CN109633605A - A kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar - Google Patents

A kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar Download PDF

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CN109633605A
CN109633605A CN201811637440.2A CN201811637440A CN109633605A CN 109633605 A CN109633605 A CN 109633605A CN 201811637440 A CN201811637440 A CN 201811637440A CN 109633605 A CN109633605 A CN 109633605A
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laser radar
robust
indicate
marine exhaust
adaptive
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杨钰潇
陈才
杜晓冬
李泽瑞
吕文君
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Anhui Youth Tiancheng Technology Co Ltd
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Anhui Youth Tiancheng Technology Co Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/48—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S17/00
    • G01S7/481—Constructional features, e.g. arrangements of optical elements
    • G01S7/4817—Constructional features, e.g. arrangements of optical elements relating to scanning
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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  • Engineering & Computer Science (AREA)
  • Artificial Intelligence (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Software Systems (AREA)
  • Health & Medical Sciences (AREA)
  • Medical Informatics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Automation & Control Theory (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Optical Radar Systems And Details Thereof (AREA)

Abstract

The present invention provides a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar, comprising steps of establishing D-H coordinate system to marine exhaust monitoring laser radar；Kinematics analysis is carried out to marine exhaust monitoring laser radar, and establishes forward kinematics equation；According to kinematics analysis result and the forward kinematics equation, the kinetic model of the marine exhaust monitoring laser radar is established；Periodical external disturbance in the kinetic model is decomposed into modeled segments and unmodel parts；Adaptive control algorithm is designed to the modeled segments；Robust H is designed to the unmodel parts∞Control algolithm；ADAPTIVE ROBUST servo follow-up tracing control law is calculated.The present invention utilizes fourier progression expanding method, by periodical external disturbance be decomposed into can modeled segments with can not modeled segments, design adaptive control algorithm and robust Robust Control Algorithm, inhibit the external disturbance that can be modeled respectively and the tracking error of external disturbance generation can not be modeled, improves control efficiency.

Description

A kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar
Technical field
The present invention relates to air pollution emission monitoring technical fields, and in particular to a kind of marine exhaust monitoring laser radar ADAPTIVE ROBUST follow-up control method.
Background technique
The situation is tense for current China atmospheric environment, and gross contamination emission is big, the area of pollutant characterized by fine particle Property atmospheric environment problem in domain becomes increasingly conspicuous.The regionality atmosphere polluting problem such as gray haze frequently occurred, with motor vehicle, engineering truck , the not qualified discharge of the moving urban pollution sources tail gas such as ship it is closely related.Moving source pollution has become In The Atmosphere Over China dirt One of most prominent, most pressing problem in dye problem.Various detection techniques are merged, moving urban pollution source discharge is integrated Monitoring is to control the direct effective means of moving source pollution.
In terms of the emission monitoring of the non-rice habitats mobile pollution source such as ship, since optical reflection unit can not be installed, it is necessary to Observation system is scanned using passive type, i.e. marine exhaust monitors laser radar, by emitting the laser of specific wavelength into atmosphere, It acquires and analyzes the scattering spectrum after physical action occurs with atmospheric medium, to obtain the concentration information of Atmospheric components.However this Kind method for monitoring and analyzing measurement optical path length is long, detection zone area is small, and the automatic positioning of observed object is extremely difficult, Er Qie In the servomechanism process of observation system, microvibration can bring about great detection error.
Summary of the invention
In view of the deficiencies of the prior art, the ADAPTIVE ROBUST that the present invention provides a kind of marine exhaust monitoring laser radar is servo-actuated Control method enables to laser radar quickly and stably to track target, and resists PERIODIC INTERFERENCE.
In order to achieve the above object, the present invention is achieved by the following technical programs:
A kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar, the marine exhaust monitor laser Radar includes pedestal B0, orientation rotation part B1With roll rotary part B2, the pedestal B0, orientation rotation part B1It is revolved with roll Rotation member B2Successively it is rotatablely connected, the method includes the steps:
Step 1: establishing D-H coordinate system to marine exhaust monitoring laser radar；
Step 2: being moved according to the corresponding DH parameter list of the D-H coordinate system to marine exhaust monitoring laser radar Credit analysis, and establish forward kinematics equation；
Step 3: establishing the marine exhaust according to the kinematics analysis result of step 2 and the forward kinematics equation Monitor the kinetic model of laser radar；
Step 4: the periodical external disturbance in the kinetic model is decomposed into modeled segments and unmodel parts；
Step 5: designing adaptive control algorithm to modeled segments described in step 4；
Step 6: designing robust H to unmodel parts described in step 4∞Control algolithm；
Step 7: the comprehensive adaptive control algorithm and the robust H∞ADAPTIVE ROBUST is calculated in control algolithm Servo follow-up tracing control law.
Further, the D-H coordinate system includes 3 link rod coordinate systems, respectively corresponds pedestal B0, orientation rotation part B1 With roll rotary part B2；Determine O0, O1, O2The coordinate origin of respectively 3 link rod coordinate systems, S0, S1, S2Respectively B0, B1, B2Mass center；θ1, θ2Respectively indicate azimuth and the roll angle of each coordinate system；τ1, τ2It respectively indicates outside and is applied to B1, the power of B Square；Wherein, O0O1Length be d1, O1O2Length be d2。
Further, the forward kinematics equation is
Wherein,It indicates from O0Coordinate system is to O1The homogeneous transform matrix of coordinate system；Indicate cos θ1、cos θ2,Indicate sin θ1、sinθ2,Indicate O0Coordinate system is to O1One step homogeneous transform matrix of coordinate system,It indicates O1Coordinate system is to O2One step homogeneous transform matrix of coordinate system.
Further, the kinetic model includes forward recursion formula:
Wherein,Indicate BiAngular speed,The unit vector in the z-axis direction of indicates coordinate system i,Indicate OiAcceleration Degree,Indicate SiAcceleration,Indicate vectorIndicate the angular acceleration of rotor, kriFor The gear deceleration Than,For the unit vector in the direction of rotor shaft；
Backward recursion formula:
Wherein,Indicate the active force that connecting rod i-1 applies connecting rod i, miIndicate BiQuality,Indicate connecting rod i-1 to even Bar i is about coordinate system i-1 origin Oi-1Torque,Indicate vector Indicate BiInertia about coordinate system i Moment matrix,Indicate the rotary inertia of rotor around the shaft,ForComponent in the z-axis of coordinate system i.
Further, the parameter preset of the marine exhaust monitoring laser radar includes m1=100, m2=46.5, r0,1= 0.18, r1,2=0.4,
Further, the parameter preset that laser radar is monitored according to the marine exhaust, calculates to obtain kinetics equation:
Enable τ=(τ1 τ2)T, q=(θ1 θ2)T, obtain
Wherein, M (q) is broad sense inertial matrix,For centripetal force and Coriolis force matrix, G (q) is gravity,D is external disturbance.
Further, it is decomposed into modeled segments in the step 4 and the specific decomposition method of unmodel parts is
D (t)=dm(t)+dl(t)
Wherein, dmIt (t) is modeled segments, dlIt (t) is unmodel parts；For modeled segments dm(t), meet:
Am, BmFor known matrix, and haveIt sets up.
Further, the step 5 is specifically, external disturbance u to the modeled segmentsdSelf adaptive control is designed to calculate Method
Wherein, udFor modeling disturbance adaptive controller output,By adaptive updates restrain obtain, it is described from Adapting to more new law is
Wherein,It is defined as the tracking error of state Pm For positively definite matrix, and meet
Further, the robust H∞The control law of control algolithm is
Wherein, yhFor robust H∞The output of controller；rh> 0, rhFor robust H∞Controller gain.
Compared with prior art, the invention has the following advantages:
The present invention passes through the summation of the external disturbance and unmodeled external disturbance that will model as the general of external disturbance Periodical external disturbance is decomposed into modeled segments and unmodel parts, design is adaptive using fourier progression expanding method by model Control algolithm and robust H∞Control algolithm, the tracking for inhibiting the external disturbance of modeling and unmodeled external disturbance to generate respectively miss Difference constructs a kind of adaptive neural network system and carrys out the external disturbance of approximate modeling, while weakening modeling external disturbance and causing Tracking error influence.Robust H proposed by the present invention∞Control program, be only required to reduce unmodeled external disturbance to The influence of track error reduces control cost, reduces the operand in algorithm implementation procedure, improves control efficiency.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with It obtains other drawings based on these drawings.
Fig. 1 is control method flow chart of the present invention；
Fig. 2 is the corresponding control system block diagram of the present invention；
Fig. 3 is that marine exhaust monitors laser radar structure chart in the present invention；
Fig. 4 is that marine exhaust monitors laser radar centroid figure in the present invention；
Fig. 5 is that marine exhaust monitors laser radar D-H link rod coordinate system structure chart in the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art Every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
The present invention provides a kind of ADAPTIVE ROBUST follow-up control methods of marine exhaust monitoring laser radar, such as Fig. 3 institute Show, it includes pedestal B which, which monitors laser radar,0, orientation rotation part B1With pitching rotary part B2, the pedestal B0、 Orientation rotation part B1With roll rotary part B2Successively it is rotatablely connected.
As shown in Figure 1, specific implementation step of the present invention is as follows:
S1, D-H coordinate system is established to marine exhaust monitoring laser radar；As shown in Figures 4 and 5, using Denavit- Hartenberg (DH) method establishes link rod coordinate system；Wherein, O0, O1, O2The coordinate origin of respectively 3 coordinate systems, S0, S1, S2 Respectively B0, B1, B2Centroid position, θ1, θ2Respectively azimuth and roll angle, τ1, τ2Respectively motor is applied to B1, B2's Torque.O0O1Length be d1, O1O2Length be d2。
According to D-H method, the corresponding DH parameter list of the built coordinate system of the present invention are as follows:
Wherein connecting rod 1 is B1And B1Upper driving B2Motor, connecting rod 2 be B2, aiFor axis ziWith zi-1Common vertical line length Degree；αiFor axis zi-1With ziBetween angle, when around axis xiIt is positive when rotating counterclockwise；diFor axis ziWith zi-1Common vertical line and zi-1 Intersection point along zi-1Coordinate；θiFor axis xi-1With xiBetween angle, when around axis zi-1It is positive when rotating counterclockwise.
S2, kinematics analysis is carried out to marine exhaust monitoring laser radar；According to DH parameter list, forward kinematics equation is established It is as follows:
Wherein,It indicates from O0Coordinate system is to O1The homogeneous transform matrix of coordinate system；Indicate cos θ1、cos θ2,Indicate sin θ1、sinθ2,Indicate O0Coordinate system is to O1One step homogeneous transform matrix of coordinate system,It indicates O1Coordinate system is to O2One step homogeneous transform matrix of coordinate system.
S3, the kinetic model for establishing marine exhaust monitoring laser radar；According to Newton-Euler method, forward recursion Formula is
Wherein,Indicate BiAngular speed,The unit vector in the z-axis direction of indicates coordinate system i,Indicate OiAcceleration Degree,Indicate SiAcceleration,Indicate vectorIndicate the angular acceleration of rotor, kriSubtract for gear Speed ratio,For the unit vector in the direction of rotor shaft.
Backward recursion formula is
Wherein,Indicate the active force that connecting rod i-1 applies connecting rod i, miIndicate BiQuality,Indicate connecting rod i-1 to even Bar i is about coordinate system i-1 origin Oi-1Torque,Indicate vector Indicate BiInertia about coordinate system i Moment matrix,Indicate the rotary inertia of rotor around the shaft,ForComponent in the z-axis of coordinate system i, i.e. torque.
The parameter that marine exhaust monitors laser radar scanning mechanism is m1=100, m2=46.5, r0,1=0.18, r1,2= 0.4, The above are in current connecting rods coordinate system Coordinate.
The parameter for bringing laser radar scanning mechanism into is derived, and the kinetics equation of laser radar scanning mechanism is obtained Are as follows:
Being arranged is matrix form, enables τ=(τ1 τ2) T, q=(θ1 θ2)T, obtain
Wherein, M (q) is broad sense inertial matrix,For centripetal force and Coriolis force matrix, G (q) is gravity,D is external disturbance:
The kinetic model of marine exhaust monitoring laser radar scanning mechanism can be written as follow the expression shape of state space Formula:
M(x1)x2=-C (x1, x2)x2+G(x1, x2)+τ+d
Wherein x1(t)=q (t),
Define tracking errorWith filter link error
Wherein p > 0 is gain, then can derive useThe error dynamics equation of expression:
Wherein, F(xe) contain the parameter matrix of kinetic model.
S4, periodical external disturbance is decomposed into modeled segments and unmodel parts；Unknown external disturbance d (t) can be with It is decomposed as the following formula:
D (t)=dm(t)+dl(t)
Wherein, dmIt (t) is modeled segments, dlIt (t) is unmodel parts.For modeled segments dm(t), meet:
Am, BmFor known matrix, and there are positive definite matrix Pm, so thatIt sets up.
S5, adaptive control algorithm is designed to the external disturbance of modeled segments in S4, the outside that weakening can model in S4 is disturbed The influence of the raw tracking error of movable property, to the external disturbance u of modeled segments in S4dDesign adaptive control algorithm:
Wherein, udFor modeling disturbance adaptive controller output,It is restrained and is obtained by following adaptive updates:
Wherein,It is defined as the tracking error of state
PmFor positively definite matrix and satisfaction
S6, design robust H∞Control algolithm reduces the external disturbance bring tracking error that can not be modeled in S4；To in S4 The external disturbance design robust H that can not be modeled∞Control algolithm, control law i.e.:
Wherein, uhFor robust H∞The output of controller, rh> 0, it is robust H∞Controller gain.
S7, the above content of integration obtain the ADAPTIVE ROBUST servo follow-up tracing control for marine exhaust monitoring laser radar Rule:
T=F (xe)+uh+ud
As constant α > 0, ρ > 0, p > 0, Q=QT> 0 and when meeting following inequality,
Self-adaptive robust controller proposed by the present invention ensures stateful, signal all bounded.The present invention will be by that will build Universal model of the summation of the external disturbance of mould and unmodeled external disturbance as external disturbance, utilizes fourier series exhibition It opens, periodical external disturbance is decomposed into modeled segments and unmodel parts, designs adaptive control algorithm and robust H∞Control Algorithm, the tracking error for inhibiting the external disturbance of modeling and unmodeled external disturbance to generate respectively, constructs a kind of adaptive mind Carry out the external disturbance of approximate modeling through network system, while weakening the influence of tracking error caused by modeling external disturbance.This hair The robust H of bright proposition∞Control program is only required to reduce influence of the unmodeled external disturbance to tracking error, reduces control This is made, reduces the operand in algorithm implementation procedure, improves control efficiency.
It should be noted that, in this document, relational terms such as first and second and the like are used merely to a reality Body or operation are distinguished with another entity or operation, are deposited without necessarily requiring or implying between these entities or operation In any actual relationship or order or sequence.Moreover, the terms "include", "comprise" or its any other variant are intended to Non-exclusive inclusion, so that the process, method, article or equipment including a series of elements is not only wanted including those Element, but also including other elements that are not explicitly listed, or further include for this process, method, article or equipment Intrinsic element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that There is also other identical elements in process, method, article or equipment including the element.
The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to the foregoing embodiments Invention is explained in detail, those skilled in the art should understand that: it still can be to aforementioned each implementation Technical solution documented by example is modified or equivalent replacement of some of the technical features；And these modification or Replacement, the spirit and scope for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution.

Claims (9)

1. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar, the marine exhaust monitor laser thunder Up to including pedestal B0, orientation rotation part B1With roll rotary part B2, the pedestal B0, orientation rotation part B1It is rotated with roll Part B2Successively it is rotatablely connected, which is characterized in that the method includes the steps:
Step 1: establishing D-H coordinate system to marine exhaust monitoring laser radar；
Step 2: carrying out movement credit to marine exhaust monitoring laser radar according to the corresponding DH parameter list of the D-H coordinate system Analysis, and establish forward kinematics equation；
Step 3: establishing the marine exhaust monitoring according to the kinematics analysis result of step 2 and the forward kinematics equation The kinetic model of laser radar；
Step 4: the periodical external disturbance in the kinetic model is decomposed into modeled segments and unmodel parts；
Step 5: designing adaptive control algorithm to modeled segments described in step 4；
Step 6: designing robust H to unmodel parts described in step 4∞Control algolithm；
Step 7: the comprehensive adaptive control algorithm and the robust H∞It is servo-actuated that ADAPTIVE ROBUST is calculated in control algolithm Tracing control rule.
2. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 1, Be characterized in that: the D-H coordinate system includes 3 link rod coordinate systems, respectively corresponds pedestal B0, orientation rotation part B1It is revolved with roll Rotation member B2；Determine O0, O1, O2The coordinate origin of respectively 3 link rod coordinate systems, S0, S1, S2Respectively B0, B1, B2Mass center； θ1, θ2Respectively indicate azimuth and the roll angle of each coordinate system；τ1, τ2It respectively indicates outside and is applied to B1, B2Torque；Wherein, O0O1Length be d1, O1O2Length be d2。
3. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 2, Be characterized in that: the forward kinematics equation is
Wherein,It indicates from O0Coordinate system is to O1The homogeneous transform matrix of coordinate system；Indicate cos θ1、cosθ2,Indicate sin θ1、sinθ2,Indicate O0Coordinate system is to O1One step homogeneous transform matrix of coordinate system,Indicate O1It sits Mark system arrives O2One step homogeneous transform matrix of coordinate system.
4. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 3, It is characterized in that, the kinetic model includes forward recursion formula:
Wherein,Indicate BiAngular speed,The unit vector in the z-axis direction of indicates coordinate system i,Indicate OiAcceleration,Indicate SiAcceleration,Indicate vector Indicate the angular acceleration of rotor, kriFor gear reduction ratio,For the unit vector in the direction of rotor shaft；
Backward recursion formula:
Wherein,Indicate the active force that connecting rod i-1 applies connecting rod i, miIndicate BiQuality,Indicate connecting rod i-1 to connecting rod i About coordinate system i-1 origin Oi-1Torque,Indicate vector Indicate BiInertial tensor about coordinate system i Matrix,Indicate the rotary inertia of rotor around the shaft,ForComponent in the z-axis of coordinate system i.
5. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 4, Be characterized in that: the parameter preset of the marine exhaust monitoring laser radar includes m1=100, m2=46.5, r0,1=0.18, r1,2 =0.4,
6. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 5, It is characterized in that: monitoring the parameter preset of laser radar according to the marine exhaust, calculate to obtain kinetics equation:
Enable τ=(τ1 τ2)T, q=(θ1 θ2)T, obtain
Wherein, M (q) is broad sense inertial matrix,For centripetal force and Coriolis force matrix, G (q) is gravity, D is external disturbance.
7. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 6, Be characterized in that: the specific decomposition method that modeled segments and unmodel parts are decomposed into the step 4 is d (t)=dm(t)+dl (t)
Wherein, dmIt (t) is modeled segments, dlIt (t) is unmodel parts；For modeled segments dm(t), meet:
Am, BmFor known matrix, and haveIt sets up.
8. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 7, Be characterized in that: the step 5 is specifically, external disturbance u to the modeled segmentsdDesign adaptive control algorithm
Wherein, udFor modeling disturbance adaptive controller output,Restrained and obtained by adaptive updates, it is described it is adaptive more New law is
Wherein,It is defined as the tracking error of state PmIt is positive Determine battle array, and meets
9. a kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar according to claim 1, It is characterized in that: the robust H∞The control law of control algolithm is
Wherein, uhFor robust H∞The output of controller；rh> 0, rhFor robust H∞Controller gain.
CN201811637440.2A 2018-12-29 2018-12-29 A kind of ADAPTIVE ROBUST follow-up control method of marine exhaust monitoring laser radar Withdrawn CN109633605A (en)

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