CN108656114B - Control method of flexible mechanical arm - Google Patents

Control method of flexible mechanical arm Download PDF

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CN108656114B
CN108656114B CN201810469011.2A CN201810469011A CN108656114B CN 108656114 B CN108656114 B CN 108656114B CN 201810469011 A CN201810469011 A CN 201810469011A CN 108656114 B CN108656114 B CN 108656114B
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CN108656114A (en
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杨春雨
许一鸣
周林娜
薛雨凝
赵建国
孟凡仪
汤瑶汉
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China University of Mining and Technology CUMT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1635—Programme controls characterised by the control loop flexible-arm control

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Abstract

The invention discloses a control method of a flexible mechanical arm, which comprises the following steps: designing a slow controller by using a self-adaptive dynamic programming algorithm according to given position information and feedback position information under a slow time scale; performing vibration estimation on the slow time scale to obtain a vibration quantity estimation value on the slow time scale; reconstructing a fast variable according to the vibration quantity estimated value and the feedback vibration information under the slow time scale under the fast time scale, and designing a fast controller by using an adaptive dynamic programming algorithm according to the fast variable; the slow controller and the fast controller are combined to control the position and the vibration of the flexible mechanical arm. According to the control method provided by the invention, the optimal control on the position and the vibration of the flexible mechanical arm can be realized under the condition of not using a system model.

Description

Control method of flexible mechanical arm
Technical Field
The invention relates to the technical field of flexible mechanical arm control, in particular to a control method of a flexible mechanical arm.
Background
The flexible mechanical arm has the advantages of high moving speed, high weight ratio of effective load to the robot, low manufacturing consumption, large working space and the like, and is widely applied to the fields of aviation, buildings and the like. Considering the special structural characteristics of the object, the motion of the flexible mechanical arm comprises macroscopic rigid body rotation and microscopic flexible vibration, and the macroscopic rigid body rotation and the microscopic flexible vibration are highly coupled. And the flexible mechanical arm has the characteristics of nonlinearity, infinite order, uncertain parameters and the like, so that the problem of improving the positioning accuracy and avoiding the vibration caused by flexibility is a challenging problem.
The method has the advantages that the dynamic characteristics of the flexible mechanical arm are fully considered and utilized, and the controller can be designed by applying the traditional methods such as PID control, variable structure control, robust control, neural network control, fuzzy control, self-adaptive control and the like. On the other hand, in consideration of the double-time scale characteristic of the flexible mechanical arm, the singular perturbation method is introduced into modeling and control of a complex flexible mechanical arm system, the controllers are respectively designed under different time scales, and the existing research results show that the controller designed by the method is simple in design process and good in performance.
Although much work has been done on flexible robotic arm control, most control strategies are based on kinetic models. However, flexible robotic arm systems have uncertainty. Therefore, it is a hot problem to study the control of the flexible robot arm using the input and the system status. Through the search and discovery of the existing relevant documents about the flexible mechanical arm control method, the model-free composite controller of the flexible mechanical arm is realized by utilizing the fuzzy controller, and relevant research is already carried out. However, the fuzzy controller needs to adjust a plurality of parameters at the same time, and the optimal control performance is difficult to achieve. While existing optimal controllers using linear quadratic designs have good control performance, they require precise system parameters. Therefore, the research on model-free optimal control of the flexible mechanical arm has important practical significance.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the art described above. Therefore, an object of the present invention is to provide a method for controlling a flexible robot arm, which can realize optimal control of the position and vibration of the flexible robot arm without using a system model.
In order to achieve the above object, the present invention provides a method for controlling a flexible manipulator, comprising: designing a slow controller by using an Adaptive Dynamic Programming (ADP) algorithm according to given position information and feedback position information under a slow time scale; performing vibration estimation on the slow time scale to obtain a vibration quantity estimation value on the slow time scale; reconstructing a fast variable according to the vibration quantity estimated value and the feedback vibration information under the slow time scale under the fast time scale, and designing a fast controller by using an adaptive dynamic programming algorithm according to the fast variable; and combining the slow controller and the fast controller to realize the control of the position and the vibration of the flexible mechanical arm.
According to the control method of the flexible mechanical arm, the slow controller is designed by using the adaptive dynamic programming algorithm according to the given position information and the feedback position information under the slow time scale, the vibration estimation value under the slow time scale is obtained, the fast variable is reconstructed according to the vibration estimation value and the feedback vibration information under the slow time scale under the fast time scale, the fast controller is designed by using the adaptive dynamic programming algorithm according to the fast variable, and then the slow controller and the fast controller are combined to realize the control of the position and the vibration of the flexible mechanical arm, so that the optimal control of the position and the vibration of the flexible mechanical arm can be realized under the condition of not using a system model.
In addition, the control method of the flexible mechanical arm provided by the above embodiment of the invention may further have the following additional technical features:
according to one embodiment of the invention, the adaptive dynamic programming algorithm comprises:
the method comprises the following steps: given an initial control law u-K0x + K, wherein K0∈Rm×nCalculate δ for the initial gain matrix, κ for the detection noisexx、Ixx、IxuUntil it is satisfied
Figure BDA0001662607940000031
Wherein, deltaxx、Ixx、IxuTo learn the matrices used to collect state and input information,
δxx＝[μ(x(t1))-μ(x(t0)),μ(x(t2))-μ(x(t1)),...,μ(x(tl))-μ(x(tl-1)
Figure BDA0001662607940000032
Figure BDA0001662607940000033
Figure BDA0001662607940000034
0≤t0＜t1＜...＜tl
wherein,
Figure BDA0001662607940000035
represents the kronecker product;
step two: using formulas
Figure BDA0001662607940000036
Solving for PkAnd Kk+1，PkFor the normalized solution of the Riccati equation, K, found in an iterative processkIs a feedback gain matrix in an iterative process, wherein,
Figure BDA0001662607940000037
Figure BDA0001662607940000038
γ(Pk)＝[p11p12...2p1n p222p23...2pn-1pnn]T
vec (M) denotes vectorization of matrix M, i.e., vec (M)g×h)＝[m11m21...m1h m2h...mgh]T；
Step three: let k ← k +1, if | | Pk-Pk-1If the | is more than alpha and the alpha is more than 0, returning to the step two, otherwise, entering the step four;
step four: let K*＝KkObtaining the optimal control law u ═ K*x。
According to an embodiment of the present invention, a slow controller is designed by using an adaptive dynamic programming algorithm according to given position information and feedback position information under a slow time scale, which specifically comprises:
defining a position error ec＝θ-θdWherein, thetadGiven position information, theta is feedback position information;
defining new variables
Figure BDA0001662607940000041
Rewriting a model of a slow subsystem describing a flexible robotic arm as
Figure BDA0001662607940000042
Wherein,
Figure BDA0001662607940000043
Figure BDA0001662607940000044
superscript s denotes slow dynamics;
selecting an evaluation function
Figure BDA0001662607940000045
Wherein Q iss＝(Qs)T≥0,Rs＝(Rs)T＞0，(As,(Qs)1/2) Considerable;
using the adaptive dynamic programming algorithm, wherein x is xs，u＝us，
Figure BDA0001662607940000046
Obtaining a slow controller for the initial feedback gain matrix
Figure BDA0001662607940000047
According to an embodiment of the present invention, the estimating vibration on a slow time scale to obtain an estimated value of vibration amount on the slow time scale specifically includes:
estimating the vibration quantity in slow time scale by considering the existence of random errorEvaluating zsAnd usThe relation z betweens＝a+busIs written into
Figure BDA0001662607940000048
Wherein v isiWhich represents a random error, is presented to the user,
Figure BDA0001662607940000049
is measured data;
defining the evaluation function J as
Figure BDA00016626079400000410
And (3) extreme value calculation:
Figure BDA00016626079400000411
approximate values for a and b were obtained:
Figure BDA0001662607940000051
thereby obtaining the vibration quantity estimated value under the slow time scale
Figure BDA0001662607940000052
According to one embodiment of the invention, the fast variable zf＝k·q-zsAnd K is the minimum value in the rigidity matrix K, and q is the feedback vibration information.
According to an embodiment of the present invention, a fast controller is designed by using an adaptive dynamic programming algorithm according to the fast variable, which specifically includes:
defining new variables
Figure BDA0001662607940000053
Rewriting a fast subsystem model describing a flexible manipulator as
Figure BDA0001662607940000054
Wherein,
Figure BDA0001662607940000055
superscript f denotes fast dynamics;
selecting an evaluation function
Figure BDA0001662607940000056
Wherein Q isf＝(Qf)T≥0，Rf＝(Rf)T＞0，(Af,(Qf)1/2) Considerable;
using the adaptive dynamic programming algorithm, wherein x is xf，u＝uf，
Figure BDA0001662607940000057
For the initial feedback gain matrix, a fast controller is obtained
Figure BDA0001662607940000058
According to an embodiment of the present invention, the slow controller and the fast controller are combined to control the position and the vibration of the flexible mechanical arm, specifically including:
will uGeneral assembly＝us+ufAs a dynamic model of the flexible manipulator
Figure BDA0001662607940000061
And (c) implementing control of the position and vibration of the flexible manipulator, wherein M is a positive definite inertial matrix and G is a nonlinear term.
Drawings
FIG. 1 is a flow chart of a method of controlling a flexible robotic arm according to an embodiment of the present invention;
FIG. 2 is a schematic view of a control system for a flexible robotic arm according to one embodiment of the present invention;
FIG. 3 is a block diagram of an embodiment of the present invention
Figure BDA0001662607940000062
Tracking KsdA convergence graph;
FIG. 4 shows an embodiment of the present invention
Figure BDA0001662607940000063
Tracking KfdA convergence graph;
FIG. 5 is a comparison graph of the control method and the trajectory tracking under the action of the fuzzy controller according to the embodiment of the present invention;
FIG. 6 is a comparison graph of a first-order modal curve under the control method and the fuzzy controller according to the embodiment of the present invention;
FIG. 7 is a comparison graph of second-order modal curves under the control method and the fuzzy controller according to the embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
A control method of a flexible robot arm according to an embodiment of the present invention is described below with reference to the drawings.
Firstly, a dynamic model of the flexible mechanical arm can be established by using a Lagrange method and an assumed modal method:
Figure BDA0001662607940000071
where M is a positive definite inertial matrix, G is a nonlinear term, K is a stiffness matrix, uGeneral assemblyTo input of a motor driving the flexible robot arm, θ represents position information and q represents vibration information.
Based on the singular perturbation theory, the control system of the flexible mechanical arm can be decomposed into a fast subsystem and a slow subsystem.
Wherein, the slow subsystem:
Figure BDA0001662607940000072
Figure BDA0001662607940000073
a fast subsystem:
Figure BDA0001662607940000074
wherein,
Figure BDA0001662607940000075
ε＝1/k，εz＝q，β＝εK，
Figure BDA0001662607940000076
k is the minimum value in the stiffness matrix K, and the superscripts s, f respectively represent slow dynamics and fast dynamics.
Combining the slow and fast controllers together to obtain:
ugeneral assembly＝us+uf (5)
Based on the Tikhonov theorem, the relationship between the state variables of the slow subsystem and the fast subsystem and the state variables of the original system is as follows:
Figure BDA0001662607940000077
q＝1/k(zs+zf)+O(ε) (7)
most of the existing flexible mechanical arm controller design methods are based on completely known or partially unknown dynamic models, and the invention researches the problem of model-free combined control of the flexible mechanical arm.
In view of the fast and slow subsystems based on the singular perturbation theory decomposition, the controller can be designed under different time scales, and the controllers designed under different time scales are combined to control the flexible mechanical arm, which is as follows.
As shown in fig. 1, a method for controlling a flexible robot arm according to an embodiment of the present invention includes the following steps:
and S1, designing the slow controller by using a self-adaptive dynamic programming algorithm according to the given position information and the feedback position information under the slow time scale.
The self-adaptive dynamic programming algorithm comprises the following steps:
the method comprises the following steps: given an initial control law:
u＝-K0x+κ (8)
wherein, K0∈Rm×nCalculate δ for the initial gain matrix, κ for the detection noisexx、Ixx、IxuUntil the following conditions are met:
Figure BDA0001662607940000081
wherein, deltaxx、Ixx、IxuTo learn the matrices used to collect state and input information,
δxx＝[μ(x(t1))-μ(x(t0)),μ(x(t2))-μ(x(t1)),...,μ(x(tl))-μ(x(tl-1)
Figure BDA0001662607940000082
Figure BDA0001662607940000083
Figure BDA0001662607940000084
0≤t0＜t1＜...＜tl
wherein,
Figure BDA0001662607940000085
represents the kronecker product;
step two: solving for P using equation (10)kAnd Kk+1，PkFor the normalized solution of the Riccati equation, K, found in an iterative processkIs a feedback gain matrix in an iterative process.
Figure BDA0001662607940000086
Wherein:
Figure BDA0001662607940000087
Figure BDA0001662607940000091
γ(Pk)＝[p11p12...2p1np222p23...2pn-1pnn]T
vec (M) denotes vectorization of matrix M, i.e., vec (M)g×h)＝[m11m21...m1h m2h...mgh]T；
Step three: let k ← k +1, if | | Pk-Pk-1If the | is more than alpha and the alpha is more than 0, returning to the step two, otherwise, entering the step four;
step four: let K*＝KkAnd obtaining an optimal control law:
u＝-K*x (11)
as shown in the above equation (2), the slow subsystem represents the rigid motion of the flexible manipulator system, and as can be seen from the above equation (6), the position state of the flexible manipulator can be directly used for the slow controller design.
Specifically, a position error may be defined:
ec＝θ-θd (12)
wherein, thetadFor given position information, θ isAnd feeding back the position information.
Defining new variables
Figure BDA0001662607940000092
The slow subsystem model describing the flexible robotic arm, equation (2) above, is rewritten as:
Figure BDA0001662607940000093
wherein,
Figure BDA0001662607940000094
selecting an evaluation function:
Figure BDA0001662607940000095
wherein Q iss＝(Qs)T≥0,Rs＝(Rs)T＞0，(As,(Qs)1/2) It is considerable.
Using the adaptive dynamic programming algorithm described above, where x is xs，u＝us，
Figure BDA0001662607940000096
For the initial feedback gain matrix, a slow controller is obtained:
Figure BDA0001662607940000097
further, the position information theta and the first guide thereof fed back by the flexible mechanical arm
Figure BDA0001662607940000101
Let us＝-Ks 0xs+κsCalculating
Figure BDA0001662607940000102
Then pass through
Figure BDA0001662607940000103
Solving for Ps kAnd Ks k+1. Then judging whether | P is present or not when k is more than 1s k-Ps k-1If not, let k ← k +1, then solve Ps kAnd Ks k+1(ii) a If so, then
Figure BDA0001662607940000104
As shown in fig. 2, the slow controller designed in the embodiment of the present invention is an ADP-based slow controller, and inputs the given position information θdAnd feedback position information theta, output slow parameter us。
And S2, performing vibration estimation in a slow time scale to obtain a vibration quantity estimation value in the slow time scale.
According to the above equation (7), the vibration information q includes the vibration amount z at a slow time scalesAnd vibration amount z at fast time scalef. To design a fast controller, first, z needs to be estimatedsAs can be seen from the above formula (6), zsAnd usThe approximate structure between is as follows:
zs＝a+bus (16)
where a and b are the parameters to be estimated. Considering the existence of random error, estimating the vibration amount z in slow time scalesAnd usThe relationship (16) between is written as:
Figure BDA0001662607940000105
wherein v isiWhich represents a random error, is presented to the user,
Figure BDA0001662607940000106
are measured data.
Using the least squares method, the evaluation function J is defined as:
Figure BDA0001662607940000107
and (3) extreme value calculation:
Figure BDA0001662607940000108
approximate values for a and b were obtained:
Figure BDA0001662607940000111
thereby obtaining the vibration amount estimated value z under the slow time scales：
Figure BDA0001662607940000112
And S3, reconstructing a fast variable according to the vibration quantity estimated value and the feedback vibration information under the slow time scale under the fast time scale, and designing a fast controller by using an adaptive dynamic programming algorithm according to the fast variable.
Reconstructed fast variables zf＝k·q-zs. Where K is the minimum value in the stiffness matrix K, and q is the feedback vibration information shown in fig. 2.
As shown in equation (4) above, the snap subsystem represents the flexible vibration of the flexible arm system.
In particular, new variables may be defined
Figure BDA0001662607940000118
The fast subsystem model describing the flexible robot arm, i.e. equation (4) above, is rewritten as:
Figure BDA0001662607940000113
wherein,
Figure BDA0001662607940000114
selecting an evaluation function:
Figure BDA0001662607940000115
wherein Q isf＝(Qf)T≥0，Rf＝(Rf)T＞0，(Af,(Qf)1/2) It is considerable.
Using the adaptive dynamic programming algorithm described above, where x is xf，u＝uf，
Figure BDA0001662607940000116
For the initial feedback gain matrix, a fast controller is obtained:
Figure BDA0001662607940000117
further, vibration information q fed back by the flexible mechanical arm and a first derivative thereof
Figure BDA0001662607940000121
Let z be kq or more,
Figure BDA0001662607940000122
estimate z and
Figure BDA0001662607940000123
then find zf＝z-zs，
Figure BDA0001662607940000124
Then let uf＝-Kf 0xf+κfCalculating
Figure BDA0001662607940000125
Then pass through
Figure BDA0001662607940000126
Solving for Pf kAnd Kf k+1. Then judging whether | P is present or not when k is more than 1f k-Pf k-1| ≦ α, if not, let k ← k +1, then solve for Pf kAnd Kf k+1(ii) a If so, then
Figure BDA0001662607940000127
As shown in fig. 2, the fast controller designed in the embodiment of the present invention is an ADP-based fast controller, and inputs a fast variable zf and outputs a fast parameter uf.
And S4, combining the slow controller and the fast controller to realize the control of the position and the vibration of the flexible mechanical arm.
After obtaining the slow and fast parameters, u may be transformed as shown in FIG. 2General assembly＝us+ufDynamic model as flexible mechanical arm
Figure BDA0001662607940000128
And outputting the position information theta and the vibration information q, thereby realizing the control of the position and the vibration of the flexible mechanical arm.
The invention can verify the effectiveness of position and vibration control in Matlab environment, and the parameters of the flexible mechanical arm are as shown in Table 1:
TABLE 1
Physical ginseng (Unit) Parameter value
Arm length L (m) 1.2
Moment of inertia J of jointh(kg·m2) 2
Moment of inertia J of loadp(kg·m2) 0.001
Arm lever mass m (kg) 0.2
Load mass M (kg) 0.1
Bending stiffness EI (N.m)2) 60
According to the singular perturbation theory, the flexible mechanical arm can be decomposed into a fast subsystem and a slow subsystem, theta and
Figure BDA0001662607940000129
and (4) approximately equalizing, and designing a slow controller by using the self-adaptive dynamic programming algorithm. First, an initial feedback gain matrix is given
Figure BDA0001662607940000131
Evaluation matrix Qs＝diag(1,0.1)，RsObtaining an optimal feedback gain matrix after finite iteration (I)
Figure BDA0001662607940000132
By solving the Raccati equation directly, where A ═ As,B＝Bs,Q＝Qs,R＝RsTo obtain an optimal feedback gain matrix Ksd＝[1 2.1406]. It can be seen that
Figure BDA0001662607940000133
And KsdApproximately equal, FIG. 3 shows
Figure BDA0001662607940000134
Converge to the optimum value KsdProcess, it can be seen that the slow controller enables optimal control of the slow subsystem.
Obtaining the vibration quantity of the flexible mechanical arm under the slow time scale by using a least square method:
Figure BDA0001662607940000135
Figure BDA0001662607940000136
obtaining a fast variable z from equations (7) and (21)fAnd designing a fast controller by using the self-adaptive dynamic programming algorithm. First, an initial feedback gain matrix is given
Figure BDA0001662607940000137
Evaluation matrix Qf＝diag(1,0.1,1,0.1)，RfObtaining an optimal feedback gain matrix after finite iteration (I)
Figure BDA0001662607940000138
By solving the Raccati equation directly, where A ═ Af,B＝Bf,Q＝Qf,R＝RfTo obtain an optimal feedback gain matrix Kfd＝[-0.0556-0.6739-0.0674-0.3017]. It can be seen that
Figure BDA0001662607940000139
And KfdApproximately equal, FIG. 4 shows
Figure BDA00016626079400001310
Converge to the optimum value KfdThe process, it can be seen, that the fast controller enables optimal control of the fast subsystem.
In order to further verify the effectiveness of the invention on position and vibration Control, the Control effect of the flexible mechanical arm Control method, namely the Control effect of the ADP-based combined controller is compared with the Control effect of the classic FLC- (Fuzzy Logic Control ) -based combined controller, fig. 5 shows that the flexible mechanical arm can reach a specified position more quickly and accurately under the action of the Control method provided by the invention, and fig. 6 and 7 show that the invention has a better inhibition effect on the vibration of the flexible mechanical arm.
In summary, according to the control method of the flexible mechanical arm in the embodiment of the present invention, the adaptive dynamic programming algorithm is used to design the slow controller according to the given position information and the feedback position information on the slow time scale, the vibration estimation is performed on the slow time scale to obtain the vibration amount estimation value on the slow time scale, the fast variable is reconstructed according to the vibration amount estimation value on the slow time scale and the feedback vibration information on the fast time scale, the adaptive dynamic programming algorithm is used to design the fast controller according to the fast variable, and then the slow controller and the fast controller are combined to realize the control of the position and the vibration of the flexible mechanical arm, so that the optimal control of the position and the vibration of the flexible mechanical arm can be realized without using a system model.
In the description of the present invention, it is to be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the present invention and to simplify the description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and are therefore not to be considered limiting of the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (2)

1. A control method of a flexible mechanical arm is characterized by comprising the following steps:
designing a slow controller by using a self-adaptive dynamic programming algorithm according to given position information and feedback position information under a slow time scale;
the method for estimating the vibration under the slow time scale to obtain the vibration quantity estimated value under the slow time scale specifically comprises the following steps:
considering the existence of random error, estimating the vibration amount z in slow time scalesAnd a slow controller usThe relation z betweens＝a+busIs written into
Figure FDA0002949956620000011
Wherein v isiWhich represents a random error, is presented to the user,
Figure FDA0002949956620000012
for measurement data, a, b are the parameters to be estimated,
Figure FDA0002949956620000013
a slow controller output obtained for the ith sample;
defining the evaluation function J as
Figure FDA0002949956620000014
Figure FDA0002949956620000015
And (3) solving an extreme value for the vibration quantity under the slow time scale obtained by the ith sampling:
Figure FDA0002949956620000016
approximate values for a and b were obtained:
Figure FDA0002949956620000017
thereby obtaining the vibration quantity estimated value under the slow time scale
Figure FDA0002949956620000018
Reconstructing a fast variable according to the vibration quantity estimated value and the feedback vibration information under the slow time scale under the fast time scale, and designing a fast controller by using an adaptive dynamic programming algorithm according to the fast variable;
and combining the slow controller and the fast controller to realize the control of the position and the vibration of the flexible mechanical arm.
2. The method of controlling a flexible robot arm as claimed in claim 1, wherein the fast variable z is set to be a valuef＝k·q-zsAnd K is the minimum value in the rigidity matrix K, and q is the feedback vibration information.
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