CN105467996A - Four-wheel steering automobile track tracking control method based on differential flat and active disturbance rejection - Google Patents

Abstract

The invention discloses a four-wheel steering automobile track tracking control method based on differential flat and active disturbance rejection, and the method can improve a tracking effect of the four-wheel steering automobile to a reference track. The method comprises the steps of (1) establishing a monorail control model of a four-wheel steering automobile in three degrees of freedom; (2) switching an underactuated controlled model to an input-and-output coupling model with disturbance and without a zero dynamic subsystem based on the control model established in step (1) according to the differential flat theory; (3) designing a linear active disturbances rejection controller (ADRC) based on the input-and-output coupling model established in step (2), and the ADRC mainly comprises a higher-order linear tracking differentiator, a higher-order expansion state observer and a linear feedback control law. In this way, a real controlled variable can be obtained.

Description

Based on the four-wheel steering automobile Trajectory Tracking Control method of differential flat and active disturbance rejection

Technical field

The invention belongs to four-wheel steering automobile Trajectory Tracking Control field, relate to a kind of four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection.

Background technology

Four-wheel steering system (all-wheel control system) is the important component part of vehicle handling stability, and its feature is the anti-phase rotation of front and back wheel when low speed, reduces radius of turn; With rotating during high speed, changing Lane is easier.Under the prerequisite improved constantly vehicle handling stability and vehicle intellectualized requirement, the requirement that four-wheel steering automobile carries out tracing control accurately to reference locus (path planning) is more and more urgent.Along with the development of modern control theory, outside the scope of classical control theory, open up the new way of more effective raising tracing control effect, become the important topic of current four-wheel steering automobile control field.

Differential flat theory is the effective approach solving drive lacking problem.Relative additive method, differential flat theory both can process minimum phase system (static feedback linearization), non-minimum phase system (dynamic feedback linearization) can be processed again, nonlinear system is equivalent to the system being input to smooth output not having zero dy namics subsystem.But differential flat condition is for very harsh a nonlinear system.Therefore usually adopt some rational Approximation Methods, consider the differential flat attribute of its approximation system, then residual error estimated as disturbance and indeterminate and compensate.

Classical PID control theory has certain interference rejection ability, use for reference the thought of " based on error concealment error ", Auto Disturbances Rejection Control Technique be absorb modern control theory achievement, develop PID thought marrow, novel practical technology that development and usage Special Nonlinear effect develops.Auto Disturbances Rejection Control Technique is totally independent of the mathematical model of controlled device, and its most outstanding feature is exactly the effect of all uncertain factors acting on controlled device is all summed up as " unknown disturbance " and utilizes the inputoutput data of object estimate in real time it and recompense.The meaning of active disturbance rejection is just this, does not need here to disturb effect outside directly measurement, does not also need the action rule realizing knowing disturbance.This also makes the occasion requiring to realize high-speed, high precision control in rugged environment, and Auto Disturbances Rejection Control Technique more can show its superiority.The advantage of auto-disturbance rejection technology control inputs output system estimation compensation disturbance is just in time applicable to solve the estimation being input to disturbance and the indeterminate existed in the system of smooth output and the compensation problem of carrying out model conversion through differential flat theory.

Summary of the invention

The present invention be directed to the defect of prior art, propose a kind of four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection, the tracking effect of four-wheel steering automobile to reference locus can be improved.

The present invention is achieved through the following technical solutions:

Based on a four-wheel steering automobile Trajectory Tracking Control method for differential flat and active disturbance rejection, comprise the following steps:

Step one: set up Three Degree Of Freedom four-wheel steering automobile single track Controlling model;

Step 2: the Controlling model set up according to step one, theoretical according to differential flat, controlled for drive lacking model is transformed to the input and output coupling model not having zero dy namics subsystem with disturbance;

Step 3: the input and output coupling model set up according to step 2, designs linear automatic disturbance rejection controller, mainly comprises high order linear Nonlinear Tracking Differentiator, high-order extended state observer and linear Feedback Control and restrain three aspects, finally obtain working control amount.

Beneficial effect of the present invention:

The present invention uses differential flat theory to carry out model conversion to drive lacking Three Degree Of Freedom four-wheel steering automobile, non-linear, coupling, drive lacking model be transformed into do not have zero dy namics subsystem be passed to smooth enter export model, and consider the out of true part of model and inside and outside disturb, indeterminate etc. is all classified as disturbance suffered by system, then CONTROLLER DESIGN controls.Differential flat system can by interior lively state feedback equivalence in a linear system (feedback linearization), by having followed the tracks of the reference locus of smooth output, just can follow the tracks of the reference locus that state variable and system export.

Accompanying drawing explanation

Fig. 1. four-wheel steering automobile single track model.

Embodiment

The invention will be described further below.

A kind of four-wheel steering automobile tracking and controlling method based on differential flat and Auto Disturbances Rejection Control Technique of the present invention, comprises the following steps:

The first step: set up four-wheel steering automobile Three Degree Of Freedom drive lacking single track Controlling model, be described below:

$\left\{\begin{array}{c}m({\stackrel{\·}{v}}_x-{\mathrm{rv}}_y)=f_{lf}{\mathrm{cos\δ}}_f-f_{sf}{\mathrm{sin\δ}}_f+f_{lr}{\mathrm{cos\δ}}_r-f_{sr}{\mathrm{sin\δ}}_r+F_x\\ m({\stackrel{\·}{v}}_y+{\mathrm{rv}}_x)=f_{lf}{\mathrm{sin\δ}}_f+f_{sf}{\mathrm{cos\δ}}_f+f_{lr}{\mathrm{sin\δ}}_r+f_{sr}{\mathrm{cos\δ}}_r+F_y\\ J\stackrel{\·}{r}=l_f(f_{lf}{\mathrm{sin\δ}}_f+f_{sf}{\mathrm{cos\δ}}_f)-l_r(f_{lr}{\mathrm{sin\δ}}_r+f_{fr}{\mathrm{cos\δ}}_r)+T_z\end{array}\right.$

Wherein, v _x, v _y, r is longitudinal, transverse direction and the yaw velocity of four-wheel steering automobile respectively, f _lfand f _lrbe the longitudinal force caused by engine, brake torque and friction, provided by following formula:

$\left\{\begin{array}{c}{f}_{lf}={\mathrm{\ϵf}}_m\\ f_{lr}=(1-\mathrm{\ϵ})f_m\end{array}\right.$

Wherein, ε is longitudinal resultant force f _mthe constant value partition factor of the longitudinal force in front and back wheel, its span is from 0 (rear wheel drive truck) to 1 (front-wheel-drive cars), considers that automobile is only by the situation of front-wheel drive, gets ε=1 herein.

F _sfand f _srthe horizontal lateral deviation power of tire

$\left\{\begin{array}{c}{f}_{sf}=C_f{\mathrm{\α}}_f\\ f_{sr}=C_r{\mathrm{\α}}_r\end{array}\right.$

Wherein

$\left\{\begin{array}{c}{\mathrm{\α}}_f={\mathrm{\δ}}_f\frac{v_y+l_{f}r}{v_x}\\ {\mathrm{\α}}_r={\mathrm{\δ}}_r\frac{v_y-l_{r}r}{v_x}\end{array}\right.$

Wherein, α _fand α _rrepresent front and back wheel side drift angle respectively.F in model _x, F _yand T _zrepresent external force and torque disturbance respectively, such as windage, crosswind interference and load transfer etc.Consider lateral deviation power f _sfand f _srdriving/braking effect relative to longitudinally driving/damping force f _lfand f _lrdriving/braking effect very little, therefore, the f in model first equation can be made _sf=f _sr=0.The formula of above-mentioned power is brought in model, and carries out small angle approximation, following equation can be obtained

$\left\{\begin{array}{c}m({\stackrel{\·}{v}}_x-{\mathrm{rv}}_y)=f_m+F_x+F_x^{\′}\\ m({\stackrel{\·}{v}}_y+{\mathrm{rv}}_x)=f_m{\mathrm{\δ}}_f+C_f({\mathrm{\δ}}_f-\frac{v_y+l_{f}r}{v_x})+C_r({\mathrm{k\δ}}_f-\frac{v_y-l_{r}r}{v_x})+F_y+F_y^{\′}\\ J\stackrel{\·}{r}=l_f(f_m{\mathrm{\δ}}_f+C_f({\mathrm{\δ}}_f-\frac{v_y+l_{f}r}{v_x}\left)\right)-l_r{C}_r({\mathrm{k\δ}}_f-\frac{v_y-l_{r}r}{v_x})+T_z+T_z^{\′}\end{array}\right.$

Wherein, F ' _x, F ' _ywith T ' _zit is the residual error after small angle approximation.Get v _x, v _y, r is state variable, δ _fand f _mfor control variable, by the above-mentioned form being modeled as state space

$\stackrel{\·}{x}=f(x,r)+g(x,r)u+g_1(x,r)u_1{u}_2+\mathrm{\ψ}(x,u,r)$

Wherein

$f(x,t)=\left[\begin{array}{c}{x}_2{x}_3\\ -x_1{x}_3-\frac{C_f}{m}\frac{x_2+l_f{x}_3}{x_1}-\frac{C_r}{m}\frac{x_2-l_r{x}_3}{x_1}\\ -\frac{l_f{C}_f}{J}\frac{x_2+l_f{x}_3}{x_1}+\frac{l_r{C}_r}{J}\frac{x_2-l_r{x}_3}{x_1}\end{array}\right],g(x,t)=\left[\begin{array}{cc}0& \frac{1}{m}\\ \frac{C_f+{\mathrm{kC}}_r}{m}& 0\\ \frac{l_f{C}_f-{\mathrm{kl}}_r{C}_r}{J}& 0\end{array}\right],g_1(x,t)=\left[\begin{array}{c}0\\ \frac{1}{m}\\ \frac{l_f}{J}\end{array}\right],$

$x=\left[\begin{array}{c}{v}_x\\ v_y\\ r\end{array}\right],u=\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]$

G ₁(x, t) u ₁u ₂disturb or indeterminate inside and outside+ψ (x, u, t) regards as, real system equation becomes

$\stackrel{\·}{x}=f(x,r)+g(x,r)u+\mathrm{\ξ}(x,u,r)$

Second step: according to the Controlling model of the foundation in the first step, utilizes differential flat theory to convert Controlling model, turns to Multivariable Coupling and be input to smooth output model, solve the problem of drive lacking.

Approximation system

$\stackrel{\·}{x}=f(x,r)+g(x,r)u$

Smooth output be

$\left\{\begin{array}{c}{y}_1=x_1\\ y_2=\frac{l_f{C}_f-{\mathrm{kl}}_r{C}_r}{J}{x}_2-\frac{C_f+{\mathrm{kC}}_r}{m}{x}_3\end{array}\right.$

State variable can be expressed as by smooth output and limited order derivative thereof

$x=x(y_1,y_2,{\stackrel{\·}{y}}_2)=\left[\begin{array}{c}{y}_1\\ \frac{k_2{y}_1{\stackrel{\·}{y}}_2+k_8{y}_2}{k_1{k}_8+k_2{k}_7}\\ \frac{k_1{y}_1{\stackrel{\·}{y}}_2-k_7{y}_2}{k_1{k}_8+k_2{k}_7}\end{array}\right]$

Wherein

$\begin{array}{c}{k}_1=\frac{l_f{C}_f-{\mathrm{kl}}_r{C}_r}{J},k_2=\frac{C_f+{\mathrm{kC}}_r}{m},k_3=\frac{k_1{C}_f}{m},k_4=\frac{k_1{C}_r}{m},\\ k_5=\frac{k_2{l}_f{C}_f}{J},k_6=-\frac{k_2{l}_r{C}_r}{J},k_7=k_3+k_4+k_5+k_6,\\ k_8=-k_1{y}_1^2+(k_3+k_5)l_f-(k_4+k_6)l_r=-k_1{y}_1^2+k_9\\ k_1{k}_8+k_2{k}_7\≠0\end{array}$

And have

$\left[\begin{array}{c}{\stackrel{\·}{y}}_1\\ {\stackrel{\·\·}{y}}_2\end{array}\right]=\mathrm{\Δ}(y_1,y_2,{\stackrel{\·}{y}}_2)\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]+\mathrm{\Λ}(y_1,y_2,{\stackrel{\·}{y}}_2)$

So

$u=u(y_1,y_2,{\stackrel{\·}{y}}_2)={\mathrm{\Δ}}^{-1}(y_1,y_2,{\stackrel{\·}{y}}_2)(\left[\begin{array}{c}{\stackrel{\·}{y}}_1\\ {\stackrel{\·\·}{y}}_2\end{array}\right]-\mathrm{\Λ}(y_1,y_2,{\stackrel{\·}{y}}_2\left)\right)$

Wherein

$\left\{\begin{array}{c}{\mathrm{\Δ}}_{11}(y_1,y_2,{\stackrel{\·}{y}}_2)=0\\ {\mathrm{\Δ}}_{12}(y_1,y_2,{\stackrel{\·}{y}}_2)=\frac{1}{m}\\ {\mathrm{\Δ}}_{21}(y_1,y_2,{\stackrel{\·}{y}}_2)=-k_1^2{x}_1+\frac{k_2{k}_7}{x_1}+\frac{k_1{k}_9}{x_1}\\ {\mathrm{\Δ}}_{22}(y_1,y_2,{\stackrel{\·}{y}}_2)=-\frac{k_1}{m}{x}_3-\frac{k_7}{m}\frac{x_2}{x_1^2}-\frac{k_9}{m}\frac{x_3}{x_1^2}\end{array}\right.$

$\left\{\begin{array}{c}{\mathrm{\Λ}}_1(y_1,y_2,{\stackrel{\·}{y}}_2)=x_2{x}_3\\ {\mathrm{\Λ}}_2(y_1,y_2,{\stackrel{\·}{y}}_2)=-k_1({\stackrel{\·}{x}}_1{x}_3+x_1{\stackrel{\·}{x}}_3)+k_7(\frac{{\stackrel{\·}{x}}_2}{x_1}-\frac{x_2}{x_1^2}{\stackrel{\·}{x}}_1)+k_9(\frac{{\stackrel{\·}{x}}_3}{x_1}-\frac{x_3}{x_1^2}{\stackrel{\·}{x}}_1)\end{array}\right.$

As long as so matrix namely reversible, so approximation system is exactly differential flat,

$\det \left(\mathrm{\Δ}\right(y_1,y_2,{\stackrel{\·}{y}}_2\left)\right)={\mathrm{\Δ}}_{11}{\mathrm{\Δ}}_{22}-{\mathrm{\Δ}}_{12}{\mathrm{\Δ}}_{21}=-\frac{1}{m}(-k_1^2{x}_1+\frac{k_2{k}_7+k_1{k}_9}{x_1})\≠0\⇔k_1{k}_8+k_2{k}_7\≠0$

This condition is easy to meet in practice.

So real system can turn to

Wherein, comprise the item of all influential system, comprising: inside and outside disturb, the residual error etc. of indeterminate, small angle approximation, can also comprise approximate in vertical transverse force formula after residual error.

3rd step: the Multivariable Coupling input/output model set up according to second step, adopts LADRC controller to control.The complicacy of disturbing inside and outside considering, and the advantage of auto-disturbance rejection technology, and then adopt automatic disturbance rejection controller to control, for the sake of simplicity, adopt linear active disturbance rejection controller (LADRC), Controller gain variations step is as follows:

1. the design of Nonlinear Tracking Differentiator TD:

$\left\{\begin{array}{c}{v}_{11}=v_{11}+{\mathrm{hv}}_{12}\\ v_{12}=v_{12}-h(-r_1^2(v_{11}-y_{1r})-2r_1{v}_{12})\\ v_{21}=v_{21}+{\mathrm{hv}}_{22}\\ v_{22}=v_{22}+{\mathrm{hv}}_{23}\\ v_{23}=v_{23}+h(-r_2^3(v_{21}-y_{2r})-3r_2^2{v}_{22}-3r_2{v}_{23})\end{array}\right.$

The linearity tracking differentiator herein designed is higher than conventional design method single order is the derivative of the higher order in order to obtain reference signal, to add feedforward term in the controlling.The Main Function of Nonlinear Tracking Differentiator carries out filtering to the reference signal of the band measurement noise that sensor records.

2. the design of high order linear extended state observer LESO

$\left\{\begin{array}{c}{e}_1=z_{11}-y_1\\ z_{11}=z_{11}+h(z_{12}-b_{11}{e}_1+U_1)\\ z_{12}=z_{12}+h(z_{13}-b_{12}{e}_1)\\ z_{13}=z_{13}+h(z_{14}-b_{13}{e}_1)\\ z_{14}=z_{14}+h(-b_{14}{e}_1)\\ e_2=z_{21}-y_2\\ z_{21}=z_{21}+h(z_{22}-b_{21}{e}_2)\\ z_{22}=z_{22}+h(z_{23}-b_{22}{e}_2+U_2)\\ z_{23}=z_{23}+h(z_{24}-b_{23}{e}_2)\\ z_{24}=z_{24}+h(z_{25}-b_{24}{e}_2)\\ z_{25}=z_{25}+h(-b_{25}{e}_2)\end{array}\right.$

Consider complicacy, have employed high order linear extended state observer.

3. the design of Feedback Control Laws:

$\left\{\begin{array}{c}{e}_{11}=v_{11}-z_{11}\\ U_{10}=c_{11}{e}_{11}\\ e_{21}=v_{21}-z_{21}\\ e_{22}=v_{22}-z_{22}\\ U_{20}=c_{21}{e}_{21}+c_{22}{e}_{22}\end{array}\right.$

$\left\{\begin{array}{c}{U}_1=v_{12}+U_{10}-z_{12}\\ U_2=v_{23}+U_{20}-z_{23}\end{array}\right.$

Working control amount

$\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]={\mathrm{\Δ}}^{-1}(y_1,y_2,{\stackrel{\·}{y}}_2)\left[\begin{array}{c}{U}_1\\ U_2\end{array}\right]$

In order to verify the validity of the contrail tracker combined based on differential flat and Auto Disturbances Rejection Control Technique of above-mentioned design, the present invention utilizes hardware-in-the-loop environment to debug automatic disturbance rejection controller, tests, study the through engineering approaches application of model, the simulation parameter adopted in the present embodiment is as follows

l f(l r)	1.51(1.32)[m]
		m	1864[kg]
J	3654[kg·m 2]
		C f(C r)	101600(213800)[N/rad]

Concrete emulation implementation step comprises two aspects:

1, PID controller and LADRC controller can both pairing approximation system realize better following the tracks of, and tracking effect difference is little.From the angle of feedback linearization, approximation system is equivalent in fact a linear system, and what difference PID controller and LADRC controller do not have in the effect of the situation not having disturbance.

2, the controlled quentity controlled variable of PID controller control approximation system is joined in real system, the reason done like this is gain matrix g ₁the amplitude of (x, t) is relatively little, does not have very large error by the controlled quentity controlled variable of approximation system, but from partial enlarged drawing, tracking effect with do not have the tracking effect of LADRC controller good.

3, when initial, a given larger initial error: given longitudinal velocity initial value is 24.5m/s, transverse velocity initial value is 0.1m/s, yaw velocity initial value is 0.001rad/s, the controlled quentity controlled variable of PID controller is the controlled quentity controlled variable controlling approximation system, relative LADRC controller, does not have large fluctuation when initial, but tracking effect is obviously not as the tracking effect of LADRC controller.

What 4, the present invention followed the tracks of is the overtake other vehicles track of vehicle when running at high speed, because vehicle when running at high speed from the disturbance that the windage of longitudinal direction is very important, simultaneously in order to verify the advantage of auto-disturbance rejection technology in estimation compensation disturbance, add that the side of 2 seconds emulates in the side direction of vehicle, compare the control effects of PID and LADRC controller.Can see that the aircraft pursuit course of PID controller deviate from reference locus gradually when there is large windage and crosswind disturbance, but LADRC controller still can realize Trajectory Tracking Control preferably.

Claims (6)

1., based on a four-wheel steering automobile Trajectory Tracking Control method for differential flat and active disturbance rejection, it is characterized in that, comprise the following steps:

Step one: set up Three Degree Of Freedom four-wheel steering automobile single track Controlling model;

Step 2: the Controlling model set up according to step one, theoretical according to differential flat, controlled for drive lacking model is transformed to the input and output coupling model not having zero dy namics subsystem with disturbance;

Step 3: the input and output coupling model set up according to step 2, designs linear automatic disturbance rejection controller, mainly comprises high order linear Nonlinear Tracking Differentiator, high-order extended state observer and linear Feedback Control and restrain three aspects, finally obtain working control amount.

2. a kind of four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection as claimed in claim 1, is characterized in that, adopt following methods to set up Controlling model:

Wherein, m is car mass, v _x, v _y, r is longitudinal, transverse direction and the yaw velocity of four-wheel steering automobile respectively, δ _rthe front-and rear-wheel steer angle of automobile, l _f, l _rfor the distance of automobile barycenter CG and front and rear wheel, C _f, C _rforward and backward tire cornering stiffness, f _lfand f _lrbe the longitudinal force caused by engine, brake torque and friction, provided by following formula:

Wherein, ε is longitudinal resultant force f _mthe constant value partition factor of the longitudinal force in front and back wheel, span be from 0 that is rear wheel drive truck to 1 i.e. front-wheel-drive cars, f _sfand f _srthe horizontal lateral deviation power of tire, F _x, F _yand T _zrepresent external force and torque disturbance respectively, consider lateral deviation power f _sfand f _srdriving/braking effect relative to longitudinally driving/damping force f _lfand f _lrdriving/braking effect very little, therefore make the f in first equation _sf=f _sr=0, front and back wheel corner adopts simple ratio to control, i.e. δ _r=k δ _f, k is front and back wheel corner proportional control factor, obtains following equation

Wherein, v is got _x, v _y, r is state variable, δ _fand f _mfor control variable, by the above-mentioned form being modeled as state space

Wherein

G ₁(x, t) u ₁u ₂disturb or indeterminate inside and outside+ψ (x, u, t) regards as, real system equation becomes

3. the controlled model of drive lacking Three Degree Of Freedom coupling nonlinear four-wheel steering automobile as claimed in claim 2, utilizes differential flat theory to convert controlled model, is converted into input and output with multiple variable model, solves the problem of drive lacking.

Approximation system

Smooth output be

State variable is expressed as by smooth output and limited order derivative thereof

Wherein

k ₁k ₈+k ₂k ₇≠0

And have

So

Wherein

As long as so matrix namely reversible, so approximation system is exactly differential flat,

This condition is easy to meet in practice.

So real system can turn to

Wherein, comprise the item of all influential system, comprising: inside and outside disturb, the residual error etc. of indeterminate, small angle approximation, can also comprise approximate in vertical transverse force formula after residual error.It is characterized in that, further, described constant value partition factor ε=1, proportional control factor k=1.

4. a kind of four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection as described in claim 1 or 2 or 3, is characterized in that, further, described high order linear Nonlinear Tracking Differentiator adopts following methods design:

Reference signal for the band measurement noise recorded sensor carries out filtering, wherein, and v ₁₁(v ₂₁) be used for following the tracks of smooth output reference signal y _1r(y _2r), v ₁₂(v ₂₂, v ₂₃) be used for obtaining reference signal y _1r(y _2r) first order derivative, r ₁, r ₂be the velocity factor of Nonlinear Tracking Differentiator, h is sampling step length.

5. a kind of four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection as described in claim 1 or 2 or 3, is characterized in that, further, described high-order extended state observer adopts following methods design:

Wherein, e ₁, e ₂observational error, z _1i(i=1,2,3,4), z _2j(j=1,2,3,4,5) are the output of extended state observer, b _1i(i=1,2,3,4), b _2j(j=1,2,3,4,5) are the gains of extended state observer, U ₁, U ₂it is virtual controlling amount.

6. a kind of four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection as described in claim 1 or 2 or 3, is characterized in that, further, described linear Feedback Control rule adopts following methods design:

Wherein, e ₁₁, e ₂₁, e ₂₂state error, U ₁₀, U ₂₀state error feedback rate control, c ₁₁, c ₂₁, c ₂₂it is Error Feedback control coefrficient.

Working control amount