Enhanced active disturbance rejection control method and stability analysis method of adaptive extended state observer for permanent magnet linear motor

Abstract

This invention provides an enhanced active disturbance rejection control (ADRC) method and its stability analysis method for an adaptive extended state observer (AESO) for permanent magnet linear motors, belonging to the field of high-performance control technology for permanent magnet linear motors. The enhanced ADRC method includes: Step S1, establishing a kinematic model based on the electromagnetic parameters of the permanent magnet linear motor; Step S2, calculating the integral sliding mode control surface based on the kinematic model, and calculating the final sliding mode control law based on the kinematic model and the integral sliding mode control surface; Step S3, obtaining the total disturbance estimate based on the structure of the LESO, and then calculating the bandwidth adaptive law to obtain the adaptive extended state observer (AESO) based on the bandwidth adaptive law; Step S4, realizing enhanced ADRC for the permanent magnet linear motor based on the final sliding mode control law and the AESO. This invention effectively solves the problems of high-speed tracking performance and anti-interference performance, achieving two-degree-of-freedom control of speed loop speed and disturbance rejection.

Description

Technical Field

[0001] This invention belongs to the field of high-performance control technology for permanent magnet linear motors, and specifically relates to an enhanced active disturbance rejection control method and its stability analysis method for an adaptive extended state observer used in permanent magnet linear motors. Background Technology

[0002] The Linear Flux-switching Permanent Magnet Motor (LFSPM) has its permanent magnets and armature windings located on the primary side, while the secondary side consists only of magnetically conductive silicon steel laminations. It has the advantages of high thrust density and high efficiency, as well as simple structure and low secondary cost, which makes LFSPM uniquely advantageous for long-stroke applications in rail transit.

[0003] However, due to the direct drive structure, load disturbances and parameter disturbances are directly applied to the mover of the LFSPM, causing a significant decrease or increase in speed. Furthermore, in practical applications, the motor parameters constantly change due to the continuous variation in the air gap within the LFSPM. In traditional speed control systems based on proportional-integral (PI) controllers, high-speed tracking performance and anti-interference performance cannot be simultaneously achieved. Summary of the Invention

[0004] The purpose of this invention is to provide an enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor, which addresses the issues of high-speed tracking performance and anti-interference performance.

[0005] A first aspect of the present invention provides an enhanced active disturbance rejection control method for an adaptive extended state observer (AESO) for a permanent magnet linear motor. The enhanced AESO method includes: step S1, establishing a kinematic model of the permanent magnet linear motor based on its electromagnetic parameters; step S2, calculating an integral sliding mode control surface based on the kinematic model, and calculating a final sliding mode control law based on the kinematic model and the integral sliding mode control surface; step S3, obtaining a total disturbance estimate based on the structure of the linear extended state observer (LESO), and calculating a bandwidth adaptive law based on the total disturbance estimate to obtain an adaptive extended state observer (AESO) based on the bandwidth adaptive law; and step S4, implementing enhanced AESO for the permanent magnet linear motor based on the final sliding mode control law and the adaptive extended state observer (AESO).

[0006] A second aspect of the present invention provides a stability analysis method for enhanced active disturbance rejection control (ADRC) of an adaptive extended state observer for a permanent magnet linear motor. This method is used to perform stability analysis on the enhanced ADRC method for an adaptive extended state observer for a permanent magnet linear motor provided by the present invention. The stability analysis method includes: step S5, constructing a Lyapunov function based on an integral sliding mode surface, and determining the stability of the integral sliding mode control based on the constructed Lyapunov function; step S6, obtaining the characteristic equation of the extended state observer ESO in the discrete complex frequency domain based on the structure of the linear extended state observer LESO and the integral sliding mode control surface; and step S7, determining the bandwidth stability of the adaptive extended state observer AESO in the discrete complex frequency domain based on the characteristic equation of the extended state observer ESO in the discrete complex frequency domain and the Juli stability criterion.

[0007] The beneficial effects of this invention are as follows:

[0008] This invention relates to an enhanced active disturbance rejection control method for an adaptive extended state observer used in permanent magnet linear motors (LFSPMs). Based on the kinematic model of LFSPMs, a mathematical model of an enhanced adaptive active disturbance rejection controller with strong anti-interference capability and bandwidth adaptation is established, effectively solving the problems of high-speed tracking performance and anti-interference performance. Stability analysis reveals that the enhanced active disturbance rejection controller (EAADRC) with improved adaptive extended state observer provided by this invention has excellent dynamic performance and anti-interference capability, achieving two-degree-of-freedom control of speed loop speed and disturbance rejection. Attached Figure Description

[0009] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0010] Figure 1 This is a flowchart of the enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor provided by the present invention;

[0011] Figure 2 This invention provides the relationship between bandwidth and low-pass filtering under different ξ values;

[0012] Figure 3 This is the overall control block diagram of the LFSPM system using the EAADRC scheme provided by the present invention;

[0013] Figure 4(a) shows the motor speed tracking under PI control when the trapezoidal speed is 0.5 m / s, as provided by the present invention.

[0014] Figure 4(b) shows the speed tracking error of the motor under PI control when the trapezoidal speed is 0.5 m / s, as provided by the present invention.

[0015] Figure 4(c) shows the motor speed tracking under LADRC control when the trapezoidal speed is 0.5 m / s, as provided by the present invention.

[0016] Figure 4(d) shows the speed tracking error of the motor under LADRC control when the trapezoidal speed is 0.5 m / s, as provided by the present invention.

[0017] Figure 4(e) shows the motor speed tracking under EAADRC control when the trapezoidal speed is 0.5 m / s, as provided by the present invention.

[0018] Figure 4(f) shows the speed tracking error of the motor under EAADRC control when the trapezoidal speed is 0.5 m / s, as provided by the present invention.

[0019] Figure 5(a) shows the motor speed tracking under PI control when the trapezoidal speed is 1.0 m / s, as provided by the present invention.

[0020] Figure 5(b) shows the speed tracking error of the motor under PI control when the trapezoidal speed is 1.0 m / s, as provided by the present invention.

[0021] Figure 5(c) shows the motor speed tracking under LADRC control when the trapezoidal speed is 1.0 m / s, as provided by the present invention.

[0022] Figure 5(d) shows the tracking error of the motor under LADRC control when the trapezoidal speed is 1.0 m / s, as provided by the present invention.

[0023] Figure 5(e) shows the motor speed tracking under EAADRC control when the trapezoidal speed is 1.0 m / s, as provided by the present invention.

[0024] Figure 5(f) shows the speed tracking error of the motor under EAADRC control when the trapezoidal speed is 1.0 m / s, as provided by the present invention.

[0025] Figure 6(a) shows the motor speed tracking under PI control when the trapezoidal speed is 1.5 m / s, as provided by the present invention.

[0026] Figure 6(b) shows the speed tracking error of the motor under PI control when the trapezoidal speed is 1.5 m / s, as provided by the present invention.

[0027] Figure 6(c) shows the motor speed tracking under LADRC control when the trapezoidal speed is 1.5 m / s, as provided by the present invention.

[0028] Figure 6(d) shows the speed tracking error of the motor under LADRC control when the trapezoidal speed is 1.5 m / s, as provided by the present invention.

[0029] Figure 6(e) shows the motor speed tracking under EAADRC control when the trapezoidal speed is 1.5 m / s, as provided by the present invention.

[0030] Figure 6(f) shows the speed tracking error of the motor under EAADRC control when the trapezoidal speed is 1.5 m / s, as provided by the present invention.

[0031] Figure 7 This is the real-time bandwidth adjustment waveform of the adaptive law provided by the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail 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. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0033] This invention aims to simultaneously achieve high-speed tracking performance and anti-interference capability in permanent magnet linear motors (e.g., linear flux-switched permanent magnet motors). It investigates the influence of nonlinear factors such as cogging force, end force, parameter variations, and external disturbances on the motor's operational stability, proposing an enhanced adaptive active disturbance rejection controller (EAADRC) with strong anti-interference capability and bandwidth adaptation. First, a robust integral sliding mode control (ISMC) law is used to construct the EADRC, improving the system's dynamic tracking performance. Second, due to the complex disturbances present during LFSPM motion, an improved adaptive extended state observer (AESO) is proposed. This AESO adjusts the control bandwidth in real time based on estimation error feedback to achieve a balance between disturbance estimation and noise reduction. Then, the stability of the proposed EAADRC is analyzed using the Jury stability criterion and the Lyapunov method. Experimental results show that the EAADRC possesses excellent dynamic performance and anti-interference capability, achieving two-degree-of-freedom control with both high speed and disturbance rejection in the speed loop.

[0034] This invention provides an enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor. The permanent magnet linear motor in this invention can be a linear flux-switching permanent magnet motor (LFSPM). Figure 1 This is a flowchart of the enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor provided by the present invention, as shown below. Figure 1 As shown, the enhanced active disturbance rejection control method includes:

[0035] Step S1: Based on the electromagnetic parameters of the permanent magnet linear motor, establish the kinematic model of the permanent magnet linear motor. The permanent magnet linear motor can be considered as a rigid body model, and the resonant modes can be ignored to establish a mathematical model of the permanent magnet linear motor.

[0036] Step S2 involves calculating the integral sliding mode control surface based on the kinematic model, and then calculating the final sliding mode control law based on the kinematic model and the integral sliding mode control surface. The integral sliding mode control surface is used to suppress system chattering and improve convergence accuracy, thereby improving the dynamic performance of the system.

[0037] Step S3: Obtain the total disturbance estimate based on the structure of the Linear Extended State Observer (LESO). Calculate the bandwidth adaptive law based on the total disturbance estimate to obtain the Adaptive Extended State Observer (AESO) based on the bandwidth adaptive law. This bandwidth adaptive law ensures accurate total disturbance estimation for the permanent magnet linear motor under different operating conditions. The Adaptive Extended State Observer (AESO) combines the Linear Extended State Observer (LESO) and the bandwidth adaptive law.

[0038] Step S4: Based on the final sliding mode control law and the adaptive extended state observer AESO, the enhanced active disturbance rejection control of the permanent magnet linear motor is realized.

[0039] The permanent magnet linear motor in this invention is a linear flux-switching permanent magnet motor, more specifically, it adopts the structure of a 12 / 13-pole linear flux-switching permanent magnet motor (LFSPM). The mover is composed of multiple silicon steel laminations, with permanent magnets of opposite magnetization directions embedded in the gaps between adjacent laminations. The non-overlapping coils of the permanent magnet linear motor are wound around a pair of primary teeth and permanent magnets. The stator of the permanent magnet linear motor is composed of stacked silicon steel laminations. Due to its unique structure, the LFSPM has the advantages of high efficiency and low cost, exhibiting unique performance in long-stroke direct-drive linear motion fields such as rail transit.

[0040] Step S1 includes:

[0041] Electromagnetic thrust of permanent magnet linear motor on dq axis The calculation is as follows:

[0042] (1)

[0043] In formula (1), ψ is the stator pole pitch of a permanent magnet linear motor. f It is a permanent magnet flux linkage. It is the d-axis current. It is the q-axis current, L d It is the d-axis inductance, L q It is a q-axis inductor.

[0044] The motion equation of the mover of a permanent magnet linear motor is as follows:

[0045] (2)

[0046] In formula (2), M is the mass of the moving part, B is the coefficient of friction, and F is the mass of the moving part. L For load capacity, Let F be the velocity of the mover, t be time, and F be the velocity of the mover. d This refers to thrust fluctuation disturbances caused by end effects.

[0047] Treating the permanent magnet linear motor as a rigid body model, the motion equation of the permanent magnet linear motor is simplified to a second-order kinematic model as follows:

[0048] (3)

[0049] In formula (3), Let be the derivative of the mover velocity, and u be the control signal. For the control gain estimate, b0=k f / M,k f Let d(v) be the thrust coefficient, M be the mover mass, ω(t) be the external disturbance, and d(v) be the thrust coefficient. s ω(t),t) represents the total disturbance of the permanent magnet linear motor.

[0050] The LFSPM control system is based on a Linear Active Disturbance Rejection Controller (LADRC). The LADRC consists of a Tracking Differentiator (TD), an Extended State Observer (ESO), and a State Error Feedback (SEF) control law. Because... It is a smooth curve, so tracking the differentiator TD is unnecessary.

[0051] The LFSPM system is a first-order system. Therefore, the structure of the Linear Extended State Observer (LESO) is as follows:

[0052] (4)

[0053] In formula (4), It is the velocity of the mover. Compared with the observed values ​​of the moving part velocity The error between them is given by l1, where l1 is the state observation error feedback gain and l2 is the disturbance observation error feedback gain. This is the estimated total disturbance.

[0054] The control signal design is as follows:

[0055] (5)

[0056] in, The output control signal is for the Linear Active Disturbance Rejection Controller (LADRC). K is the integral variable. p K is the proportional parameter of the Linear State Error Feedback (LSEF). i It is the integration parameter. It is a time integral variable. In the time integral variable The error between the lower mover velocity and the observed mover velocity.

[0057] The structural expression of formula (4) LESO is rewritten in matrix form:

[0058] (6)

[0059] In formula (6), Let LESO be the state vector. , , , , , , for The derivative, Includes mover velocity estimates Total disturbance estimate , The observable for the linearly extended state observer LESO, namely the mover velocity. That is, the actual value of the mover velocity; This is the input to the linearly extended state observer LESO, i.e. Shaft current reference value , This is to control the gain coefficient.

[0060] To simplify the parameter tuning process and reduce the number of parameters, pole configuration is described as follows:

[0061] (7)

[0062] In formula (7), It is the determinant of a matrix. For the Laplace operator, for The identity matrix, ω0 is the bandwidth of the linearly extended state observer LESO.

[0063] The gain is configured as follows:

[0064] (8)

[0065] Compared to LADRC, EAADRC adds two components. First, it employs a robust integral sliding mode control (ISMC) law to construct the EADRC (Enhanced Active Disturbance Rejection Controller), improving the system's dynamic performance. Second, it improves the adaptive law of AESO based on the rate of change of the estimated disturbance derivative.

[0066] To improve the dynamic performance of the system, the discontinuous switching term in ISMC can generate rapid and strong control actions, thereby immediately compensating for deviations caused by sudden disturbances, which is something that traditional LSEF cannot provide. Furthermore, ISMC exhibits strong robustness to system parameter variations and external uncertainties, thus enhancing overall anti-interference capability.

[0067] Step S2 includes:

[0068] The integral sliding mode control surface calculated based on the kinematic model is as follows:

[0069] (9)

[0070] In formula (9), It is the integral sliding mode control surface for speed tracking error. It is the integral sliding mode control surface The derivative, It is a preset speed reference value. c1 is the derivative of the speed reference value, c2 is the weighting coefficient of the error term, and c2 is the weighting coefficient of the error integral term. This is the actual operating speed of the permanent magnet linear motor. It is a time integral variable. In the time integral variable The speed reference value is set below. The sliding mode convergence rate is chosen as an exponential rate. Because chattering can occur in sliding mode control, the sign function... Saturated function Replaced, saturation function It can be defined as follows:

[0071] (10)

[0072] In formula (10), It is the boundary layer value of the saturation function. .

[0073] Based on the kinematic model and integral sliding mode control surface, including equations (1), (2), (3), (9) and (10), the final sliding mode control law is calculated as follows:

[0074] (11)

[0075] In formula (11), It is the output of integral sliding mode control. It is the gain of the switching item. It is the derivative of the speed reference value. is the total disturbance estimate, and k1 is the gain of the exponential term.

[0076] Based on the derivative of the observed disturbance, a novel adaptive law is proposed. Specifically, the faster the disturbance changes, the larger the bandwidth. Therefore, step S3 includes:

[0077] The bandwidth adaptive law is calculated as follows:

[0078] (12)

[0079] In formula (12), This refers to the bandwidth of the Adaptive State Observer (AESO), which should be understood. This is the instantaneous calculated value of the adaptively adjusted observer bandwidth. It is an adaptive adjustment of the intensity coefficient. It is a characteristic quantity of the normalized rate of change of disturbance. It is an exponential function with base e, used to construct a hyperbolic tangent bandwidth adjustment curve, ensuring that bandwidth changes are smooth and bounded. It is the bandwidth of the Adaptive State Observer (AESO). The lower limit, It is the bandwidth of the Adaptive State Observer (AESO). The upper limit of ξ, where ξ is a positive coefficient. It is the derivative of the total disturbance estimate after passing through a low-pass filter. It is the derivative of the total disturbance estimate.

[0080] As can be seen from formula (12), the bandwidth of AESO is adjusted in real time according to the change of the total disturbance estimate. When the estimation error is relatively large during the acceleration process of the permanent magnet linear motor, the bandwidth of AESO is relatively high, which ensures fast convergence. Under steady state, the bandwidth of AESO is relatively low, thus reducing noise sensitivity. AESO is suitable for nonlinear systems with both model uncertainty and random noise.

[0081] When ω 0min =20、ω 0max =80, Follow The changing curve is as follows Figure 2 As shown, Figure 2 This invention provides the relationship between bandwidth and low-pass filtering under different ξ values. Figure 2 It can be seen that the larger the value of ξ, The faster the response to changes in disturbances, the better. However, if ξ is too large, It may be sensitive to noise, which may lead to inaccurate bandwidth changes. In the experiment, ξ=0.1 can be selected.

[0082] This invention analyzes the stability of EAADRC using the Jury stability criterion and the Lyapunov stability criterion. Experiments compare the control effects of PID, LADRC, and EAADRC, including the proposed EAADRC control strategy consisting of AESO and ISMC. First, based on the selected integral sliding surface, a Lyapunov function is constructed to prove the stability of ISMC. Second, from the discrete complex frequency domain, the stability of AESO is proven using the Jury stability criterion.

[0083] Accordingly, the present invention also provides a stability analysis method for enhanced active disturbance rejection control (ADRC) of an adaptive extended state observer for a permanent magnet linear motor, used to perform stability analysis on the enhanced ADRC method for an adaptive extended state observer for a permanent magnet linear motor described above. The stability analysis method includes: step S5, constructing a Lyapunov function based on the integral sliding mode surface, and judging the stability of the integral sliding mode control based on the constructed Lyapunov function; step S6, obtaining the characteristic equation of the extended state observer ESO in the discrete complex frequency domain based on the structure of the linear extended state observer LESO and the integral sliding mode control surface; step S7, judging the bandwidth stability of the adaptive extended state observer AESO in the discrete complex frequency domain based on the characteristic equation of the extended state observer ESO in the discrete complex frequency domain and the Juli stability criterion.

[0084] Step S5 involves a stability analysis of the sliding mode control (SMC). Step S5 includes:

[0085] Based on the pre-selected integral sliding surface of the velocity tracking error, the Lyapunov function is constructed as follows:

[0086] (13)

[0087] In formula (13), It is a Lyapunov function, V is the variable symbol of the Lyapunov function, and s m The integral sliding surface for velocity tracking error is obtained by differentiating the Lyapunov function of equation (13):

[0088] (14)

[0089] in, Let s be the derivative of the Lyapunov function. m For the integral sliding surface of velocity tracking error, For the integral sliding surface s m The derivative, For the velocity of the mover, For the coefficients of the exponential approaching term; according to the derivative of the Lyapunov function, in In the case of >0, Thus, under the condition of exponential convergence, the tracking error of the integral sliding mode control is bounded and stable.

[0090] Specifically, because and The function always maintains the same sign, that is, in In this case, ,exist In this case, , and when When, satisfy Therefore, under the condition of exponential convergence, the tracking error of the integral sliding mode control is bounded and stable.

[0091] In practical applications, the bandwidth of the Linear Extended State Observer (LESO) It will be affected by the sampling period T s Due to limitations, its range needs further discussion in the discrete domain. To determine... The constraints are determined by the forward Euler discretization formula (4). That is, under the condition that the bandwidth is limited by the sampling period, the structure of the linear extended state observer LESO is discretized by forward Euler to obtain the discretized second-order ESO structure:

[0092] (15)

[0093] In formula (15), This is the velocity estimate for the (k+1)th sampling period. This is the velocity estimate for the k-th sampling period. This is the estimated total disturbance value for the (k+1)th sampling period. For the control period of a discrete control system, The speed value of the kth sampling period, This is the estimated total disturbance value for the k-th sampling period. For the control input of the kth sampling period, This is the estimated control gain. , , This is the bandwidth of the Adaptive State Observer (AESO).

[0094] According to formulas (9) and (15), the characteristic equation of the extended state observer ESO in the discrete complex frequency domain can be obtained. That is, based on the integral sliding mode control surface and the structure of the forward Euler discretized second-order extended state observer ESO, the characteristic equation of the extended state observer ESO in the discrete complex frequency domain is as follows:

[0095] (16)

[0096] In formula (16), , The system matrix of the discrete extended state observer is... , Let z be the determinant of a matrix, z be the discrete complex frequency domain variable of the discrete-time system, and diag([z,z]) represent a diagonal matrix with the discrete complex frequency domain variable z as the main diagonal element;

[0097] The characteristic equation of the extended state observer (ESO) in the discrete complex frequency domain is calculated as follows: , , .

[0098] To ensure that all poles of the characteristic equation lie within the unit circle, the Jury stability criterion can be used to derive the corresponding criteria. In other words, the Jury stability criterion conditions are as follows:

[0099] (17)

[0100] The bandwidth stability of the adaptive extended state observer (AESO) in the discrete complex frequency domain is determined using the Julius stability criterion condition (17). According to the Julius stability criterion condition, all poles of the characteristic equation lie within the unit circle.

[0101] In formula (17), J1 is the first condition of the Jury stability criterion, which is used to test the relationship between the moduli of the characteristic polynomial coefficients to ensure that the poles are located inside the unit circle; J2 is the second condition of the Jury stability criterion, which is used to test the value of the characteristic polynomial at z=1, which requires that it be greater than 0; J3 is the third condition of the Jury stability criterion, which is used to test the value of the characteristic polynomial at z=-1, which requires that it be greater than 0.

[0102] Will , , , , Substituting into formula (17), we get:

[0103] (18)

[0104] The bandwidth stability of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is determined based on the Juli stability criterion, including:

[0105] Based on the Julius stability criterion, the bandwidth stability criteria for the adaptive extended state observer (AESO) in the discrete complex frequency domain are as follows:

[0106] (19)

[0107] in, It is the bandwidth of the Adaptive State Observer (AESO). The lower limit, It is the bandwidth of the Adaptive State Observer (AESO). The upper limit, when the bandwidth of the adaptive state observer AESO If the bandwidth stability condition of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is met, then the bandwidth stability of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is guaranteed.

[0108] Figure 3 This is the overall control block diagram of the LFSPM system using the EAADRC scheme provided by the present invention, as follows: Figure 3 As shown, the outer speed loop uses EAADRC control, outputting q-axis current commands. An adaptive extended state observer estimates the speed and total disturbance in real time and adjusts the bandwidth online according to the disturbance rate of change. The disturbance estimate is fed forward to the speed loop. The inner current loop uses... Vector control involves the three-phase current being regulated by a proportional-integral (PI) controller after coordinate transformation, and then driving the motor via space vector pulse width modulation (SVPWM). An encoder provides position and speed feedback.

[0109] To verify the effectiveness and superiority of the proposed control method, the acceleration during the acceleration process of the permanent magnet linear motor was set to 2.6 m / s² under the given speed trapezoidal command. 2 The acceleration during the deceleration process of the permanent magnet linear motor is set to -2.6 m / s². 2 The velocity tracking performance at 0.5 m / s, 1 m / s, and 1.5 m / s will be discussed below.

[0110] This invention provides the tracking effect and tracking error of different control methods on motor speed.

[0111] When the trapezoidal speed is 0.5 m / s, Figure 4(a) shows the motor's rotor speed tracking under PI control, Figure 4(b) shows the speed tracking error under PI control, Figure 4(c) shows the motor's rotor speed tracking under LADRC control, Figure 4(d) shows the speed tracking error under LADRC control, Figure 4(e) shows the motor's rotor speed tracking under EAADRC control, and Figure 4(f) shows the speed tracking error under EAADRC control. In Figures 4(a) and 4(b), the rise time of PI control is 0.41 s, and the speed tracking error is 0.1 m / s. In Figures 4(c) and 4(d), the rise time of LADRC is 0.37 s, and the speed tracking error is 0.06 m / s. Compared with PI control, the rise time is reduced by 9.8%, and the speed tracking error is reduced by 40%. In Figures 4(e) and 4(f), the rise time of EAADRC is 0.33s and the speed tracking error is 0.02m / s. Compared with PI control, the rise time is reduced by 19.5% and the speed tracking error is reduced by 80%. In comparison, the technical solution provided by the present invention exhibits excellent dynamic performance and disturbance rejection performance.

[0112] When the trapezoidal speed is 1.0 m / s, Figure 5(a) shows the motor's rotor speed tracking under PI control, Figure 5(b) shows the speed tracking error under PI control, Figure 5(c) shows the motor's rotor speed tracking under LADRC control, Figure 5(d) shows the speed tracking error under LADRC control, Figure 5(e) shows the motor's rotor speed tracking under EAADRC control, and Figure 5(f) shows the speed tracking error under EAADRC control. In Figures 5(a) and 5(b), the rise time of PI control is 0.93 s, and the speed tracking error is 0.19 m / s. In Figures 5(c) and 5(d), the rise time of LADRC is 0.87 s, and the speed tracking error is 0.12 m / s. Compared with PI control, the rise time is reduced by 6.5%, and the speed tracking error is reduced by 36.8%. In Figures 5(e) and 5(f), the rise time of EAADRC is 0.85s and the speed tracking error is 0.05m / s. Compared with PI control, the rise time is reduced by 8.6% and the speed tracking error is reduced by 73.7%. In comparison, the technical solution provided by the present invention exhibits excellent dynamic performance and disturbance rejection performance.

[0113] When the trapezoidal speed is 1.5 m / s, Figure 6(a) shows the motor's rotor speed tracking under PI control, Figure 6(b) shows the speed tracking error under PI control, Figure 6(c) shows the motor's rotor speed tracking under LADRC control, Figure 6(d) shows the speed tracking error under LADRC control, Figure 6(e) shows the motor's rotor speed tracking under EAADRC control, and Figure 6(f) shows the speed tracking error under EAADRC control. In Figures 6(a) and 6(b), the rise time of PI control is 1.21 s, and the speed tracking error is 0.26 m / s. In Figures 6(c) and 6(d), the rise time of LADRC is 1.17 s, and the speed tracking error is 0.17 m / s. Compared with PI control, the rise time is reduced by 3.3%, and the speed tracking error is reduced by 34.6%. In Figures 6(e) and 6(f), the rise time of EAADRC is 1.07s and the speed tracking error is 0.1m / s. Compared with PI control, the rise time is reduced by 11.6% and the speed tracking error is reduced by 61.5%. In comparison, the technical solution provided by the present invention exhibits excellent dynamic performance and disturbance rejection performance.

[0114] Figure 7 This invention provides a real-time bandwidth adjustment waveform for an adaptive law, such as... Figure 7 As shown, taking 1.0 m / s as an example, the bandwidth-adaptive EAADRC control strategy exhibits differences between the startup and steady-state phases. The upper figure represents the reference velocity and feedback velocity, while the lower figure shows the adaptive change in bandwidth during velocity following. Specifically, in the startup phase, a larger observer bandwidth can improve position accuracy. Through adaptive law adjustment, =Approximately 60 rad / s. However, in the steady state phase, and cannot be increased by... This further improves positioning accuracy. Conversely, in the steady-state phase, disturbances change slowly, therefore... A bandwidth of 20 rad / s is sufficient to estimate the disturbance and reduce observation noise. Therefore, the proposed bandwidth adaptive strategy achieves a good balance between disturbance suppression and observation noise.

[0115] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0116] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0117] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. An enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor, characterized in that, The enhanced active disturbance rejection control method includes: Step S1: Establish the kinematic model of the permanent magnet linear motor based on its electromagnetic parameters; Step S2: Calculate the integral sliding mode control surface based on the kinematic model, and calculate the final sliding mode control law based on the kinematic model and the integral sliding mode control surface; Step S3: Obtain the total perturbation estimate based on the structure of the linear extended state observer (LESO), and calculate the bandwidth adaptive law based on the total perturbation estimate to obtain the adaptive extended state observer (AESO) based on the bandwidth adaptive law. Step S4: Based on the final sliding mode control law and the adaptive extended state observer AESO, enhanced active disturbance rejection control of the permanent magnet linear motor is achieved.

2. The enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor according to claim 1, characterized in that, The permanent magnet linear motor is a linear flux switching type permanent magnet motor, and step S1 includes: The electromagnetic thrust of the permanent magnet linear motor on the dq axis The calculation is as follows: ； in, This refers to the stator pole pitch of a permanent magnet linear motor. It is a permanent magnet flux linkage. It is the d-axis current. It is the q-axis current, L d It is the d-axis inductance, L q It is a q-axis inductor; The motion equation of the mover of a permanent magnet linear motor is as follows: ； Where M is the mass of the mover, B is the coefficient of friction, and F L For load capacity, Let F be the velocity of the mover, t be time, and F be the velocity of the mover. d This refers to thrust fluctuation disturbances caused by end effects. Treating the permanent magnet linear motor as a rigid body model, the motion equation of the permanent magnet linear motor is simplified into a second-order kinematic model as follows: ； in, Let be the derivative of the mover velocity, and u be the control signal. For the control gain estimate, b0=k f / M,k f Let M be the thrust coefficient, M be the mover mass, and ω(t) be the external disturbance. This represents the total disturbance of the permanent magnet linear motor.

3. The enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor according to claim 2, characterized in that, Step S2 includes: The integral sliding mode control surface calculated based on the kinematic model is as follows: ； in, It is the integral sliding mode control surface for speed tracking error. It is the integral sliding mode control surface The derivative, It is a preset speed reference value. c1 is the derivative of the speed reference value, c2 is the weighting coefficient of the error term, and c2 is the weighting coefficient of the error integral term. This is the actual operating speed of the permanent magnet linear motor. It is a time integral variable. In the time integral variable The following speed reference value; Define saturation function as follows: ； in, It is the boundary layer value of the saturation function. ; Based on the kinematic model and the integral sliding mode control surface, the final sliding mode control law is calculated as follows: ； in, It is the output of integral sliding mode control. It is the gain of the switching item. It is a speed reference value. The derivative, is the total disturbance estimate, and k1 is the gain of the exponential term.

4. The enhanced active disturbance rejection control method for an adaptive extended state observer of a permanent magnet linear motor according to claim 3, characterized in that, Step S3 includes: The bandwidth adaptive law is calculated as follows: ； in, It is the bandwidth of the Adaptive State Observer (AESO). It is an adaptive adjustment of the intensity coefficient. It is a characteristic quantity of the normalized rate of change of disturbance. It is an exponential function with base e. It is the bandwidth of the Adaptive State Observer (AESO). The lower limit, It is the bandwidth of the Adaptive State Observer (AESO). The upper limit of ξ, where ξ is a positive coefficient. It is the derivative of the total disturbance estimate after passing through a low-pass filter. It is the derivative of the total disturbance estimate. It is the bandwidth of the Adaptive State Observer (AESO).

5. A stability analysis method for enhanced active disturbance rejection control (ADRC) using an adaptive extended state observer for a permanent magnet linear motor, used for stability analysis of the enhanced ADRC method for an adaptive extended state observer for a permanent magnet linear motor as described in claim 4, characterized in that... The stability analysis method includes: Step S5: Construct a Lyapunov function based on the integral sliding surface, and determine the stability of the integral sliding control based on the constructed Lyapunov function. Step S6: Based on the structure of the linear extended state observer (LESO) and the integral sliding mode control surface, obtain the characteristic equation of the extended state observer (ESO) in the discrete complex frequency domain. Step S7: Determine the bandwidth stability of the adaptive extended state observer (AESO) in the discrete complex frequency domain based on the characteristic equation of the extended state observer (ESO) in the discrete complex frequency domain and the Julius stability criterion.

6. The stability analysis method for enhanced active disturbance rejection control of an adaptive extended state observer for a permanent magnet linear motor according to claim 5, characterized in that, Step S5 includes: Based on the pre-selected integral sliding surface of the velocity tracking error, the Lyapunov function is constructed as follows: ； in, It is a Lyapunov function, V is the variable symbol of the Lyapunov function, and s m The integral sliding surface for velocity tracking error; Differentiating the Lyapunov function yields: ； in, Let s be the derivative of the Lyapunov function. m For the integral sliding surface of velocity tracking error, For the integral sliding surface s m The derivative, For the velocity of the mover, Gain of the switching item; Among them, under the condition of exponential convergence, the tracking error of the integral sliding mode control law is bounded and stable.

7. The stability analysis method for enhanced active disturbance rejection control of an adaptive extended state observer for a permanent magnet linear motor according to claim 6, characterized in that, The structure of the Linear Extended State Observer (LESO) is as follows: ； in, It is the velocity of the mover. Compared with the observed values ​​of the moving part velocity The error between them This is the estimated total disturbance. , ω0 is the bandwidth of the linearly extended state observer LESO.

8. The stability analysis method for enhanced active disturbance rejection control of an adaptive extended state observer for a permanent magnet linear motor according to claim 7, characterized in that, Step S6 includes: With bandwidth limited by the sampling period, the structure of the linear extended state observer (LESO) is discretized using forward Euler discretization to obtain a discretized second-order ESO structure: ； in, This is the velocity estimate for the (k+1)th sampling period. This is the velocity estimate for the k-th sampling period. This is the estimated total disturbance value for the (k+1)th sampling period. For the control period of a discrete control system, The speed value of the kth sampling period, This is the estimated total disturbance value for the k-th sampling period. For the control input of the kth sampling period, This is the estimated control gain. , , For the bandwidth of the adaptive state observer AESO; Based on the structure of the integral sliding mode control surface and the forward Euler discretized second-order extended state observer ESO, the characteristic equation of the extended state observer ESO in the discrete complex frequency domain is as follows: ； in, , The system matrix of the discrete extended state observer is... , Let z be the determinant of a matrix, z be the discrete complex frequency domain variable of the discrete-time system, and diag([z,z]) represent a diagonal matrix with the discrete complex frequency domain variable z as the main diagonal element; The characteristic equation of the extended state observer (ESO) in the discrete complex frequency domain is calculated as follows: , , .

9. The stability analysis method for enhanced active disturbance rejection control of an adaptive extended state observer for a permanent magnet linear motor according to claim 8, characterized in that, Step S7 includes: According to the Julius stability criterion, the conditions for the Julius stability criterion are as follows: ； The bandwidth stability of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is determined based on the Juli stability criterion.

10. The stability analysis method for enhanced active disturbance rejection control of an adaptive extended state observer for a permanent magnet linear motor according to claim 9, characterized in that, The bandwidth stability of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is determined based on the Juli stability criterion, including: Based on the Julius stability criterion, the bandwidth stability criteria for the adaptive extended state observer (AESO) in the discrete complex frequency domain are as follows: ； in, It is the bandwidth of the Adaptive State Observer (AESO). The lower limit, It is the bandwidth of the Adaptive State Observer (AESO). The upper limit, when the bandwidth of the adaptive state observer AESO If the bandwidth stability judgment condition of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is met, then the bandwidth stability of the Adaptive Extended State Observer (AESO) in the discrete complex frequency domain is guaranteed.

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