High-speed motor continuous terminal sliding mode current decoupling method based on adaptive observer

Abstract

The invention discloses a high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer, and belongs to the technical field of motor control. The method comprises the following steps: constructing a rapid continuous terminal sliding mode surface based on a hyperbolic tangent function for permanent magnet synchronous motor current loop control so as to improve the convergence speed and suppress buffeting; a linear expansion state observer based on adaptive parameters is designed, and d-axis and q-axis currents and total disturbance are accurately observed in real time; and performing feedforward compensation on the observed disturbance value to a voltage control law derived from the sliding mode surface. The method effectively solves the problems that a traditional control method is slow in convergence, large in buffeting, weak in anti-interference capacity and incomplete in decoupling, and the dynamic response speed, control precision and robustness of the system under parameter change and external disturbance are remarkably improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of motor control, in particular to a high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer. BACKGROUND

[0002] High-speed permanent magnet synchronous motor (HPMSM) systems have broad application prospects in high-end driving equipment application fields such as aerospace, high-speed machine tool flywheel energy storage, distributed power generation, natural gas exploration and transportation, vacuum ion pumps and the like due to the advantages of small size, high power density and high integration. At present, the magnetic field oriented control technology is widely used in the HPMSM system, and the proportional integral (PI) control is generally adopted. Because the PI control method has simple structure and is easy to implement, it has become the mainstream method of motor control. However, in the actual HPMSM application, the motor parameter changes and uncertain disturbances caused by external environment changes will affect the control performance of the motor system, and if only linear control such as PI control is adopted, it is difficult to meet the application of HPMSM in high-performance occasions.

[0003] In order to meet the high-performance application of HPMSM, many nonlinear control methods have been proposed by domestic and foreign scholars, such as adaptive control, fuzzy control, predictive control, sliding mode control (SMC) and the like. Due to the large-scale application of digital signal processors, the SMC with discontinuous high-frequency switching terms is outstanding among these nonlinear control methods due to its strong anti-interference ability and insensitivity to system uncertainty.

[0004] The traditional integral sliding mode control method adopts a linear sliding mode surface, and this method has few parameters and is easy to implement, but when tracking a larger step value, it is easy to produce a larger overshoot, and the convergence speed is slow; the traditional terminal sliding mode control method has a faster response speed, but when the system state passes through the zero point, singularity will be caused, thereby reducing the system tracking accuracy; the non-singular terminal sliding mode control sacrifices the response speed to solve the singularity problem. Therefore, in order to improve the tracking accuracy, response speed and anti-interference performance of the current loop of the permanent magnet synchronous motor, an advanced control method needs to be sought to realize the fast and high-precision response of the permanent magnet synchronous motor under the interference condition.

[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] Further, the convergence time of the fast continuous terminal sliding mode surface is determined by the following procedure: When S TH = 0, the system variable will converge from x0 to a value x(t1) near zero, and has Integrate both sides of the expression of the fast continuous terminal sliding mode surface to obtain the convergence time t of the fast continuous terminal sliding mode surface: .

[0010] Further, the construction process of the linear extended state observer based on adaptive parameters is as follows: Establish a traditional linear extended state observer: ; ; Where, and are the estimated currents of the d-axis and q-axis, respectively; i d and i q are the actual measured currents of the d-axis and q-axis, respectively; u d and u q are the control input voltages of the d-axis and q-axis, respectively; and are the estimated disturbances of the d-axis and q-axis, respectively; e id and e iq are the current errors of the d-axis and q-axis, respectively; α 1 and α 2 are observer gain parameters; Introduce adaptive parameters to adjust the observer parameters online: ; Where, Ψ is the flux linkage; ω 0 is the current loop bandwidth; ω e is the electromagnetic angular velocity; β belongs to e id or e iq the maximum value in; T is the sampling time.

[0011] Further, the observer gain parameters α 1and α 2are set as: α 1=2 ω 0, α 2= ω 0.

[0012] Further, the voltage equation of the permanent magnet synchronous motor in the ideal state is: ; wherein R is the motor stator resistance; Ψ f is the motor permanent magnet flux linkage; L is the motor stator inductance.

[0013] Further, the derivation process of the voltage control law is as follows: According to the permanent magnet synchronous motor under the condition of parameter change and external disturbance, the voltage equation of the permanent magnet synchronous motor is: ; wherein, f d and f q are the total disturbances of the d-axis and the q-axis respectively; Define the current error state function and derive it: ; wherein, , ; and are the expected currents of the d-axis and the q-axis respectively; e d and e q are the current errors of the d-axis and the q-axis respectively; Combined with the fast continuous terminal sliding mode surface and the exponential reaching law, the voltage control law of the d-axis and the q-axis is obtained: ; wherein h d , h q are the coefficients of the sliding mode surface s d and s q ; , are real numbers greater than 0; 、 is an equivalent control law.

[0014] Further, the equivalent control law is calculated by the following formula: ; ; wherein q d , q q is an exponential term coefficient of an exponential reaching law; s d , s q is a sliding surface variable; 、 is an equal speed term coefficient of an exponential reaching law.

[0015] In a second aspect, the present application further provides a computer terminal, comprising: a memory storing an executable program; a processor configured to run the program, wherein the program, when running, performs the method for continuous terminal sliding mode current decoupling of high-speed motor based on an adaptive observer.

[0016] In a third aspect, the present application further provides a computer readable storage medium, comprising a stored executable program, wherein the executable program, when running, controls a device where the computer readable storage medium is located to perform the method for continuous terminal sliding mode current decoupling of high-speed motor based on an adaptive observer.

[0017] In a fourth aspect, the present application further provides a computer program product, comprising a computer program, wherein the computer program, when executed by a processor, implements the method for continuous terminal sliding mode current decoupling of high-speed motor based on an adaptive observer.

[0018] Compared with the prior art, the present application has the beneficial effects that: the fast continuous terminal sliding mode surface (FCTSMC) based on the hyperbolic tangent function adopted by the present application has the finite time convergence characteristics of the terminal sliding mode and the continuity of the hyperbolic tangent function, overcomes the singularity problem of the traditional terminal sliding mode and the slow convergence speed of the non-singular terminal sliding mode, enables the system state to quickly and accurately converge to the equilibrium point, and significantly improves the dynamic response performance and steady-state tracking accuracy of the current loop. By using the smooth and continuous hyperbolic tangent function to replace the sign function in the traditional sliding mode control, the control output is fundamentally smoothed, the chattering phenomenon of the controller is greatly weakened, high-performance continuous smooth control is achieved, and the switching loss and impact on the actuator are reduced. The present application designs an adaptive parameter linear extended state observer (AESO) which can accurately observe and estimate the total disturbance of the system (including parameter variation, unmodeled dynamics and external disturbance) in real time, and feed forward the estimated value to the control law, effectively eliminating the influence of the disturbance on the system, so that the control system has strong robustness to internal parameter variation and external load disturbance. Through the real-time observation and compensation of the cross-coupling term in the d-q axis current and the disturbance by the AESO, the strong inter-axis coupling effect under high-speed operation is effectively suppressed, high-performance dynamic decoupling control of the d-axis and q-axis currents is achieved, and the controller design is simplified. The proposed AESO introduces adaptive parameters related to the system state (such as current error and electric angular velocity), which can adjust the observer gain online according to the actual operating conditions of the motor, and compared with the ESO with fixed parameters, it can maintain better observation accuracy and faster convergence speed under various operating conditions, and has wider adaptability. BRIEF DESCRIPTION OF DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments or the prior art, the drawings needed in the following embodiment or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the drawings, and other drawings can be obtained by those skilled in the art without creative labor.

[0020] Figure 1 The method flowchart of the present application; Figure 2 The overall block diagram of the method of the present application; Figure 3 The control performance graph of five control methods tracking step speed; Figure 4 The q-axis current response graph corresponding to the five control methods; Figure 5 The d-axis current response graph corresponding to the five control methods. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is described and explained below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. Based on the examples provided by the present application, all other examples obtained by those of ordinary skill in the art without creative labor fall within the scope of the present application.

[0022] The present application provides a high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer, as shown in Figure 1 The method specifically comprises the following steps: S1, constructing a fast continuous terminal sliding mode surface based on a hyperbolic tangent function, for permanent magnet synchronous motor current loop control; S2, constructing a linear extended state observer based on adaptive parameters, for observing the d-axis and q-axis currents and disturbances of the permanent magnet synchronous motor; S3, feeding forward the d-axis and q-axis disturbance values observed by the adaptive extended state observer to the voltage control law derived by the fast continuous terminal sliding mode surface, to realize decoupling and anti-disturbance control of the d-q axis currents.

[0023] The sliding surface used by the traditional integral sliding mode control (ISMC) is as follows: (1); Wherein, c is a constant greater than zero; x1 is a state variable, and has .

[0024] When the system state variable converges to the sliding surface, i.e. s I =0, the above formula (1) is rewritten as: (2); Taking the integral of both sides of the above formula (2), when the system state variable converges from x0 to a value x(t1) near zero, and has , the convergence time t can be obtained: (3); Wherein, t1 represents the time when the system state variable x converges to the vicinity of zero.

[0025] In the above formula (3), if x(t1) is infinitely close to zero, the convergence time will also be infinitely extended. Therefore, the traditional integral sliding surface will make the system state variable asymptotically converge 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 is the sliding surface variable; tanh() is the hyperbolic tangent function; sgn() is the sign function.

[0031] When the system state variable will converge from x0 to the value x(t1) near zero, and there is , the convergence time t of the two sides of formula (8) can be obtained by integration: (9).

[0032] The FCTSMC proposed in the application has the following characteristics: 1) compared with the traditional TSMC and NTSMC, the sliding surface proposed will make the system state variable have a faster convergence speed; 2) the sliding surface has higher convergence accuracy.

[0033] Further, the specific method of designing the high-speed permanent magnet synchronous motor current controller is as follows: Suppose the permanent magnet synchronous motor model is in an ideal state, and the stator voltage equation is obtained as: (10); The stator flux equation is: (11); When L d = L q = L , combined with formula (10) and formula (11), we have: (12); where, Ψ d and Ψ q are the d-axis and q-axis stator fluxes, respectively; u d and u q are the d-axis and q-axis control input voltages, respectively; R is the motor stator resistance; i d and i q are the d-axis and q-axis actual measured currents, respectively; ω e is the electromagnetic angular velocity; L d , L q are the d-axis and q-axis inductances, respectively; Ψ fFor the motor permanent magnet flux linkage.

[0034] The voltage equation of surface-mounted permanent magnet synchronous motor (PMSM) considering parameter variation can be expressed as: L d = L q =L (13); (14); Where, Δ L , Δ R and Δ Ψ are the deviations between the actual values and the nominal values of the system parameters L , R and Ψ f f d and f q are various external disturbances and unmodeled parts, respectively; f d1 and f q1 are unknown disturbances.

[0035] Specifically, in the actual system, the motor parameters will change, and the actual parameters are the nominal values plus the deviation values, which are brought into the ideal voltage equation (12) to obtain the actual d-axis and q-axis voltage equations: ; Where, and are the actual control input voltages of the d-axis and q-axis, respectively.

[0036] The above equation is expanded and grouped into the nominal part and the disturbance part: The nominal part is: .

[0037] The disturbance part is: .

[0038] Based on the above disturbance part, equation (14) is obtained.

[0039] Simplifying equation (13) gives: (15); Where, , .

[0040] Define the state function of the current error of the permanent magnet synchronous motor as: ​​ (16); where, and are the desired currents of d-axis and q-axis, respectively; e d and e q are the current errors of d-axis and q-axis, respectively.

[0041] Taking the derivative of equation (16) and combining equation (15), we have (17).

[0042] Combining equation (17), the d-axis and q-axis voltage control laws based on exponential reaching law can be obtained by using hyperbolic tangent terminal sliding mode control as (18); (19); where, h d , h q are the coefficients of sliding surface s d and s q , the sliding surfaces sdand sqrefer to s TH ; q d , q q are the exponential term coefficients of exponential reaching law; , are the constant term coefficients of exponential reaching law; , are the parameters, the references s TH ; , are the equivalent control laws.

[0043] Specifically, equation (16) and equation (17) are brought into equation (8), and s TH =0 is set, so we have ; ; There are F d , F q in the above equation. In order to eliminate the influence of F d , F q on the system, the traditional exponential reaching law is introduced to suppress the disturbance F d , F qThe influence of the current loop control performance, namely 、 Therefore, the above formula can be changed to .

[0044] In formula (17), F d And F q There are electronic resistance voltage drops, cross-coupling terms, unmodeled dynamics, and external disturbances, etc. In order to eliminate the influence of the above disturbances, an adaptive parameter extended state observer is used for compensation.

[0045] The adaptive parameter extended state observer AESO is designed as follows: According to formula (16), an adaptive parameter based extended state observer is constructed, and the expression of the extended state observer is as follows: (20); (21).

[0046] Wherein, And The estimated current of the d-axis and the q-axis respectively; And The estimated disturbance of the d-axis and the q-axis respectively; e id And e iq The current error of the d-axis and the q-axis respectively; α 1=2 ω 0, α 2= ω 0, ω 0 is the current loop bandwidth, α 1 and α 2 are observer gain parameters.

[0047] In order to improve the observation accuracy of the extended state observer, the application designs an adaptive parameter, that is (22); Wherein, Ψ The flux linkage; ω e The electromagnetic angular velocity; Beta belongs to e id Or e iq The maximum value in T is the sampling time.

[0048] As Figure 2 shown, the working principle of the application is as follows: First, the actual mechanical angular velocity of the permanent magnet synchronous motor (PMSM) is detected in real time by the sensor, which is compared with the given reference angular velocity, and the obtained speed error is processed by the sliding mode speed controller to generate the reference current signal of the q axis.

[0049] Subsequently, the above-mentioned reference q-axis current is compared with the actual q-axis current fed back by the current sensor, and the obtained current error is input into the fast continuous terminal sliding mode controller (FCTSMC) based on the hyperbolic tangent function for current loop adjustment. At the same time, the adaptive parameter extended state observer (AESO) is used to observe and estimate the total disturbance (including parameter variation, coupling term and external disturbance) in the d-axis and q-axis currents in real time. The estimated value of the q-axis disturbance obtained by observation is used as a feedforward compensation, and the control amount output by the FCTSMC is integrated, and finally the q-axis voltage command is obtained. The d-axis control process is the same as the q-axis.

[0050] Next, the obtained d-axis and q-axis voltage commands are converted to the stationary two-phase coordinate system by Park inverse transformation, and then synthesized into space vector pulse width modulation (SVPWM) signals for driving the inverter power switching device (IGBT Inverter), realizing accurate control of the motor stator voltage, and finally achieving the purpose of regulating the motor speed and torque.

[0051] The permanent magnet synchronous motor MATLAB simulation is built, and the tracking performance of SMC, TSMC, FCTSMC, FCTSMC+ESO (extended state observer) and the proposed FCTSMC+AESO (adaptive parameter extended state observer) is compared. The parameters of the high-speed permanent magnet synchronous motor are shown in Table 1.

[0052] Table 1 Permanent magnet synchronous motor parameters

[0053] Figure 3 The control performance chart for tracking step speed for five control methods, the reference speed tracked within 1s is 2000rpm, the reference speed tracked after 1s is 10000rpm, and a step load of 3N·m is applied at t=1.5s. From Figure 3It can be seen from the partial enlarged view in that the speed fluctuation of the proposed FCTSMC method is smaller than that of the TSMC and SMC methods when tracking the speed of 2000 rpm, and the speed fluctuation of the FCTSMC is ± 30 rpm, while the speed fluctuation of the TSMC and SMC methods is greater than ± 40 rpm. When the disturbance observer is added to the FCTSMC method, the speed waveform tracked at 2000 rpm presents a smaller speed fluctuation (± 5 rpm). When tracking the speed of 10000 rpm, the speed fluctuation of the proposed FCTSMC method is also smaller than that of the TSMC and SMC, and the above three methods all have overshoot, and the response speed of the proposed FCTSMC method is faster than that of the above two methods. The two methods of adding the observer 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, and after improving the traditional ESO to AESO, the steady-state accuracy of the speed waveform is obviously improved.

[0054] Figure 4 and Figure 5 It can be seen from the q-axis current that the proposed FCTSMC+AESO method has the smallest current waveform whether in the 2000 rpm-10000 rpm stage or after the load disturbance. Figure 5 It can also be seen from the d-axis current in that after the external load disturbance is applied at 1.5 s, the proposed FCTSMC+AESO method recovers to zero at the fastest speed and with the smallest fluctuation, while the recovery of the other methods is slower and has a larger current fluctuation, which shows that the method of the application can better suppress the cross-coupling problem; in addition, the d-axis current error of the proposed method is less than ± 0.2 A, while the d-axis current error of the other four methods is greater than 0.5 A, which shows that the proposed method can effectively suppress the disturbances such as parameter changes in the motor system and external load. The above test shows that the proposed FCTSMC+AESO method can effectively improve the robustness of the current loop.

[0055] It should be noted that the application is not limited to the above embodiments. The above embodiments are only examples, and embodiments having the same technical idea and playing the same role within the scope of the technical solutions of the application are all included in the technical scope of the application. In addition, within the scope of the main idea of the application, various modifications that can be thought of by those skilled in the art, and other ways constructed by combining part of the components in the embodiments are also included in the scope of the application.

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 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.

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; 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.

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: 。 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. 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; ω 0 represents the current loop bandwidth; ω e Electromagnetic angular velocity; β belongs to e id or 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 4, characterized in that, The observer gain parameter α 1 and α 2 is set as: α 1=2 ω 0， α 2= ω 0。 6. 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: ； 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.

7. 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 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 desired 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.

8. The high-speed motor continuous terminal sliding mode current decoupling method based on an adaptive observer as described in claim 7, characterized in that, 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.

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