CN103970138A

CN103970138A - ALV transverse control method based on active disturbance rejection and differential smoothing

Info

Publication number: CN103970138A
Application number: CN201410194055.0A
Authority: CN
Inventors: 夏元清; 孙中奇; 阮广凯; 高源�; 李春明; 付梦印; 邓志红; 蒲钒; 娜茜泰; 叶镭
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2014-05-08
Filing date: 2014-05-08
Publication date: 2014-08-06
Anticipated expiration: 2034-05-08
Also published as: CN103970138B

Abstract

The invention provides an ALV transverse control method based on active disturbance rejection and differential smoothing. The control effect and robustness of the method that differential smoothing and active disturbance rejection are combined on an underactuation system are proved through simulation under different conditions. The ALV transverse control method comprises the steps that firstly, an ALV transverse kinetic model is established; then, the differential smoothing output is designed according to the kinetic model; at last, according to the differential smoothing output, the control law and an active disturbance rejection controller, a composite controller of the ALV transverse control system is designed. The active disturbance rejection controller comprises a tracking differentiator, an expansion state observer and a nonlinear feedback control law.

Description

ALV (active disturbance rejection) transverse control method based on active disturbance rejection and differential smoothing

Technical Field

The invention belongs to the field of transverse control of a ground autonomous driving vehicle system, and relates to an ALV transverse control method based on active disturbance rejection and differential smoothing.

Background

The ground Autonomous driving Vehicle (ALV) is a key component of a Future Combat System (FCS) and an Intelligent Transportation System (ITS), and is one of the most active research directions in the fields of current intelligent robots, artificial intelligence and the like. An ALV should not only have the conventional moving functions of acceleration, deceleration, forward, backward, turning, etc., but also have autonomous capabilities of task analysis, environment perception, path planning, path tracking, automatic obstacle avoidance, etc. The research relates to the scientific and technical fields of machinery, kinematics and dynamics, electronics, computers, information processing, control, artificial intelligence and the like.

The theory of differential smoothing was first proposed by Fliess M, Levine J, Martin P and Rouchon P. For under-actuated ground mobile platform control, after an initial position and a target position are given, the problem of relocation can be solved by utilizing a differential smoothing theory. The concept of differential smoothing characterizes an original system as equivalent to another system after suitable dynamic expansion. The smoothed output has an important role for the problem of trajectory generation, and if the smoothed output is known, the corresponding state variables and control variables can be obtained. However, this method has the disadvantage that it is only effective for differential smoothing systems and the smooth output is not easily found. The introduction of differential smoothing systems has led to the widespread use of differential smoothing theory in control problems. Differential smoothing has been applied in the research of under-actuated spacecraft as a feasible trajectory generation method.

The active disturbance rejection control technology is a novel practical technology which absorbs modern control theory achievement, develops PID thought essence (eliminates errors based on errors) and develops and applies special nonlinear effect to develop. The active disturbance rejection control technology is completely independent of a mathematical model of a controlled object, and has the most prominent characteristic that the action of all uncertain factors acting on the controlled object is reduced to unknown disturbance, and the input and output data of the object are used for estimating and compensating the unknown disturbance in real time. The significance of the active disturbance rejection lies in that here, the external disturbance action does not need to be directly measured, and the action rule of the disturbance does not need to be known. The advantages of the active disturbance rejection control technology can be further shown in the occasions where high-speed and high-precision control is required to be realized in the severe environment.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides an ALV (equivalent-to-average-value) transverse control method based on active disturbance rejection and differential smoothing, and the control effect and robustness of the differential smoothing and active disturbance rejection combined method on an under-actuated system are proved through simulation under different conditions.

The technical scheme of the invention is as follows:

an ALV transverse control method based on active disturbance rejection and differential smoothing is characterized by firstly establishing a transverse dynamic model of a ground autonomous driving vehicle; then designing differential smooth output according to the dynamic model; and finally, designing a composite controller of a transverse control system of the ground autonomous driving vehicle according to the differential smooth output and control law and the active disturbance rejection controller.

The active disturbance rejection controller comprises a tracking differentiator, an extended state observer and a nonlinear feedback control law.

The invention has the beneficial effects that:

1. when the vehicle speed is high, the transverse dynamic linear model of the mobile platform can meet the requirement of transverse motion control;

2. under the control of the controller combining the differential smoothing and the ADRC, the mobile platform realizes stable and high-precision transverse motion within the speed range of 0-40 m/s, has strong robustness on the change of self parameters, road conditions, lane changing time and the like, and can meet the requirement of high-performance control, thereby showing that the controller combining the differential smoothing and the ADRC is feasible for controlling the transverse motion of the high-speed mobile platform;

3. the invention can provide guidance for the engineering design of the high-speed high-mobility platform under study.

Drawings

FIG. 1 is a diagram of a lateral control model of a ground autonomous driving vehicle system;

FIG. 2 shows a controller U₁Lower system S₁The output response of (1);

FIG. 3 shows a controller U₁Lower system S₂The output response of (1);

FIG. 4 shows a controller U₂Lower system S₂The output response of (1);

FIG. 5 is a graph of expected lateral displacement of a rail;

FIG. 6. reference trajectory of body angle;

FIG. 7.V_xThe parameters of the platform and 1m/s are output curves under nominal values;

FIG. 8.V_xThe 20m/s and the platform parameters are output curves under nominal values;

FIG. 9.V_x13m/s and the platform parameter is an output curve under a non-nominal value;

FIG. 10 is a graph of output for a platform with perturbation and perturbation.

Detailed Description

The present invention will be described in detail with reference to the accompanying drawings.

The invention discloses a vehicle system transverse control method based on differential smoothing and active disturbance rejection control technology, which comprises the following steps:

firstly, a transverse control model of a ground autonomous driving vehicle system is established, which is shown in the attached figure 1 and described as follows:

wherein l_fIs the distance between the center of mass and the front axis,/_rIs the distance between the center of mass and the rear axle, m is the equipment mass of the whole vehicle, C_f、C_rCornering stiffness, δ, of front and rear tires, respectively_fFor the turning angle of the front wheels of the vehicle, I_zRepresenting moment of inertia about the Z axis, v_xRepresenting longitudinal velocity, v_yThe lateral velocity is indicated in the form of,the yaw rate is shown.

And step two, designing differential smooth output according to the control model established in the step one:

equation (1) has a differential smoothing characteristic, and its differential smoothing output is:

F = \frac{m}{2 C_{af}} V_{y} - \frac{I_{z}}{{2 l}_{f} C_{af}} r - - - (2)

control quantity delta of front wheel_fThe inputs are represented as:

all states of the system, V_yR and control input delta_fBoth can be represented by a function of the smoothed output F and its derivative, so that the under-actuated motion control system has the characteristic of differential smoothing when implementing track control according to the definition of the differential smoothing system.

And thirdly, designing a controller based on differential smoothing and ADRC.

1. Mathematical model transformation of transverse motion smoothing system of ground autonomous mobile platform

In order to design the ADRC controller of the platform transverse motion smoothing system, the smoothing system model (3) needs to be converted into a simulated model. To this end, let x₁＝F，When u is δ, formula (3) is rewritten to formula (4).

\{\begin{matrix} {\dot{x}}_{1} = x_{2} \\ {\dot{x}}_{2} = f (x_{1}, x_{2}) + Bu \end{matrix} - - - (4)

Wherein,

f (x_{1}, x_{2}) = [E_{1} + E_{2}] \dot{F} + [E_{3} + E_{4}] \dot{F}, B = \frac{1}{C_{1} B_{1} + C_{2} B_{2}}, E_{1} = \frac{D_{2} (C_{1} A_{1} + C_{2} A_{3})}{V (C_{1} D_{2} - C_{2} D_{1})}

E_{2} = \frac{D_{1} (C_{1} A_{2} - C_{1} V^{2} + C_{2} A_{4})}{V (C_{2} D_{1} - C_{1} D_{2})}, E_{3} = \frac{C_{2} (C_{1} A_{1} + C_{2} A_{3})}{V (C_{2} D_{1} - C_{1} D_{2})}, E_{4} = \frac{C_{1} (C_{1} A_{2} - C_{1} V^{2} + C_{2} A_{4})}{V (C_{1} D_{2} - C_{2} D_{1})} .

in order to make the system a pure integral system, we should design an extended state observer to eliminate the internal and external disturbances. We write equation (4) in the form of an expanded state space expression, as in equation (5):

\{\begin{matrix} {\dot{x}}_{1} = x_{2} \\ {\dot{x}}_{2} = x_{3} + Bu \\ {\dot{x}}_{3} = g (x_{1}, x_{2}) \end{matrix} - - - (5)

wherein, g (x)₁,x₂) Is f (x)₁,x₂) The derivative of (c).

2. Controller design based on differential smoothing and ADRC

In the following, we design the controller of the autonomous mobile platform lateral motion smoothing system based on equation (5) and the active disturbance rejection control method.

The active disturbance rejection controller of the autonomous mobile platform transverse motion smoothing system based on the formula (5) is expressed as formulas (6) to (9):

\{\begin{matrix} e_{1} = v_{1} - z_{1}, e_{2} = v_{2} - z_{2} \\ u_{0} = k (e_{1}, e_{2}, p) \end{matrix} - - - (8)

wherein F_rIs a reference track of a smoothing function andV_yrand r_rReference trajectories for the lateral velocity and the body attitude angular velocity, respectively.

3. Differential smoothing and ADRC based parameter tuning of a controller

The underactuated system control of the transverse motion of the ground autonomous mobile platform is realized by designing differential smooth output and controlling the track tracking of the differential smooth output. The designed differential smooth output is controlled by using Active Disturbance Rejection (ADRC), and the controller is shown in formulas (6) to (9).

The most critical part of the controller design is parameter debugging, and since the adjustment of the parameters with overlarge coefficient and overlarge time scale of the smooth output system designed by the method is difficult to carry out and cannot be directly obtained through multiple times of debugging, a time scale method is selected to adjust the parameters.

Firstly, a reference system is selected

\overset{. .}{F} + \dot{F} + 2 F = u - - - (10)

The time scale p of the system (10) is obtained by adjusting parameters by a time scale method₁0.241 and adjust its parameters.

According to model G_S1Can adjust ADRC controller U₁Is composed of

r₁₁＝0.1,r₁₂＝0.02,h＝0.01,

h₁＝0.02,c＝100,β₁＝100,

β₂＝200,β₃＝30000.

Substituting the system parameters into the system (3) to obtain

\overset{. .}{F} + 326 \dot{F} + 26490 F = 12.1 u - - - (11)

The time scale p of the system (11) is obtained by adjusting parameters by a time scale method₂2.83. First, using ADRC controller U₁For the non-linear model, i.e. the system S₁And S₂And performing control simulation, wherein the obtained output F is shown in the attached figures 2 and 3.

FIGS. 2 and 3 show the results of controller U₁Although S can be well matched₁Implementing smooth control; however, for S₂The control process of (1) can not follow the track to be dispersed completely, and at the moment, U can be seen₁Has not been adapted to S₂。

From S₁And S₂Time scale ratio m ═ p₂/p₁Is approximately equal to 10, and then can be obtained according to the controller U by the ADRC parameter setting method of the time scale of the controlled system₁Obtaining the controller U after parameter adjustment₂：

r₁₁＝0.1,r₁₂＝0.2,h＝0.001,

h₁＝0.002,c＝200,β₁＝1000,

β₂＝2800,β₃＝30000000.

Then respectively utilize the controllers U₁And U₂To system S₂Control simulation is carried out, and the obtained output y is shown in figure 4. As shown.

FIG. 4 shows a phase comparison controller U₁Controller U₂To S₂A satisfactory control effect is obtained, and the controller U is visible₂Is applicable to S₂In (1).

In order to verify the method for realizing the design of the transverse controller of the ground autonomous driving vehicle system based on the combination of differential smoothing and active disturbance rejection, the control effect and robustness of the differential smoothing method on the under-actuated system are verified through simulation under different conditions.

The dynamic equation of the transverse control of the ground autonomous driving vehicle system established in the invention is as follows:

wherein l_fIs the distance between the center of mass and the front axle of 1.05m, l_rThe distance between the mass center and the rear axle is 1.63m, and m is 1480Kg of the whole vehicle equipment mass, C_fThe cornering stiffness of the front tyre is 67500N/rad, C_rThe cornering stiffness of the rear tire is 47500N/rad, delta_fFor the turning angle of the front wheels of the vehicle, I_zRepresenting moment of inertia around the Z axis 2350Kg im²，v_xRepresenting longitudinal velocity, v_yThe lateral velocity is indicated in the form of,the yaw rate is shown.

The invention takes the model as an example, and the specific simulation implementation steps are as follows:

simulation environment

Assuming that the platform is moving in a double line at a fixed longitudinal speed, the track change trajectory (the transition of the arrangement) is shown in fig. 5. The trajectory is generated using a sine function planning algorithm, the planning formula being shown in equation (12). In the formula, v₀(t): a desired lateral displacement; w: lane width; t is t₁: the time to turn from the right lane to the left lane; t is t₂: the time to start driving on the left lane; t is t₃: the time to turn from the left lane to the right lane; t is t₄: and returning to the right lane. Assuming that the ideal posture of the vehicle body is the tangential direction of the transverse track, the reference track of the vehicle body angle is shown in fig. 6.

During simulation, parameters of the platform and the steering mechanism and the longitudinal speed V are changed_xTo examine the robustness of the ADRC controller, wherein the tire angular stiffness C_sf,C_srThe change of (a) may represent both a perturbation of the tyre's own parameters and a variation (disturbance) of the road-ground conditions; changes in platform centroid to front and rear axle distances can then represent both mass distribution and changes in road longitudinal unevenness (disturbances) thus, the above-described set of simulation parameters can examine the ability of the designed ADRC controller to adapt to "internal" and "external" uncertainties.

Simulation result

See the attached figures 7-8, each is V_x1m/s, 40m/s and platform parameters are simulation results under nominal values; FIG. 9 is a simulation result of the following parameters: v_x35m/s, 2220kg (1.5 times the nominal value), I_z＝3290kg·m²(1.4 times the nominal value), l_f1.2m (center of mass shifted backward 0.15 m), lr 1.48m, C_sf40500N/rad (60% of nominal), C_sr28500N/rad (60% of nominal). FIG. 10 is at C_sf＝[0.85+0.15(2U(0,1)-1)]C_{sf_nom}、C_sr＝[0.85+0.15(2U(0,1)-1)]C_{sr_nom}The results for the same other parameters as the simulation conditions of FIG. 9, where U (0,1) is a unity uniform distribution function. The conditions corresponding to fig. 4.7 and 4.8 are very harsh for automatic control of the lateral motion of the platform. The blue track represents a reference track, the red track represents an actual track of the controller controlled trolley designed based on the ADRC method, and the green track represents an actual running track of the controller controlled trolley designed based on the neural network and the fuzzy control method.

The results of the attached figures 7-8 show that compared with a method combining a neural network and fuzzy control, a controller combining differential smoothing and ADRC has good adaptability to the change of the platform speed, and the stable and high-precision control on the transverse motion of the system is successfully realized. The results of fig. 9-10 show that even if the road switching time is shortened and the platform parameters and the road conditions are greatly changed, the platform still has ideal lateral motion performance under the control of the ADRC controller.

Claims

1. An ALV lateral control method based on active disturbance rejection and differential smoothing is characterized in that: firstly, establishing a transverse dynamic model of a ground autonomous driving vehicle; then designing differential smooth output according to the dynamic model; and finally, designing a composite controller of a transverse control system of the ground autonomous driving vehicle according to the differential smooth output and control law and the active disturbance rejection controller.

2. The ALV lateral control method based on active disturbance rejection and differential smoothing as claimed in claim 1, wherein: the active disturbance rejection controller comprises a tracking differentiator, an extended state observer and a nonlinear feedback control law.

3. The ALV lateral displacement tracking system control method based on active disturbance rejection as claimed in claim 2, characterized in that: the tracking differentiator adopts the following model:

wherein

And sgn is a function of the sign,

wherein,d＝rh,d₀＝dh,y₀＝v₁-v₀-hv₂

where r is the parameter to be adjusted and also the velocity factor of the tracking differentiator, h₀Is the filter factor, h is the sampling step, v₀Is a lateral control reference input, v, of a ground autonomous driving vehicle system₁(k) For input signals to track, v₂(k) Is to obtain an approximately differential signal of the input signal, d₀,a,a₀,y,y₀Intermediate variables in the equation solving process are eliminated in iteration; by solving this equation, an approximate differential signal is obtained, that is, an approximate differential signal is obtained while tracking the input signal.

4. The ALV lateral displacement tracking system control method based on active disturbance rejection as claimed in claim 2 or 3, characterized in that: the extended state observer adopts the following model:

wherein:

wherein z is₁,z₂,z₃Is the output of the extended state observer, z₁Tracking system state v₁,z₂Tracking the state v of the system₂,z₃Estimating the internal disturbance and the external disturbance of the system, h is a sampling step length, b₀Coefficient z being a control variable₁(k+1),z₂(k+1),z₃(k +1) is the output of the extended state observer, z₁(k +1) tracking System State v₁(k),z₂(k +1) tracking the State v of the System₂(k),z₃(k +1) is the internal and external disturbance, β, of the estimated system₀₁,β₀₂,β₀₃Is the coefficient of the observer, reflects the observation ability of the observer, e is the state error, u (k) is the control quantity of the system, y is the system output, delta is the linear segment interval length of the power function fal, and the requirement of delta epsilon [0,1]Taking δ to be 0.01, α represents the power of a power function fal, and α is represented as α in both fal functions₁α₂Satisfy 0<α₂<α₁<1, take alpha₁＝0.5，α₂＝0.25。

5. The ALV lateral displacement tracking system control method based on active disturbance rejection of claim 4, wherein: the nonlinear feedback control law adopts the following model:

wherein e is₁、e₂Respectively the error between the observed quantity and the input signal and the differential, K_p、K_DFor error feedback gain, the control capability of the controller is embodied, and delta in the formula satisfies delta epsilon [0,1 ∈]Taking delta to be 0.01, the power of two power functions satisfies 0<α_p<1<α_DTaking alpha_p＝0.5，α_D2; the expression of the control law of the active disturbance rejection controller is obtained as follows:

u(k)＝u₀-z₃(k)/b₀。