1. A fuzzy self-adaptive control method of a single-link mechanical arm is characterized by comprising the following steps:

establishing a nonlinear model and a hysteresis model of the single-link mechanical arm; the input of the nonlinear model is a linear function of magnetic hysteresis;

determining a virtual controller model and a virtual adaptive law according to the error model and the nonlinear model;

determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the nonlinear model and the event trigger model; the event trigger model is updated according to a dynamic threshold value;

and controlling the actuator of the single-link mechanical arm according to the virtual controller model, the virtual adaptive law, the fuzzy adaptive trigger controller model and the trigger adaptive law.

2. The method of claim 1, wherein the hysteresis model is determined based on a derivative of the output signal with respect to time and a derivative of the input signal with respect to time.

3. The method of claim 1, wherein the event-triggered model determines the dynamic threshold based on a trigger control input signal.

4. The method of claim 1, wherein the virtual controller model is determined based on an exponential function of an error variable and a known nonlinear system function.

5. The method of claim 1, wherein the determining a fuzzy adaptive trigger controller model and a trigger adaptation law based on the non-linear model and the event trigger model comprises:

determining an event trigger function according to the nonlinear model and the error variable;

and determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the event trigger function and the event trigger model.

6. A fuzzy adaptive control system for a single link robotic arm, comprising:

the first model determining module is used for establishing a nonlinear model and a hysteresis model of the single-link mechanical arm; the input of the nonlinear model is a linear function of magnetic hysteresis;

the second model determining module is used for determining a virtual controller model and a virtual adaptive law according to the error model and the nonlinear model;

the third model determining module is used for determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the nonlinear model and the event trigger model; the event trigger model is updated according to a dynamic threshold value;

and the comprehensive control module is used for controlling the actuator of the single-link mechanical arm according to the virtual controller model, the virtual adaptive law, the fuzzy adaptive trigger controller model and the trigger adaptive law.

7. A fuzzy adaptive control system for a single link robotic arm, comprising:

at least one processor;

at least one memory for storing at least one program;

when executed by the at least one processor, cause the at least one processor to implement the method for fuzzy adaptive control of a single link robotic arm of any one of claims 1-5.

8. A storage medium having stored therein a processor-executable program, wherein the processor-executable program, when executed by a processor, is configured to perform the method for fuzzy adaptive control of a single link robot arm as claimed in any one of claims 1 to 5.

9. A fuzzy adaptive control system of a single-link mechanical arm is characterized by comprising a controller, an actuator and the single-link mechanical arm, wherein the actuator is connected with the controller and the single-link mechanical arm, and the controller comprises:

at least one processor;

at least one memory for storing at least one program;

when executed by the at least one processor, cause the at least one processor to implement the method for fuzzy adaptive control of a single link robotic arm of any one of claims 1-5.

Background

In recent years, with the development of robotics, a robot structure applying high speed, high precision, and high load-to-weight ratio has been receiving attention in the fields of industry and aerospace. Hysteresis is common in the actual control of robotic arm systems. The hysteresis reduces the tracking performance of the system and affects the stability of the control system, so how to compensate the hysteresis and make the system have good performance is a hot topic. In addition, in an actual control system, since network transmission resources are very limited, and the control amount required by the system is quite large, saving network communication bandwidth while considering input delay is also an urgent problem to be solved.

Interpretation of terms

The limited time control method comprises the following steps: the method means that the system state track reaches the equilibrium within the preset limit in the set time interval.

A reverse step design method: the feedback controller is obtained by recursively constructing a Lyapunov function of the closed-loop system, a control law is selected to enable the derivative of the Lyapunov function along the track of the closed-loop system to have certain performance, the boundedness and convergence of the track of the closed-loop system to a balance point are enabled, and the selected control law is a solution of a system stabilization problem, a tracking problem, an interference suppression problem or a combination of several problems.

Uncertain nonlinear systems: the system has the characteristics of both an uncertain system and a nonlinear system, namely the system with uncertain parameters, uncertain dynamics (system perturbation) and external interference, wherein the output of the system is not in direct proportion to the input of the system.

Time triggering: triggering is carried out at fixed intervals.

An event triggering mechanism: and determining whether to trigger according to the current state of the system, and performing various operations if the system state meets the trigger condition.

Hysteresis: a characteristic of the output quantity of the measuring device is related to the sequence of previously input quantities. When the input quantity reaches the same quantity from the increasing direction and the decreasing direction, respectively, the difference between the two output quantities is called a hysteresis error.

Lyapunov stability (Lyapunov stability): in the field of automatic control, lyapunov stability may be used to describe the stability of a powertrain system. If the trajectory of any initial condition of the powertrain system near the equilibrium state is maintained near the equilibrium state, it may be referred to as at-lyapunov stabilization. Lyapunov stability can be used in both linear and non-linear systems. However, the stability of a linear system can be determined in other ways, and therefore lyapunov stability is mostly used to analyze the stability of a nonlinear system. The concept of Lyapunov stability can be extended to infinite-dimensional manifolds, i.e., structural stability, which is the behavior of a group of different but "close" solutions to a differential equation. Input-state stability (ISS) is the application of lyapunov stability to systems with input. If any initial condition eventually approaches the trajectory near the equilibrium state, the system may be said to asymptotically stabilize at that point. The exponential stability can be used for ensuring the minimum decay rate of the system and also can be used for estimating the speed of track convergence.

Adaptive compensation (Adaptive compensation): the method is a control method which designs a self-adaptive compensation control law according to the redundancy condition of a system actuator, achieves the control aim of tracking the motion of a reference model by utilizing an effective actuator, and simultaneously keeps better dynamic and steady-state performances, and mainly solves the fault-tolerant control problem of the actuator fault of the MIMO nonlinear system.

Fuzzy Logic Systems (Fuzzy Logic Systems, FLSs): fuzzy logic systems refer to systems that are constructed using fuzzy concepts and fuzzy logic. When it is used to act as a Controller, it is called a Fuzzy Logic Controller (Fuzzy Logic Controller). Due to the liberty in selecting fuzzy concepts and fuzzy logic, a wide variety of fuzzy logic systems can be constructed. The most common fuzzy logic systems fall into three categories: pure fuzzy logic systems, high wood-gatekeeper fuzzy logic systems, and fuzzy logic systems with fuzzy generators and fuzzy cancellers.

Sesamol behaviour (Zeno behavior): in event-triggered control, control is triggered an unlimited number of times within a limited time.

Disclosure of Invention

It is therefore an object of the present invention to provide a fuzzy adaptive control method, system and storage medium for a single link mechanical arm, which can achieve dynamic compensation of hysteresis, converge in a limited time and save communication resources.

In a first aspect, an embodiment of the present invention provides a fuzzy self-adaptive control method for a single-link mechanical arm, including:

establishing a nonlinear model and a hysteresis model of the single-link mechanical arm; the input of the nonlinear model is a linear function of magnetic hysteresis;

determining a virtual controller model and a virtual adaptive law according to the error model and the nonlinear model;

determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the nonlinear model and the event trigger model; the event trigger model is updated according to a dynamic threshold value;

and controlling the actuator of the single-link mechanical arm according to the virtual controller model, the virtual adaptive law, the fuzzy adaptive trigger controller model and the trigger adaptive law.

Optionally, the hysteresis model is determined from a derivative of the output signal with respect to time and a derivative of the input signal with respect to time.

Optionally, the event trigger model determines the dynamic threshold value from a trigger control input signal.

Optionally, the virtual controller model is determined from an exponential function of the error variable and a known nonlinear system function.

Optionally, the determining a fuzzy adaptive trigger controller model and a trigger adaptive law according to the nonlinear model and the event trigger model includes:

determining an event trigger function according to the nonlinear model and the error variable;

and determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the event trigger function and the event trigger model.

In a second aspect, an embodiment of the present invention provides a fuzzy adaptive control system for a single link manipulator, including:

the first model determining module is used for establishing a nonlinear model and a hysteresis model of the single-link mechanical arm; the input of the nonlinear model is a linear function of magnetic hysteresis;

the second model determining module is used for determining a virtual controller model and a virtual adaptive law according to the error model and the nonlinear model;

the third model determining module is used for determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the nonlinear model and the event trigger model; the event trigger model is updated according to a dynamic threshold value;

and the comprehensive control module is used for controlling the actuator of the single-link mechanical arm according to the virtual controller model, the virtual adaptive law, the fuzzy adaptive trigger controller model and the trigger adaptive law.

In a third aspect, an embodiment of the present invention provides a fuzzy adaptive control system for a single link manipulator, including:

at least one processor;

at least one memory for storing at least one program;

when the at least one program is executed by the at least one processor, the at least one program causes the at least one processor to implement the fuzzy adaptive control method of the first aspect.

In a fourth aspect, an embodiment of the present invention provides a storage medium, in which a processor-executable program is stored, and the processor-executable program is used to execute the fuzzy adaptive control method described in the first aspect when executed by a processor.

In a fifth aspect, an embodiment of the present invention provides a fuzzy adaptive control system for a single link robot, including a controller, an actuator, and the single link robot, where the actuator connects the controller and the single link robot, and the controller includes:

at least one processor;

at least one memory for storing at least one program;

when the at least one program is executed by the at least one processor, the at least one program causes the at least one processor to implement the fuzzy adaptive control method of the first aspect.

The implementation of the embodiment of the invention has the following beneficial effects: the nonlinear model in the embodiment of the invention considers the influence of input delay, the event trigger model is updated according to a dynamic threshold, the virtual control virtual controller and the virtual adaptive law are determined according to the error model and the nonlinear model, and the fuzzy adaptive trigger controller model and the trigger adaptive law are determined according to the event trigger model and the nonlinear model; thereby realizing the dynamic supplement of the lag and saving communication resources, and converging in a limited time.

Drawings

FIG. 1 is a schematic flow chart illustrating the steps of a fuzzy adaptive control method for a single link manipulator according to an embodiment of the present invention;

FIG. 2 is a block diagram of a fuzzy adaptive control system for a single link robotic arm according to an embodiment of the present invention;

FIG. 3 is a flow chart illustrating a simulation of a fuzzy adaptive control system for a single link robotic arm according to an embodiment of the present invention;

FIG. 4 is a graph comparing the system output signal and the reference output signal of a fuzzy adaptive control system for a single link robotic arm according to an embodiment of the present invention;

FIG. 5 is a tracking error diagram of a fuzzy adaptive control system for a single link robotic arm according to an embodiment of the present invention;

FIG. 6 is a signal comparison of a typical control input for a single link robot arm as provided by an embodiment of the present invention and a trigger control input as provided by an embodiment of the present invention;

FIG. 7 is a timing diagram illustrating the timing intervals between the fuzzy adaptive control system of a single link robot arm according to an embodiment of the present invention;

FIG. 8 is a block diagram of a fuzzy adaptive control system for a second single link robotic arm according to an embodiment of the present invention;

fig. 9 is a block diagram of a third fuzzy adaptive control system for a single link manipulator according to an embodiment of the present invention.

Detailed Description

The invention is described in further detail below with reference to the figures and the specific embodiments. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

As shown in fig. 1, an embodiment of the present invention provides a fuzzy adaptive control method for a single link robot arm, which includes the following steps.

S100, establishing a nonlinear model and a hysteresis model of the single-link mechanical arm; the input to the nonlinear model is a linear function of hysteresis.

Optionally, the hysteresis model is determined from a derivative of the output signal with respect to time and a derivative of the input signal with respect to time.

Specifically, consider the following single link robotic arm system, consider the following class of uncertain nonlinear systems:

wherein x is [ x ]₁,…,x_n]^T∈RⁿIs a state variable of the system; u (t) is the input signal of the system; f. of_i(·)∈R,(i＝1,…N) is an uncertain non-linear function in the system,is a known smooth non-linear function in the system; q ∈ R denotes an unknown constant parameter.

The system output response is denoted v, taking into account the presence of input hysteresis in the system_c＝B(u_c) Wherein u is_cIs a designed controller. The hysteresis model can be expressed as:

wherein the content of the compound A is A,and B is a constant value,and isThis makes it possible to obtain:

wherein p (u)_c) A bounded variable is represented. Let p be p (u)_c) The model of the input hysteresis can be expressed as:

and S200, determining a virtual controller model and a virtual adaptive law according to the error model and the nonlinear model.

Optionally, the virtual controller model is determined from an exponential function of the error variable and a known nonlinear system function.

In summary, the nonlinear system of the single link robot arm is designed as follows:

wherein x is₁Denotes the displacement, x₂Representing velocity, I is inertia, m is mass, G is gravitational acceleration, l is center of mass to joint length, B is viscous coefficient of friction, d_kIs an unknown disturbance.

Specifically, the following error equation is introduced:

in the formula of alpha_i(i is 1,2) is a virtual control law, z is_i(i-1, 2) is an error variable. Before designing a program, defineThe design process is as follows.

Step 1 design the virtual control law as

In the formula, c₁Is a normal quantity, xi₁(·):Rⁿ→R^rIs a known smooth nonlinear function of the gamma order (gamma is more than or equal to 1), beta is a constant and satisfiesIs a variable of unknown parameter theta₁An estimated value of, i.e.Γ₁Is a positive definite matrix of order r x r.

The self-adaptation law is designed as follows:

step 2 design of virtual control law alpha₂Comprises the following steps:

s300, determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the nonlinear model and the event trigger model; the event trigger model is updated according to a dynamic threshold value;

optionally, the event trigger model determines the dynamic threshold value from a trigger control input signal.

In particular, due to limitations of communication channel bandwidth and computational power, in order to save network resources of the communication network, the following event triggering schemes are considered:

wherein t is_k，k∈R⁺Indicating the triggering time of the controller, t_k+1The next trigger moment. w (t) is the input of an event-triggered controller, f_E(. cndot.) is a varying threshold.

Optionally, the determining a fuzzy adaptive trigger controller model and a trigger adaptive law according to the nonlinear model and the event trigger model includes:

determining an event trigger function according to the nonlinear model and the error variable;

and determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the event trigger function and the event trigger model.

Specifically, in the control strategy, a Fuzzy Logic System (FLS) is employed to approximate an unknown continuous function.

K^TΓ (X) denotes the estimated parameter vector in the FLSs; k ═ K (K)₁,K₂,…,K_N)^TIs a parameter variable; Γ (X) ═ Γ (Γ)₁(X),Γ₂(X),…,Γ_N(X)) represents a known fuzzy basis function vector; n represents the number of fuzzy rules; x ═ X₁,x₂,…,x_k]Is the input vector of the approximator. Set the center of the area asThe fuzzy basis function Γ_i(X) is:

assuming that the direction of 1, q is known but the magnitude is unknown, q ≠ 0,

assuming 2, the desired signal r is known and bounded, there is a 3 rd derivative.

In particular, the triggering condition of the event-triggered communication scheme is based on the control signal u_c(t) is a non-periodic event-triggered mechanism. When the control signal u_cAnd (t) when the change exceeds a threshold value, updating the output signal of the trigger to prolong the updating interval, thereby saving resources. In the running process of the system, as the system state gradually tends to be stable, the updating frequency of the trigger is gradually reduced, and then the system can be kept stable only by consuming smaller resources. The definition of the event triggering scheme is as follows:

wherein, t_k>0，k∈Z⁺，γ₁＝|w(t)-u_c(t)|，σ>0，m₁>0，0<δ<1，m₁Is a constant type parameter.

u is a control law defined as:

wherein the parametersAnd_pis present in the actual case, but is unknown, which makes the subsequent analysis quite complicated. To solve this problem, the text is provided withIs composed ofIs determined by the estimated value of (c),is composed ofThe estimated value of (a), wherein,

the self-adaptation law is designed as follows:

and S400, controlling the actuator of the single-link mechanical arm according to the virtual controller model, the virtual adaptive law, the fuzzy adaptive trigger controller model and the trigger adaptive law.

As shown in fig. 2, the virtual controller model is applied to a virtual controller, and the virtual controller includes an adaptive law; the fuzzy self-adaptive trigger controller model is applied to a fuzzy self-adaptive trigger controller, and the fuzzy self-adaptive trigger controller comprises a trigger self-adaptive law; the single-link mechanical arm in the embodiment of the invention comprises a virtual controller and a virtual adaptive law corresponding to the virtual controller, a fuzzy adaptive trigger controller and a trigger adaptive law corresponding to the fuzzy adaptive trigger controller which jointly form a controller, and the controller controls an actuator.

The implementation of the embodiment of the invention has the following beneficial effects: the nonlinear model in the embodiment of the invention considers the influence of input delay, the event trigger model is updated according to a dynamic threshold, the virtual control virtual controller and the virtual adaptive law are determined according to the error model and the nonlinear model, and the fuzzy adaptive trigger controller model and the trigger adaptive law are determined according to the event trigger model and the nonlinear model; thereby realizing the dynamic supplement of the lag and saving communication resources, and converging in a limited time.

The system stability of the embodiment of the present invention was analyzed as follows.

First, a Lyapunov function V is selected_iCan be expressed as According to theoretical analysis, for any 0<κ_i<1, there is a positive constantWherein a is_iAnd b_iIs a constant value, is

Wherein, 0<κ_i<1，0<β<1, whenThen, the virtual control law and the self-adaptive law are combined to be analyzed, and theoretical analysis is carried out to obtain

V can be derived from equation (18)_iIs bounded. z is a radical of_i，Andare all bounded, and in addition theta_iτ and k are both constants, soAndis also bounded. At the same time, z₁Y-r and r are bounded, indicating that y is bounded. It can be seen that x₁Is probabilistically semi-globally consistent bounded. Alpha is alpha₁From z₁Andcomposition of, thus alpha₁Is bounded, meaning x₁Is also bounded. For the same reason, x₂Are bounded. This means that this control lawAnd is also bounded. Thus, all output and tracking errors of the closed loop system are bounded. Furthermore, the above results need to be satisfiedFrom the above analysis, it can be proved that the method proposed by the present application can make all the outputs y within a limited time₁，y₂Can locate a given signal r₁，r₂A small area of (a).

Because of the fact thate(t_k) 0, which can be analyzed according to the Lagrange median theoremTherefore, in the guaranteed time interval t^*Is satisfied byIn this case, the system can effectively avoid Zeno behavior.

The following description is given with reference to a specific embodiment.

Referring to the simulation flow chart of fig. 3, first the reference input r, the initial tracking error, and the controller parameters c1, c2 are determined; then determining a single-link mechanical arm model, initializing partial parameters and determining a trigger adaptation lawThen, a tracking error model, a virtual control law alpha of a virtual controller is determined₁α₂(ii) a Then determining the fuzzy adaptive trigger controller,

Law of controlAnd (4) acting the determined model on an event trigger and iterating, and ending the simulation if the iteration times meet the requirement.

Setting the disturbance obstacle as d_kSin (t); the reference signal is r ═ sin (t).

The fuzzy adaptive controller membership function is as follows:

selecting parameters: gamma-shaped₁＝Γ₂＝1，q＝1，γ₁＝γ₂＝1，a₁＝1，a₂＝10，ζ＝1，λ₁＝0.8，λ₂＝0.8，c₁＝10，c₂＝15，σ＝40，δ＝0.2，m₁＝0.6，q＝1；m＝1；g＝9.8；l＝0.4；B＝1；Initial value x₁(0)＝0.3。

Fig. 4-7 are corresponding simulation results, which show that: the control method realizes the tracking control of the single-link mechanical arm, realizes the globally consistent bounded state of the system and ensures the performance of the system in limited time. It can be seen from fig. 4 and 5 that, in the state that the initial value of the output is 0.3, the system can realize fast tracking within a limited time, so that the tracking error is rapidly close to 0 from 0.3, and fluctuation is kept within an expected error range of 0.05, and the output of the subsequent system almost coincides with the reference input, thereby realizing accurate tracking. In fig. 6, the dotted line is the continuous control signal input, and the solid line is the step-type event-triggered control input, so that it can be seen that the bandwidth resource can be well saved. The results in fig. 7 show that the minimum bandwidth is 0.04s, and the maximum bandwidth is 0.31s, which indicates that the trigger frequency is low, and the bandwidth resources can be effectively saved. As can be seen from Table 1, it saves 85.5% of the bandwidth between 0 and 2 seconds, 87% between 2 and 4 seconds, 90.5% between 4 and 6 seconds, 88% between 6 and 8 seconds, and 86.5% between 8 and 10 seconds. It saves 87.5% of the bandwidth in 10 seconds. Therefore, the control method not only realizes the tracking control of the single arm, but also achieves the effect of saving the bandwidth.

TABLE 1 number of triggers of single link arm over time

Time(s)	0-2	2-4	4-6	6-8	8-10
						Number of triggers	29	26	19	24	27

As shown in fig. 8, an embodiment of the present invention provides a fuzzy adaptive control system for a single link robot arm, including:

the first model determining module is used for establishing a nonlinear model and a hysteresis model of the single-link mechanical arm; the input of the nonlinear model is a linear function of magnetic hysteresis;

the second model determining module is used for determining a virtual controller model and a virtual adaptive law according to the error model and the nonlinear model;

the third model determining module is used for determining a fuzzy self-adaptive trigger controller model and a trigger self-adaptive law according to the nonlinear model and the event trigger model; the event trigger model is updated according to a dynamic threshold value;

and the comprehensive control module is used for controlling the actuator of the single-link mechanical arm according to the virtual controller model, the virtual adaptive law, the fuzzy adaptive trigger controller model and the trigger adaptive law.

It can be seen that the contents in the foregoing method embodiments are all applicable to this system embodiment, the functions specifically implemented by this system embodiment are the same as those in the foregoing method embodiment, and the advantageous effects achieved by this system embodiment are also the same as those achieved by the foregoing method embodiment.

As shown in fig. 9, an embodiment of the present invention further provides a fuzzy adaptive control system for a single link manipulator, including:

at least one processor;

at least one memory for storing at least one program;

when executed by the at least one processor, cause the at least one processor to implement the fuzzy adaptive control method steps of the single link robotic arm of the above-described method embodiments.

It can be seen that the contents in the foregoing method embodiments are all applicable to this system embodiment, the functions specifically implemented by this system embodiment are the same as those in the foregoing method embodiment, and the advantageous effects achieved by this system embodiment are also the same as those achieved by the foregoing method embodiment.

In addition, the embodiment of the application also discloses a computer program product or a computer program, and the computer program product or the computer program is stored in a computer readable storage medium. The computer program may be read by a processor of a computer apparatus from a computer-readable storage medium, and the computer program is executed by the processor, so that the computer apparatus executes the method of fuzzy adaptive control of a single link robot arm described above. Likewise, the contents of the above method embodiments are all applicable to the present storage medium embodiment, the functions specifically implemented by the present storage medium embodiment are the same as those of the above method embodiments, and the advantageous effects achieved by the present storage medium embodiment are also the same as those achieved by the above method embodiments.

As shown in fig. 2, an embodiment of the present invention further provides a fuzzy adaptive control system for a single link robot arm, including a controller, an actuator and the single link robot arm, where the actuator is connected to the controller and the single link robot arm, and the controller includes:

at least one processor;

at least one memory for storing at least one program;

when the at least one program is executed by the at least one processor, the at least one processor is caused to implement the above-described fuzzy adaptive control method.

It can be seen that the contents in the foregoing method embodiments are all applicable to this system embodiment, the functions specifically implemented by this system embodiment are the same as those in the foregoing method embodiment, and the advantageous effects achieved by this system embodiment are also the same as those achieved by the foregoing method embodiment.

While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.