Non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization

Abstract

The invention discloses a non-singleton interval type-2 fuzzy PID space manipulator tracking control method for improving particle swarm optimization, and relates to the field of space manipulator control, in particular to a PID space manipulator tracking control method. The invention aims to improve the control accuracy and rapidity of the existing space manipulator. The method comprises the following steps: 1, establishing a flexible joint space manipulator model; judging whether the space manipulator has a fault or not, and if not, executing the steps 2-4; if the steps exist, executing the fifth to sixth steps; 2, constructing a traditional PID (Proportion Integration Differentiation) controller and a non-singleton interval type-2 fuzzy PID controller; 3, obtaining parameters of the optimal non-singleton interval type-2 fuzzy PID controller, namely obtaining the optimal non-singleton interval type-2 fuzzy PID controller; fourthly, the flexible joint space manipulator model is controlled based on the third step; 5, constructing a traditional PID (Proportion Integration Differentiation) controller, a non-singleton interval type-2 fuzzy PID controller and a signal compensation fuzzy PID; and sixthly, the flexible joint space manipulator model is controlled based on the fifth step.

Description

Technical Field

[0001] The present invention relates to the field of space manipulator control, and specifically relates to a non-singleton interval type-2 fuzzy PID space manipulator tracking control method with improved particle swarm optimization, as well as a fault-tolerant control design based on fuzzy PID signal compensation. Background Art

[0002] The development of the space industry is of great significance for maintaining national security, promoting scientific research, improving the quality of human life, and exploring unknown fields. In recent years, China's space industry has made remarkable progress. The lunar exploration project has successfully completed the "orbiting, landing, and returning" phases, Tianwen-1 has successfully landed on Mars, and the Beidou-3 system has achieved global networking. According to the plan, China will achieve the first landing of Chinese astronauts on the moon before 2030, and carry out lunar scientific investigations and related technical experiments. At the same time, space exploration is constantly deepening, and space missions are becoming increasingly complex, which puts higher requirements on space exploration equipment.

[0003] During the process of space exploration, astronauts need to overcome difficulties such as space radiation, microgravity environment, and extreme temperatures when performing extravehicular space missions. This not only reduces the mission efficiency but also seriously threatens the safety of astronauts. With the rapid development of space technology, space robots are being used more and more widely. Space robots are special robots used to assist or replace humans in performing extravehicular operations, space exploration, and other activities in the space environment. A space manipulator is a special space robot, similar to a human arm, usually composed of a base and multiple links. A space manipulator can not only assist astronauts in moving but also replace astronauts in performing equipment installation, repair, and replacement work, which can reduce the extravehicular time of astronauts and ensure the safety of astronauts. In addition, a space manipulator has strong capture and rendezvous and docking capabilities as well as load-carrying and handling capabilities, and has become an indispensable equipment for the construction, maintenance, and use of space stations.

[0004] The space manipulator controller is very important for a space manipulator, which directly relates to the performance, accuracy of the space manipulator, and whether it can successfully complete various tasks. An efficient control algorithm can ensure high-precision and stable control of the manipulator, optimize the motion trajectory and force distribution of the space manipulator, reduce energy consumption, lower mission costs, and improve mission success rates. Therefore, it is imperative to develop an advanced and efficient space manipulator controller. Summary of the Invention

[0005] The purpose of the present invention is to improve the control accuracy and rapidity of existing space manipulators, and to propose a non-singleton interval type-2 fuzzy PID space manipulator tracking control method with improved particle swarm optimization.

[0006] The specific process of the non-singleton interval type-2 fuzzy PID space manipulator tracking control method with improved particle swarm optimization is as follows:

[0007] Step 1: Establish a flexible joint space manipulator model;

[0008] Determine whether there is a fault in the space manipulator. If not, execute Steps 2 to 4; if so, execute Steps 5 to 6;

[0009] Step 2: Construct a traditional PID controller and a non-singleton interval type-2 fuzzy PID controller;

[0010] Step 3: Use the particle swarm optimization algorithm to optimize the parameters of the non-singleton interval type-2 fuzzy PID controller to obtain the optimal parameters of the non-singleton interval type-2 fuzzy PID controller, that is, obtain the optimal non-singleton interval type-2 fuzzy PID controller;

[0011] Step 4: Control the flexible joint space manipulator model established in Step 1 based on the optimal non-singleton interval type-2 fuzzy PID controller;

[0012] Step 5: Construct a traditional PID controller, a non-singleton interval type-2 fuzzy PID controller, and a signal compensation fuzzy PID (the signal compensation fuzzy PID is FPID);

[0013] Step 6: Control the flexible joint space manipulator model established in Step 1 based on the traditional PID controller, the non-singleton interval type-2 fuzzy PID controller, and the signal compensation fuzzy PID constructed in Step 5.

[0014] The beneficial effects of the present invention are as follows:

[0015] Based on the dynamic model of a planar two-link flexible-joint space manipulator considering faults, a non-singleton interval type-2 fuzzy PID controller and a fault-tolerant control method with fuzzy PID signal compensation are designed, and an improved particle swarm optimization algorithm is used to optimize its control performance. The present invention designs a tracking control method for a non-singleton interval type-2 fuzzy PID space manipulator optimized by an improved particle swarm optimization, which is mainly as follows: First, a dynamic simulation model of a planar two-link flexible-joint space manipulator is established, and the generalized force of the model input and the generalized coordinates of the output are clarified. In addition, the manipulator faults are considered in this model, and a fault vector is introduced. Second, for the tracking control task of the space manipulator, an interval type-2 fuzzy PID controller is designed. The interval type-2 fuzzy PID controller designed in the present invention uses interval type-2 fuzzy logic to optimize the PID controller parameters in real time, and can solve the problem that the traditional PID parameters cannot be adjusted in real time. For the fuzzification link of the fuzzy system, the present invention adopts a non-singleton fuzzification method, and realizes the function of non-singleton fuzzification through simulation software programming, and applies it to the interval type-2 fuzzy PID controller. Compared with the traditional singleton fuzzification method, this method can trigger more fuzzy rules and has stronger ability to handle uncertainties. Third, the present invention adopts a fault-tolerant control method with interval type-2 fuzzy PID signal compensation. For the error between the output of the faulty system and the ideal output, the input signal is compensated by fuzzy PID, and then the output of the system is corrected. It can be seen from the simulation experiment results that this method can well cope with the faults of the manipulator actuators. Fourth, the present invention uses the particle swarm optimization algorithm to optimize the fuzzy scaling factors of the interval type-2 fuzzy PID controller. Compared with the traditional particle swarm optimization, the present invention improves its inertia coefficient, which enhances the global search ability in the early stage and the local search ability in the later stage of the algorithm. According to the simulation experiment situation and the characteristics of the multi-input multi-output of the controlled object, the present invention proposes a new fitness calculation method to simultaneously consider the accuracy and rapidity of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is the flowchart of the present invention; Figure 2 is the model diagram of a planar two-link space manipulator; Figure 3 is the curve diagram of the angle output of joint 1; Figure 4 is the curve diagram of the angle output of joint 2; Figure 5 is the curve diagram of the angle output of joint 1; Figure 6 is the curve diagram of the angle output of joint 2. DETAILED DESCRIPTION OF THE INVENTION

[0017] The specific implementation method 1: The specific process of the tracking control method for a non-singleton interval type-2 fuzzy PID space manipulator optimized by the improved particle swarm optimization in this implementation method is as follows:

[0018] Step 1: Establish a flexible-joint space manipulator model considering faults;

[0019] Determine whether there is a fault in the space manipulator. If there is no fault, execute Steps 2 to 4; if there is a fault, execute Steps 5 to 6;

[0020] Step 2: Construct a traditional PID controller and a non-singleton interval type-2 fuzzy PID controller;

[0021] Step 3: Use the particle swarm optimization algorithm to optimize the parameters ΔK P24 、ΔK I24 、ΔK D24 、ΔK P25 、ΔK I25 、ΔK D25 of the non-singleton interval type-2 fuzzy PID controller to obtain the optimal parameters of the non-singleton interval type-2 fuzzy PID controller, that is, obtain the optimal non-singleton interval type-2 fuzzy PID controller;

[0022] Step 4: Control the flexible joint space manipulator model established in Step 1 based on the optimal non-singleton interval type-2 fuzzy PID controller;

[0023] Step 5: Construct a traditional PID controller, a non-singleton interval type-2 fuzzy PID controller, and a signal compensation fuzzy PID (the signal compensation fuzzy PID is FPID);

[0024] Step 6: Control the flexible joint space manipulator model established in Step 1 based on the traditional PID controller, the non-singleton interval type-2 fuzzy PID controller, and the signal compensation fuzzy PID constructed in Step 5.

[0025] Specific Embodiment 2: The difference between this embodiment and Specific Embodiment 1 is that: in Step 1, a flexible joint space manipulator model considering faults is established; the specific process is as follows:

[0026] Assume that the space manipulator is not affected by external forces such as gravity, can be modeled in an inertial system, and all joints are flexible and rotatable. As shown in Table 1, where the upper left superscript of the vector represents the coordinate system, and the meanings of each quantity of the manipulator are as follows.

[0027] Table 1 Physical quantities of the space manipulator and their meanings

[0028]

[0029]

[0030] Applying the manipulator moving in a certain plane to carry out research on the controller design and other issues of the present invention is also general. In this paper, a planar two-link flexible joint space manipulator is used as the controlled object for modeling, such as Figure 2 ;

[0031] The dynamic model of a planar two-link flexible joint space manipulator considering faults is as follows:

[0032]

[0033] In the formula, q represents the generalized coordinates of the manipulator, represents the derivative of the generalized coordinates of the manipulator, represents the second derivative of the generalized coordinates of the manipulator;

[0034] D(q) represents the inertia matrix, represents the centrifugal force and Coriolis force matrix, K(q) represents the stiffness matrix, represents the fault vector;

[0035] u represents the generalized force of the manipulator, γ(t) represents the time distribution of the fault, and t represents time;

[0036] The generalized coordinates q and the generalized force u of the manipulator are as follows:

[0037] q = [r bx r by q bz q m1 q m2 T (2)

[0038] u = [F bx F by τ bz τ m1 τ m2 T (3)

[0039] In the formula, r bx represents the position of the manipulator base in the X direction in the inertial system; r by represents the position of the manipulator base in the Y direction in the inertial system; q bz represents the rotation angle of the manipulator base in the Z direction in the inertial system;

[0040] q m1 represents the rotation angle of joint 1; q m2 represents the rotation angle of joint 2; The superscript T represents taking the transpose;

[0041] F bx represents the force acting on the manipulator base in the X direction in the inertial system; F by represents the force acting on the manipulator base in the Y direction in the inertial system;

[0042] τ bz represents the torque acting on the manipulator base in the Z direction in the inertial system;

[0043] τ m1 ​​The torque exerted by the controller on joint 1; τ m2 The torque exerted by the controller on joint 2;

[0044] The controlled object, i.e., the robotic arm, has an input of the generalized force u, which is provided by the controller, and an output value of the generalized coordinate q. This invention focuses on the input torque τ of joint 1 among them m1 , the input torque τ of joint 2 m2 , and the angles and angular velocities of joints 1 and 2: q m1 、q m2 、

[0045] Other steps and parameters are the same as those in the first specific implementation manner.

[0046] Specific implementation manner three: What is different between this implementation manner and the first or second specific implementation manner is that in step two, a traditional PID controller and a non-singleton interval type-2 fuzzy PID controller are constructed; the specific process is as follows:

[0047] Different from the singleton interval type-2 fuzzy PID, this invention adopts a non-singleton interval type-2 fuzzy PID that is more suitable for dealing with uncertainties; the input signals of the interval type-2 fuzzy logic system are the error signal e and its differential signal

[0048] The number of channels of the PID controller is 5, which are F bx 、F by 、τ bz 、τ m1 and τ m2 ; i = 1, 2, 3, 4, 5;

[0049] The expression of the traditional PID controller is:

[0050]

[0051] The force F bx acting on the X direction of the robotic arm base in the inertial system is the output of the first-channel traditional PID;

[0052] The force F by acting on the Y direction of the robotic arm base in the inertial system is the output of the second-channel traditional PID;

[0053] The torque τ bz acting on the Z direction of the robotic arm base in the inertial system is the output of the third-channel traditional PID;

[0054] The expression of the non-singleton interval type-2 fuzzy PID controller is:

[0055]

[0056] The torque τ of the non-singleton interval type-2 fuzzy controller acting on joint 1 m1 is the output of the fuzzy PID of the fourth channel;

[0057] The torque τ of the non-singleton interval type-2 fuzzy controller acting on joint 2 m2 is the output of the fuzzy PID of the fifth channel;

[0058] In the formula,

[0059] K P1 is the proportional coefficient of the traditional PID controller for F bx ; K I1 is the integral coefficient of the traditional PID controller for F bx ; K D1 is the derivative coefficient of the traditional PID controller for F bx ; where K P1 = 10, K I1 = 1, K D1 = 2;

[0060] K P2 is the proportional coefficient of the traditional PID controller for F by ; K I2 is the integral coefficient of the traditional PID controller for F by ; K D2 is the derivative coefficient of the traditional PID controller for F by ; where K P2 = 10, K I2 = 1, K D2 = 2;

[0061] K P3 is the proportional coefficient of the traditional PID controller for τ bz ; K I3 is the integral coefficient of the traditional PID controller for τ bz ; K D3 is the derivative coefficient of the traditional PID controller for τ bz ; where K P3 = 11, K I3 = 1, K D3 = 2.5;

[0062] K P4 is the proportional coefficient of the non-singleton interval type-2 fuzzy PID controller for τ m1 ; K I4 is the integral coefficient of the non-singleton interval type-2 fuzzy PID controller for τ m1 ; K D4 is the derivative coefficient of the non-singleton interval type-2 fuzzy PID controller for τ m1The differential coefficient of the non-singleton interval type-2 fuzzy PID controller; where K P4 = 16, K I4 = 0.5, K D4 = 2;

[0063] K P5 is the proportional coefficient of the non-singleton interval type-2 fuzzy PID controller for τ m2 ; K I5 is the integral coefficient of the non-singleton interval type-2 fuzzy PID controller for τ m2 ; K D5 is the differential coefficient of the non-singleton interval type-2 fuzzy PID controller for τ m2 ; where K P5 = 10, K I5 = 0.1, K D5 = 1.5;

[0064] e 1 represents the error signal of the traditional PID controller for F bx ; represents the differential of e 1 ; e 2 represents the error signal of the traditional PID controller for F by ; represents the differential of e 2 ; e 3 represents the error signal of the traditional PID controller for τ bz ; represents the differential of e 3 ; e 4 represents the error signal of the non-singleton interval type-2 fuzzy PID controller for τ m1 ; represents the differential of e 4 ; e 5 represents the error signal of the non-singleton interval type-2 fuzzy PID controller for τ m2 ; represents the differential of e 5 ;

[0065] ΔK P24 represents the real-time tuning of the proportional coefficient K P4 of the PID controller by the crisp value output from the non-singleton interval type-2 fuzzy PID controller; ΔK I24 represents the real-time tuning of the integral coefficient K I4 of the PID controller by the crisp value output from the non-singleton interval type-2 fuzzy PID controller; ΔK D24 represents the real-time tuning of the differential coefficient K D4 of the PID controller by the crisp value output from the non-singleton interval type-2 fuzzy PID controller;

[0066] ΔK P25 represents the crisp value output by the non-singleton interval type-2 fuzzy PID controller for real-time tuning of the proportional coefficient K of the PID controller P5 ; ΔK I25 represents the crisp value output by the non-singleton interval type-2 fuzzy PID controller for real-time tuning of the integral coefficient K of the PID controller I5 ; ΔK D25 represents the crisp value output by the non-singleton interval type-2 fuzzy PID controller for real-time tuning of the derivative coefficient K of the PID controller D5 ;

[0067] The non-singleton interval type-2 fuzzy PID controller u i represents F bx , F by , τ bz , τ m1 or τ m2 ;

[0068] The present invention adopts a fault-tolerant control method of interval type-2 fuzzy PID signal compensation to cope with faults. For the error between the output of the faulty system and the ideal output, the input signal can be compensated in time through fuzzy PID, thereby correcting the output of the system

[0069] Other steps and parameters are the same as those in the first or second specific implementation manner

[0070] Specific implementation manner four: The difference between this implementation manner and one of the first to third specific implementation manners is that the solution processes of the said ΔK P24 , ΔK I24 , ΔK D24 , ΔK P25 , ΔK I25 , ΔK D25 are as follows

[0071] 1), Select 5 fuzzy subsets: NB, NS, Z, PS, PB

[0072] NB is negative large, NS is negative small, Z is zero, PS is positive small, and PB is positive large

[0073] The error signal e of the non-singleton interval type-2 fuzzy PID controller i is divided into 5 fuzzy subsets: NB, NS, Z, PS, and PB; e i represents e 4 or e 5 ;

[0074] The error signal e of the non-singleton interval type-2 fuzzy PID controller i derivative It is divided into 5 fuzzy subsets: NB, NS, Z, PS, and PB; denote or

[0075] Based on the error signal e of the non - singleton interval type - 2 fuzzy PID controller i and e i differential Construct 25 fuzzy rules; e 4 and correspond to 25 fuzzy rules; e 5 and correspond to 25 fuzzy rules;

[0076] The fuzzy rules are (i represents 4 or 5):

[0077] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is NB, and the differential of e i is NB, the fuzzy subset of K is PS, the fuzzy subset of K Pi is NB, and the fuzzy subset of K Ii is PB; Di

[0078] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is NS, and the differential of e i is NB, the fuzzy subset of K is PS, the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is NS; Di

[0079] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is Z, and the differential of e i is NB, the fuzzy subset of K is NS, and the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is NS; Di

[0080] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is PS, and the differential of e i is NB, the fuzzy subset of K is PS, and the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is NS; Di

[0081] ​When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PB, and the differential of e i is NB, the fuzzy subset of K is PB, the fuzzy subset of K Pi is Z, and the fuzzy subset of K Ii is Z; Di

[0082] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NB, and the differential of e i is NS, the fuzzy subset of K is PS, the fuzzy subset of K Pi is NB, and the fuzzy subset of K Ii is PS; Di

[0083] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NS, and the differential of e i is NS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is Z; Di

[0084] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is Z, and the differential of e i is NS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is Z; Di

[0085] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PS, and the differential of e i is NS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is Z, and the fuzzy subset of K Ii is Z; Di

[0086] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PB, and the differential of e i is NS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is PS, and the fuzzy subset of K Ii is Z; Di ​​​​​​

[0087] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NB and the derivative of e i is Z, the fuzzy subset of K is NS, the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is NS, and the fuzzy subset of K Di is PS;

[0088] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NS and the derivative of e i is Z, the fuzzy subset of K is Z, the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is NS, and the fuzzy subset of K Di is PS;

[0089] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is Z and the derivative of e i is Z, the fuzzy subset of K is Z, the fuzzy subset of K Pi is Z, and the fuzzy subset of K Ii is Z, and the fuzzy subset of K Di is Z;

[0090] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PS and the derivative of e i is Z, the fuzzy subset of K is Z, the fuzzy subset of K Pi is PS, and the fuzzy subset of K Ii is PS, and the fuzzy subset of K Di is PS;

[0091] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PB and the derivative of e i is Z, the fuzzy subset of K is NS, the fuzzy subset of K Pi is PS, and the fuzzy subset of K Ii is PS, and the fuzzy subset of K Di is PS;

[0092] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NB and the derivative of e i is PS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is NS, and the fuzzy subset of K Ii is NS, and the fuzzy subset of K Di is Z;

[0093] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NS, and the derivative of e i is PS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is Z, the fuzzy subset of K Ii is Z, the fuzzy subset of K Di is Z;

[0094] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is Z, and the derivative of e i is PS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is Z, the fuzzy subset of K Ii is PS, the fuzzy subset of K Di is Z;

[0095] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PS, and the derivative of e i is PS, the fuzzy subset of K is Z, the fuzzy subset of K Pi is Z, the fuzzy subset of K Ii is PS, the fuzzy subset of K Di is Z;

[0096] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is PB, and the derivative of e i is PS, the fuzzy subset of K is PS, the fuzzy subset of K Pi is PS, the fuzzy subset of K Ii is PB, the fuzzy subset of K Di is PS;

[0097] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NB, and the derivative of e i is PB, the fuzzy subset of K is PB, the fuzzy subset of K Pi is PB, the fuzzy subset of K Ii is Z, the fuzzy subset of K Di is Z;

[0098] When the system error signal e of the non-singleton interval type-2 fuzzy PID controller i is NS, and the derivative of e i is PB, the fuzzy subset of K is PS, the fuzzy subset of K Pi is PS, the fuzzy subset of K Ii is PS, the fuzzy subset of K DiThe fuzzy subset of is NS;

[0099] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is Z, the differential of e i is PB, the fuzzy subset of K Pi is NS, the fuzzy subset of K Ii is PS, the fuzzy subset of K Di is NS;

[0100] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is PS, the differential of e i is PB, the fuzzy subset of K Pi is PS, the fuzzy subset of K Ii is PS, the fuzzy subset of K Di is NS;

[0101] When the system error signal e of the non - singleton interval type - 2 fuzzy PID controller i is PB, the differential of e i is PB, the fuzzy subset of K Pi is PS, the fuzzy subset of K Ii is PB, the fuzzy subset of K Di is PB;

[0102] The fuzzy rules of the interval type - 2 fuzzy PID are shown in the following table. The fuzzy inference inputs are the system error and its differential, denoted as e i and in the table. Taking the lower - right cell of the table as an example, the corresponding fuzzy rule is:

[0103] Table 2 Fuzzy rules table of KP / KI / KD

[0104]

[0105] Due to the multi - input and multi - output characteristics of the controlled object, the present invention adopts a 5 - channel PID controller, and the basic parameters are shown in Table 3;

[0106] Table 3 Basic parameters of the fuzzy PID controller

[0107]

[0108] 2), Let be the input of the non - singleton interval type - 2 fuzzy PID controller, and the triggering interval F j (x) of the j - th fuzzy rule is

[0109]

[0110] Among them, e i is the error signal of the non-singleton interval type-2 fuzzy PID controller; is the differential of e i ; j = 1, 2, …, 25; e i represents e 4 or e 5 ; represents or

[0111] Among them, the upper bound of the triggering interval lower bound f j is:

[0112]

[0113] In the formula, is the fuzzy subset corresponding to the j-th fuzzy rule for τ m1 (the fuzzy subsets of K Pi , K Ii , K Di corresponding to the 25 rules, such as PS / PB / PB), is the fuzzy subset corresponding to the j-th fuzzy rule for τ m2 . Taking the lower-right cell of Table 3 as an example, for the j-th fuzzy rule,

[0114] represents the lower bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for e i , represents the lower bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for ;

[0115] represents the upper bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for e i , represents the upper bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for ;

[0116] 3) The output interval y j of the j-th fuzzy rule is:

[0117]

[0118] Among them, y j is the lower bound of the fuzzy subset output interval, is the upper bound of the fuzzy subset output interval;

[0119] Upper bound of the output interval of the NB fuzzy subset Upper bound of the output interval of the NS fuzzy subset Upper bound of the output interval of the Z fuzzy subset Upper bound of the output interval of the PS fuzzy subset Upper bound of the output interval of the PB fuzzy subset

[0120] Lower bound of the output interval of the NB fuzzy subset y j =-1; Lower bound of the output interval of the NS fuzzy subset y j =-0.6; Lower bound of the output interval of the Z fuzzy subset y j =-0.1; Lower bound of the output interval of the PS fuzzy subset y j =0.4; Lower bound of the output interval of the PB fuzzy subset y j =0.9;

[0121] The output intervals of the five fuzzy subsets are shown in the following table, where y j is the lower bound of the output interval of the fuzzy subset, is the upper bound of the output interval of the interval type-2 fuzzy subset.

[0122] Table 4 Output intervals

[0123]

[0124] 4), Based on the upper bound of the triggering interval Lower bound f j And y j , Calculate the center y of the lower bound set l And the center y of the upper bound set u ; Expressed as:

[0125]

[0126] Where, l and u are the switching points obtained by the KM iteration method; n = 25;

[0127] 5), Based on the center y of the lower bound set l And the center y of the upper bound set u , Calculate the average value of the center y of the lower bound set l And the center y of the upper bound set u , That is, the crisp value of the final output;

[0128]

[0129] 6), based on the clear value of the final output obtained in 5) and K P4 , obtain ΔK P24 ; expressed as:

[0130]

[0131] wherein, is the scale factor of K m1 for τ P4 ;

[0132] is the clear value y of the final output of K m1 for τ P4 ;

[0133] Based on the clear value of the final output obtained in 5) and K I4 , obtain ΔK I24 ; expressed as:

[0134]

[0135] wherein, is the integral factor of K m1 for τ I4 ;

[0136] is the clear value y of the final output of K m1 for τ I4 ;

[0137] Based on the clear value of the final output obtained in 5) and K D4 , obtain ΔK D24 ; expressed as:

[0138]

[0139] wherein,

[0140] is the integral factor of K m1 for τ D4 ;

[0141] is the clear value y of the final output of K m1 for τ D4 ;

[0142] 7), based on the clear value of the final output obtained in 5) and K P5 , obtain ΔK P25 ; expressed as:

[0143]

[0144] wherein, is the scale factor of K m2 for τ P5 ;

[0145] is the clear value y of the final output of K m2 for τ P5 ;

[0146] Based on the clear value of the final output obtained in 5) and K I5 , ΔK I25 is obtained; expressed as:

[0147]

[0148] wherein, is the scale factor of K m2 for τ I5 ;

[0149] is the clear value y of the final output of K m2 for τ P5 ;

[0150] Based on the clear value of the final output obtained in 5) and K D5 , ΔK D25 is obtained; expressed as:

[0151]

[0152] wherein, is the integral factor of K m2 for τ D5 ;

[0153] is the clear value y of the final output of K m2 for τ P5 ;

[0154] takes different values;

[0155] The present invention selects 5 fuzzy subsets: NB, NS, Z, PS, PB, and adopts the bottom-width isosceles triangle membership function, as follows:

[0156]

[0157]

[0158] wherein, x is the function independent variable, A iis a certain fuzzy subset, where i = 1, 2, 3, 4, 5, corresponding to NB, NS, Z, PS, PB respectively; is A i the output value of the upper bound membership function; is A i the output value of the lower bound membership function; x i is the abscissa of the center of the isosceles triangle; a and b are constants, and a and b represent the width of the isosceles triangle, satisfying b > a > 0.

[0159] Other steps and parameters are the same as those in any one of the specific embodiments one to three.

[0160] Specific embodiment five: The difference between this embodiment and any one of the specific embodiments one to four is that in step three, the particle swarm optimization algorithm is used to optimize the parameters ΔK P24 、ΔK I24 、ΔK D24 、ΔK P25 、ΔK I25 、ΔK D25 of the non-singleton interval type-2 fuzzy PID controller (optimize 6 parameters together), and obtain the optimal parameters of the non-singleton interval type-2 fuzzy PID controller, that is, obtain the optimal non-singleton interval type-2 fuzzy PID controller; the specific process is as follows:

[0161] The present invention uses the particle swarm optimization algorithm to optimize the interval type-2 fuzzy PID parameters to obtain more suitable parameters ΔK P24 、ΔK I24 、ΔK D24 、ΔK P25 、ΔK I25 、ΔK D25 of the non-singleton interval type-2 fuzzy PID controller; the specific parameters to be optimized are the fuzzy proportionality factors of channels 4 and 5, a total of 6 parameters. Therefore, in this particle swarm optimization algorithm, the particle position is a 6-dimensional vector.

[0162] First, generate multiple particles within a certain range. Each particle has two basic attributes: position and velocity. Its initial position and initial velocity are randomly generated, and then start iterative search for the optimal solution until the search target is reached.

[0163] In the particle swarm optimization algorithm, the inertia coefficient w decays with the number of iterations, as shown in the following formula:

[0164]

[0165] In the formula, i is the number of iterations, i max is the maximum number of iterations, w min is the minimum inertia coefficient, w max is the maximum inertia coefficient;

[0166] In the traditional particle swarm optimization algorithm, the inertia coefficient w is a fixed value. The present invention improves this to enhance the global search ability in the early stage and the local search ability in the later stage of the algorithm;

[0167] In the particle swarm optimization algorithm, the fitness calculation method is as follows:

[0168]

[0169] In the formula, |e 1 (t)| is the absolute value of the joint 1 angle error; |e 2 (t)| is the absolute value of the joint 2 angle error; t is time; T 1 is the upper integration time; T 2 is the upper integration time; T 2 <T 1 ; α 1 , α 2 , β 1 , β 2 are weight factors; J is the particle fitness;

[0170] The particle fitness attribute is calculated from the particle position. For the optimization of the traditional particle swarm control system, generally, the control system performance evaluation index ITAE is directly set equal to the particle fitness J. The smaller this index value, the better the control system performance. This type of fitness calculation method helps to reduce the system adjustment time and overshoot. However, because the error has little influence on ITAE when time t is small, the system rapidity decreases. Therefore, the present invention proposes a new fitness calculation method to simultaneously take into account the system accuracy and rapidity.

[0171] Other steps and parameters are the same as those in the first to fourth specific embodiments.

[0172] Specific embodiment six: The difference between this embodiment and any one of the first to fifth specific embodiments is that in step five, a traditional PID controller, a non-singleton interval type-2 fuzzy PID controller, and a signal compensation fuzzy PID (the signal compensation fuzzy PID is FPID) are constructed; the specific process is as follows:

[0173] The expression of the signal compensation fuzzy PID is:

[0174]

[0175] The signal compensation fuzzy PID compensation q m1 is the output of the first-channel fuzzy PID;

[0176]

[0177] The signal compensation fuzzy PID compensation q m2 is the output of the second-channel fuzzy PID;

[0178] In the formula, q m1 represents the rotation angle of joint 1; q m2 represents the rotation angle of joint 2;

[0179] K PF1 is the signal compensation fuzzy PID proportional coefficient for q m1 ; K IF1 is the signal compensation fuzzy PID integral coefficient for q m1 ; K DF1 is the signal compensation fuzzy PID derivative coefficient for q m1 ; where K PF1 = 5, K IF1 = 0.1, K DF1 = 0.01;

[0180] K PF2 is the signal compensation fuzzy PID proportional coefficient for q m2 ; K IF2 is the signal compensation fuzzy PID integral coefficient for q m2 ; K DF2 is the signal compensation fuzzy PID derivative coefficient for q m2 ; where K PF2 = 5, K IF2 = 0.1, K DF2 = 0.01;

[0181] e F1 represents the signal compensation fuzzy PID error signal for q m1 ; represents the derivative of e F1 ;

[0182] e F2 represents the signal compensation fuzzy PID error signal for q m2 ; represents the derivative of e F2 ;

[0183] ΔK PF1 represents the real-time tuning of the proportional coefficient K PF1 of the PID controller by the crisp value output by the signal compensation fuzzy PID; ΔK IF1 represents the real-time tuning of the integral coefficient K IF1 of the PID controller by the crisp value output by the signal compensation fuzzy PID; ΔK DF1 represents the real-time tuning of the derivative coefficient K DF1 of the PID controller by the crisp value output by the signal compensation fuzzy PID;

[0184] ΔK PF2It represents the clear value output by the signal-compensated fuzzy PID for real-time tuning of the proportional coefficient K of the PID controller PF2 ; ΔK IF2 It represents the clear value output by the signal-compensated fuzzy PID for real-time tuning of the integral coefficient K of the PID controller IF2 ; ΔK DF2 It represents the clear value output by the signal-compensated fuzzy PID for real-time tuning of the derivative coefficient K of the PID controller DF2 ; for real-time tuning

[0185] The parameters are shown in Table 5, and the fuzzy rules are designed for it separately, as shown in Table 6

[0186] Table 5 Signal-compensated fuzzy PID parameters

[0187]

[0188] Other steps and parameters are the same as those in Embodiments 1 to 5

[0189] Embodiment 7: The difference between this embodiment and Embodiment 1 to 6 is that the solution process of the ΔK PF1 , ΔK IF1 , ΔK DF1 , ΔK PF2 , ΔK IF2 , ΔK DF2 is as follows

[0190] 1), Select 5 fuzzy subsets: NB, NS, Z, PS, PB

[0191] NB is negative large, NS is negative small, Z is zero, PS is positive small, and PB is positive large

[0192] For the signal-compensated fuzzy PID error signal e m1 of q F1 , it is divided into 5 fuzzy subsets: NB, NS, Z, PS, and PB; for the derivative of e F1

[0193] For the signal-compensated fuzzy PID error signal e m2 of q F2 , it is divided into 5 fuzzy subsets: NB, NS, Z, PS, and PB; for the derivative of e F2 is divided into 5 fuzzy subsets: NB, NS, Z, PS, and PB

[0194] Based on the signal-compensated fuzzy PID error signal for and Differential of Construct 25 fuzzy rules;

[0195] Denote q m1 or q m2 ; Denote e F1 or e F2 ; Denote or

[0196] Based on the signal-compensated fuzzy PID error signal e for q m1 and the differential of e F1 and e F1 Differential of Construct 25 fuzzy rules;

[0197] Based on the signal-compensated fuzzy PID error signal e for q m2 and the differential of e F2 and e F2 Differential of Construct 25 fuzzy rules;

[0198] The fuzzy rules are ( Denote 1 or 2):

[0199] When the signal-compensated fuzzy PID error signal for is NB, and the differential of is NB, then the fuzzy subset of is PB, the fuzzy subset of is NB,

[0200] Denote K PF1 or K PF2 ; Denote K IF1 or K IF2 ; Denote K DF1 or K DF2 ; When the signal-compensated fuzzy PID error signal for is NB, and the differential of for is NS, then the fuzzy subset of is PS, the fuzzy subset of is NS,

[0201] When the signal-compensated fuzzy PID error signal for ​ For NB, for the differential is Z, the fuzzy subset of is PS, the fuzzy subset of

[0202] When for the signal compensation fuzzy PID error signal is NB, for the differential is PS, the fuzzy subset of is PS, the fuzzy subset of

[0203] When for the signal compensation fuzzy PID error signal is NB, for the differential is PB, the fuzzy subset of is Z, the fuzzy subset of

[0204] When for the signal compensation fuzzy PID error signal is NS, for the differential is NB, the fuzzy subset of is PS, the fuzzy subset of

[0205] When for the signal compensation fuzzy PID error signal is NS, for the differential is NS, the fuzzy subset of is PS, the fuzzy subset of

[0206] When for the signal compensation fuzzy PID error signal is NS, for the differential is Z, the fuzzy subset of is PS, the fuzzy subset of

[0207] When for the signal - compensated fuzzy PID error signal is NS, for the differential is PS, the fuzzy subset of is Z, the fuzzy subset of

[0208] When for the signal - compensated fuzzy PID error signal is NS, for the differential is PB, the fuzzy subset of is NS, the fuzzy subset of

[0209] When for the signal - compensated fuzzy PID error signal is Z, for the differential is NB, the fuzzy subset of IF1 is PS, K the fuzzy subset of

[0210] When for the signal - compensated fuzzy PID error signal is Z, for the differential is NS, the fuzzy subset of is PS, the fuzzy subset of

[0211] When for the signal - compensated fuzzy PID error signal is Z, for the differential is Z, the fuzzy subset of is Z, the fuzzy subset of

[0212] When for the signal - compensated fuzzy PID error signal is Z, for the differential is PS, the fuzzy subset of The fuzzy subset of is PS;

[0213] When the signal compensation fuzzy PID error signal for is Z, and the differential for is PB, the fuzzy subset of is NS, the fuzzy subset of is PS, the fuzzy subset of

[0214] When the signal compensation fuzzy PID error signal for is PS, and the differential for is NB, the fuzzy subset of is PS, the fuzzy subset of is NS, the fuzzy subset of

[0215] When the signal compensation fuzzy PID error signal for is PS, and the differential for is NS, the fuzzy subset of is Z, the fuzzy subset of is Z, the fuzzy subset of

[0216] When the signal compensation fuzzy PID error signal for is PS, and the differential for is Z, the fuzzy subset of is NS, the fuzzy subset of is PS, the fuzzy subset of

[0217] When the signal compensation fuzzy PID error signal for is PS, and the differential for is PS, the fuzzy subset of is NS, the fuzzy subset of is PS, the fuzzy subset of

[0218] When the signal compensation fuzzy PID error signal for is PS, and the differential for is PS, the fuzzy subset of When it is PB, the fuzzy subset of is NS, the fuzzy subset of

[0219] When targeting the signal-compensated fuzzy PID error signal of is PB, and when targeting the differential of is NB, the fuzzy subset of is Z, the fuzzy subset of

[0220] When targeting the signal-compensated fuzzy PID error signal of is PB, and when targeting the differential of is NS, the fuzzy subset of is PS, the fuzzy subset of

[0221] When targeting the signal-compensated fuzzy PID error signal of is PB, and when targeting the differential of is Z, the fuzzy subset of is NS, the fuzzy subset of

[0222] When targeting the signal-compensated fuzzy PID error signal of is PB, and when targeting the differential of is PS, the fuzzy subset of is NS, the fuzzy subset of

[0223] When targeting the signal-compensated fuzzy PID error signal of is PB, and when targeting the differential of is PB, the fuzzy subset of is NB, the fuzzy subset of

[0224] Table 6 Fuzzy PID Signal Compensation KPF / KIF / KDF Rule Table

[0225]

[0226] 2), Let be the input of the signal compensation fuzzy PID, and the triggering interval F j (x) of the j-th fuzzy rule is

[0227]

[0228] where is the error signal of the signal compensation fuzzy PID; is the differential of the error signal e i of the signal compensation fuzzy PID; j = 1, 2,..., 25; represents e F1 or e F2 ; represents or

[0229] where the upper bound and the lower bound f j of the triggering interval are:

[0230]

[0231] In the formula, is the fuzzy subset corresponding to the j-th fuzzy rule for q m1 (the fuzzy subsets of K Pi , K Ii , K Di corresponding to the 25 rules, such as PS / PB / PB), is the fuzzy subset corresponding to the j-th fuzzy rule for q m2 . Taking the lower right cell of Table 3 as an example, for the j-th fuzzy rule,

[0232] represents the lower bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for ,

[0233] represents the lower bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for ;

[0234] represents the upper bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for ,

[0235] represents the upper bound membership function value of the fuzzy subset corresponding to the j-th fuzzy rule for The membership function value of the upper bound of the j-th fuzzy rule corresponding to the fuzzy subset;

[0236] 3), the output interval y of the j-th fuzzy rule j is:

[0237]

[0238] where y j is the lower bound of the output interval of the fuzzy subset, is the upper bound of the output interval of the fuzzy subset;

[0239] The upper bound of the output interval of the fuzzy subset NB The upper bound of the output interval of the fuzzy subset NS The upper bound of the output interval of the fuzzy subset Z The upper bound of the output interval of the fuzzy subset PS The upper bound of the output interval of the fuzzy subset PB

[0240] The lower bound of the output interval of the fuzzy subset NB y j = -1; The lower bound of the output interval of the fuzzy subset NS y j = -0.6; The lower bound of the output interval of the fuzzy subset Z y j = -0.1; The lower bound of the output interval of the fuzzy subset PS y j = 0.4; The lower bound of the output interval of the fuzzy subset PB y j = 0.9;

[0241] The output intervals of the five fuzzy subsets are shown in the following table, where y j is the lower bound of the output interval of the fuzzy subset, is the upper bound of the output interval of the fuzzy subset.

[0242] Table 7 Output Interval

[0243]

[0244] 4), based on the upper bound of the trigger interval lower bound f j and y j , calculate the lower bound set center y l and the upper bound set center y u ; expressed as:

[0245]

[0246] Among them, l and u are the conversion points obtained by the KM iteration method; n = 25;

[0247] 5), Based on the lower bound set center y l and the upper bound set center y u , calculate the average value of the lower bound set center y l and the upper bound set center y u , which is the final output clear value;

[0248]

[0249] 6), Based on the final output clear value obtained in 5) and K PF1 , obtain ΔK PF1 ; Expressed as:

[0250]

[0251] Among them, is the proportionality factor of K m1 for q PF1 ;

[0252] is the final output clear value y of K m1 for q PF1 ;

[0253] Based on the final output clear value obtained in 5) and K IF1 , obtain ΔK IF1 ; Expressed as:

[0254]

[0255] Among them, is the integral factor of K m1 for q IF1 ;

[0256] is the final output clear value y of K m1 for q IF1 ;

[0257] Based on the final output clear value obtained in 5) and K DF1 , obtain ΔK DF1 ; Expressed as:

[0258]

[0259] Among them, is the integral factor of K m1 for q DF1 ;

[0260] For q m1 Regarding K DF1 The clear value y of the final output;

[0261] 7), based on the clear value of the final output obtained in 5) and K P5 , obtain ΔK PF2 ; Expressed as:

[0262]

[0263] Among them, For q m2 Regarding K P5 The scale factor;

[0264] For q m2 Regarding K P5 The clear value y of the final output;

[0265] Based on the clear value of the final output obtained in 5) and K IF2 , obtain ΔK IF2 ; Expressed as:

[0266]

[0267] Among them, For q m2 Regarding K IF2 The scale factor;

[0268] For q m2 Regarding K IF2 The clear value y of the final output;

[0269] Based on the clear value of the final output obtained in 5) and K DF2 , obtain ΔK DF2 ; Expressed as:

[0270]

[0271] Among them, For q m2 Regarding K DF2 The integral factor;

[0272] For q m2 Regarding K DF2 The clear value y of the final output;

[0273] The present invention selects 5 fuzzy subsets: NB, NS, Z, PS, PB, and adopts a bottom-width isosceles triangle membership function, as follows:

[0274]

[0275]

[0276] where x is the independent variable of the function, and A i is a certain fuzzy subset, and i = 1, 2, 3, 4, 5, corresponding to NB, NS, Z, PS, PB respectively; is the output value of the upper bound membership function of A i ; is the output value of the lower bound membership function of A i ; x i is the abscissa of the center of the isosceles triangle; a and b are constants, and a and b represent the width of the isosceles triangle, satisfying b > a > 0.

[0277] Other steps and parameters are the same as those in any one of the specific embodiments one to six.

[0278] The following embodiments are used to verify the beneficial effects of the present invention:

[0279] Embodiment 1:

[0280] In order to verify and demonstrate the effectiveness of the improved particle swarm optimization-based non-singleton interval type-2 fuzzy PID controller and the interval type-2 fuzzy PID signal compensation fault-tolerant control in the present invention, the following simulation experiments were carried out. The parameters of the robotic arm are shown in Table 8, and the parameters of the interval type-2 fuzzy membership function are a = 0.25, b = 0.5, and x i is shown in Table 9.

[0281] Table 8 Specific values of various physical quantities of the two-link robotic arm

[0282]

[0283] Table 9 Parameters of the interval type-2 fuzzy membership function

[0284]

[0285] First, assume that no fault occurs, input the desired generalized coordinates q = [0 0 -1 1 1] T , run the simulation program and compare the output curves, such as Figure 3 , Figure 4 . "PSO" represents particle swarm optimization, and "S" and "N" represent traditional singleton fuzzification and non-singleton fuzzification respectively. The control performance indicators are as follows in the table.

[0286] Table 10 Performance indicators of the fault-free system

[0287]

[0288] It can be seen from the output curve that the performance of the interval type-2 fuzzy PID controller without particle swarm optimization is relatively poor, with a large overshoot and it is difficult to meet the stability requirements. However, the improved particle swarm optimization algorithm for the interval type-2 fuzzy PID controller has improved this shortcoming, enabling the system to meet the task requirements. It can be seen from Table 10 that the performance indicators of the non-singleton fuzzification system are better than those of the singleton fuzzification, and the control effect is better.

[0289] Actuator faults τ are simultaneously added to the two joints of the robotic arm at t = 4 s mi (t)=τ mi (t)+1, i = 1, 2. The input desired generalized coordinates q = [0 0 -1 1 1] T , run the simulation program to compare the output curves, such as Figure 5 、 Figure 6 . "SC" indicates that the fuzzy PID signal compensation fault-tolerant control method is adopted. The control performance indicators are as follows in the table.

[0290] Table 11 Performance indicators of the faulty system

[0291]

[0292] After the actuator of the robotic arm joint fails, the joint angle of the system without fuzzy PID signal compensation is difficult to return to the expected value, while the system with fuzzy PID signal compensation is less affected by the fault. In addition, for the faulty system, the performance indicators of the non-singleton fuzzification system are better than those of the singleton fuzzification, indicating that the non-singleton fuzzy PID has stronger fault tolerance than the traditional singleton fuzzy PID. This shows that the controller designed in the present invention has good robustness and can better handle faults during the task execution of the flexible joint space robotic arm.

[0293] The present invention can also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. Improved particle swarm optimization non-singleton interval type-2 fuzzy PID space manipulator tracking control method, characterized by: The specific process of the method is: Step 1: Establish a flexible joint space robot model; Determine whether the space robot arm has a fault. If not, execute steps 2 to 4. If yes, execute steps 5 to 6. Step 2: Construct a traditional PID controller and a non-singleton interval type-2 fuzzy PID controller; Step 3, using particle swarm optimization algorithm to optimize the parameters of the non-singleton interval type-two fuzzy PID controller to obtain the optimal non-singleton interval type-two fuzzy PID controller parameters, that is, to obtain the optimal non-singleton interval type-two fuzzy PID controller; Step 4: Control the flexible joint space manipulator model established in step 1 based on the optimal non-singleton interval type-II fuzzy PID controller; Step 5: Construct a traditional PID controller, a non-singleton interval type-II fuzzy PID controller, and a signal compensation fuzzy PID; Step six: Based on the traditional PID controller, non-singleton interval type-II fuzzy PID controller and signal compensation fuzzy PID constructed in step five, the flexible joint space robot model established in step one is controlled.

2. The non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization according to claim 1, characterized in that: In the step 1, a flexible joint space robot model is established; the specific process is as follows: The dynamic model of the planar two-link flexible joint space manipulator considering faults is as follows: In the formula, q represents the generalized coordinates of the robot arm, represents the generalized coordinate derivative of the manipulator, represents the second-order derivative of the generalized coordinates of the manipulator; D(q) represents the inertia matrix, represents the centrifugal force and Coriolis force matrix, K(q) represents the stiffness matrix, represents the fault vector; u represents the generalized force of the robot, γ(t) represents the time distribution of the fault, and t represents time; The generalized coordinates q of the manipulator and the generalized force u of the manipulator are as follows: q=[r bx r by q bz q m1 q m2 ] T (2) u=[F bx F by t bz t m1 t m2 ] T (3) In the formula, r bx Indicates the position of the robot base in the X direction under the inertial system; r by Indicates the position of the robot base in the Y direction under the inertial system; q bz Indicates the rotation angle of the robot base in the Z direction under the inertial system; q m1 represents the rotation angle of joint 1; q m2 Indicates the rotation angle of joint 2; The superscript T means to find the transpose; F bx Indicates the force acting on the base of the robot in the X direction in the inertial system; F by It represents the force acting on the Y direction of the robot base in the inertial system; τ bz It represents the moment acting on the Z direction of the robot base in the inertial system; τ m1 represents the torque applied by the controller to joint 1; τ m2 Represents the torque applied by the controller to joint 2.

3. The non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization according to claim 2, characterized in that: In the step 2, a traditional PID controller and a non-singleton interval type II fuzzy PID controller are constructed; the specific process is: The traditional PID controller expression is: The force F acting on the base of the robot in the X direction in the inertial system bx It is the output of the first channel traditional PID; The force F acting on the Y direction of the robot base in the inertial system by It is the output of the traditional PID of the second channel; The moment τ acting on the Z direction of the robot base in the inertial system bz It is the output of the third channel traditional PID; The expression of non-singleton interval type-2 fuzzy PID controller is: The torque τ of the non-singleton interval type-2 fuzzy controller acting on joint 1 m1 It is the output of the fourth channel fuzzy PID; The torque τ of the non-singleton interval type-2 fuzzy controller acting on joint 2 m2 is the output of the fifth channel fuzzy PID; In the formula, K P1 For F bx The proportional coefficient of the traditional PID controller; K I1 For F bx The traditional PID controller integral coefficient; K D1 For F bx The traditional PID controller differential coefficient; where K P1 =10, K I1 =1, K D1 =2; K P2 For F by The proportional coefficient of the traditional PID controller; K I2 For F by The traditional PID controller integral coefficient; K D2 For F by The traditional PID controller differential coefficient; where K P2 =10, K I2 =1, K D2 =2; K P3 For τ bz The proportional coefficient of the traditional PID controller; K I3 For τ bz The traditional PID controller integral coefficient; K D3 For τ bz The traditional PID controller differential coefficient; where K P3 =11, K I3 =1, K D3 =2.5; K P4 For τ m1 The proportional coefficient of the non-singleton interval type-II fuzzy PID controller; K I4 For τ m1 The integral coefficient of the non-singleton interval type-II fuzzy PID controller; K D4 For τ m1 The differential coefficient of the non-singleton interval type-II fuzzy PID controller; where K P4 =16, K I4 =0.5, K D4 =2; K P5 For τ m2 The proportional coefficient of the non-singleton interval type-II fuzzy PID controller; K I5 For τ m2 The integral coefficient of the non-singleton interval type-II fuzzy PID controller; K D5 For τ m2 The differential coefficient of the non-singleton interval type-II fuzzy PID controller; where K P5 =10, K I5 =0.1, K D5 =1.5; e1 indicates that the bx The error signal of the traditional PID controller; represents the differential of e1; e2 represents the differential of F by The error signal of the traditional PID controller; represents the differential of e2; e3 represents the differential of τ bz The error signal of the traditional PID controller; represents the differential of e3; e4 represents the differential of τ m1 The error signal of the non-singleton interval type-II fuzzy PID controller; represents the differential of e4; e5 represents the differential of τ m2 The error signal of the non-singleton interval type-II fuzzy PID controller; represents the differential of e5; ΔK P24 Indicates the clear value output by the non-singleton interval type-II fuzzy PID controller; ΔK I24 Indicates the clear value output by the non-singleton interval type-II fuzzy PID controller; ΔK D24 It indicates that the crisp value is output by the non-singleton interval type-2 fuzzy PID controller; ΔK P25 Indicates the clear value output by the non-singleton interval type-II fuzzy PID controller; ΔK I25 Indicates the clear value output by the non-singleton interval type-II fuzzy PID controller; ΔK D25 Represents the crisp value output by the non-singleton interval type-2 fuzzy PID controller.

4. The non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization according to claim 3, characterized in that: The ΔK P24 , ΔK I24 , ΔK D24 , ΔK P25 , ΔK I25 , ΔK D25 The solution process is: 1) Select 5 fuzzy subsets: NB, NS, Z, PS, and PB; NB is negative and large, NS is negative and small, Z is zero, PS is positive and small, and PB is positive and large; Non-singleton interval type-II fuzzy PID controller error signal e i Divided into 5 fuzzy subsets: NB, NS, Z, PS and PB; e i It means e4 or e5; Non-singleton interval type-II fuzzy PID controller error signal e i Differential Divided into 5 fuzzy subsets: NB, NS, Z, PS and PB; express or Based on the error signal of non-singleton interval type-II fuzzy PID controller i and e i Differential Construct 25 fuzzy rules; The fuzzy rules are: When the error signal of the non-singleton interval type II fuzzy PID controller system is i For NB, e i Differential When it is NB, K Pi The fuzzy subsets are PS, K Ii The fuzzy subset is NB, K Di The fuzzy subset of is PB; When the error signal of the non-singleton interval type II fuzzy PID controller system is i NS, e i Differential When it is NB, K Pi The fuzzy subsets are PS, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is NS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i is Z, e i Differential When it is NB, K Pi The fuzzy subsets are NS, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is NS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For PS, e i Differential When it is NB, K Pi The fuzzy subsets are PS, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is NS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i PB, e i Differential When it is NB, K Pi The fuzzy subsets are PB, K Ii The fuzzy subsets are Z, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For NB, e i Differential When NS, K Pi The fuzzy subsets are PS, K Ii The fuzzy subset is NB, K Di The fuzzy subset of is PS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i NS, e i Differential When NS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i is Z, e i Differential When NS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For PS, e i Differential When NS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are Z, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i PB, e i Differential When NS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For NB, e i Differential When Z, K Pi The fuzzy subsets are NS, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is PS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i NS, e i Differential When Z, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is PS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i is Z, e i Differential When Z, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are Z, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For PS, e i Differential When Z, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is PS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i PB, e i Differential When Z, K Pi The fuzzy subsets are NS, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is PS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For NB, e i Differential When it is PS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are NS, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i NS, e i Differential When it is PS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are Z, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i is Z, e i Differential When it is PS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For PS, e i Differential When it is PS, K Pi The fuzzy subsets are Z, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i PB, e i Differential When it is PS, K Pi The fuzzy subsets are PS, K Ii The fuzzy subsets are PB, K Di The fuzzy subset of is PS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For NB, e i Differential When PB is Pi The fuzzy subsets are PB, K Ii The fuzzy subsets are Z, K Di The fuzzy subset of is Z; When the error signal of the non-singleton interval type II fuzzy PID controller system is i NS, e i Differential When PB is Pi The fuzzy subsets are PS, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is NS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i is Z, e i Differential When PB is Pi The fuzzy subsets are NS, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is NS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i For PS, e i Differential When PB is Pi The fuzzy subsets are PS, K Ii The fuzzy subsets are PS, K Di The fuzzy subset of is NS; When the error signal of the non-singleton interval type II fuzzy PID controller system is i PB, e i Differential When PB is Pi The fuzzy subsets are PS, K Ii The fuzzy subsets are PB, K Di The fuzzy subset of is PB; 2) Set is the input of the non-singleton interval type-II fuzzy PID controller, and the triggering interval F of the jth fuzzy rule j (x) is Among them, e i is the error signal of the non-singleton interval type-II fuzzy PID controller; for e i Differential of; j = 1, 2, ..., 25; e i It means e4 or e5; express or The upper bound of the trigger interval The Nether f j for: In the formula, For τ m1 The jth fuzzy rule of corresponds to the fuzzy subset, For τ m2 The jth fuzzy rule of corresponds to the fuzzy subset; Indicates for e i The jth fuzzy rule corresponds to the lower bound membership function value of the fuzzy subset. Indicates for The jth fuzzy rule corresponds to the lower bound membership function value of the fuzzy subset; Indicates for e i The jth fuzzy rule corresponds to the fuzzy subset upper bound membership function value, Indicates for The jth fuzzy rule corresponds to the fuzzy subset upper bound membership function value; 3) Output interval y of the jth fuzzy rule j for: in, y j is the lower bound of the fuzzy subset output interval, The upper bound of the fuzzy subset output interval; Fuzzy subset NB output interval upper bound Upper bound of NS output interval of fuzzy subset Upper bound of fuzzy subset Z output interval Upper bound of fuzzy subset PS output interval Upper bound of fuzzy subset PB output interval Fuzzy subset NB output interval lower bound y j =-1; Fuzzy subset NS output interval lower bound y j =-0.6; Fuzzy subset Z output interval lower bound y j =-0.1; Fuzzy subset PS output interval lower bound y j =0.4; Fuzzy subset PB output interval lower bound y j =0.9; 4) Based on the upper limit of the trigger interval The Nether f j as well as y j , Calculate the lower bound set center y l and the center of the upper bound set y u ; expressed as: Where l and u are the transformation points obtained by the KM iterative method; n = 25; 5) Based on the lower bound set center y l and the center of the upper bound set y u , calculate the lower bound set center y l and the center of the upper bound set y u The average value of is the final output clarity value; 6) The clarity value and K of the final output obtained based on 5) P4 , and obtain ΔK P24 ; expressed as: in, For τ m1 About K P4 The scaling factor of For τ m1 About K P4 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) I4 , and obtain ΔK I24 ; expressed as: in, For τ m1 About K I4 The integrating factor of For τ m1 About K I4 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) D4 , and obtain ΔK D24 ; expressed as: in, For τ m1 About K D4 The integrating factor of For τ m1 About K D4 The final output clear value y; 7) The clarity value and K of the final output obtained based on 5) P5 , and obtain ΔK P25 ; expressed as: in, For τ m2 About K P5 The scaling factor of For τ m2 About K P5 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) I5 , and obtain ΔK I25 ; expressed as: in, For τ m2 About K I5 The scaling factor of For τ m2 About K P5 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) D5 , and obtain ΔK D25 ; expressed as: in, For τ m2 About K D5 The integrating factor of For τ m2 About K P5 The final output clear value y.

5. The non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization according to claim 4, characterized in that: In the step 3, the particle swarm optimization algorithm is used to optimize the parameters of the non-singleton interval type-two fuzzy PID controller to obtain the optimal non-singleton interval type-two fuzzy PID controller parameters, that is, to obtain the optimal non-singleton interval type-two fuzzy PID controller; The specific process is: The inertia coefficient w in the particle swarm optimization algorithm decays with the number of iterations, as shown in the following formula: In the formula, i is the number of iterations, i max is the maximum number of iterations, w min is the minimum inertia coefficient, w max is the maximum inertia coefficient; The fitness calculation method in the particle swarm optimization algorithm is: Where, |e1(t)| is the absolute value of the angle error of joint 1; |e2(t)| is the absolute value of the angle error of joint 2; t is time; T1 is the upper bound time of integration; T2 is the upper bound time of integration; T2<T1; α1, α2, β1, β2 are weight factors; J is the particle fitness.

6. The non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization according to claim 5, characterized in that: In the step 5, a traditional PID controller, a non-singleton interval type II fuzzy PID controller and a signal compensation fuzzy PID are constructed; the specific process is: The signal compensation fuzzy PID expression is: Signal compensation fuzzy PID compensation q m1 is the output of the first channel fuzzy PID; Signal compensation fuzzy PID compensation q m2 is the output of the second channel fuzzy PID; In the formula, q m1 represents the rotation angle of joint 1; q m2 Indicates the rotation angle of joint 2; K PF1 For q m1 Signal compensation fuzzy PID proportional coefficient; K IF1 For q m1 Signal compensation fuzzy PID integral coefficient; K DF1 For q m1 The signal compensation fuzzy PID differential coefficient; where K PF1 =5, K IF1 =0.1, K DF1 =0.01; K PF2 For q m2 Signal compensation fuzzy PID proportional coefficient; K IF2 For q m2 Signal compensation fuzzy PID integral coefficient; K DF2 For q m2 The signal compensation fuzzy PID differential coefficient; where K PF2 =5, K IF2 =0.1, K DF2 =0.01; e F1 Indicates that for q m1 The signal compensates the fuzzy PID error signal; Indicates e F1 The differential of e F2 Indicates that for q m2 The signal compensates the fuzzy PID error signal; Indicates e F2 The differential of ΔK PF1 Indicates the clear value of the fuzzy PID output compensated by the signal; ΔK IF1 Indicates the clear value of the fuzzy PID output compensated by the signal; ΔK DF1 Indicates the clear value output by the signal compensation fuzzy PID; ΔK PF2 Indicates the clear value of the fuzzy PID output compensated by the signal; ΔK IF2 Indicates the clear value of the fuzzy PID output compensated by the signal; ΔK DF2 Indicates the clear value output by signal compensation fuzzy PID.

7. The non-singleton interval type-2 fuzzy PID space manipulator tracking control method based on improved particle swarm optimization according to claim 6, characterized in that: The ΔK PF1 , ΔK IF1 , ΔK DF1 , ΔK PF2 , ΔK IF2 , ΔK DF2 The solution process is: 1) Select 5 fuzzy subsets: NB, NS, Z, PS, and PB; NB is negative and large, NS is negative and small, Z is zero, PS is positive and small, and PB is positive and large; For q m1 The signal compensation fuzzy PID error signal e F1 It is divided into five fuzzy subsets: NB, NS, Z, PS and PB; for e F1 Differential Divided into 5 fuzzy subsets: NB, NS, Z, PS and PB; For q m2 The signal compensation fuzzy PID error signal e F2 It is divided into five fuzzy subsets: NB, NS, Z, PS and PB; for e F2 Differential Divided into 5 fuzzy subsets: NB, NS, Z, PS and PB; Based on targeting The signal compensates the fuzzy PID error signal and Differential Construct 25 fuzzy rules; Indicates q m1 or q m2 ; Indicates e F1 or e F2 ; express or The fuzzy rules are: When targeting The signal compensates the fuzzy PID error signal For NB, Differential When it is NB, The fuzzy subset of is PB, The fuzzy subset of is NB, The fuzzy subset of is PB; K PF1 or K PF2 ; K IF1 or K IF2 ; K DF1 or K DF2 ; When targeting The signal compensates the fuzzy PID error signal For NB, Differential When it is NS, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is NS; When targeting The signal compensates the fuzzy PID error signal For NB, Differential When Z, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is NS; When targeting The signal compensates the fuzzy PID error signal For NB, Differential When it is PS, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is NS; When targeting The signal compensates the fuzzy PID error signal For NB, Differential When PB is The fuzzy subset of is Z, The fuzzy subset of is Z, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For NS, Differential When it is NB, The fuzzy subset of is PS, The fuzzy subset of is NB, The fuzzy subset of is PS; When targeting The signal compensates the fuzzy PID error signal For NS, Differential When it is NS, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For NS, Differential When Z, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For NS, Differential When it is PS, The fuzzy subset of is Z, The fuzzy subset of is Z, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For NS, Differential When PB is The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For Z, Differential When it is NB, The fuzzy subsets are PS, K IF1 The fuzzy subset of is NS, The fuzzy subset of is PS; When targeting The signal compensates the fuzzy PID error signal For Z, Differential When it is NS, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is PS; When targeting The signal compensates the fuzzy PID error signal For Z, Differential When Z, The fuzzy subset of is Z, The fuzzy subset of is Z, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For Z, Differential When it is PS, The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is PS; When targeting The signal compensates the fuzzy PID error signal For Z, Differential When PB is The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is PS; When targeting The signal compensates the fuzzy PID error signal For PS, Differential When it is NB, The fuzzy subset of is PS, The fuzzy subset of is NS, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For PS, Differential When it is NS, The fuzzy subset of is Z, The fuzzy subset of is Z, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For PS, Differential When Z, The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For PS, Differential When it is PS, The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For PS, Differential When PB is The fuzzy subset of is NS, The fuzzy subset of is PB, The fuzzy subset of is PS; When targeting The signal compensates the fuzzy PID error signal For PB, Differential When it is NB, The fuzzy subset of is Z, The fuzzy subset of is Z, The fuzzy subset of is Z; When targeting The signal compensates the fuzzy PID error signal For PB, Differential When it is NS, The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is NS; When targeting The signal compensates the fuzzy PID error signal For PB, Differential When Z, The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is NS; When targeting The signal compensates the fuzzy PID error signal For PB, Differential When it is PS, The fuzzy subset of is NS, The fuzzy subset of is PS, The fuzzy subset of is NS; When targeting The signal compensates the fuzzy PID error signal is PB, the differential of When PB is The fuzzy subset of is NB, The fuzzy subset of is PB, The fuzzy subset of is NB; 2) Set is the signal compensation fuzzy PID input, the triggering interval F of the jth fuzzy rule j (x) is in, To compensate the fuzzy PID error signal for the signal; The fuzzy PID error signal e is compensated for by the signal i Differentiation of; j = 1, 2, ..., 25; Indicates e F1 or e F2 ; express or The upper bound of the trigger interval The Nether f j for: In the formula, For q m1 The jth fuzzy rule of corresponds to the fuzzy subset, For q m2 The jth fuzzy rule of corresponds to the fuzzy subset; Indicates for The jth fuzzy rule corresponds to the lower bound membership function value of the fuzzy subset. Indicates for The jth fuzzy rule corresponds to the lower bound membership function value of the fuzzy subset; Indicates for The jth fuzzy rule corresponds to the fuzzy subset upper bound membership function value, Indicates for The jth fuzzy rule corresponds to the fuzzy subset upper bound membership function value; 3) Output interval y of the jth fuzzy rule j for: in, y j is the lower bound of the fuzzy subset output interval, The upper bound of the fuzzy subset output interval; Fuzzy subset NB output interval upper bound Upper bound of NS output interval of fuzzy subset Upper bound of fuzzy subset Z output interval Upper bound of fuzzy subset PS output interval Upper bound of fuzzy subset PB output interval Fuzzy subset NB output interval lower bound y j =-1; Fuzzy subset NS output interval lower bound y j =-0.6; Fuzzy subset Z output interval lower bound y j =-0.1; Fuzzy subset PS output interval lower bound y j =0.4; Fuzzy subset PB output interval lower bound y j =0.9; 4) Based on the upper limit of the trigger interval The Nether f j as well as y j , Calculate the lower bound set center y l and the center of the upper bound set y u ; expressed as: Where l and u are the transformation points obtained by the KM iterative method; n = 25; 5) Based on the lower bound set center y l and the center of the upper bound set y u , calculate the lower bound set center y l and the center of the upper bound set y u The average value of is the final output clarity value; 6) The clarity value and K of the final output obtained based on 5) PF1 , and obtain ΔK PF1 ; expressed as: in, For q m1 About K PF1 The scaling factor of For q m1 About K PF1 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) IF1 , and obtain ΔK IF1 ; expressed as: in, For q m1 About K IF1 The integrating factor of For q m1 About K IF1 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) DF1 , and obtain ΔK DF1 ; expressed as: in, For q m1 About K DF1 The integrating factor of For q m1 About K DF1 The final output clear value y; 7)、 Based on the clarity value and K of the final output obtained in 5) P5 , and obtain ΔK PF2 ; expressed as: in, For q m2 About K P5 The scaling factor of For q m2 About K P5 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) IF2 , and obtain ΔK IF2 ; expressed as: in, For q m2 About K IF2 The scaling factor of For q m2 About K IF2 The final output clear value y; Based on the clarity value and K of the final output obtained in 5) DF2 , and obtain ΔK DF2 ; expressed as: in, For q m2 About K DF2 The integrating factor of For q m2 About K DF2 The final output clear value y.

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