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CN112338914B - A fuzzy control algorithm for single-link manipulator based on stochastic system with limited output and input time delay - Google Patents

A fuzzy control algorithm for single-link manipulator based on stochastic system with limited output and input time delay Download PDF

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CN112338914B
CN112338914B CN202011167915.3A CN202011167915A CN112338914B CN 112338914 B CN112338914 B CN 112338914B CN 202011167915 A CN202011167915 A CN 202011167915A CN 112338914 B CN112338914 B CN 112338914B
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王迎春
张佳鑫
杨珺
郑煜
仇小洁
李海峰
柴琦
姚禹池
朱保鹏
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Abstract

本发明公开了一种在输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，由模糊自适应控制器、视觉传感器、机械臂控制电枢和末端灵巧手组成。本发明通过利用模糊逻辑系统，对存在随机扰动和高度非线性的机械手系统模型设计模糊自适应控制器并设计了相对应的自适应算法，使其在遭受进行网络控制时的控制器输入延时和输出信号受限以及各种转矩随机扰动的情况下能够依然精确地跟踪参考信号，操作目标。

Figure 202011167915

The invention discloses a fuzzy control algorithm of a single-link manipulator based on a random system under the condition of limited output and input time delay. By using the fuzzy logic system, the present invention designs a fuzzy adaptive controller for the manipulator system model with random disturbance and high nonlinearity, and designs a corresponding adaptive algorithm, so that it suffers from the input delay of the controller during network control. In the case of limited output signal and various torque random disturbances, it can still accurately track the reference signal and operate the target.

Figure 202011167915

Description

Single-link manipulator fuzzy control algorithm based on random system under output limitation and input hysteresis
Technical Field
The invention belongs to the technical field of manipulator structures and control, and particularly relates to a single-link manipulator fuzzy control algorithm based on a random system when output is limited and input is delayed.
Background
Nowadays, science and technology development is so rapid, and the robot technology slowly emerges, and becomes one of indispensable technical fields of human social progress and development due to the characteristics of wide application range, high flexibility, capability of working in a limit environment and the like. In the related art, the manipulator is widely applied to the fields of mechanical manufacturing, aerospace, medicine, atomic energy and the like, and plays a vital role in automatic production. In the stressed movement of the manipulator, the manipulator interacts with the external environment, and the specified work tasks such as grinding, drilling, polishing, grabbing and the like are completed by contact. In the stressed movement, the manipulator collects the target position through the visual sensor, then the controller sends a command to drive the armature of the manipulator to drive the manipulator to move, and the dexterous hand operates the target. By utilizing the characteristic of flexible control, the precision and the force of the manipulator meet the actual operation requirements, and the application range and the safety of the manipulator are greatly expanded.
Although the application of the manipulator is wide and the safety is high, when the manipulator is controlled by a control console of the robot system through a network, input delay in the aspect of the controller is inevitable due to the characteristics of network communication, so that the command of the controller cannot reach an execution mechanism in time, and a target is not operated and processed in time. Meanwhile, the tail end of the manipulator is limited by different motion areas when a dexterous hand is executed due to different characteristics of operation objects, so that the control performance of the controller is seriously influenced, and the manipulator system is very easy to be unstable in the operation process and even is difficult to operate according to a plan to cause the whole system to be crashed.
In the existing control algorithm, for the fuzzy controller design process based on the backstepping method of the manipulator, it is often assumed that the virtual control symbol of the previous state is known, and the assumption greatly limits the applicability of the controller. Meanwhile, when describing external disturbance, the disturbance is considered to be from certainty, and in the actual operation process, the random torque disturbance suffered by different manipulators or different operating environments is different, so that the whole system modeling can be considered to be in accordance with the actual engineering significance under the framework of a random system.
Disclosure of Invention
In view of the above, the invention provides a fuzzy controller designed based on a random system, which solves the problem of input delay and output limitation of a robot system console by introducing a Pade approximation technology and nonlinear transformation, and designs a self-adaptive algorithm and combines the designed fuzzy controller to solve the problem that the robot system can be self-adjusted under the condition that the robot system suffers from input delay and output limitation and random torque disturbance, thereby improving the control accuracy and the production efficiency.
The technical scheme of the invention is as follows:
a fuzzy control algorithm for single-link manipulator based on stochastic system under limited output and input lag is realized by fuzzy adaptive controller, visual sensor, manipulator control armature and tail end dexterous hand.
The fuzzy control algorithm is constructed by a fuzzy controller and a self-adaptive algorithm;
the fuzzy control algorithm is based on the following random Uncertain Non-strict feedback (Stochastic Uncertain Non-linear feedback) mathematical model, which can be expressed as follows:
Figure GDA0003379334210000021
Figure GDA0003379334210000031
Y(t)＝X1(t)
wherein f isi(X) denotes an unknown non-linear function in the system, X being X1To XnThe set of vectors of (a) is,
Figure GDA0003379334210000032
i.e. the various stages of the robot manipulator system, where
Figure GDA0003379334210000033
Indicating an unknown control gain, the sign of which is unknown; u and Y (t) are the input and output of the system and-kc＜Y(t)＜kcWherein k iscRepresents the constraint to which the output of the system is subjected, τ being the input delay of the control signal to the robotic system;
Figure GDA0003379334210000034
is a random perturbation and ω is an independent standard brownian motion factor defined over the full probability space.
First order state x of the original system1I.e., Y, is constrained to the interval (-k)c,kc) The nonlinear transformation method proposed by the present invention is used for processing as follows
Figure GDA0003379334210000035
The reference signal is then transformed into the form
Figure GDA0003379334210000036
The rest of each order state xi1,2, n, in the form of x in the mathematical model described aboveiThe correspondence is equal.
The manipulator system controller input delay can be processed by the following Pade approximation technology, and is characterized in that:
Figure GDA0003379334210000041
wherein v is a laplace variable; for further study, another intermediate variable xn+1Is introduced and satisfies (assuming the original system order is n):
Figure GDA0003379334210000042
then using the inverse laplace transform one can get:
Figure GDA0003379334210000043
where λ is 2/τ, then the dynamic equation for the entire single link manipulator system can be simply expressed as:
Figure GDA0003379334210000044
the fuzzy control algorithm for converting the whole system model from input time lag to no time lag is completed through Pade approximation, and the fuzzy control algorithm comprises the following steps:
1): the visual sensor captures the operation target as a reference signal yd；
2): reference signal ydState x of the manipulator at this time1Making a difference to obtain an error z of the two1And carrying out differential solution of a dynamic equation;
3): and (2) approximating strong nonlinear terms and coupling terms in a model in the manipulator system by using a Fuzzy Logic system (Fuzzy Logic Systems), wherein the Fuzzy Logic system is established as follows:
the ith fuzzy model rule is established as follows:
Ri: if Z is1Belong to F1 i，……，ZnBelong to
Figure GDA0003379334210000051
Then y belongs to Bi(ii) a 1,2, N is a fuzzy rule number;
after single-valued fuzzifier, product inference and center-averaged deblurring, any nonlinear function f (z) that needs to be approximated can be expressed as:
Figure GDA0003379334210000052
wherein Z ═ Z1,...,Zn]TFor an input vector of dimension n in the real number domain,
Figure GDA0003379334210000053
is that
Figure GDA0003379334210000054
Of the membership function, thetaT＝[θ1,...,θN]The weight vector is a vector of weights,
Figure GDA0003379334210000055
and is
Figure GDA0003379334210000056
Wherein the input signal of the ith-order system to the fuzzy logic is
Figure GDA0003379334210000057
Wherein
Figure GDA0003379334210000058
Is represented by ydThe ith order derivative of (a) is,
Figure GDA0003379334210000059
is representative of
Figure GDA00033793342100000510
Figure GDA00033793342100000511
Modeling the state x of a manipulator system1Operation target state y of manipulatordAnd first derivative
Figure GDA00033793342100000512
As input to fuzzy logic systems, output being first order systems
Figure GDA00033793342100000513
And contains a corresponding precision level error epsilon1；
4): two signals theta output by using fuzzy logic system1And
Figure GDA0003379334210000061
establishing information about theta1Adaptive algorithm of
Figure GDA0003379334210000062
Wherein theta is1Is theta1 *An estimate of (d). Optimal weight vector θ1 *The selection method comprises the following steps:
Figure GDA0003379334210000065
where ε >0 is the precision order constant. Here we give the invention directly as theta for each orderiThe adaptive algorithm of (1) is as follows:
Figure GDA0003379334210000066
Figure GDA0003379334210000067
is representative of
Figure GDA0003379334210000068
M is the custom relaxation coefficient, and i represents the order of the physical model of the manipulator system.
5): error signal z1Input to the Nussbaum function N as the argument ξ1And establishes an argument ξ about the function1Adaptive algorithm of
Figure GDA0003379334210000069
Wherein the function N must have the following properties:
Figure GDA00033793342100000610
Figure GDA00033793342100000611
here, we directly give the function argument ξiThe adaptive algorithm at each stage is:
Figure GDA00033793342100000612
Figure GDA00033793342100000613
i denotes the order of the model of the manipulator system.
6): self-setting corresponding given parameter sigma by using the self-adaptive algorithm established by 4) and 5)1，γ1，k1，m1Design of virtual controller alpha1Here we directly give the virtual control of each step of the invention as follows:
αi＝N(ξi)∈i
i represents the order of the model of the manipulator system;
7): utilizing 6) designed controller and adaptive algorithm to process the state x of the next order of the manipulator system2Processing the data to obtain a control error signal z corresponding to the virtual controller of the previous stage system2Inputting the 2 nd order corresponding fuzzy logic system and Nussbaum function, and outputting them respectively
Figure GDA0003379334210000071
And xi2And self-assigns a corresponding given parameter sigma2,γ2,k2,m2Design of virtual controller alpha2。
8): then the first order state x3With the virtual control signal a derived from the 2 nd order2Differencing to obtain a 3 rd order error signal z3And then proceeds with the work done in 7). Repeating the above steps for each step state x of the manipulator systemiSequentially processing the control signals to obtain corresponding virtual control alphaiAnd adaptive algorithm
Figure GDA0003379334210000072
And
Figure GDA0003379334210000073
until the last stage of the system is reached, outputting a corresponding self-adaptive algorithm and an actual fuzzy controller u;
9): and (4) continuously comparing the state of the manipulator at the next moment with the state of the operation target, returning to the step 1, and continuously circulating.
The invention has the advantages of
The invention has the advantages that: the fuzzy control algorithm is invented, so that when the manipulator system suffers input time lag and output is restricted, random disturbance of torque can be overcome, a controlled target can still be operated, self-adjustment can be realized, and the robustness and the production efficiency of the system are improved.
Drawings
FIG. 1 is a diagram of a fuzzy controller control methodology;
FIG. 2 is a graph of membership function;
FIG. 3 is a flow chart of a fuzzy control algorithm.
Detailed Description
The invention is further illustrated by the following description in conjunction with the figures and the specific embodiments.
Referring to fig. 1-3, the invention is a fuzzy control algorithm of a single link manipulator based on a stochastic system with limited output and input lag, comprising the following steps:
firstly, the output of the system is processed by utilizing nonlinear transformation:
first order state x of the original system1I.e., Y, is constrained to the interval (-k)c,kc) The nonlinear transformation method proposed by the present invention is used for processing as follows
Figure GDA0003379334210000081
The reference signal is then transformed into the form
Figure GDA0003379334210000082
Each of the remaining states is defined as xi1,2, n, in the form of x in the mathematical model described aboveiThe correspondence is equal.
The manipulator system controller input delay can be processed by the following Pade approximation technology, and is characterized in that:
Figure GDA0003379334210000091
where v is the laplace variable. For further study, another intermediate variable xn+1Is introduced and satisfies (assuming the original system order is n):
Figure GDA0003379334210000092
then using the inverse laplace transform one can get:
Figure GDA0003379334210000093
where λ is 2/τ, then the dynamic equation for the entire single link manipulator system can be simply expressed as:
Figure GDA0003379334210000094
the fuzzy control algorithm for converting the whole system model from input time lag to no time lag is completed through Pade approximation, and the fuzzy control algorithm comprises the following steps:
1): the visual sensor captures the operation target as a reference signal yd；
2): reference signal ydState x of the manipulator at this time1Making a difference to obtain an error z of the two1And carrying out differential solution of a dynamic equation;
3): and (2) approximating strong nonlinear terms and coupling terms in a model in the manipulator system by using a Fuzzy Logic system (Fuzzy Logic Systems), wherein the Fuzzy Logic system is established as follows:
the ith fuzzy model rule is established as follows:
Ri: if Z is1Belong to F1 i，……，ZnBelong to
Figure GDA0003379334210000101
Then y belongs to Bi(ii) a 1,2, N is a fuzzy rule number;
after single-valued fuzzifier, product inference and center-averaged deblurring, any nonlinear function f (z) that needs to be approximated can be expressed as:
Figure GDA0003379334210000102
wherein Z ═ Z1,...,Zn]TFor an input vector of dimension n in the real number domain,
Figure GDA0003379334210000103
is that
Figure GDA0003379334210000104
Of the membership function, thetaT＝[θ1,...,θN]The weight vector is a vector of weights,
Figure GDA0003379334210000105
and is
Figure GDA0003379334210000106
Wherein the input signal of the ith-order system to the fuzzy logic is
Figure GDA0003379334210000107
Wherein
Figure GDA0003379334210000108
Is represented by ydThe ith order derivative of (a) is,
Figure GDA0003379334210000109
is representative of
Figure GDA00033793342100001010
An estimate of (d).
Modeling the state x of a manipulator system1Operation target state y of manipulatordAnd first derivative
Figure GDA00033793342100001011
As input to fuzzy logic systems, output being first order systems
Figure GDA00033793342100001012
And contains a corresponding precision level error epsilon1；
4): two signals theta output by using fuzzy logic system1And
Figure GDA0003379334210000111
establishing information about theta1Adaptive algorithm of
Figure GDA0003379334210000112
Wherein theta is1Is theta1 *An estimate of (d). Optimal weight vector θ*The selection method comprises the following steps:
Figure GDA0003379334210000114
where ε >0 is the precision order constant. Here we give the invention directly as theta for each orderiThe adaptive algorithm of (1) is as follows:
Figure GDA0003379334210000115
Figure GDA0003379334210000116
is representative of
Figure GDA0003379334210000117
M is the custom relaxation coefficient, γiAnd σiRepresenting the custom parameters and i representing the order of the model of the manipulator system.
5): error signal z1Input to the Nussbaum function N as the argument ξ1And establishes an argument ξ about the function1Adaptive algorithm of
Figure GDA0003379334210000118
Wherein the function N must have the following properties:
Figure GDA0003379334210000119
Figure GDA00033793342100001110
here, we directly give the function argument ξiThe adaptive algorithm at each stage is:
Figure GDA00033793342100001111
Figure GDA00033793342100001112
i denotes the order of the model of the manipulator system.
6): self-setting corresponding given parameter sigma by using the self-adaptive algorithm established by 4) and 5)1，γ1，k1，m1Design of virtual controller alpha1Here we directly give the virtual control of each step of the invention as follows:
αi＝N(ξi)∈i
i denotes the order of the model of the manipulator system.
7): utilizing 6) designed controller and adaptive algorithm to carry out mechanical control on the systemState x of the next order2Processing the data to obtain a control error signal z corresponding to the virtual controller of the previous stage system2Inputting the 2 nd order corresponding fuzzy logic system and Nussbaum function, and outputting them respectively
Figure GDA0003379334210000121
And xi2And self-assigns a corresponding given parameter sigma2，γ2，k2，m2Design of virtual controller alpha2.
8): then the first order state x3With the virtual control signal a derived from the 2 nd order2Differencing to obtain a 3 rd order error signal z3And then proceeds with the work done in 7). Repeating the above steps for each step state x of the manipulator systemiSequentially processing the control signals to obtain corresponding virtual control alphaiAnd adaptive algorithm
Figure GDA0003379334210000122
And
Figure GDA0003379334210000123
until the last stage of the system is reached, outputting a corresponding self-adaptive algorithm and an actual fuzzy controller u;
9): and (4) continuously comparing the state of the manipulator at the next moment with the state of the operation target, returning to the step 1, and continuously circulating.
In summary, the above is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Note: in fig. 3, i is the order of the manipulator system model, the initial value is 1, the orders of different manipulators are not necessarily the same, and n represents the last order.

Claims (5)

1.一种在输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，其特征在于：由模糊自适应控制器、自适应调节算法、视觉传感器、机械臂控制电枢和末端灵巧手实现；由随机系统为基础设计的模糊控制器，通过引入Pade逼近技术和非线性变换来解决机器人系统控制台输入延时和输出受限的问题，并设计自适应算法，结合设计的模糊控制器，解决了在机械手系统遭受输入延时输出受限以及伴随随机转矩扰动的情况下，能够自调节，从而提高控制精度和生产效率；1. a single-link manipulator fuzzy control algorithm based on random system under output limited and input time lag, it is characterized in that: by fuzzy adaptive controller, adaptive adjustment algorithm, vision sensor, mechanical arm control armature and The terminal is realized by dexterous hand; the fuzzy controller is designed based on the random system, and the input delay and output limitation of the robot system console are solved by introducing the Pade approximation technology and nonlinear transformation, and an adaptive algorithm is designed, combined with the designed The fuzzy controller solves the problem that the manipulator system can self-adjust when the input delay and output are limited and accompanied by random torque disturbance, thereby improving the control accuracy and production efficiency; 通过Pade逼近完成整个系统模型的从有输入时滞到无时滞转换模糊控制算法，包括以下步骤：Through Pade approximation, the fuzzy control algorithm for transforming the entire system model from input delay to no delay is completed, including the following steps: 步骤1：视觉传感器捕捉操作目标，作为参考信号yd；Step 1: the visual sensor captures the operation target as the reference signal y d ; 步骤2：参考信号yd与机械手此时的状态x1做差，得出两者的误差z1，并进行动态学方程微分求解；Step 2: The difference between the reference signal y d and the state x 1 of the manipulator at this time is obtained, the error z 1 between the two is obtained, and the differential solution of the dynamic equation is performed; 步骤3：利用模糊逻辑系统(Fuzzy Logic Systems)对机械手系统中模型中的强非线性项和耦合项进行逼近，将机械手系统模型的状态x1，机械手的操作目标状态yd及一阶导数
Figure FDA0003396302310000011
作为模糊逻辑系统的输入，输出为一阶系统的
Figure FDA0003396302310000012
并含有相应的精确级误差ε1；Step 3: Using Fuzzy Logic Systems to approximate the strong nonlinear terms and coupling terms in the model of the manipulator system, the state x 1 of the manipulator system model, the manipulator's operating target state y d and the first derivative
Figure FDA0003396302310000011
As the input of the fuzzy logic system, the output is the first-order system
Figure FDA0003396302310000012
and contains the corresponding precision level error ε 1 ; 步骤4：利用模糊逻辑系统输出的两种信号θ1和
Figure FDA0003396302310000013
建立关于θ1的自适应算法
Figure FDA0003396302310000014
其中θ1是
Figure FDA0003396302310000015
的估计值；Step 4: Use the two signals θ1 and θ1 output by the fuzzy logic system
Figure FDA0003396302310000013
Building an adaptive algorithm with respect to θ 1
Figure FDA0003396302310000014
where θ1 is
Figure FDA0003396302310000015
estimated value; 步骤5：将误差信号z1输入给Nussbaum函数，作为自变量ξ1的输入信号，并建立关于该函数自变量ξ1的自适应算法
Figure FDA0003396302310000021
Step 5: Input the error signal z 1 to the Nussbaum function as the input signal of the independent variable ξ 1 , and establish an adaptive algorithm about the independent variable ξ 1 of the function
Figure FDA0003396302310000021
 步骤6：利用步骤4与步骤5建立的自适应算法，自给定应的给定参数σ1,γ1,k1,m1，设计虚拟控制器α1；Step 6: Use the adaptive algorithm established in Step 4 and Step 5 to design a virtual controller α 1 from the given parameters σ 1 , γ 1 , k 1 , m 1 ; 步骤7：利用步骤6设计的控制器和自适应算法，对机械手系统下一阶的状态x2进行处理，求得与前一阶系统的虚拟控制器对应的控制误差信号z2，输入第2阶相对应模糊逻辑系统与Nussbaum函数，分别输出θ2与ξ2的自适应算法
Figure FDA0003396302310000022
和
Figure FDA0003396302310000023
并自给定相应的给定参数σ2,γ2,k2,m2,设计虚拟控制器α2；Step 7: Use the controller and adaptive algorithm designed in Step 6 to process the state x 2 of the next stage of the manipulator system, obtain the control error signal z 2 corresponding to the virtual controller of the previous stage system, and input the second stage. Adaptive algorithm of order corresponding fuzzy logic system and Nussbaum function, output θ 2 and ξ 2 respectively
Figure FDA0003396302310000022
and
Figure FDA0003396302310000023
And design the virtual controller α 2 from the corresponding given parameters σ 2 , γ 2 , k 2 , m 2 ; 步骤8：然后将一阶状态x3与第2阶得到的虚拟控制信号α2做差求得第3阶的误差信号z3，然后继续进行步骤7所做工作；重复如此，依次对机械手系统的各阶状态xi依次处理，得出相应的虚拟控制αi及自适应算法
Figure FDA0003396302310000024
与
Figure FDA0003396302310000025
直至进行到系统最后一阶输出相应的自适应算法和实际模糊控制器u；Step 8: Then make the difference between the first-order state x 3 and the virtual control signal α 2 obtained in the second order to obtain the error signal z 3 of the third order, and then continue the work done in step 7; The state x i of each order is processed in turn, and the corresponding virtual control α i and adaptive algorithm are obtained.
Figure FDA0003396302310000024
and
Figure FDA0003396302310000025
Until the last order of the system outputs the corresponding adaptive algorithm and the actual fuzzy controller u; 步骤9：将下一刻的机械手的状态继续与操作目标的状态进行比较，返回步骤1，继续循环；Step 9: Continue to compare the state of the manipulator at the next moment with the state of the operation target, return to step 1, and continue the cycle; 步骤6所述的自适应算法和控制器，其特征为：The adaptive algorithm and controller described in step 6 are characterized by:
Figure FDA0003396302310000026
Figure FDA0003396302310000026
 其中，ki是自设定增益系数
Figure FDA0003396302310000027
是代表
Figure FDA0003396302310000028
的估计值,m是自定义松弛系数，i表示机械手系统的物理模型的阶数，且最后一阶的虚拟控制器αn为实际的模糊控制器u；
Figure FDA0003396302310000031
表示的是一个中间变量，以简便算法的表述形式，其内容为
Figure FDA0003396302310000032
Among them, ki is the self-set gain coefficient
Figure FDA0003396302310000027
is a representative
Figure FDA0003396302310000028
The estimated value of , m is the self-defined relaxation coefficient, i represents the order of the physical model of the manipulator system, and the virtual controller α n of the last order is the actual fuzzy controller u;
Figure FDA0003396302310000031
Represents an intermediate variable, in the form of a simple algorithm, its content is
Figure FDA0003396302310000032
 该针对输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，由模糊自适应控制器、视觉传感器、机械臂控制电枢和末端灵巧手实现；模糊控制算法由模糊控制器和自适应算法构建而成；The fuzzy control algorithm for a single-link manipulator based on a stochastic system with limited output and input time delay is implemented by a fuzzy adaptive controller, a vision sensor, a robotic arm controlling the armature and a terminal dexterous hand; the fuzzy control algorithm is implemented by a fuzzy controller and self-adaptive algorithms; 模糊自适应控制器和自适应调节算法的设计，基于下述随机不确定非严格反馈(Stochastic Uncertain Non-strict feedback)数学模型，可表示为：The design of fuzzy adaptive controller and adaptive adjustment algorithm is based on the following mathematical model of Stochastic Uncertain Non-strict feedback, which can be expressed as:
Figure FDA0003396302310000033
Figure FDA0003396302310000033
Figure FDA0003396302310000034
Figure FDA0003396302310000034
 Y(t)＝X1(t)Y(t)=X 1 (t) 其中的fi(X)表示的是系统中未知的非线性函数，X为X1到Xn的向量集合，
Figure FDA0003396302310000035
也就是机器人机械手系统的各阶状态，这里
Figure FDA0003396302310000036
表示的是未知的控制增益，符号是未知的；u与Y(t)是系统的输入与输出且-kc<Y(t)<kc,其中kc表示系统的输出所遭受到的约束条件，τ是机械手系统该控制信号的输入延迟；
Figure FDA0003396302310000037
是随机扰动，ω是一个独立的标准的定义在全概率空间上的布朗运动因子。where f i (X) represents the unknown nonlinear function in the system, X is the vector set from X 1 to X n ,
Figure FDA0003396302310000035
That is, the state of each order of the robot manipulator system, here
Figure FDA0003396302310000036
Represents the unknown control gain, and the sign is unknown; u and Y(t) are the input and output of the system and -k c <Y(t)<k c , where k c represents the constraints on the output of the system condition, τ is the input delay of the control signal of the manipulator system;
Figure FDA0003396302310000037
is a random perturbation, and ω is an independent standard Brownian motion factor defined in the full probability space. 2.根据权利要求1所述的一种在输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，步骤2，x1与yd应为经过非线性变换得到的新的状态信号；原系统的第一阶状态x1即Y，被约束在区间(-kc,kc),利用本发明提出的非线性变换方法处理如下2. a kind of single-link manipulator fuzzy control algorithm based on random system under the condition of limited output and input time delay according to claim 1, step 2, x 1 and y d should be the new obtained through nonlinear transformation. State signal; the first-order state x 1 of the original system, namely Y, is constrained in the interval (-k c , k c ), and the nonlinear transformation method proposed by the present invention is used to process as follows
Figure FDA0003396302310000041
Figure FDA0003396302310000041
 参考信号则被变换为下述形式The reference signal is then transformed into the following form
Figure FDA0003396302310000042
Figure FDA0003396302310000042
 3.根据权利要求1所述的一种在输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，步骤3，模糊逻辑系统建立如下：3. a kind of single-link manipulator fuzzy control algorithm based on random system under output limited and input time lag according to claim 1, step 3, fuzzy logic system is established as follows: 第i个模糊模型规则建立如下：The i-th fuzzy model rule is established as follows: Ri：如果Z1属于F1 i，……，Zn属于
Figure FDA0003396302310000043
那么y属于Bi；R i : if Z 1 belongs to F 1 i , ..., Z n belongs to
Figure FDA0003396302310000043
then y belongs to B i ; i＝1,2,...,N,N是模糊规则数；i=1,2,...,N,N is the number of fuzzy rules; 经过单值模糊器,乘积推理和中心平均反模糊器处理，则任意需要被逼近的非线性函数f(z)可以表示为：After processing by single-valued fuzzer, product inference and center-averaged defuzzifier, any nonlinear function f(z) that needs to be approximated can be expressed as:
Figure FDA0003396302310000044
Figure FDA0003396302310000044
 其中，Z＝[Z1,…,Zn]T为实数域上n维的输入向量，
Figure FDA0003396302310000045
是
Figure FDA0003396302310000046
的隶属度关系函数，θT＝[θ1,…,θN]，是权向量，
Figure FDA0003396302310000047
且
Figure FDA0003396302310000048
本发明中，第i阶的系统输入给模糊逻辑的输入信号为
Figure FDA0003396302310000049
其中
Figure FDA00033963023100000410
表示的是yd的第i阶导数，
Figure FDA00033963023100000411
是代表
Figure FDA00033963023100000412
的估计值。Among them, Z=[Z 1 ,...,Z n ] T is the n-dimensional input vector on the real number domain,
Figure FDA0003396302310000045
Yes
Figure FDA0003396302310000046
The membership function of , θ T =[θ 1 ,…,θ N ], is the weight vector,
Figure FDA0003396302310000047
and
Figure FDA0003396302310000048
In the present invention, the input signal of the i-th order system input to the fuzzy logic is
Figure FDA0003396302310000049
in
Figure FDA00033963023100000410
represents the ith derivative of y d ,
Figure FDA00033963023100000411
is a representative
Figure FDA00033963023100000412
estimated value of . 4.根据权利要求1所述的一种在输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，步骤4所述，最优权向量θ*的选取方法如下：4. a kind of single-link manipulator fuzzy control algorithm based on random system under output limited and input time lag according to claim 1, described in step 4, the selection method of optimal weight vector θ * is as follows:
Figure FDA0003396302310000051
Figure FDA0003396302310000051
 其中，ε>0是精确级常数；Among them, ε>0 is the precision level constant; 步骤5所述，Nussbaum函数应具有下述特征：As described in step 5, the Nussbaum function should have the following characteristics: 对于任意的连续函数N(ξ)，满足For any continuous function N(ξ), satisfy
Figure FDA0003396302310000052
Figure FDA0003396302310000052
Figure FDA0003396302310000053
Figure FDA0003396302310000053
 步骤6所述的自适应算法和控制器，其特征为：The adaptive algorithm and controller described in step 6 are characterized by:
Figure FDA0003396302310000054
Figure FDA0003396302310000054
 其中，ki是自设定增益系数，
Figure FDA0003396302310000055
是代表
Figure FDA0003396302310000056
的估计值,m是自定义松弛系数，i表示机械手系统的物理模型的阶数，且最后一阶的虚拟控制器αn为实际的模糊控制器u；
Figure FDA0003396302310000057
表示的是一个中间变量，以简便算法的表述形式，其内容为
Figure FDA0003396302310000058
Among them, k i is the self-set gain coefficient,
Figure FDA0003396302310000055
is a representative
Figure FDA0003396302310000056
The estimated value of , m is the self-defined relaxation coefficient, i represents the order of the physical model of the manipulator system, and the virtual controller α n of the last order is the actual fuzzy controller u;
Figure FDA0003396302310000057
Represents an intermediate variable, in the form of a simple algorithm, whose content is
Figure FDA0003396302310000058
 步骤8所述的每一阶状态xi，i＝1,2,...,n，其形式与数学模型中xi对应相等。Each order state x i described in step 8, i =1, 2, . 5.根据权利要求1所述一种在输出受限和输入时滞下基于随机系统的单连杆机械手模糊控制算法，机械手系统控制器输入延时可进行如下Pade逼近技术处理，其特征在于：5. a kind of single-link manipulator fuzzy control algorithm based on random system under the limited output and input time lag according to claim 1, the manipulator system controller input time delay can carry out the following Pade approximation technique processing, it is characterized in that:
Figure FDA0003396302310000061
Figure FDA0003396302310000061
 其中v是拉普拉斯变量；为了更进一步研究，另外一个中间变量xn+1被引进来并且满足(假设原系统阶数为n)：where v is the Laplace variable; for further study, another intermediate variable x n+1 is introduced and satisfied (assuming the original system order is n):
Figure FDA0003396302310000062
Figure FDA0003396302310000062
 然后利用拉普拉斯逆变换可以得到：Then use the inverse Laplace transform to get:
Figure FDA0003396302310000063
Figure FDA0003396302310000063
 这里λ＝2/τ，然后整个单连杆机械手系统的动态方程就可以简单的表示为：Here λ=2/τ, then the dynamic equation of the entire single-link manipulator system can be simply expressed as:
Figure FDA0003396302310000064
Figure FDA0003396302310000064
 通过Pade逼近完成整个系统模型的从有输入时滞到无时滞转换；Complete the conversion of the entire system model from input delay to no delay through Pade approximation; 根据机器人系统机械手的控制经验，确定语言变量的隶属度函数曲线。According to the control experience of the manipulator of the robot system, the membership function curve of the language variable is determined.
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