Cross arm and insulator installation robot motor control method based on T-S fuzzy model

Abstract

The invention discloses a cross arm and insulator installation robot motor control method based on a T-S fuzzy model, and the method comprises the following steps: building a permanent magnet synchronous motor nonlinear model according to electromagnetism and motor dynamics; based on a sector nonlinear method, establishing a permanent magnet synchronous motor T-S fuzzy model; designing an observer to obtain a load torque estimated value; designing an L-infinity robust controller to ensure that the angular velocity of the motor can track a reference instruction; and an anti-control gain matrix solving criterion is formulated, and it is ensured that the system meets performance indexes. According to the method, the nonlinear control problem of the permanent magnet synchronous motor system is effectively solved, the influence of continuous interference signals on the system can be effectively suppressed, and the robustness of the system is enhanced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of intelligent monitoring of power systems, and particularly relates to a motor control method for a cross arm and insulator installation robot based on a T-S fuzzy model. BACKGROUND

[0002] With the continuous expansion of rural distribution networks and the continuous improvement of supporting facilities, new distribution lines are continuously increasing. When a new rural distribution network line is built, a cross arm and insulator need to be installed on the erected cement pole to support the overhead conductor. The traditional method adopts a manual high-altitude operation mode: the worker puts the cross arm into the top of the pole, adjusts the position and direction, and then fastens the bolt. However, this operation mode is low in efficiency and has safety risks. In order to improve the installation efficiency of the cross arm and insulator and ensure the safety of the workers, the inventors have developed a rural distribution network cross arm installation robot system, which uses a permanent magnet synchronous motor as an execution unit and automatically completes the lifting, leveling and fixing of the cross arm on the cement pole by controlling the motor. However, the permanent magnet synchronous motor has strong nonlinear characteristics, especially when the motor is running at high speed, the nonlinear characteristics will be further increased, which increases the control difficulty of the system.

[0003] Therefore, the application provides a permanent magnet synchronous motor control strategy based on a T-S fuzzy model, which fully utilizes the ability of the T-S fuzzy model to approximate nonlinear dynamics and effectively solves the nonlinear control problem of the permanent magnet synchronous motor system. In addition, there are external disturbances in the operation process of the motor system, which have an adverse effect on the operation performance of the motor system. Therefore, the application provides a robust control strategy based on an L∞ performance index, which can effectively suppress the influence of continuous disturbance signals on the system and enhance the robustness of the system. SUMMARY

[0004] In order to overcome the above-mentioned shortcomings of the prior art, the application provides a permanent magnet synchronous motor control method for a cross arm and insulator installation robot based on a T-S fuzzy model, which effectively solves the nonlinear control problem of the permanent magnet synchronous motor system, can effectively suppress the influence of continuous disturbance signals on the system, and enhances the robustness of the system.

[0005] The application provides a permanent magnet synchronous motor control method for a cross arm and insulator installation robot based on a T-S fuzzy model, which comprises the following steps: Step 1: establishing a nonlinear model of the permanent magnet synchronous motor according to electromagnetism and motor dynamics; Step 2: establishing a T-S fuzzy model of the permanent magnet synchronous motor based on a sector nonlinear method; Step 3: designing an observer to obtain an estimated value of the load torque; Step 4: designing an L∞ robust controller to ensure that the motor angular velocity can track the reference command; Step 5: Develop a criterion for solving the inverse control gain matrix to ensure that the system meets the performance indicators.

[0006] Furthermore, the specific content of step 1 includes: The voltage equations and mechanical equations of the permanent magnet synchronous motor in the d-q axis coordinate system are shown below: ; ; (1) in, V d and V q These represent the stator voltages respectively. d-q Axial components, i d and i q These are the stator currents. d-q Axial components, d 1 and d 2 Indicates external interference; L d and L q They are respectively d-q Shaft inductance component, R s Stator resistance; ω It is electric angular velocity. φ It is a permanent magnet flux chain; J It is the moment of inertia. B The damping coefficient is... p It is the number of magnetic pole pairs; T l and T e These are the load torque and the electromagnetic torque, respectively. T e satisfy: (2); The system uses a surface-mounted permanent magnet synchronous motor, and the electronic inductance satisfies: L=Lq=Ld. Therefore, the electromagnetic torque can be further simplified to: (3); Combining equations (1) and (3), the nonlinear model of the permanent magnet synchronous motor can be obtained as follows: (4); in, .

[0007] Further, the specific content in the step S2 includes the following steps: The angular velocity ω is selected as the antecedent variable, and the following is considered where M1 and M2 are the minimum and maximum speeds of the motor, respectively, and a T-S fuzzy model of the permanent magnet synchronous motor is established, and the fuzzy rules are as follows: Object rule i: when ω(t) is Mi, then: (5); where ; Through the single-point fuzzification, product inference machine, and defuzzification process, a global T-S fuzzy model can be obtained, which is as follows: (6); where hi (6) i=1,2 is a membership function, .

[0008] Further, the specific content in the step S3 includes: (7); where and are the estimated values of the state and load torque, respectively; L1i and L2i are the to-be-designed observer gain matrices; y is the system output, y = Cx, C is the system output matrix.

[0009] Combined with equations (6)-(7), the following estimated error system can be obtained: (8); where ; Based on the system (8), the solution criterion for the load torque observer gain matrix is given: For a given α>0, if there exist a positive definite matrix Q and matrices (i=1,2) such that the following inequality condition is satisfied: (9); then the state of the system (8) is uniformly ultimately bounded, and the observer gain matrix can be calculated by the formula ; Further, the specific method for proving that the state of the system (8) is uniformly ultimately bounded is as follows: A Lyapunov function is constructed as follows: ; Where Q is the Lyapunov matrix; Calculating the derivative of function V1, we get: (10); By variable substitution Combining this with equation (10), we can obtain (11); in, ; According to equation (10), when equation (9) holds, the following conditions also hold: (12); From equation (12), we can see that: when hour, ,in .

[0010] estimation error Will remain in the collection Inside, among them, This represents the smallest eigenvalue of matrix Q; In summary, it is proven that the state of system (8) is consistent and eventually bounded.

[0011] Furthermore, in step 4, ensuring that the motor angular velocity can track the reference command is achieved through the following method: The q-axis current reference signal is constructed as follows: (13); Where iqr is the q-axis current reference signal and ωr is the angular velocity reference signal.

[0012] In practical use, due to Tl The value is usually unknown and can be replaced by an estimate provided by the load torque observer (7); Considering that the system load torque typically varies little within a small range, it can be ignored, and thus, we obtain... q Derivative of the shaft current reference signal: (14); In addition, due to d shaft current id =0, therefore, d shaft current reference signal idr Set to zero; Combining model (4) with equations (13)-(14), the tracking error system can be obtained as follows: (15); According to the tracking error system (15), a controller is designed As follows: (16); Wherein, u1 is a feedforward control law, which is used to offset the adverse effects of tracking signal on tracking error; u2 is a feedback control law, which is used to stabilize the tracking error system, and the related design method will be given later; According to the tracking error system (15) and the control law (16), and referring to the obtaining process of the global fuzzy model (6), the T-S fuzzy model of the tracking error system can be obtained as follows: (17); Wherein, ; For the system (17), the feedback control law u2 is designed as follows: Controller rule i: when ω(t) is Wi, then: ; Wherein, Ki is a feedback control gain matrix, Wi is a fuzzy set; Similar to the process of obtaining the global model, the global fuzzy control law can be obtained as follows: (18); Wherein, is a membership function designed freely, and satisfies ; Substitute the feedback control law u2 into the model (17), and the closed-loop tracking control system can be obtained as follows: (19).

[0013] Further, step 4 also defines the L performance index: (20); Wherein, γ is L the performance index, and ||d||∞ is the infinite norm.

[0014] Further, step 5 is specifically: For a given β>0, ρ>0 and a membership function μi - ρhi ≥0, if there exist positive definite matrices P Ω i and matrices Ni (i=1, 2), such that the following inequality condition is satisfied: (21); (22); (23); (24); wherein, , the system (19) satisfies the L performance index (20), and the controller gain matrix can be obtained by the formula .

[0015] Compared with the prior art, the present application has the beneficial effects that: The present application provides a permanent magnet synchronous motor control strategy based on T-S fuzzy model, which makes full use of the ability of T-S fuzzy model to approximate nonlinear dynamics and effectively solves the problem of nonlinear control of permanent magnet synchronous motor system. In addition, during the operation of the motor system, there are external disturbances, which have an adverse effect on the operation performance of the motor system. Therefore, the present application provides a robust control strategy based on L performance index. This strategy can effectively suppress the influence of continuous disturbance signals on the system, overcoming the shortcoming of traditional H∞ robust control strategy that can only handle energy-bounded disturbances, thereby enhancing the robustness of the system. BRIEF DESCRIPTION OF DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description.

[0017] Figure 1 is a permanent magnet synchronous motor system control block diagram of a cross arm and insulator installation robot motor control method based on T-S fuzzy model according to an embodiment of the present application.

[0018] Figure 2 is a comparison chart of μ1 and ρh1 in the membership function of a cross arm and insulator installation robot motor control method based on T-S fuzzy model according to an embodiment of the present application.

[0019] Figure 3 is a comparison chart of μ2 and ρh2 in the membership function of a cross arm and insulator installation robot motor control method based on T-S fuzzy model according to an embodiment of the present application.

[0020] Figure 4 is a load torque estimation effect chart of a cross arm and insulator installation robot motor control method based on T-S fuzzy model according to an embodiment of the present application.

[0021] Figure 5 is a tracking control effect comparison chart of a cross arm and insulator installation robot motor control method based on T-S fuzzy model according to an embodiment of the present application. DETAILED DESCRIPTION

[0022] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0023] As shown in the figure, the motor control method of the cross arm and insulator mounting robot based on a T-S fuzzy model according to an embodiment of the present application comprises the following steps: Figure 1 Step 1: establishing a nonlinear model of a permanent magnet synchronous motor according to electromagnetism and motor dynamics; the specific content of step 1 comprises: The voltage equation and mechanical equation of the permanent magnet synchronous motor in a d-q axis coordinate system are as follows: ; ; ; (1) wherein, V d and V q represent the d-axis and q-axis components of the stator voltage respectively, d-q d and i q are the d-axis and q-axis components of the stator current respectively, i 1 and d-q 2 represent external disturbances; d d and d q are the d-axis and q-axis inductance components respectively, L s is the stator resistance; L is the electrical angular velocity, d-q is the permanent magnet flux linkage; R is the moment of inertia, ω is the damping coefficient, φ is the number of pole pairs; J l and B e are the load torque and electromagnetic torque respectively, p e satisfy: T T T (2); ​​​​The system uses a surface-mounted permanent magnet synchronous motor, and the electronic inductance satisfies: L=Lq=Ld. Therefore, the electromagnetic torque can be further simplified to: (3); Combining equations (1) and (3), the nonlinear model of the permanent magnet synchronous motor can be obtained as follows: (4); in, .

[0024] Step 2: Based on the sector nonlinearity method, establish the TS fuzzy model of the permanent magnet synchronous motor; the specific content of step S2 includes the following steps: Choose angular velocity ω as the antecedent variable, and consider... ,in, M 1 and M 2 The minimum and maximum speeds of the motor are given, and a fuzzy model of the permanent magnet synchronous motor TS is established with the following fuzzy rules: Object rules i When ω(t) is M i Then: (5); in, ; Through single-point fuzzification, product inference, and defuzzification, a global TS fuzzy model can be obtained, in the following form: (6); in, hi ( i=1,2 ) is the membership function. .

[0025] Step 3: Design an observer to obtain the load torque estimate; the specific contents of step S3 include: (7); in, and These are the estimated values ​​for the state and the load torque, respectively; L1i and L2i The gain matrix of the observer to be designed; y For system output, y = Cx, C This is the system output matrix.

[0026] Combining equations (6) and (7), the following estimation error system can be obtained: (8); wherein, ; Based on the system (8), a load torque observer gain matrix solving criterion is given: For a given α>0, if there exists a positive definite matrix Q and matrices (i=1,2) such that the following inequality condition is satisfied: (9); then the state of the system (8) is uniformly ultimately bounded, and the observer gain matrix can be obtained by formula ; And the specific method to prove that the state of the system (8) is uniformly ultimately bounded is: Construct a Lyapunov function as follows: ; Wherein, Q is the Lyapunov matrix; Calculate the derivative of the function V1, and get: (10); Through variable substitution , and combined with formula (10), we can get (11); wherein, ; According to formula (10), when formula (9) is established, the following conditions are established: (12); From formula (12), it can be seen that when , wherein .

[0027] The estimation error will be kept in the set , wherein, denotes the minimum eigenvalue of the matrix Q; In summary, it is proved that the state of the system (8) is uniformly ultimately bounded.

[0028] Step 4: Design an L∞robust controller to ensure that the motor angular velocity can track the reference command; In step 4, to ensure that the motor angular velocity can track the reference command, the specific method is: Construct the q-axis current reference signal as follows: (13); Wherein, iqr is the q-axis current reference signal, and ωr is the angular velocity reference signal.

[0029] In practical use, due to Tl The value is usually unknown and can be replaced by an estimate provided by the load torque observer (7); Considering that the system load torque typically varies little within a small range, it can be ignored, and thus, we obtain... q Derivative of the shaft current reference signal: (14); In addition, due to d shaft current id =0, therefore, d shaft current reference signal idr Set to zero; Combining model (4) with equations (13)-(14), the tracking error system can be obtained as follows: (15); Design a controller based on the tracking error system (15). as follows: (16); Where u1 is the feedforward control law, used to counteract the adverse effects of the tracking signal on the tracking error; u2 is the feedback control law, used to stabilize the tracking error system, and the relevant design method will be given later. Based on the tracking error system (15) and the control law (16), and referring to the process of obtaining the global fuzzy model (6), the TS fuzzy model of the tracking error system can be obtained as follows: (17); in, ; For system (17), the feedback control law u2 is designed as follows: Controller rule i: When ω(t) is Wi, then: ; in, Ki For feedback control gain matrix, Wi It is a fuzzy set; Similar to the process of obtaining the global model, the global fuzzy control law can be obtained as follows: (18); in, For a freely designed membership function, and satisfying ; Substituting the feedback control law u2 into model (17), the closed-loop tracking control system is obtained as follows: (19).

[0030] Further, step 4 also defines the L performance index: (20). where γ is L the performance index, and ||d||∞ is the infinity norm.

[0031] Step 5: Formulate the anti-control gain matrix solving criterion to ensure that the system meets the performance index. Step 5 is specifically: For a given β>0, ρ>0 and membership function satisfying μi - ρhi ≥0, if there exists a positive definite matrix P Ω i and matrix Ni (i=1, 2), such that the following inequality conditions are met: (21). (22). (23). (24). where , then the system (19) meets the L performance index (20), and the controller gain matrix can be calculated by the formula .

[0032] The following proves that the system (19) meets the L performance index (20): Construct a Lyapunov function: ; where is the Lyapunov matrix.

[0033] Calculate the derivative of the function V2, which can be obtained: (25). Combined with formula (25), the following condition can be obtained: (26). From formula (26), when the following conditions are met: (27). Contract the formula (27), that is, multiply the matrix before and after, which can obtain the following condition: (28). where , By variable substitution is obtained.

[0034] Combining equations (26)-(29), it is known that when the following equation is established (29) ; then (30) ; In order to reduce the conservatism of condition (29), consider the property , it can be obtained that: (31) ; From equation (31), it is known that conditions μi - ρhi ≥0 and (21)-(23) can guarantee that equation (29) is established, and then condition (30) can be obtained.

[0035] Multiply the exponential operator on both ends of the inequality in equation (30) e-βt , and integrate the equation, it can be obtained that: (32) ; On the other hand, apply the Schur complement lemma to equation (24), it can be obtained that: (33) ; Consider the zero initial condition, i.e., V2(0)=0, and from equations (32)-(33), it can be obtained that: ; That is, system (19) satisfies the L performance index.

[0036] The effectiveness of the tracking control algorithm proposed is verified through simulation experiments.

[0037] The parameter values are shown in Table 1: Table 1 Parameter value table The parameters set by the method are as follows: ρ=0.3, α=0.1, β=0.2, γ=1.1, M1=2000, M2=-2000, the load torque observer and the feedback control gain matrix can be calculated by solving condition (9) and conditions (21)-(24) as follows: ; ; ; ; .

[0038] Further, the controller membership function is determined as follows: ; Figure 2 and Figure 3 The controller membership function is shown as μi and the model membership function is shown as hi ( i =1,2), according to Figure 2 and Figure 3 , the condition μi - ρhi ≥0 is established.

[0039] Suppose the system is disturbed as ; ; The system tracking signal is For the above conditions, the load torque estimation and tracking control effect are verified, and the related results are shown in Figures 4-5 .

[0040] Figure 4 The estimation effect diagram of the load torque is shown, and it can be seen from Figure 4 that even in the presence of disturbance, the proposed observer strategy can still achieve fast and good load torque estimation. Figure 5 is the comparison effect diagram of the proposed L∞ robust control method and the non-robust control method. From the diagram, it can be seen that compared with the non-robust control, the proposed algorithm has higher tracking accuracy and stronger disturbance suppression ability.

[0041] From the above results, it can be seen that the proposed algorithm effectively solves the nonlinear problem existing in the permanent magnet synchronous motor control and has good robustness.

[0042] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A T-S fuzzy model based cross arm and insulator mounting robot motor control method, characterized in that, The method comprises the following steps: Step 1: according to electromagnetism and motor dynamics, a nonlinear model of a permanent magnet synchronous motor is established; Step 2: based on a sector nonlinear method, a T-S fuzzy model of the permanent magnet synchronous motor is established; Step 3: an observer is designed to obtain an estimated value of a load torque; Step 4: an L∞ robust controller is designed to ensure that the motor angular velocity can track a reference instruction; Step 5: a solving criterion of a control gain matrix is formulated to ensure that the system meets a performance index.

2. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, characterized in that, The specific content of the step 1 comprises: The voltage equation and the mechanical equation of the permanent magnet synchronous motor in a d-q axis coordinate system are as follows: ； ； ；（1） in, V d and V q These represent the stator voltages respectively. d-q Axial components, i d and i q These are the stator currents. d-q Axial components, d 1 and d 2 Indicates external interference; L d and L q They are respectively d-q Shaft inductance component, R s Stator resistance; ω It is electric angular velocity. φ It is a permanent magnet flux chain; J It is the moment of inertia. B The damping coefficient is... p It is the number of magnetic pole pairs; T l and T e These are the load torque and the electromagnetic torque, respectively. T e satisfy: （2）； The system uses a surface-mounted permanent magnet synchronous motor, and the electronic inductance satisfies: L=L q =L d Therefore, the electromagnetic torque can be further simplified as: （3）； In combination with the formula (1) and the formula (3), the nonlinear model of the permanent magnet synchronous motor can be obtained, and the specific content is as follows: （4）； wherein .

3. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, characterized in that, The specific content in the step S2 comprises the following steps: The selection angular velocity ω is the antecedent variable, and the following is considered wherein, M 1 The minimum and maximum rotational speeds of the motor are respectively M 2 The minimum and maximum rotational speeds of the motor are respectively Object Rules i When ω(t) is M i then: （5）； Wherein, ； Through a single-point fuzzification, a product inference machine and a defuzzification process, a global T-S fuzzy model can be obtained, and the form is as follows: （6）； wherein hi ( i=1,2 ) is a membership function, .

4. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, characterized in that, The specific content in the step S3 comprises: （7）； wherein, and are the estimated values of the state and load torque, respectively; L1i and L2i is the observer gain matrix to be designed; y is the system output, y = Cx, C is the system output matrix; In combination with the formula (6)-(7), the following estimated error system can be obtained: （8）； wherein ; Based on the system (8), a solving criterion of a load torque observer gain matrix is given: For a given a > 0, if there exist positive definite matrices Q and matrices (i = 1, 2) such that the following inequality conditions are satisfied: （9）； The state of the system (8) is consistent eventually bounded, and the observer gain matrix can be obtained by the formula is calculated.

5. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, characterized in that, The specific method for proving that the state of the system (8) is uniformly ultimately bounded is as follows: A Lyapunov function is constructed as follows: ； Wherein, Q is a Lyapunov matrix; The derivative of the function V1 is calculated, and the following can be obtained: (10)； By variable substitution and in combination with equation (10), we obtain （11）； wherein ; According to the formula (10), when the formula (9) is established, the following conditions are established: （12）； From equation (12), it is known that when , where . estimating error will be kept in the set wherein, denotes the smallest eigenvalue of the matrix Q; According to the above, it is proved that the state of the system (8) is uniformly ultimately bounded.

6. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, wherein In the step 4, the specific method for ensuring that the motor angular velocity can track the reference instruction is as follows: A q-axis current reference signal is constructed as follows: （13）； Wherein, iqr is a q-axis current reference signal, and ωr is an angular velocity reference signal. In practical use, due to Tl Typically unknown, the estimate provided by the load torque observer (7) can be used instead; Considering that the system load torque usually varies little within small intervals, it can be neglected, and thus, the following is obtained q Derivative of the shaft current reference signal: （14）； In addition, due to d shaft current id =0, therefore, d shaft current reference signal idr Set to zero; In combination with the model (4) and the formula (13)-(14), the tracking error system can be obtained as follows: （15）； According to the tracking error system (15), a controller is designed As follows: （16）； Wherein, u1 is a feedforward control law, which is used to offset the adverse effects of a tracking signal on the tracking error; u2 is a feedback control law, which is used to stabilize the tracking error system, and the related design method will be given later; According to the tracking error system (15) and the control law (16), and with reference to the obtaining process of the global fuzzy model (6), the T-S fuzzy model of the tracking error system can be obtained as follows: （17）； wherein ; For the system (17), the feedback control law u2 is designed as follows: Controller rule i: when ω(t) is Wi, then: ； wherein, Ki is a feedback control gain matrix, Wi is a fuzzy set; Similar to the process of obtaining the global model, the global fuzzy control law can be obtained as follows: （18）； wherein is a freely designed membership function and satisfies ; The feedback control law u2 is substituted into the model (17), and the closed-loop tracking control system can be obtained as follows: (19)。 7. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, characterized in that, The step 4 further defines an L∞ performance index: （20） ； where γ is L ∞ is the infinity norm.

8. The T-S fuzzy model-based motor control method for a cross arm and insulator mounting robot according to claim 1, characterized in that, The step 5 is as follows: For given β > 0, p > 0 and membership function satisfying μi - ρhi ≥ 0, if there exist positive definite matrices P and Ω i and matrices Ni (i = 1, 2) such that the following inequality conditions are satisfied: （21）； （22）； （23）； (24)； wherein If the system (19) satisfies the L performance index (20), then the controller gain matrix can be obtained by the formula ​

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