High-speed motor continuous terminal sliding mode current decoupling method based on adaptive observer
Patent Information
- Application Number
- CN202511653730.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-12
- Publication Date
- 2026-09-15
- Estimated Expiration
- 2045-11-12
AI Technical Summary
基于模型的解耦控制策略主要有前馈解耦和反馈解耦,但该策略对电机参数敏感,在参数误差较大的情况甚至会导致系统不稳定,且无法做到完全解耦,动态解耦性能差,因而限制了其应用范围,后两种解耦控制策略是当前的研究热点
[0018]Compared with existing technologies, the beneficial effects of this invention are as follows: The Fast Continuous Terminal Sliding Surface (FCTSMC) based on the hyperbolic tangent function adopted in this invention combines the finite-time convergence characteristics of terminal sliding mode with the continuity of the hyperbolic tangent function, overcoming the singularity problem of traditional terminal sliding mode and the slow convergence speed of non-singular terminal sliding mode. This enables the system state to converge to the equilibrium point quickly and accurately, significantly improving the dynamic response performance and steady-state tracking accuracy of the current loop. By replacing the sign function in traditional sliding mode control with a smooth and continuous hyperbolic tangent function, the control output is fundamentally smoothed, greatly reducing the chattering phenomenon of the controller, achieving high-performance continuous smooth control, and reducing switching losses and impact on the actuator. This invention designs an Adaptive Parametric Linear Extended State Observer (AESO), which can accurately observe and estimate the total system disturbance (including parameter changes, unmodeled dynamics, and external disturbances) in real time, and feedforward the estimated value to the control law, effectively eliminating the influence of disturbances on the system, and making the control system highly robust to internal parameter changes and external load disturbances. By using AESO to observe and compensate for cross-coupling terms and disturbances in the d- and q-axis currents in real time, the strong inter-axis coupling effect under high-speed operation is effectively suppressed, achieving high-performance dynamic decoupling control of the d- and q-axis currents and simplifying controller design. The proposed AESO introduces adaptive parameters related to system states (such as current error and electric angular velocity), which can adjust the observer gain online according to the actual operating conditions of the motor. Compared with ESO with fixed parameters, it can maintain better observation accuracy and faster convergence speed under various operating conditions, and has wider adaptability.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of motor control technology, and in particular to a method for decoupling continuous terminal sliding mode current of a high-speed motor based on an adaptive observer. Background Technology
[0002] High-speed permanent magnet synchronous motor (HPMSM) systems have broad application prospects in high-end drive equipment fields such as aerospace, high-speed machine tool flywheel energy storage, distributed power generation, natural gas extraction and transportation, and vacuum ion pumps due to their advantages of small size, high power density, and high integration. Currently, field-oriented control technology is widely used in HPMSM systems, typically employing proportional-integral (PI) control. Because of its simple structure and ease of implementation, PI control has become the mainstream method for motor control. However, in practical HPMSM applications, changes in motor parameters and uncertain disturbances caused by external environmental variations can affect the control performance of the motor system. Using only linear control methods such as PI control is insufficient to meet the requirements of HPMSM applications in high-performance environments.
[0003] To meet the high-performance requirements of HPMSM, scholars both domestically and internationally have proposed many nonlinear control methods, such as adaptive control, fuzzy control, predictive control, and sliding mode control (SMC). Due to the widespread application of digital signal processors, SMC, with its discontinuous high-frequency switching terms, stands out among these nonlinear control methods because of its strong anti-interference capability and insensitivity to system uncertainties.
[0004] Traditional integral sliding mode control uses a linear sliding surface, which is easy to implement with few parameters, but it is prone to large overshoot when tracking large step values and has a slow convergence speed. Traditional terminal sliding mode control, while having a fast response speed, introduces singularities when the system state crosses zero, thus reducing the system's tracking accuracy. Non-singular terminal sliding mode control sacrifices response speed to solve the singularity problem. Therefore, to improve the tracking accuracy, response speed, and anti-interference performance of the permanent magnet synchronous motor's current loop, an advanced control method is needed to achieve a fast and high-precision response of the permanent magnet synchronous motor under disturbance conditions.
[0005] Furthermore, to address the severe system coupling problem caused by high operating fundamental frequencies, current research focuses primarily on decoupling control strategies. These strategies can be broadly categorized into model-based decoupling control, disturbance compensation-based decoupling control, and complex vector controller-based decoupling control. Model-based decoupling control strategies mainly include feedforward decoupling and feedback decoupling. However, this strategy is sensitive to motor parameters, and large parameter errors can even lead to system instability. It also cannot achieve complete decoupling and exhibits poor dynamic decoupling performance, thus limiting its application. The latter two decoupling control strategies are currently the focus of research. Summary of the Invention
[0006] To address the above problems, this invention provides a method for decoupling the continuous terminal sliding mode current of a high-speed motor based on an adaptive observer. This system aims to solve the problems of slow convergence, chattering and singularity in traditional sliding mode control, and parameter sensitivity of traditional decoupling strategies by combining a fast continuous terminal sliding mode control based on hyperbolic tangent function (FCTSMC) with an adaptive parameter extended state observer (AESO). Ultimately, it achieves high dynamic, high precision, and robust decoupling control of the dq axis current of a high-speed permanent magnet synchronous motor under parameter changes and external disturbances.
[0007] In a first aspect, the present invention provides a method for decoupling continuous terminal sliding mode current of a high-speed motor based on an adaptive observer, comprising the following steps: S1, Construct a fast continuous terminal sliding surface based on the hyperbolic tangent function for current loop control of permanent magnet synchronous motor; S2, Construct a linear extended state observer based on adaptive parameters to observe the current and disturbances of the d-axis and q-axis of the permanent magnet synchronous motor; S3, feedforward the disturbance values of the d-axis and q-axis observed by the adaptive extended state observer to the voltage control law derived from the fast continuous terminal sliding surface, thereby achieving decoupling and disturbance-resistant control of the dq-axis current.
[0008] Furthermore, the expression for the fast continuous terminal sliding surface is: ; in, x 1 represents a state variable; x 2 is x The derivative of 1; ε, λ, and h are real numbers greater than zero, and 0 < ε < 1; S TH For sliding surface variables; tanh() is the hyperbolic tangent function; sgn() is a symbolic function.
[0009] Furthermore, the convergence time of the fast continuous terminal sliding surface is determined through the following process: When S TH =0, the system variable will converge from x0 to a value x(t1) near zero, and has Integrating both sides of the expression for the fast continuous terminal sliding surface, the convergence time t of the fast continuous terminal sliding surface is obtained: .
[0010] Furthermore, the construction process of the linearly extended state observer based on adaptive parameters is as follows: Establish a traditional linear extended state observer: ; ; in, and These are the estimated currents along the d-axis and q-axis, respectively. i d and i q These are the actual measured currents along the d-axis and q-axis, respectively. u d and u q These are the control input voltages for the d-axis and q-axis, respectively. and These are the estimated perturbations along the d-axis and q-axis, respectively. e id and e iq These are the current errors along the d-axis and q-axis, respectively. α 1 and α 2 is the observer gain parameter; Introducing adaptive parameters to adjust the observer parameters online: ; in, ψ For magnetic linkage; oh 0 represents the current loop bandwidth; oh e Electromagnetic angular velocity; β belongs to e id or e iq The maximum value in; T is the sampling time.
[0011] Furthermore, the observer gain parameter α 1 and α 2 is set as: α 1=2 oh 0, α 2= oh 0.
[0012] Furthermore, the voltage equation of the permanent magnet synchronous motor under ideal conditions is: ; Where R is the stator resistance of the motor; ψ f For permanent magnet flux linkage in motors; L is the stator inductance of the motor.
[0013] Furthermore, the derivation process of the voltage control law is as follows: Based on the parameter variations and external disturbances, the voltage equation of a permanent magnet synchronous motor is as follows: ; in, f d and f q These are the total disturbances along the d-axis and q-axis, respectively; Define the current error state function and find its derivative: ; in, , ; and These are the expected currents along the d-axis and q-axis, respectively. e d and e q These are the current errors along the d-axis and q-axis, respectively. Combining the aforementioned fast continuous terminal sliding surface and exponential reaching law, the voltage control laws for the d-axis and q-axis are obtained: ; Among them, h d h q Sliding surfaces s d and s q The coefficient; , It is a real number greater than 0; , This is an equivalent control law.
[0014] Furthermore, the equivalent control law is calculated using the following formula: ; ; Where, q d q q For the coefficient of the exponential term of the exponential convergence law; s d s q For the synovial surface variable; , For the coefficient of the constant-rate term of the exponential approach law.
[0015] Secondly, the present invention also provides a computer terminal, comprising: Memory, which stores executable programs; A processor is configured to run the program, wherein the program executes the method for decoupling continuous terminal sliding mode current of a high-speed motor based on an adaptive observer.
[0016] Thirdly, the present invention also provides a computer-readable storage medium comprising a stored executable program, wherein, when the executable program is executed, it controls the device where the computer-readable storage medium is located to execute the aforementioned method for decoupling continuous terminal sliding mode current of a high-speed motor based on an adaptive observer.
[0017] Fourthly, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned method for decoupling continuous terminal sliding mode current of a high-speed motor based on an adaptive observer.
[0018] Compared with existing technologies, the beneficial effects of this invention are as follows: The Fast Continuous Terminal Sliding Surface (FCTSMC) based on the hyperbolic tangent function adopted in this invention combines the finite-time convergence characteristics of terminal sliding mode with the continuity of the hyperbolic tangent function, overcoming the singularity problem of traditional terminal sliding mode and the slow convergence speed of non-singular terminal sliding mode. This enables the system state to converge to the equilibrium point quickly and accurately, significantly improving the dynamic response performance and steady-state tracking accuracy of the current loop. By replacing the sign function in traditional sliding mode control with a smooth and continuous hyperbolic tangent function, the control output is fundamentally smoothed, greatly reducing the chattering phenomenon of the controller, achieving high-performance continuous smooth control, and reducing switching losses and impact on the actuator. This invention designs an Adaptive Parametric Linear Extended State Observer (AESO), which can accurately observe and estimate the total system disturbance (including parameter changes, unmodeled dynamics, and external disturbances) in real time, and feedforward the estimated value to the control law, effectively eliminating the influence of disturbances on the system, and making the control system highly robust to internal parameter changes and external load disturbances. By using AESO to observe and compensate for cross-coupling terms and disturbances in the d- and q-axis currents in real time, the strong inter-axis coupling effect under high-speed operation is effectively suppressed, achieving high-performance dynamic decoupling control of the d- and q-axis currents and simplifying controller design. The proposed AESO introduces adaptive parameters related to system states (such as current error and electric angular velocity), which can adjust the observer gain online according to the actual operating conditions of the motor. Compared with ESO with fixed parameters, it can maintain better observation accuracy and faster convergence speed under various operating conditions, and has wider adaptability. Attached Figure Description
[0019] To more clearly illustrate the technical solutions in the embodiments of this drawing or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this drawing. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.
[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is an overall block diagram of the method of the present invention; Figure 3 Control performance diagrams for five control methods tracking step speed; Figure 4 The diagram shows the q-axis current response for the five control methods. Figure 5 The diagram shows the d-axis current response for the five control methods. Detailed Implementation
[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments provided by this invention without inventive effort are within the scope of protection of this invention.
[0022] This invention provides a method for decoupling the continuous terminal sliding mode current of a high-speed motor based on an adaptive observer, such as... Figure 1 As shown, the specific steps include the following: S1, Construct a fast continuous terminal sliding surface based on the hyperbolic tangent function for current loop control of permanent magnet synchronous motor; S2, Construct a linear extended state observer based on adaptive parameters to observe the current and disturbances of the d-axis and q-axis of the permanent magnet synchronous motor; S3, feedforward the disturbance values of the d-axis and q-axis observed by the adaptive extended state observer to the voltage control law derived from the fast continuous terminal sliding surface, thereby achieving decoupling and disturbance-resistant control of the dq-axis current.
[0023] The sliding surface used in traditional integral sliding mode control (ISMC) is shown below: (1); Where c is a constant greater than zero; x1 is a state variable, and has .
[0024] When the system state variables converge to the sliding surface, i.e., s I =0, so the above equation (1) can be rewritten as: (2); Integrating both sides of equation (2) above, when the system state variable converges from x0 to a value x(t1) near zero, and we have The convergence time t can be obtained as follows: (3); Where t1 represents the time it takes for the system state variable x to converge to near zero.
[0025] In equation (3) above, if x(t1) approaches zero infinitely, the convergence time will also be extended infinitely. Therefore, the traditional integral sliding surface will cause the system state variables to converge asymptotically to zero in an infinite time.
[0026] Traditional terminal sliding mode control (TSMC) methods employ the following sliding surface: (4); Where r and α are any positive real numbers, and 0 <r<1。
[0027] When s T When = 0, integrating both sides of equation (4) above, we can obtain the convergence time t: (5); As can be seen from the analysis of the above equation (5), increasing α or decreasing r can reduce the convergence time.
[0028] To solve the singularity problem, x1 and x2 in TSMC are interchanged to obtain Non-singular Terminal Sliding Control (NTSMC), whose sliding surface is: (6).
[0029] When s N When = 0, integrating both sides of equation (6) above, we can obtain the convergence time t: (7); Analysis of equation (7) shows that increasing α reduces the convergence time. Compared to equation (3), both equations (5) and (7) converge within a finite time, indicating that the terminal sliding mode control method can make the system state variables converge within a finite time. Observing equations (5) and (7), it can be seen that when the initial state x0 is large, the convergence speed of the system is slow.
[0030] Traditional terminal sliding mode control suffers from singularity issues, while traditional non-singular terminal sliding mode control exhibits slow convergence. To address these problems, this invention proposes a Fast Continuous Terminal Sliding Mode Control (FCTSMC) based on the hyperbolic tangent function. This method solves the non-singularity problem and improves convergence speed. The expression for its sliding surface is shown below: (8); in, x 1 represents the state variable, specifically the error between the reference and feedback values of the dq-axis current; x 2 is x The derivative of 1; ε, λ, and h are real numbers greater than zero, and 0 < ε < 1; STH For sliding surface variables; tanh() is the hyperbolic tangent function; sgn() is a symbolic function.
[0031] When the system state variable converges from x0 to a value x(t1) near zero, and has Integrating both sides of equation (8), we can obtain the convergence time t: (9).
[0032] The FCTSMC proposed in this invention has the following characteristics: 1) Compared with traditional TSMC and NTSMC, the proposed sliding surface enables the system state variables to have a faster convergence speed; 2) The proposed sliding surface has higher convergence accuracy.
[0033] Furthermore, the specific method for designing a current controller for a high-speed permanent magnet synchronous motor is as follows: Assuming the permanent magnet synchronous motor model is in an ideal state, the stator voltage equation can be obtained as follows: (10); The stator flux linkage equation is: (11); when L d = L q = L Combining equations (10) and (11), we can obtain: (12); in, ψ d and ψ q These are the stator flux linkages along the d-axis and q-axis, respectively. u d and u q These are the control input voltages for the d-axis and q-axis, respectively. R is the stator resistance of the motor; i d and i q These are the actual measured currents along the d-axis and q-axis, respectively. oh e Electromagnetic angular velocity; L d L q These are the d-axis and q-axis inductances, respectively. ψ fFor permanent magnet flux linkage in motors.
[0034] Considering parameter variations, surface-mounted permanent magnet synchronous motors ( L d = L q =L The voltage equation for () can be expressed as: (13); (14); Where, Δ L Δ R and Δ ψ System parameters L , R and ψ f The deviation between the actual value and the nominal value; f d and f q These are various external disturbances and unmodeled components; f d1 and f q1 All of these are unknown disturbances.
[0035] Specifically, in the actual system, the motor parameters will change. The actual parameters are the nominal values plus the deviation values. Substituting these into the ideal voltage equation (12), we obtain the actual d-axis and q-axis voltage equations: ; in, and These are the actual control input voltages for the d-axis and q-axis, respectively.
[0036] Expanding the above equation, we divide it into a nominal part and a perturbation part: The nominal portion is: .
[0037] The disturbance part is: .
[0038] Based on the above perturbation part, we obtain equation (14).
[0039] The simplified formula (13) yields: (15); in, , .
[0040] The state function for the current error of a permanent magnet synchronous motor is defined as follows: (16); in, and These are the expected currents along the d-axis and q-axis, respectively. e d and e q These are the current errors along the d-axis and q-axis, respectively.
[0041] Differentiating equation (16) and combining it with equation (15), we get: (17).
[0042] Combining equation (17), and using hyperbolic tangent terminal sliding mode control, the d-axis and q-axis voltage control laws based on the exponential reaching law can be obtained as follows: (18); (19); Among them, h d h q These are the sliding surfaces s d and s q The coefficients, sliding surface sd and sq reference s TH ; q d q q It is the coefficient of the exponential term in the exponential approach law; , It is the coefficient of the constant-rate term of the exponential approach law; , These are parameters, see reference. s TH ; , It is an equivalent control law.
[0043] Specifically, substitute equations (16) and (17) into equation (8), and let s TH =0, resulting in: ; ; F exists in the above formula d F q In order to eliminate F d F q Regarding the impact on the system, the traditional exponential reaching law is introduced to suppress the disturbance F. d F qThe impact of this on improving the current loop control performance, i.e. , Therefore, the above formula can be changed to .
[0044] In equation (17), F d and F q The system contains disturbances such as electronic resistance voltage drop, cross-coupling terms, unmodeled dynamics, and external disturbances. To eliminate the influence of these disturbances, an adaptive parameter extended state observer is used for compensation.
[0045] The adaptive parameter extended state observer (AESO) is designed as follows: Based on equation (16), an extended state observer based on adaptive parameters is constructed, and the expression of the extended state observer is as follows: (20); (twenty one).
[0046] in, and These are the estimated currents along the d-axis and q-axis, respectively. and These are the estimated perturbations along the d-axis and q-axis, respectively. e id and e iq These are the current errors along the d-axis and q-axis, respectively. α 1=2 oh 0, α 2= oh 0, oh 0 represents the current loop bandwidth. α 1 and α 2 is the observer gain parameter.
[0047] To improve the observation accuracy of the extended state observer, this invention designs an adaptive parameter, namely... (twenty two); in, ψ For magnetic linkage; oh e Electromagnetic angular velocity; β belongs to e id or e iq The maximum value in; T is the sampling time.
[0048] like Figure 2 As shown, the working principle of this invention is as follows: First, the actual mechanical angular velocity of the permanent magnet synchronous motor (PMSM) is detected in real time by a sensor and compared with a given reference angular velocity. The resulting speed error is processed by a sliding mode speed controller to generate a reference current signal for the q-axis.
[0049] Subsequently, the reference q-axis current is compared with the actual q-axis current fed back by the current sensor. The resulting current error is input to a Fast Continuous Terminal Sliding Mode Controller (FCTSMC) based on the hyperbolic tangent function for current loop regulation. Simultaneously, an Adaptive Parametric Extended State Observer (AESO) is used to observe and estimate the total disturbances (including parameter variations, coupling terms, and external disturbances) in the d-axis and q-axis currents in real time. The observed q-axis disturbance estimate is used as a feedforward compensation value and combined with the control output of the FCTSMC to finally obtain the q-axis voltage command. The d-axis control flow is similar to that of the q-axis.
[0050] Next, the obtained d-axis and q-axis voltage commands are converted to a stationary two-phase coordinate system through Park inverse transformation, and then synthesized into a space vector pulse width modulation (SVPWM) signal, which is used to drive the inverter power switching device (IGBTInverter) to achieve precise control of the motor stator voltage, and ultimately achieve the purpose of adjusting the motor speed and torque.
[0051] A MATLAB simulation of a permanent magnet synchronous motor was built, and the tracking performance of SMC, TSMC, FCTSMC, FCTSMC+ESO (extended state observer) and the proposed FCTSMC+AESO (adaptive parameter extended state observer) was compared. The parameters of the high-speed permanent magnet synchronous motor are shown in Table 1 below.
[0052] Table 1 Parameters of Permanent Magnet Synchronous Motor
[0053] Figure 3 The control performance diagrams for five control methods tracking a step speed are shown. The reference speed tracked within 1 second is 2000 rpm, and the reference speed tracked after 1 second is 10000 rpm. A step load of 3 N·m is applied at t=1.5s. Figure 3The magnified view shows that when tracking a speed of 2000 rpm, the speed fluctuation of the proposed FCTSMC method is smaller than that of the TSMC and SMC methods. At this point, the speed fluctuation of FCTSMC is ±30 rpm, while the speed fluctuations of the TSMC and SMC methods are both greater than ±40 rpm. Adding a disturbance observer to the FCTSMC method results in even smaller speed fluctuations (±5 rpm) when tracking a speed of 2000 rpm. When tracking a speed of 10000 rpm, the speed fluctuation of the proposed FCTSMC method is also smaller than that of TSMC and SMC. Furthermore, all three methods exhibit overshoot, and the proposed FCTSMC method has a faster response speed than the other two. Both methods with added observers can track the target speed (10000 rpm) without overshoot. However, the speed fluctuation of the proposed FCTSMC+AESO method is smaller than that of the FCTSMC+ESO method. Improving the traditional ESO by replacing it with AESO significantly improves the steady-state accuracy of the speed waveform.
[0054] Figure 4 and Figure 5 These are the d-axis and q-axis current waveforms, respectively. As can be seen from the q-axis current, the proposed FCTSMC+AESO method has the smallest current waveform, whether in the 2000rpm-10000rpm range or after load disturbance. Figure 5 The d-axis current also shows that after an external load disturbance is applied for 1.5 seconds, the proposed FCTSMC+AESO method recovers to zero with the fastest speed and the smallest fluctuation, while the other methods recover more slowly and exhibit larger current fluctuations. This indicates that the method of this invention can effectively suppress cross-coupling problems. Furthermore, the d-axis current error of the proposed method is less than ±0.2A, while the d-axis current error of the other four methods is greater than 0.5A. This demonstrates that the proposed method can effectively suppress disturbances such as parameter changes and external loads in the motor system. The above experiments show that the proposed FCTSMC+AESO method can effectively improve the robustness of the current loop.
[0055] It should be noted that the present invention is not limited to the above-described embodiments. The above embodiments are merely examples, and any embodiments that have the same structure and perform the same effects as the technical concept within the scope of the present invention are included within the scope of the present invention. Furthermore, various modifications that can be conceived by those skilled in the art to the embodiments, and other ways of constructing by combining some of the constituent elements of the embodiments, without departing from the spirit of the present invention, are also included within the scope of the present invention.
Claims
1. A method for decoupling continuous terminal sliding mode current of a high-speed motor based on an adaptive observer, characterized in that, include: S1, Construct a fast continuous terminal sliding surface based on the hyperbolic tangent function for current loop control of permanent magnet synchronous motor; S2, Construct a linear extended state observer based on adaptive parameters to observe the current and disturbances of the d-axis and q-axis of the permanent magnet synchronous motor; S3, feedforward the disturbance values of the d-axis and q-axis observed by the linear extended state observer based on adaptive parameters to the voltage control law derived from the fast continuous terminal sliding surface, thereby achieving decoupling and disturbance-resistant control of the dq-axis current; The derivation process of the voltage control law is as follows: Based on the parameter variations and external disturbances, the voltage equation of a permanent magnet synchronous motor is as follows: ; in, f d and f q These are the total disturbances along the d-axis and q-axis, respectively; u d and u q These are the control input voltages for the d-axis and q-axis, respectively. i d and i q These are the actual measured currents along the d-axis and q-axis, respectively. and They are i d and i q The derivative with respect to time; R is the stator resistance of the motor; ψ f For permanent magnet flux linkage in motors; L is the stator inductance of the motor; ω e Electromagnetic angular velocity; Define the current error state function and find its derivative: ; in, and These are the lumped disturbance terms along the d-axis and q-axis, respectively. , ; and These are the expected currents along the d-axis and q-axis, respectively. and They are and The derivative; e d and e q These are the current errors along the d-axis and q-axis, respectively. and They are e d and e q The derivative; and They are i d and i q The derivative; Combining the aforementioned fast continuous terminal sliding surface and exponential reaching law, the voltage control laws for the d-axis and q-axis are obtained: ; Among them, h d h q These are the d-axis sliding surface variables. s d and q-axis sliding surface variables s q The coefficient; , It is a real number greater than 0; , This is an equivalent control law; ε is a real number greater than zero, and 0 < ε < 1; tanh() is the hyperbolic tangent function; sgn() is a sign function; The equivalent control law is calculated using the following formula: ; ; Where, q d q q For the coefficient of the exponential term of the exponential convergence law; , For the coefficient of the constant-rate term of the exponential approach law.
2. The high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer as described in claim 1, characterized in that, The expression for the fast continuous terminal sliding surface is: ; in, x 1 represents a state variable; x 2 is x The derivative of 1; λ and h are real numbers greater than zero; S TH For the sliding surface variable.
3. The high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer as described in claim 2, characterized in that, The convergence time of the fast continuous terminal sliding surface is determined by the following process: When S TH =0, the system state variable will converge from x0 to a value x(t1) near zero, and has Integrating both sides of the expression for the fast continuous terminal sliding surface, the convergence time t of the fast continuous terminal sliding surface is obtained: ; Where x0 is the state variable x The initial value of 1.
4. The high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer as described in claim 1, characterized in that, The construction process of the linear extended state observer based on adaptive parameters is as follows: Establish a traditional linear extended state observer: ; ; in, and These are the estimated currents along the d-axis and q-axis, respectively. and These are the estimated perturbations along the d-axis and q-axis, respectively. e id and e iq These are the current errors along the d-axis and q-axis, respectively. α 1 and α 2 is the observer gain parameter. α 1=2 ω 0, α 2= ω 0; Introducing adaptive parameters to adjust the observer gain parameters online: ; in, ψ For magnetic linkage; ω 0 represents the current loop bandwidth; β take e id and e iq The maximum value in; T is the sampling time.
5. The high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer as described in claim 1, characterized in that, The voltage equation of the permanent magnet synchronous motor under ideal conditions is: 。