CN106950999B - mobile stage trajectory tracking control method adopting active disturbance rejection control technology - Google Patents
mobile stage trajectory tracking control method adopting active disturbance rejection control technology Download PDFInfo
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Abstract
The invention discloses a track tracking control method for a mobile stage by adopting an active disturbance rejection control technology, which designs track tracking control of the mobile stage by adopting the active disturbance rejection control technology, designs an active disturbance rejection controller, decouples a multivariable and strong-coupling system into three subsystems, respectively designs the active disturbance rejection controllers for the subsystems, carries out dynamic compensation linearization treatment on a nonlinear system, improves the control performance of the system, and designs an extended state observer to effectively estimate and compensate uncertainty of a system model and internal and external disturbance quantities of the system in real time.
Description
Technical Field
The invention belongs to the technical field of stage control, relates to track tracking control of a mobile stage, and particularly relates to a track tracking control method of the mobile stage, which can eliminate the influence of perturbation of internal parameters of a system and external interference disturbance on the track tracking performance of the mobile stage and realize an effective adoption of an active disturbance rejection control technology.
background
In modern performance, in order to achieve an artistic effect better, the omnidirectional moving type stage needs to be controlled to match with actors for performing the performance. The omnidirectional moving stage is an omnidirectional moving platform formed by coupling four omnidirectional wheels, and consists of eight motors according to power and steering control requirements, each driving wheel is provided with an independent power source, and each shaft is provided with an independent steering mechanism. The movable stage with the structure has the characteristics of small turning radius, stable and easy turning and the like, and is particularly suitable for the scene requirements of complex scenes in performance.
however, the four-wheel motion control system for the omnidirectional mobile platform belongs to a multivariable, nonlinear and strongly coupled complex dynamic system, and the research on the control method is a difficult point, and particularly on the track tracking control of the omnidirectional mobile platform, the currently used methods mainly include sliding mode control, backstepping control, fuzzy control and the like. The sliding mode variable structure method has the advantages of fast response, good transient performance and robustness, is widely applied to track tracking control, but is easy to generate buffeting and directly influences the control effect. The backstepping control is an earlier trajectory tracking control method based on kinematic consideration, and is widely applied to the tracking problem, but the control structure and the design process of the backstepping control are complex, and meanwhile, the system must meet a strict feedback control structure, so that the requirement on the system is high, and the backstepping control is difficult to realize in practical situations. The fuzzy control method has certain robustness, but the fuzzy control rule can not be completely summarized due to the influence of subjective factors of people, and the self-learning capability is lacked. The omnidirectional mobile stage needs to meet the requirements of site intelligent scenery in real time in performance, and tracking control of the moving track is carried out according to the position requirements of actors and other properties, but the track tracking performance of the mobile stage is greatly reduced under the existing control method due to the fact that the omnidirectional mobile stage is perturbed by parameters in a complex system per se and various external interference factors in the performance influence the mobile stage.
Disclosure of Invention
The invention provides a track tracking control method of a mobile stage, aiming at overcoming the defect that the mobile stage in the prior art cannot meet the requirement of intelligent control of a modern performance scene, and the track tracking control method can effectively improve the artistic diversification effect of the modern performance. The method adopts the active disturbance rejection technology to design the track tracking control of the moving stage, and designs the extended state observer to effectively estimate and compensate the uncertainty of the system model and the internal and external disturbance quantities of the system in real time, and the method has strong inhibiting effect on the internal and external disturbance of the system and the uncertainty of the model.
The track tracking control method for the mobile stage by adopting the active disturbance rejection control technology is characterized by comprising the following steps of:
Step 1) establishing a kinematic model of a mobile stage:
The structure of the mobile stage is complex, the mobile stage is a multivariable, high-coupling and nonlinear under-actuated system, a controller is designed for the system, firstly, a reasonable kinematic model is established, the pose of the mobile stage is described by three quantities (x, y, theta), and the kinematic model of the mobile stage is established, as shown in formula (1):
The calculation of the control quantity U of the linear speed of the driving wheel is shown as the formula (2):
Wherein:
X-coordinate value of the moving stage on the X axis of the world coordinate system,
Y-coordinate value of the moving stage on the Y axis of the world coordinate system,
theta-rotation angle of the moving stage in the world coordinate system,
θ0Angle between diagonal and lateral edges of the body, theta for a structurally fixed body0The value of the signal is a certain value,
R is the distance from the center of mass of the vehicle body to the rotation center of the steering structure,
r-the radius of rotation of the steering structure,
w1、2、3、4-angular velocities of rotation of the four steering mechanisms,
ρ1、2、3、4-the angles of the four steering mechanisms with the X-axis of the vehicle body coordinate system;
Step 2) establishing a track tracking error model of the mobile stage, wherein the process comprises the following steps:
at any one time, its velocity vector in the world coordinate system istaking the velocity vector of the reference point in a body coordinate system asIs recorded as [ u v w ]]Terror in tracking of trackdescribed as shown in formula (3):
wherein u isr，vrRespectively representing the expected values of the speed components of the moving stage along the X and Y axes of the vehicle body coordinate system at the time t through the track decompositionrA desired value indicating a rotational angular velocity of the vehicle body;
step 3) decoupling of a multivariable system, wherein the process comprises the following steps:
For three input-three output systems
note the book
x＝[x1 x2 x3]T
f＝[f1 f2 f3]T
u＝[u1 u2 u3]T (5)
introducing "virtual control volume"The formula (4) is changed into
the I channel in the system has the input-output relationship of
Multivariable decoupling control can be realized by parallelly embedding 3 active disturbance rejection controllers between the control quantity U and the output quantity y;
wherein x1，x2，x3-a state quantity of a three-input-three-output system,
u1，u2，u3-a control input of a three-input-three-output system,
y1，y2，y3-a system output of a three-input-three-output system,
f1，f2，f3-a disturbance term for each channel,
b11,b12,b13,b21,b22,b23,b31,b32,b33-a system gain factor;
step 4), designing an active disturbance rejection controller, wherein the process comprises the following steps:
According to the trajectory tracking error model, the trajectory tracking controller is decoupled into three independent subsystems, namely excontrol circuit, eyControl loop and eθThe control loop is used for respectively designing an active disturbance rejection controller for each subsystem;
the system is a first-order system, a tracking differentiator is not needed, and the active disturbance rejection controller comprises an extended state observer and a state feedback control law, which is specifically as follows;
(1) Designing an extended state observer, and estimating and compensating the state and the disturbance of the system in real time, wherein the equation of the extended state observer is given as follows:
wherein, beta01、β02Is a set of parameters to be set,
e- -estimated value of output z1the difference with the output y is such that,
u-the control input values of the system,
b0-a compensation factor, which is a function of the compensation factor,
z2-an estimate of the dilated state;
(2) Linear state error feedback control law
wherein k is1Is a coefficient of proportionality that is,
e1- -reference input v1and the estimated value of the outputz1the difference value of (a) to (b),
u0-error feedback control quantity.
The method for tracking and controlling the track of the mobile stage by adopting the active disturbance rejection control technology is characterized in that in the step 3), the specific process is as follows:
As shown in the formula 3), the system can be regarded as a three-input three-output system, and u (t), v (t), w (t) are indirect control quantities
Let the dynamic coupling part be:
f1,f2,f3For the disturbance sum term, the static coupling part is:
By utilizing a linear active disturbance rejection control technology, the dynamic coupling part is estimated and compensated as sum disturbance on respective channels, decoupling control of the system can be realized as long as a matrix B is ensured to be reversible, and in the system, the determinant value of B is constantly-1, and decoupling control can be realized.
The method for tracking and controlling the track of the mobile stage by adopting the active disturbance rejection control technology is characterized in that in the step 4), the specific process is as follows:
With exthe active disturbance rejection controller of the control subsystem is designed as an example, and comprises an extended state observer and a state feedback control law:
(1) Designing an extended state observer, and estimating and compensating the state and the disturbance of the system in real time, wherein the equation of the extended state observer is given as follows:
wherein, beta01、β02is a set of parameters to be set,
z1--exIs detected by the measured values of (a) and (b),
z2-an observed value of the expansion state quantity;
(2) Law of state error feedback control
wherein k is1Is a scaling factor.
The method for tracking and controlling the track of the mobile stage by adopting the active disturbance rejection control technology is characterized in that the implementation process on a mobile stage control computer is operated by a main execution part and mainly comprises the following steps:
1) Setting parameters: in the parameter import interface, R, R, theta in the formula (1) are input0values, and ρ1，ρ2，ρ3，ρ4an initial value of (1); in the parameter setting interface of the active disturbance rejection controller, the gain beta of the extended state observer is input01、β02、β11、β12、β21、β22And k is1、k2、k3A value of (b), wherein11、β12is eyObserver gain, beta, of the control subsystem21、β22Is eθobserver gain, k, of the control subsystem2,k3are each ey,eθThe state error feedback control law proportionality coefficient, after the input parameter is confirmed, the control computer sends the setting data into a computer storage unit Flash for storage;
2) Setting a track: setting a motion track in a track import interface, storing preset track data into a Flash storage unit by a control computer after the import track is confirmedThe control computer decomposes the preset trajectory into ur vr wr]Tstoring the matrix and the data into a Flash storage unit for storage, wherein ur,vr,wrAre all functions of time t;
3) Off-line debugging: clicking a 'debugging' button in a configuration interface, controlling a system to enter a controller debugging stage, taking a straight line track as a test track, and adjusting beta in a parameter setting interface01、β02、β11、β12、β21、β22Value of (a) and k1、k2、k3Observing the tracking error e of the moving stage trackx、ey、eθThus, a group of parameters capable of quickly and effectively realizing the track tracking control of the moving stage is determined;
4) And (3) online operation: clicking a 'run' button on a configuration interface, reading the optimal setting parameters of the active disturbance rejection controller from the Flash storage by a control computer of the mobile stage, and reading a matrix u after the track decomposition from the Flash storager vr wr]Texecutes a 'moving stage track tracking control program', and measures the real-time pose [ x y theta ] of the moving stage on line]TAnd controlling the rotating speed of the driving motor and the rotating speed of the steering motor to realize automatic adjustment of the pose of the moving stage, measuring the real-time pose of the moving stage on line when the next adjustment period arrives, and repeating the whole execution process, wherein the steps are repeated in this way to realize automatic adjustment control of the track tracking of the moving stage.
compared with the prior art, the invention has the advantages that:
1) Aiming at the internal parameter perturbation of the system and the uncertainty of external interference and the like, the invention introduces the extended state observer to estimate the state and the internal and external disturbances of the system in real time, and compensates by utilizing the nonlinear error feedback control rate, thereby eliminating the influence of the internal and external disturbances;
2) According to the self-structure characteristics of the mobile stage, the active disturbance rejection controller is designed, a multivariable and strong-coupling system is decoupled into three subsystems, the active disturbance rejection controllers are respectively designed for the subsystems, the nonlinear system is subjected to dynamic compensation linearization treatment, and the control performance of the system is improved.
drawings
Fig. 1 is a schematic view of a mobile stage architecture;
FIG. 2 is a block diagram of a mobile stage trajectory tracking active-disturbance-rejection control;
FIG. 3 is a block diagram of a first order linear active disturbance rejection controller;
FIG. 4 moving stage trajectory tracking x-axis tracking error exA curve;
FIG. 5 tracking error e of moving stage trajectory tracking y-axisya curve;
FIG. 6 tracking error e of moving stage track tracking theta axisθcurve line.
Detailed Description
In order to make the technical scheme and the design idea of the present invention clearer, the following detailed description is made with reference to the accompanying drawings.
a method for tracking and controlling a moving stage track by adopting an active disturbance rejection control technology comprises the following processes:
step 1) establishing a kinematic model of a mobile stage:
The structure of the mobile stage is complex, the mobile stage is a multivariable, high-coupling and nonlinear under-actuated system, and a controller needs to be designed for the system, and a reasonable kinematic model needs to be established firstly. The pose of the moving stage is described by three quantities (x, y, θ). Establishing kinematic model of mobile stage, see expression (1)
the control quantity U of the linear speed of the driving wheel is as follows:
wherein
X-coordinate value of moving stage on X axis of world coordinate system
Y-coordinate value of moving stage on Y axis of world coordinate system
theta- -rotation angle of a moving stage in a world coordinate system
θ0Angle between opposite corners and sides of the body (for a fixed structure body, theta)0to a certain definite value)
R- -distance from center of mass of vehicle body to center of rotation of steering structure
r- -radius of rotation of steering Structure
w1、2、3、4angular velocities of rotation of four steering mechanisms
ρ1、2、3、4-the angle of the steering mechanism with the X-axis of the body coordinate system.
Step 2) establishing a track tracking error model of the mobile stage, wherein the process comprises the following steps:
At any one time, its velocity vector in the world coordinate system isTaking the velocity vector of the reference point in a body coordinate system asis recorded as [ u v w ]]TError in tracking of trackDescribed as formula (3):
Wherein u isr，vrrespectively representing the expected values of the speed components of the moving stage along the X and Y axes of the vehicle body coordinate system at the time t through the track decompositionrIndicating the expected value of the angular velocity of rotation of the vehicle body.
step 3) decoupling of a multivariable system, wherein the process comprises the following steps:
for three input-three output systems
Note the book
x＝[x1 x2 x3]T
f＝[f1 f2 f3]T
u＝[u1 u2 u3]T (5)
Introducing "virtual control volume"The formula (4) is changed into
The I channel in the system has the input-output relationship of
Multivariable decoupling control can be realized by embedding 3 active disturbance rejection controllers between the control quantity U and the output quantity y in parallel.
x1，x2，x3state quantities of three-input-three-output systems
u1，u2，u3Control inputs of three-input-three-output systems
y1，y2，y3System output of a three-input three-output system
f1，f2，f3Disturbance terms for each channel
b11,b12,b13,b21,b22,b23,b31,b32,b33-system gain factor
Step 4), designing an active disturbance rejection controller, wherein the process comprises the following steps:
According to the trajectory tracking error model, the trajectory tracking controller can be decoupled into three independent subsystems, and an active disturbance rejection controller is respectively designed for each subsystem.
By decouplinglaw decouples the trajectory tracking controller into three subsystems, namely excontrol circuit, eyControl loop and eθAnd a control loop.
Because the system is a first-order system, a tracking differentiator is not needed, and the active disturbance rejection controller comprises an extended state observer and a state feedback control law
(1) designing an extended state observer, and estimating and compensating the state and the disturbance of the system in real time, wherein the equation of the extended state observer is given as follows:
wherein, beta01、β02is a set of parameters to be set.
e- -estimated value of output z1Difference with output y
u- -control input value of the System
b0-compensation factor
z2-an estimate of the dilated state
(2) Linear state error feedback control law
Wherein k is1Is a scaling factor.
e1- -reference input v1with the output estimated value z1difference of (2)
u0-error feedback control quantity
Further, in the step 3), the specific process is as follows:
As shown in the formula 3), the system can be regarded as a three-input three-output system, and u (t), v (t), w (t) are indirect control quantities
Let the dynamic coupling part be:
f1,f2,f3for the disturbance sum term, the static coupling part is:
With linear active-disturbance-rejection control techniques, the dynamic coupling components are estimated and compensated as sum-disturbances on the respective channels. As long as the matrix B is ensured to be reversible, the decoupling control of the system can be realized. For the system, B is reversible, so decoupling control can be realized.
Still further, in the step 4), the specific process is as follows:
with exthe active disturbance rejection controller design of the control subsystem is an example. The active disturbance rejection controller comprises an extended state observer and a state feedback control law
(1) Designing an extended state observer, and estimating and compensating the state and the disturbance of the system in real time, wherein the equation of the extended state observer is given as follows:
Wherein, beta01、β02Is a set of parameters to be set.
z1--exobserved value of (2)
z2- -observed value of the amount of expansion state
(2) Law of state error feedback control
Wherein，k1is a scaling factor.
the embodiment is a process of tracking a track of a mobile stage, and the specific operation process comprises the following steps:
1. in the parameter setting interface, basic parameters of a kinematic model of the mobile stage are input, and the basic parameters are as follows:
r＝0.2m，R＝1.0m，
The auto-disturbance rejection controller parameters are input as follows:
β01＝β02＝β11＝β12＝β21＝β22＝1
k1＝k2＝k3＝1
2. In the track import interface, a motion track is set. The set trajectory of this example is such that the moving stage rotates itself at an angular velocity of 0.2rad/s while moving linearly along the y-axis of the world coordinate system at a velocity of 1 m/s. After trajectory decomposition, [ u ] is obtainedr vr wr]TMatrix (u)r,vr,wrAll as a function of time t), [ u ]r vr wr]Tthe matrix parameters are as follows:
[ur vr wr]T＝[0 1.0t 0.2t]TWherein u isr,vrall units of (a) are m/s, wrin units of rad/s.
Matrix u obtained by decomposing the trackr vr wr]TThe data is stored in Flash storage.
3. off-line debugging: and clicking a 'debugging' button in the configuration interface to control the system to enter a controller debugging stage. Adjusting beta in parameter setting interface by taking linear track as test track01、β02、β11、β12、β21、β22value of (a) and k1、k2、k3Observing the tracking error e of the moving stage trackx、ey、eθTherefore, a group of parameters capable of quickly and effectively realizing the tracking control of the moving stage track is determined. The parameters of the active disturbance rejection controller obtained by debugging are as follows:
[β01 β02]T＝[100 2500]T
[β11 β12]T＝[90 2025]T
[β01 β02]T＝[110 3025]T
k1＝1.5，k2＝2，k3＝2
4. And (3) online operation: clicking a 'run' button on a configuration interface, reading the optimal setting parameters of the active disturbance rejection controller from the Flash storage by a control computer of the mobile stage, and reading a matrix u after the track decomposition from the Flash storager vr wr]Texecutes a 'moving stage track tracking control program', and measures the real-time pose [ x y theta ] of the moving stage on line]TAnd the rotating speeds of the driving motor and the steering motor are controlled, so that the automatic adjustment of the pose of the movable stage is realized. And when the next adjusting period is reached, measuring the real-time pose of the movable stage on line, and then repeating the whole executing process. And repeating the steps in this way, and realizing the automatic regulation control of the track tracking of the moving stage.
The above illustrates the moving stage trajectory tracking effect that one embodiment of the present invention exhibits excellent performance. It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that any modifications made within the spirit of the invention and the scope of the appended claims fall within the scope of the invention.
Claims (3)
1. A track tracking control method for a mobile stage by adopting an active disturbance rejection control technology is characterized by comprising the following steps:
step 1) establishing a kinematic model of a mobile stage:
The structure of the mobile stage is complex, the mobile stage is a multivariable, high-coupling and nonlinear under-actuated system, a controller is designed for the system, firstly, a reasonable kinematic model is established, the pose of the mobile stage is described by three quantities (x, y, theta), and the kinematic model of the mobile stage is established, as shown in formula (1):
the calculation of the control quantity U of the linear speed of the driving wheel is shown as the formula (2):
wherein:
X-coordinate value of the moving stage on the X axis of the world coordinate system,
Y-coordinate value of the moving stage on the Y axis of the world coordinate system,
Theta-rotation angle of the moving stage in the world coordinate system,
θ0Angle between diagonal and lateral edges of the body, theta for a structurally fixed body0The value of the signal is a certain value,
R is the distance from the center of mass of the vehicle body to the rotation center of the steering structure,
r-the radius of rotation of the steering structure,
w1、2、3、4-angular velocities of rotation of the four steering mechanisms,
ρ1、2、3、4-the angles of the four steering mechanisms with the X-axis of the vehicle body coordinate system;
Step 2) establishing a track tracking error model of the mobile stage, wherein the process comprises the following steps:
at any one time, its velocity vector in the world coordinate system isTaking the velocity vector of the reference point in a body coordinate system asIs recorded as [ u v w ]]Terror in tracking of trackDescribed as shown in formula (3):
wherein u isr，vrRespectively representing the expected values of the speed components of the moving stage along the X and Y axes of the vehicle body coordinate system at the time t through the track decompositionrA desired value indicating a vehicle body rotation angle;
step 3) decoupling of a multivariable system, wherein the process comprises the following steps:
for three input-three output systems
note the book
xs＝[x1 x2 x3]T
ys＝[y1 y2 y3]T
f＝[f1 f2 f3]T
uz＝[u1 u2 u3]T (5)
Introducing virtual control quantitythe formula (4) is changed into
The I channel in the system has the input-output relationship of
At the controlled quantity U and the output quantity ysmultivariable decoupling control can be realized by embedding 3 active disturbance rejection controllers in parallel;
Wherein x1，x2，x3-a state quantity of a three-input-three-output system,
u1，u2，u3-a control input of a three-input-three-output system,
y1，y2，y3-a system output of a three-input-three-output system,
f1，f2，f3-a disturbance term for each channel,
b11,b12,b13,b21,b22,b23,b31,b32,b33-a system gain factor;
step 4), designing an active disturbance rejection controller, wherein the process comprises the following steps:
According to the trajectory tracking error model, the trajectory tracking controller is decoupled into three independent subsystems, namely exControl circuit, eyControl loop and eθThe control loop is used for respectively designing an active disturbance rejection controller for each subsystem;
the system is a first-order system, a tracking differentiator is not needed, and the active disturbance rejection controller comprises an extended state observer and a state feedback control law, which is specifically as follows;
(1) designing an extended state observer, and estimating and compensating the state and the disturbance of the system in real time, wherein the equation of the extended state observer is given as follows:
Wherein, beta01、β02is a set of parameters to be set,
e- -estimated value of output z1and output youtthe difference value of (a) to (b),
uz-the control input value of the system,
b0-a compensation factor, which is a function of the compensation factor,
z2-an estimate of the dilated state;
(2) Linear state error feedback control law
wherein k is1Is a coefficient of proportionality that is,
e1- -reference input v1With the output estimated value z1The difference value of (a) to (b),
u0-error feedback control quantity.
2. The method for tracking and controlling the track of the moving stage by using the active disturbance rejection control technology according to claim 1, wherein in the step 3), the specific process is as follows:
as shown in the formula 3), the system can be regarded as a three-input three-output system, and u (t), v (t), w (t) are indirect control quantities
Wherein u isr，vrrespectively representing the expected values of the speed components of the moving stage along the X and Y axes of the vehicle body coordinate system at the time t through the track decompositionrA desired value indicating a vehicle body rotation angle;
Let the dynamic coupling part be:
f1,f2,f3For the disturbance sum term, the static coupling part is:
By utilizing a linear active disturbance rejection control technology, the dynamic coupling part is estimated and compensated as sum disturbance on respective channels, and the decoupling control of the system can be realized as long as the matrix B is ensured to be reversible; in the system, the determinant value of B is constantly-1, and decoupling control can be realized.
3. The method for tracking and controlling the moving stage track by adopting the active disturbance rejection control technology as claimed in claim 1, wherein the implementation process on the moving stage control computer is executed by a main execution part, and mainly comprises the following steps:
1) Setting parameters: in the parameter import interface, R, R, theta in the formula (1) are input0values, and ρ1，ρ2，ρ3，ρ4An initial value of (1); in the parameter setting interface of the active disturbance rejection controller, the gain beta of the extended state observer is input01、β02、β11、β12、β21、β22And k is1、k2、k3a value of (b), wherein11、β12is eyobserver gain, beta, of the control subsystem21、β22is eθobserver gain, k, of the control subsystem2,k3are each ey,eθThe state error feedback control law proportionality coefficient, after the input parameter is confirmed, the control computer sends the setting data into a computer storage unit Flash for storage;
2) Setting a track: setting a motion track in a track import interface, storing preset track data into a Flash storage unit by a control computer after the import track is confirmed, and decomposing the preset track into u by the control computerr vr wr]TStoring the matrix and the data into a Flash storage unit for storage, wherein ur,vr,wrAre all functions of time t;
3) off-line debugging: clicking a 'debugging' button in a configuration interface, controlling a system to enter a controller debugging stage, taking a straight line track as a test track, and adjusting beta in a parameter setting interface01、β02、β11、β12、β21、β22Value of (a) and k1、k2、k3Observing the tracking error e of the moving stage trackx、ey、eθThus, a group of parameters capable of quickly and effectively realizing the track tracking control of the moving stage is determined;
4) and (3) online operation: clicking a 'run' button on a configuration interface, reading the optimal setting parameters of the active disturbance rejection controller from the Flash storage by a control computer of the mobile stage, and reading a matrix u after the track decomposition from the Flash storager vr wr]TExecutes a 'moving stage track tracking control program', and measures the real-time pose [ x y theta ] of the moving stage on line]TAnd controlling the rotating speed of the driving motor and the rotating speed of the steering motor to realize automatic adjustment of the pose of the moving stage, measuring the real-time pose of the moving stage on line when the next adjustment period arrives, and repeating the whole execution process, wherein the steps are repeated in this way to realize automatic adjustment control of the track tracking of the moving stage.
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