is solved to obtain the optimal four-wheel driving torque, four-wheel driving torque distribution is further reconstructed according to the torque loss coefficient, and the output torque of the hub motor is controlled, so that the automobile still has the capability of stable running after the motor torque is lost.
For the simulation analysis of the torque coordination distribution system, firstly, whether the torque distribution strategy considering the torque loss can ensure the driving stability of the automobile when the torque of the in-wheel motor is lost is preliminarily verified. And selecting a double-shift line working condition, setting the road adhesion coefficient to be 0.85, simulating to reduce the loss of the right front hub motor to 60% torque output, and setting the simulated initial vehicle speed and the target vehicle speed to be 60 km/h. The result is shown in fig. 6. The Torque Distribution strategy in which the Torque loss is taken into account is denoted as tdtl (Torque Distribution fire Torque loss). As can be seen from fig. 6(a), the loss of the torque of the right front wheel causes the vehicle to have a yaw rate for driving to the right, and after the torque is redistributed to the four wheels, the yaw rate of the vehicle can follow the desired value and the vehicle can be safely driven, thereby improving the maneuverability of the vehicle. As can be seen from fig. 6(b), the centroid slip angle starts to increase after the torque loss of the right front wheel of the automobile, which seriously affects the stability of the automobile, and the torque distribution strategy considering the torque loss reconstructs the four-wheel torque, so that the error between the actual value of the centroid slip angle and the reference value is reduced, and the stability of the automobile is greatly increased. As can be seen from fig. 6(c), when the torque loss occurs in the right front wheel of the vehicle, the vehicle not only has poor steering stability, but also has a certain loss in vehicle speed, and the torque distribution strategy considering the torque loss can make the vehicle speed decrease relatively smaller in the double-lane action, thereby improving the dynamic performance of the vehicle to a certain extent. Therefore, the torque distribution strategy considering the torque loss can be analyzed and obtained, and the torque distribution strategy can play a role in ensuring the running safety, the operation stability and certain dynamic property of the automobile on the road surface with good adhesion conditions.
When single-wheel torque loss simulation verification is carried out, a double-traverse-line working condition simulation test is selected, the torque loss of the right front wheel is reduced to 60%, the road adhesion coefficient is set to be 0.3, the initial vehicle speed and the target vehicle speed are both 60km/h, and the simulation result is shown in fig. 7. The torque distribution strategy in which the torque losses are taken into account is denoted TDTL. The wheel Slip constrained Torque coordinated Distribution strategy taking into account Torque losses is denoted as TDSRTL (Torque Distribution for Slip braking while Torque loss). As can be seen from the comparative simulation results of the two control strategies, in fig. 7(b), the torque coordinated split strategy (TDSRTL) taking into account the wheel slip constraint can make the vehicle yaw rate response faster, the vehicle drivability better, i.e., the driver's steering demand faster, than the torque split strategy (TDTL) taking no account of the torque constraint. In the torque distribution strategy in FIG. 7(c), the centroid slip angle of the torque distribution strategy without considering the torque constraint at the time of 10.45s is-2.845 degrees, while the centroid slip angle of the torque coordination distribution control strategy with considering the wheel slip constraint is-2.446 degrees, so that 14.02 percent is reduced, the jitter of the centroid slip angle of the automobile can be eliminated, and the driving stability of the automobile is improved. As can be seen from the four-wheel torque output curve in fig. 7(d), after the torque of the right front wheel is lost, the drive torque of the left front wheel is reduced, and the drive torque of the right rear wheel is correspondingly increased according to the yaw moment control demand, but under the constraint control considering the wheel slip, the drive torque of the right rear wheel is reduced at any time in the process of increasing the torque so as to prevent the wheel slip, and the running safety of the automobile is ensured. In fig. 7(e), although the wheel torque is limited and the vehicle driving torque is reduced to some extent, the vehicle speed is reduced by about 0.5km/h only during the double lane shifting operation. In general, when the right front wheel has torque loss, the proposed coordinated torque distribution control strategy considering wheel slip redistributes the torque, ensures the yaw moment required by the stability of the automobile, and ensures the driving safety of the automobile.
And when the two-wheel torque loss simulation verification is carried out, the working condition that the two wheels generate the torque loss is designed, and the proposed torque coordination distribution control strategy is verified. And selecting a double-shift-line simulation test. The torque loss of the two wheels on the same side is set, the torque loss of the right front wheel is reduced to 80%, the torque loss of the right rear wheel is reduced to 50%, the road adhesion coefficient is 0.3, the initial vehicle speed and the target vehicle speed are both 60km/h, and the simulation result is shown in FIG. 8. From the simulation comparison result of the torque loss of the two wheels on the same side, it is seen that the torque distribution strategy (TDTL) in fig. 8(b) without considering the torque constraint generates a certain degree of sideslip during the second lane change of the double lane shifting action, so that the automobile is in a dangerous driving state during the period, and the torque coordination distribution control strategy (TDSRTL) considering the wheel slip improves the sideslip phenomenon and ensures the driving safety of the automobile. As can be seen from fig. 8(c), although the torque distribution strategy without considering the torque constraint can reduce the centroid slip angle of the vehicle before 10s to ensure the stability of the vehicle, the centroid slip angle is increased instead to cause the wheel slip during the second lane change, and the torque coordination distribution control restrains the torque output to a certain extent under the extension judgment, but controls the wheel slip at the same time to ensure the stability of the vehicle as a whole. As can be seen from the four-wheel torque in fig. 8(d), since the torque loss occurs in both right two wheels, the yaw moment cannot be compensated by increasing the torque on the different axis side as in the case of the single-wheel loss. The left wheel torque also decreases and follows the change in the right wheel torque while the left wheel fine-tunes the torque output to maintain the yaw moment stable. As can be seen in FIG. 8(e), the lowest vehicle speed of the torque distribution strategy without considering the torque constraint is 56.5km/h, and the vehicle speed under the control of the torque coordination distribution can be kept between 57 km/h and 60km/h, so that the dynamic property of the vehicle is ensured to a certain extent.
The verification proves that the whole torque coordination distribution system can ensure that the automobile can stably and safely run when the motor torque is lost by distributing the torque of the four-wheel motor of the automobile.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.
Claims (10)
1. A nonlinear error feedback torque control method for use in an automobile to adjust a driving torque parameter of an automobile model of the automobile, the automobile having a plurality of wheels, the automobile model having a driving torque parameter for each wheel, the automobile model obtaining a driving torque actual value of a corresponding wheel according to different driving torque parameters to prevent the corresponding wheel from slipping, the nonlinear error feedback torque control method comprising the steps of:
taking one wheel of an automobile as a control object, acquiring a slip rate value and a slip rate threshold value of the wheel, and calculating a difference value between the slip rate value and the slip rate threshold value to obtain a slip rate deviation;
acquiring a driving torque actual value of the wheel, and calculating a difference value between the driving torque actual value and a preset driving torque expected value to obtain a driving torque deviation;
obtaining a nonlinear control law by nonlinear combination of the slip rate deviation and the driving torque deviation, wherein the nonlinear control rate u 0 ＝k 0 e 0 +fst(e 1 ,c 0 e 2 ,r 0 ,h 0 )，e 0 ＝∫e 1 ，k 0 Is a gain coefficient, c 0 Is a damping coefficient, h 0 For the sampling time, the coefficient r is adjusted 0 ＝0.05/h 0 Fst (-) is the steepest control synthesis function, e 1 As slip ratio deviation, e 2 Is the torque deviation;
calculating a driving torque adjustment value of the wheel through the nonlinear control rate, wherein the driving torque adjustment value
Wherein, b 0 Is a compensation factor;
and taking the driving torque adjustment value as the driving torque parameter to adjust the actual driving torque value of the wheel until the actual driving torque value of the wheel is the same as the expected driving torque value so as to prevent the wheel from skidding.
2. The nonlinear error feedback torque control method in accordance with claim 1, wherein the slip rate threshold value calculating method comprises the steps of:
acquiring yaw rate deviation and the slip rate value of the wheels;
and obtaining the slip rate threshold value by the yaw velocity deviation and the slip rate value through a fuzzy threshold value algorithm.
3. The nonlinear error feedback torque control method according to claim 2, wherein the calculation method of the yaw rate deviation includes the steps of:
acquiring an actual yaw rate value of the wheels;
and calculating the difference value between the actual value of the yaw rate and the reference value of the yaw rate of the wheels to obtain the yaw rate deviation.
4. The nonlinear error feedback torque control method according to claim 1, wherein the design method of the steepest control synthesis function includes the steps of:
calculating an intermediate variable d according to the sampling time h required by the nonlinear error feedback control and a third input variable r corresponding to the sampling time h: d ═ rh;
calculating an intermediate variable d from the intermediate variable d 0 ：d 0 ＝hd；
According to a first input variable x 1 And a second input variable x 2 Calculating an intermediate variable y: y is x 1 +hx 2 ；
Calculating the intermediate variable a 0 ：
Calculating an intermediate variable a:
calculating the steepest control synthesis function fst (x) 1 ,x 2 ,r,h 0 )：
5. The nonlinear error feedback torque control method of claim 1, wherein the slip rate value calculation method comprises the steps of:
obtaining the wheel rotation linear velocity V of the automobile ω And the speed v of the vehicle x ；
Calculating the slip rate value:
6. a nonlinear error feedback torque control system which employs the nonlinear error feedback torque control method according to any one of claims 1 to 5, comprising:
the slip rate deviation calculation module is used for taking one wheel of an automobile as a control object, acquiring a slip rate value and a slip rate threshold value of the wheel, and calculating a difference value between the slip rate value and the slip rate threshold value to obtain a slip rate deviation;
the driving torque deviation calculation module is used for acquiring a driving torque actual value of the wheel and calculating a difference value between the driving torque actual value and a preset driving torque expected value to obtain a driving torque deviation;
a nonlinear control rate calculation module for obtaining a nonlinear control law by nonlinear combination of the slip rate deviation and the driving torque deviation, wherein the nonlinear control rate u is 0 ＝k 0 e 0 +fst(e 1 ,c 0 e 2 ,r 0 ,h 0 )，e 0 ＝∫e 1 ，k 0 In order to be the gain factor,c 0 is a damping coefficient, h 0 For the sampling time, the coefficient r is adjusted 0 ＝0.05/h 0 Fst (-) is the steepest control synthesis function, e 1 As slip ratio deviation, e 2 Is the torque deviation;
a driving torque adjustment value calculating module for calculating a driving torque adjustment value of the wheel by the nonlinear control rate
Wherein, b 0 Is a compensation factor;
and the driving torque actual value adjusting module is used for taking the driving torque adjusting value as the driving torque parameter so as to adjust the driving torque actual value of the wheel until the driving torque actual value of the wheel is the same as the driving torque expected value, so as to prevent the wheel from skidding.
7. The particle swarm optimization-based control torque constraint method is applied to the nonlinear error feedback torque control method according to any one of claims 1 to 5, and comprises the following steps of:
s1, obtaining a slip rate value s of the wheel and an actual centroid slip angle beta of the vehicle as characteristic quantities to form Q (s, beta), and establishing a coordinate system of an extensible control domain by taking the slip rate value s as a horizontal coordinate and the actual centroid slip angle beta as a vertical coordinate;
s2, carrying out regional division on the extension control domain:
classical domain: ((-s) 1 ,s 1 )，(-β 1 ,β 1 ))；
And (3) extension domain: ((-s) 1 1 ,s 1 1 )，(-β 1 1 ,β 1 1 ) In which-s) 1 1 ∈(-s 2 ,-s 1 )，s 1 1 ∈(s 1 ,s 2 )，-β 1 1 ∈(-β 2 ,-β 1 )，β 1 1 ∈(β 1 ,β 2 )；
Non-domain: ((-s) 2 1 ,s 2 1 )，(-β 2 1 ,β 2 1 ) In which-s) 2 1 ∈(-∞,-s 2 )，s 2 1 ∈(s 2 ,∞)，-β 2 1 ∈(-∞,-β 2 )，β 2 1 ∈(β 2 ,∞)；
S3, acquiring a linear region boundary of the actual centroid sideslip angle gain of the vehicle as a boundary beta of a vertical coordinate of the classical domain 1 Obtaining a slip rate threshold s of the wheel max As the abscissa boundary s of the classical domain 1 I.e. s 1 ＝s max ；
S4, calculating the slip rate optimal value s of the wheel by the particle swarm algorithm according to the slip rate value s of the current state of the wheel and the actual centroid slip angle beta of the current state of the vehicle 2 And the slip rate optimum s 2 Corresponding optimal centroid slip angle beta 2 ；
S5, judging whether the characteristic quantity is in a classical domain, if so, implementing torque constraint of the classical domain on the wheels of the vehicle;
s6, when the characteristic quantity is not in the classical domain, judging whether the characteristic quantity is in an extension domain, if so, implementing torque constraint of the extension domain on the wheels of the vehicle;
and S7, when the characteristic quantity is not in an extension domain, the characteristic quantity is in a non-domain, and the non-domain torque constraint is implemented on the wheels of the vehicle.
8. The particle-swarm-based extendible control torque constraint method according to claim 7, wherein said slip rate optimum s 2 And its corresponding optimum centroid slip angle beta 2 The calculation method of (2) is as follows:
(1) obtaining an actual value ω of yaw rate of the wheels z According to the actual value omega of the yaw angular velocity z And setting a fitness function according to the actual centroid slip angle beta
Wherein v is x Is the vehicle speed of the wheel, μ is the road adhesion coefficient, g is the gravitational acceleration;
(2) taking one wheel of the vehicle as a target individual and all wheels of the vehicle as a group, and taking the actual value omega of the yaw rate of each wheel z Forming particles by taking the corresponding actual centroid side deflection angle beta as a particle parameter, and forming particle groups by all the particles;
(3) acquiring particle parameters of the population in a historical optimal state under an actual road adhesion coefficient to serve as a historical population optimal solution, and acquiring particle parameters of the target individual in the historical optimal state under the actual road adhesion coefficient to serve as a historical individual optimal solution;
(4) calculating an adaptive value of the target particle by using the target particle through the fitness function by taking the actual particle parameter of the target individual as the target particle;
(5) comparing the adaptive value of the target particle with the adaptive value of the historical individual optimal solution, if the adaptive value of the target particle is greater than the adaptive value of the historical individual optimal solution, replacing the particle parameter of the target particle with the particle parameter of the historical individual optimal solution, updating the individual optimal solution, and if the adaptive value of the target particle is less than the adaptive value of the historical individual optimal solution, keeping the particle parameter of the historical individual optimal solution inconvenient;
(6) comparing the adaptive value of the target particle with the adaptive value of the historical population optimal solution, if the adaptive value of the target particle is greater than the adaptive value of the historical population optimal solution, replacing the particle parameter of the target particle with the particle parameter of the historical population optimal solution, updating the population optimal solution, and if the adaptive value of the target particle is less than the adaptive value of the historical population optimal solution, keeping the particle parameter of the historical population optimal solution inconvenient;
(7) iteratively updating the particle parameters of the target particles according to the individual optimal solution and the new population optimal solution, and judging iterationWhether the times reach a preset maximum iteration number or not, if not, returning the updated target particles to the step (3), if so, stopping the iteration, and calculating the optimal value s of the slip rate according to the actual value of the yaw velocity after the iteration of the target particles is finished through a slip rate calculation formula 2 Taking the actual centroid slip angle after the target particle iteration is finished as the optimal centroid slip angle beta 2 。
9. The particle swarm scalable control torque constraint method according to claim 8, wherein the iterative update method of the target particles comprises the steps of:
obtaining a maximum yaw rate of the target particles
The inertia weight tau of the target particle, the random number rand () of the target particle, which is more than 0 and less than 1, and the population optimal solution p of the kth generation of the target particle g Individual optimal solution p of kth generation of the target particle i Acceleration constant c of the target particle 1 And an acceleration constant c of the target particle 2 ；
Actual value of yaw rate according to k generation of target particle
And centroid slip angle of kth generation of the target particle
Calculating the k +1 th generation yaw velocity actual value of the target particles
Calculating the centroid slip angle of the k +1 th generation of the target particle
Calculating the k-th generation yaw rate actual value of the target particle
And centroid slip angle of kth generation of the target particle
Updating to the k +1 th generation actual value of the yaw rate of the target particle
And centroid slip angle of the k +1 th generation of the target particle
10. The particle swarm expandable control torque constraint method according to claim 8, wherein the inertial weight τ of the target particle is updated as the number of iterations changes, and the calculation method of the inertial weight comprises the following steps:
obtaining a maximum weight τ of the target particle max Minimum weight τ of the target particle min ；
According to the iteration times t of the target particles gen Calculating an inertial weight τ of the target particle:
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