Speed control method for permanent magnet synchronous motor system under current and speed constraints

Abstract

The application discloses a speed control method of a permanent magnet synchronous motor system constrained by current and rotating speed. The method provided by the application comprises the following steps: establishing a dynamic model of the permanent magnet synchronous motor system and converting the dynamic model into a state equation; designing a disturbance observer for unmatched disturbance; determining a penalty function according to the state equation of the permanent magnet synchronous motor system constrained by current and rotating speed obtained in step two and state constraints existing in the system; determining a corresponding adaptive speed controller of the permanent magnet synchronous motor according to the dynamic model of the permanent magnet synchronous motor, the state equation of the permanent magnet synchronous motor, the disturbance observer and the penalty function; and constructing a corresponding Lyapunov function according to the adaptive speed controller of the permanent magnet synchronous motor. The rotating speed and current of the permanent magnet synchronous motor can track a reference signal with a given precision without violating the required constraint conditions, and the method has robustness to external disturbance and uncertain parameters.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, and specifically relates to a speed control method for permanent magnet synchronous motor systems constrained by current and speed. Background Technology

[0002] In recent years, with the rapid development of power electronics and microelectronics technologies, significant progress has been made in the research of motor control theory, particularly in rare-earth permanent magnet materials and permanent magnet synchronous motors (PMSMs). Compared with traditional electrically excited synchronous motors, PMSMs offer advantages such as simple structure, light weight, high power density, low loss, and high efficiency, and have been widely applied in various industrial fields. Simultaneously, control methods for PMSMs, including field-oriented control, direct torque control, adaptive control, sliding mode variable structure control, and feedback linearization, have been proposed and successfully applied.

[0003] In practical applications, the parameters of PMSM systems often exhibit significant uncertainties; for example, the stator resistance of the motor changes with increasing temperature during operation. Robust control and adaptive control techniques are powerful tools for handling the influence of unknown parameters. Adaptive control techniques, with their lower conservatism, have been applied to PMSM systems in numerous engineering projects.

[0004] It is worth noting that most existing results only consider state-constrained PMSM systems. In the real world, for safety reasons, the current and velocity of a PMSM cannot be arbitrary, but must be contained within certain strict ranges. Currently, researchers have adopted a variety of effective methods to develop state (or output) constrained controllers, such as model predictive control (MPC) and methods based on barrier Lyapunov functions (BLF). However, the MPC method requires solving the optimization problem at each time step, and solving the optimization problem is often time-consuming. In practical applications, fast controller response is often a necessary condition for maintaining high efficiency. Therefore, there is a contradiction between the fast response of the controller required in practical applications and the time-consuming nature of the MPC method. As for the BLF method, there are two main drawbacks: (1) In order to ensure the continuity and differentiability of the virtual controller, the controller design process is often quite complex; (2) The feasibility conditions of the virtual controller must always be guaranteed to prevent violations of state constraints, which means that a lot of time and effort is needed to find a set of parameters that appropriately satisfy the feasibility conditions.

[0005] On the other hand, while these results consider state-constrained PMSM systems, they rarely account for mismatch disturbances. Mismatch disturbances are typically caused by external load torques on the PMSM, and disturbance observers have been widely used to address this issue.

[0006] Currently, there is limited research on the mismatch interference problem that is likely to be encountered in actual situations, and on the control problem of PMSM systems with constraints based on current and speed. Summary of the Invention

[0007] To address the aforementioned issues, this application provides a speed control method for permanent magnet synchronous motor systems constrained by current and speed, which solves the mismatch disturbance problem in state-constrained PMSM systems in the prior art.

[0008] This application provides a speed control method for a permanent magnet synchronous motor system constrained by current and speed, the method comprising:

[0009] Step 1: Establish the dynamic model of the permanent magnet synchronous motor system;

[0010] Step 2: For the simplified dynamic model, a coordinate transformation is introduced to convert the dynamic model of the permanent magnet synchronous motor system into state equations;

[0011] Step 3: Based on the state equations of the permanent magnet synchronous motor system with mismatched disturbances, design a disturbance observer to address the mismatched disturbances;

[0012] Step 4: Based on the state equations of the permanent magnet synchronous motor system constrained by current and speed obtained in Step 2, determine the penalty function for the state constraints of the system.

[0013] Step 5: Based on the dynamic model of the permanent magnet synchronous motor, the state equation of the permanent magnet synchronous motor, the disturbance observer, and the penalty function, determine the corresponding adaptive speed controller for the permanent magnet synchronous motor.

[0014] Step 6: Construct the corresponding Lyapunov function based on the adaptive speed control controller of the permanent magnet synchronous motor.

[0015] Alternatively, the dynamic model of the permanent magnet synchronous motor is as follows:

[0016] (1)

[0017] in: Represents the angular velocity of the rotor. Represents the moment of inertia. Represents the extreme logarithm. Represents rotor flux linkage. represent shaft current, Represents the coefficient of viscous friction. This represents the unknown mismatched load torque disturbance, and there exists a positive constant. , making Furthermore, its derivative has a positive upper bound, defined as... , represent shaft current, Representing inductance, it is an unknown positive constant. This represents the stator resistance, which is an unknown positive constant. represent shaft voltage, represent Shaft voltage, where rotational speed and current Subject to constraints and restrictions.

[0018] Optionally, for the simplified dynamic model, a coordinate transformation is introduced to convert the dynamic model of the permanent magnet synchronous motor system into state equations, including:

[0019] Step 21, let shaft current To obtain the maximum torque-to-current ratio, the dynamic model of the permanent magnet synchronous motor is simplified to:

[0020] (2)

[0021] Step 22, let To provide a speed reference tracking signal, a simplified model of the permanent magnet synchronous motor's dynamics is defined, with the coordinate transformation as follows:

[0022]

[0023] The permanent magnet synchronous motor system can then be represented by the following model using state equations:

[0024] (3)

[0025] in: Represents the speed tracking error. represent shaft current, This represents a mismatched perturbation. , derivative , These are known parameters. It is an unknown parameter, u is the control input, representing the input voltage. This is the system output, representing the speed tracking error. Based on the actual situation, we reasonably assume that the constraints on the current and speed are as follows: , ,in, A positive constant and , It is a positive constant.

[0026] Optionally, for system mismatch disturbances Design the following interference observer:

[0027] (4)

[0028] in For the observer state, To counter interference The estimated value, It is the gain coefficient;

[0029] definition ,Pick for Based on the estimate, therefore... Taking the derivative and substituting equations (3) and (4) into the equation, we get:

[0030] (5).

[0031] Optional, the penalty function is as follows:

[0032] (6)

[0033] in: A positive coefficient. .

[0034] Optional speed controllers for permanent magnet synchronous motors include:

[0035] (7)

[0036] Where: Definition , They are respectively The estimate, It is the controller coefficient. It is a positive coefficient.

[0037] Optionally, based on the adaptive speed controller of the permanent magnet synchronous motor, the corresponding Lyapunov function is constructed, including:

[0038] Step 61, Define Construct the following Lyapunov function:

[0039] (8)

[0040] in Differentiating equation (8), we can prove the output of the speed tracking error through analysis. It can converge to a small neighborhood of 0;

[0041] Step 62, construct the auxiliary Lyapunov function:

[0042] (9)

[0043] Differentiating equation (9), we can prove the output state of the speed tracking error through analysis. and shaft current state It will not violate the given constraints.

[0044] Compared with the prior art, the advantages of this invention are as follows: (1) This invention studies a real system considering mismatched disturbances. By combining constraint control with the disturbance observer method, the system's performance is guaranteed to be good; (2) This invention considers not only current constraints but also speed constraints. The requirement of full-state constraints makes controller design and subsequent stability analysis challenging, and the designed penalty function helps to handle constraint problems; (3) This invention considers PMSM systems with uncertain parameters. The introduction of adaptive parameters makes the system more robust and has high engineering practical value. Attached Figure Description

[0045] Figure 1 This is a schematic flowchart of a speed control method for a permanent magnet synchronous motor according to the present invention;

[0046] Figure 2 This is a schematic diagram of the permanent magnet synchronous motor control system of the present invention;

[0047] Figure 3 This is a simulation of the present invention. shaft current And the resulting curve that does not violate constraints;

[0048] Figure 4 The rotational speed of this invention And the resulting curve that does not violate constraints;

[0049] Figure 5 The rotational speed of this invention With reference speed The speed regulation effect curve;

[0050] Figure 6 This is the observation effect curve of the interference observer of the present invention. Detailed Implementation

[0051] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention. Figure 1 A schematic flowchart of a speed control system and method for a permanent magnet synchronous motor system according to the present invention is shown. (Refer to...) Figure 1 The method in this embodiment includes the following steps:

[0052] Step 1: Establish the dynamic model of the permanent magnet synchronous motor system;

[0053] Step 2: For the simplified dynamic model, a coordinate transformation is introduced to convert the dynamic model of the permanent magnet synchronous motor system into state equations;

[0054] Step 3: Based on the state equations of the permanent magnet synchronous motor system with mismatched disturbances, design a disturbance observer to address the mismatched disturbances;

[0055] Step 4: Based on the state equations of the permanent magnet synchronous motor system constrained by current and speed obtained in Step 2, determine the penalty function for the state constraints of the system; once the system state approaches its boundary, the designed penalty term will approach infinity, thereby achieving the purpose of constraining the state.

[0056] Step 5: Based on the dynamic model of the permanent magnet synchronous motor, the state equation of the permanent magnet synchronous motor, the disturbance observer, and the penalty function, determine the corresponding adaptive speed controller for the permanent magnet synchronous motor.

[0057] Step 6: Based on the adaptive speed controller of the permanent magnet synchronous motor, construct the corresponding Lyapunov function and prove the stability of the closed-loop system.

[0058] The steps are explained in detail below.

[0059] In step one, based on the dynamic model of the permanent magnet synchronous motor, the model of the permanent magnet synchronous motor system in the d-q axis coordinate system is as follows:

[0060] (1)

[0061] in: Represents the angular velocity of the rotor. Represents the moment of inertia. Represents the extreme logarithm. Represents rotor flux linkage. represent shaft current, Represents the coefficient of viscous friction. This represents the load torque disturbance due to mismatch, and there exists a positive constant. , making Furthermore, its derivative has a positive upper bound, defined as... , represent shaft current, Representing inductance, it is an unknown positive constant. This represents the stator resistance, which is an unknown positive constant. represent shaft voltage, represent Shaft voltage. Where rotational speed... and current Subject to constraints and restrictions.

[0062] Step two is as follows:

[0063] Step 21, let To obtain the maximum torque-to-current ratio, equation (1) simplifies to:

[0064] (2)

[0065] Step 22, let To provide a speed reference tracking signal, a simplified model of the permanent magnet synchronous motor's dynamics is defined, with the coordinate transformation as follows:

[0066] (3)

[0067] The PMSM system (2) can be written as a mathematical model represented by the following state equations:

[0068] (4)

[0069] in: Represents the speed tracking error. represent shaft current, It is a mismatched perturbation. , It is an unknown quantity, u is the control input, representing the input voltage. This is the output, representing the speed tracking error. Based on actual conditions, we reasonably assume the following constraints on the current and speed: , ,in, A positive constant and , It is a positive constant.

[0070] The system state constraints are: The control objective of system (4) is to design the control input u such that... .

[0071] In step three, due to mismatched disturbances in the system... This invention constructs an interference observer to estimate mismatched disturbances. The interference observer is designed as follows:

[0072] (5)

[0073] in For the observer state, To counter interference The estimate, It is the gain coefficient.

[0074] definition ,Pick for Based on the estimate, therefore... By taking the derivative and substituting the relevant values ​​from (4) and (5) into the calculation, we can obtain:

[0075] (6)

[0076] In step four, the system state is required to meet certain conditions. The present invention designs the following penalty function:

[0077] (7)

[0078] in: A positive coefficient. .

[0079] In step five, based on the dynamic model of the permanent magnet synchronous motor from step one, the state equation of the permanent magnet synchronous motor from step two, the disturbance observer from step three, and the penalty function from step four, considering the existence of unknown parameters, the adaptive speed controller for the permanent magnet synchronous motor is designed as follows:

[0080] (8)

[0081] Among them, the definition , They are respectively The estimate, These are design parameters. It is a positive coefficient.

[0082] The control objective of this controller is to make the system (4) .

[0083] In step six, define The Lyapunov function is constructed as follows:

[0084] (9)

[0085] It is easy to know .

[0086] Differentiating (9) yields:

[0087] (10)

[0088] Will , And by substituting the controller (8) into (9) and rearranging the data, we get:

[0089] (11)

[0090] According to the expansion and contraction of Yang's inequality, (11) can be rearranged as follows:

[0091] (12)

[0092] (12) Where:

[0093] (13)

[0094] All design parameters are positive; simply select the appropriate parameters. It can be guaranteed All are positive.

[0095] Based on the continuity of the system state, there exists a moment... , making when hour, If it is true, then it can be known that .

[0096] Therefore, (18) can be simplified to:

[0097] (14)

[0098] in .

[0099] According to Lyapunov's stability theory, the state of system (4) is... Bounded, which means that tracking control, i.e., speed control, is achieved. Therefore, when hour:

[0100] (15)

[0101] According to the designed controller (8), we can obtain ,therefore Similarly, there is

[0102] .

[0103] Construct the following auxiliary Lyapunov function:

[0104] (16)

[0105] Differentiating (16) with respect to the following, we obtain:

[0106] (17)

[0107] in It can be known that when When, there exists a constant Make .

[0108] Based on the above analysis, we can conclude that:

[0109] (18)

[0110] From (18), we know that there exists a When hour, Therefore when hour, .

[0111] like If it is a finite value, then ,set up time , Then there exists a time. , making This means that there exists a moment. , making According to (16), it can be known that This is related to hour Contradiction, therefore .

[0112] Furthermore, assuming exist The moment has reached its limit Then there exists a time. ,at this time .

[0113] For (4) Differentiate and apply the controller in (8) Substituting these values ​​and organizing them, we can obtain:

[0114] (19)

[0115] It can be known that when hour:

[0116] (20)

[0117] in .

[0118] From (20), we can see that the existence time is... , making This contradicts the previous assumption: there exists a time. ,at this time Contradictory, therefore, It will not reach the boundary Similarly, It will not reach the boundary .

[0119] In summary, none of the states in system (4) violate the given constraints.

[0120] The embodiments of this application will be further illustrated below with specific examples.

[0121] System simulation and parameter selection are performed in the Matlab environment. , , , , , , , , , , , , , , The simulation results are as follows Figures 3 to 6 As shown in the simulation curves, when subjected to mismatched disturbances, the PMSM system, constrained by current and speed, can effectively track the given reference speed signal. The designed adaptive law gives the PMSM system in this embodiment good robustness. Figure 3 Current simulation is shown. shaft current It will not violate any restrictions. Figure 4 This demonstrates that the speed tracking error of the speed control can converge to a given accuracy limit. Figure 5 This demonstrates that the rotational speed can track the given reference rotational speed signal very well. Figure 6 The observation results of the designed interference observer are shown, from Figure 6 It can be seen that the observation of mismatched interference is effective.

[0122] This application combines constraint control with the disturbance observer method to ensure good system performance. It considers not only current constraints but also speed constraints. The requirements of full-state constraints make controller design and subsequent stability analysis challenging, but the designed penalty function helps handle constraint problems. This application considers PMSM systems with uncertain parameters; the introduction of adaptive parameters improves system robustness and has high engineering practical value.

[0123] This invention proposes a speed control method for a permanent magnet synchronous motor (PMSM) system constrained by current and speed. Based on disturbance observer, adaptive control, and state constraint control techniques, a novel speed control scheme for the PMSM is proposed. Through the proposed control scheme, the speed of the PMSM can track a given reference signal with a given accuracy without violating the required constraints, demonstrating practical engineering value.

Claims

1. A speed control method for a permanent magnet synchronous motor system constrained by current and speed, characterized in that, The method includes: Step 1: Establish the dynamic model of the permanent magnet synchronous motor system; Step 2: For the simplified dynamic model, a coordinate transformation is introduced to convert the dynamic model of the permanent magnet synchronous motor system into state equations; Step 3: Based on the state equations of the permanent magnet synchronous motor system with mismatched disturbances, design a disturbance observer to address the mismatched disturbances; Step 4: Based on the state equations of the permanent magnet synchronous motor system constrained by current and speed obtained in Step 2, determine the penalty function for the state constraints of the system. Step 5: Based on the dynamic model of the permanent magnet synchronous motor, the state equation of the permanent magnet synchronous motor, the disturbance observer, and the penalty function, determine the corresponding adaptive speed controller for the permanent magnet synchronous motor. Step 6: Construct the corresponding Lyapunov function based on the adaptive speed control controller for permanent magnet synchronous motors; For the simplified dynamic model, a coordinate transformation is introduced to convert the dynamic model of the permanent magnet synchronous motor system into state equations, including: Step 21, let shaft current To obtain the maximum torque-to-current ratio, the dynamic model of the permanent magnet synchronous motor is simplified to: (2)； in: Represents the angular velocity of the rotor. Represents the moment of inertia. Represents the extreme logarithm. Represents rotor flux linkage. represent shaft current, Represents the coefficient of viscous friction. This represents the unknown mismatched load torque disturbance, and there exists a positive constant. , making Furthermore, its derivative has a positive upper bound, defined as... ; Representing inductance, it is an unknown positive constant. This represents the stator resistance, which is an unknown positive constant. represent Shaft voltage; Step 22, let To provide a speed reference tracking signal, a simplified model of the permanent magnet synchronous motor's dynamics is defined, with the coordinate transformation as follows: ； The permanent magnet synchronous motor system can then be represented by the following model using state equations: (3)； in: Represents the speed tracking error. represent shaft current, This represents a mismatched perturbation. , derivative , These are known parameters. It is an unknown parameter, u is the control input, representing the input voltage. This is the system output, representing the speed tracking error. Based on the actual situation, we reasonably assume that the constraints on the current and speed are as follows: , ,in, A positive constant and , A positive constant; To address the mismatch disturbances in the system Design the following interference observer: (4)； in For the observer state, To counter interference The estimated value, It is the gain coefficient; definition ,Pick for Based on the estimate, therefore... Taking the derivative and substituting equations (3) and (4) into the equation, we get: (5)。 2. The speed control method for a permanent magnet synchronous motor system constrained by current and speed according to claim 1, characterized in that, The dynamic model of the permanent magnet synchronous motor is as follows: (1)； in: Represents the angular velocity of the rotor. Represents the moment of inertia. Represents the extreme logarithm. Represents rotor flux linkage. represent shaft current, Represents the coefficient of viscous friction. This represents the unknown mismatched load torque disturbance, and there exists a positive constant. , making Furthermore, its derivative has a positive upper bound, defined as... , represent shaft current, Representing inductance, it is an unknown positive constant. This represents the stator resistance, which is an unknown positive constant. represent shaft voltage, represent Shaft voltage, where rotational speed and current Subject to constraints and restrictions.

3. The speed control method for a permanent magnet synchronous motor system constrained by current and speed according to claim 2, characterized in that, The penalty function is as follows: (6)； in: A positive coefficient. .

4. The speed control method for a permanent magnet synchronous motor system constrained by current and speed according to claim 3, characterized in that, The speed controller for permanent magnet synchronous motors is as follows: (7)； Where: Definition , They are respectively The estimate, It is the controller coefficient. It is a positive coefficient.

5. The speed control method for a permanent magnet synchronous motor system constrained by current and speed according to claim 4, characterized in that, Based on the adaptive speed controller for permanent magnet synchronous motors, the corresponding Lyapunov function is constructed, including: Step 61, Define Construct the following Lyapunov function: (8)； in Differentiating equation (8), we can prove the output of the speed tracking error through analysis. It can converge to a small neighborhood of 0; Step 62, construct the auxiliary Lyapunov function: (9)； Differentiating equation (9), we can prove the output state of the speed tracking error through analysis. and shaft current state It will not violate the given constraints. .

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