Hierarchical dual-mode active disturbance rejection tracking control method

Abstract

The present application belongs to the technical field of photoelectric tracking and motor servo control, and particularly relates to a layered dual-mode self-disturbance rejection tracking control method. The method comprises: S1: using a speed loop extended state model to decompose total disturbance of a current permanent magnet synchronous motor into non-periodic disturbance and periodic disturbance; S2: using a zero decoupling variable structure cascaded extended state observer to obtain a non-periodic disturbance compensation quantity; S3: orthogonally spectrum compressing a compressed regression vector of a Von Mises periodic basis radial basis function neural network to obtain an unknown order periodic disturbance compensation quantity; S4: extracting a slowly varying envelope, and calculating a known current measurement error harmonic disturbance quantity based on the slowly varying envelope; and S5: constructing a fixed time nonlinear state error feedback control law to obtain respective q-axis reference currents of all permanent magnet synchronous motors, so as to realize tracking control of a moving platform. The present application can improve the pointing accuracy, tracking stability and continuous tracking capability of a coaxial spherical parallel tracking frame.

Description

Technical Field

[0001] This invention belongs to the field of photoelectric tracking and motor servo control technology, and particularly relates to a hierarchical dual-mode active disturbance rejection tracking control method. Background Technology

[0002] The coaxial spherical parallel tracking frame is a novel parallel mechanism for photoelectric pointing and tracking of ground-based telescopes. The moving platform is connected to the base via three equidistant branches along the circumference, and is driven collaboratively by three coaxially arranged permanent magnet synchronous motors (PMSMs), forming a coaxial spherical parallel mechanism (CSPM). This allows the moving platform to perform three-degree-of-freedom pure rotational pointing motion around the center of the CSPM mechanism. This tracking frame combines high rigidity, low inertia, and fast response, eliminating overhead blind spots and achieving infinite continuous roll around the pointing axis, with a pitch angle range of approximately 48°–132°, suitable for high-dynamic continuous tracking of rapidly overhead targets. The pointing accuracy of the moving platform ultimately depends on the control quality of the speed loops of the three coaxial PMSM drive shafts: any drop, pulsation, or lag in the speed of any PMSM drive shaft speed loop will be amplified through the kinematic coupling of the parallel mechanism, resulting in pointing jitter and tracking error. Therefore, the key to achieving high-precision continuous tracking lies in designing a control strategy with strong disturbance suppression capabilities for the three-axis speed loop. However, the PMSM speed loop is simultaneously affected by two types of disturbances: aperiodic disturbances arise from load changes, wind load, inertial perturbations, friction, bus fluctuations, and current loop mismatch, exhibiting gradual or abrupt changes; periodic disturbances arise from cogging torque, inverter dead zone, flux harmonics, current sampling and position detection errors, and are related to the rotor electrical angle, manifesting as periodic jitter of the optical axis during low-speed precision pointing. The coexistence and mutual coupling of these two types of disturbances are the main factors limiting pointing accuracy.

[0003] For aperiodic disturbances, Active Disturbance Rejection Control (ADRC) aggregates various disturbances into a total disturbance and actively estimates and compensates for it. Its core is the Extended State Observer (ESO). When ESO uses high gain parameters, the disturbance estimation accuracy is high, but at the same time, it amplifies high-frequency measurement noise, causing a contradiction between disturbance suppression and noise suppression. Existing variable gain, filtering, and structural improvement methods have the problem of mutual coupling between the zero point of the disturbance channel and the fixed pole of the observer, making it difficult to achieve strong disturbance suppression and effective noise reduction in a time-division manner while keeping the observation pole unchanged. For periodic disturbances, methods using internal models of resonant and quasi-resonant controllers require prior information about the disturbance frequency. Once frequency mismatch occurs, the disturbance compensation performance will significantly degrade. The Gaussian Radial Basis Function Neural Network (RBFNN) uses rotor position as input and does not require prior frequency information, but the basis functions exhibit discontinuities at the junction of electrical angles 0° and 2π, and the network requires a large number of nodes. The Adaptive Linear Neuron (ADALINE) can compensate for known harmonics online, but the amplitude must be adaptively adjusted from zero, and the regression vector must maintain a constant amplitude. The tracking response speed is slow during operating condition changes, and it does not utilize the known physical law that the amplitude of the measurement error harmonics is calibrated with the stator current. Most of the above methods are asymptotically convergent and transiently dependent on initial values. Furthermore, the azimuth axis can roll continuously indefinitely, and the drive axis operates in a multi-turn position mode. If absolute angle commands from 0° to 360° are directly issued, non-shortest path detours are likely to occur near the full-turn angle boundaries, causing sudden speed changes. The three-axis system also requires a unified zero-position reference; improper mode switching will cause sudden changes in control commands. In summary, existing solutions mostly focus on general three-axis coordination and zero-return, without addressing the disturbance characteristics of this tracking frame at the algorithmic level. Therefore, there is an urgent need for a composite disturbance suppression method centered on an algorithm and oriented towards the three-axis velocity loop, which can improve the suppression capability and convergence speed of both aperiodic and periodic disturbances while also meeting the engineering requirements of multi-turn continuous azimuth tracking and unified three-axis zero-position. Summary of the Invention

[0004] In view of this, the present invention aims to provide a hierarchical dual-modal active disturbance rejection tracking control method to solve the problems that existing disturbance suppression methods are difficult to balance disturbance compensation, noise suppression and convergence performance. At the same time, the infinite continuous roll of the azimuth leads to multiple position rotations and inconsistent three-axis zero-position references, which cause sudden changes in commands and ultimately result in tracking frame optical axis jitter, insufficient pointing accuracy and limited dynamic continuous tracking performance. The present invention can improve the composite disturbance suppression capability and convergence speed of the three-axis velocity loop, thereby improving the pointing accuracy, tracking stability and continuous tracking capability of the coaxial spherical parallel tracking frame.

[0005] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A hierarchical dual-mode active disturbance rejection tracking control method is used to suppress coexisting aperiodic and periodic disturbances in the permanent magnet synchronous motors of a coaxial spherical parallel tracking frame. The method specifically includes the following steps: S1: Construct a speed loop expansion state model and use the speed loop expansion state model to decompose the total disturbance of the current permanent magnet synchronous motor into three types of components: non-periodic disturbance, unknown order periodic disturbance, and known current measurement error harmonics. S2: Construct a zero-point decoupled variable structure cascaded expansion state observer, and use the zero-point decoupled variable structure cascaded expansion state observer to process aperiodic disturbances and obtain aperiodic disturbance compensation amounts. S3: Input the rotor electrical angle corresponding to the current permanent magnet synchronous motor into the von Mises periodic basis radial basis function neural network, and perform orthogonal spectrum compression on the compressed regression vector of the von Mises periodic basis radial basis function neural network to obtain the unknown order periodic disturbance compensation amount. S4: Extract the slow-changing envelope using the measured q-axis current corresponding to the current permanent magnet synchronous motor, and calculate the known current measurement error harmonic disturbance based on the slow-changing envelope; S5: Construct a fixed-time nonlinear state error feedback control law. Input the non-periodic disturbance compensation, the unknown-order periodic disturbance compensation, and the known current measurement error harmonic disturbance into the fixed-time nonlinear state error feedback control law for processing to obtain the q-axis reference current. Replace the current permanent magnet synchronous motor with the next permanent magnet synchronous motor and repeat steps S1-S4 until the q-axis reference current corresponding to each permanent magnet synchronous motor is obtained, thereby realizing the tracking control of the moving platform.

[0006] Furthermore, in step S1, the expression for the velocity loop expansion state model is: ; ; ; ; in, For mechanical angular velocity, For time, This refers to the nominal control gain of the speed loop. This is the q-axis reference current. This is the nominal value of the torque coefficient. This is the nominal value of the moment of inertia. This is a non-periodic disturbance. For periodic disturbances, This is the nominal value of the damping coefficient. The viscous damping coefficient is... For rotational inertia, The torque coefficient, For load torque, For unknown internal and external disturbances. For current loop tracking error, For components of unknown order, The known measurement error harmonic components.

[0007] Furthermore, in step S2, the expression for the zero-point decoupled variable structure cascaded expansion state observer is: ; ; in, For speed estimation error, For mechanical angular velocity, This is an estimated value for the rotational speed. To The first-level estimate, To The second-order precise estimate, This refers to the nominal control gain of the speed loop. This is the q-axis reference current. This is an estimate of the perturbation derivative term. The difference between the two-level disturbance estimates. All are kernel gains. The derivative of the estimated rotational speed. To The derivative of the first-order estimate, To The derivative of the second-order precise estimate, The derivative of the estimated value of the perturbation derivative term. It is a non-periodic disturbance.

[0008] Furthermore, in step S2, the formula for calculating the aperiodic disturbance compensation amount is: ; ; in, This is the compensation amount for non-periodic disturbances. and All are variables that switch with binary values. The changing output composite weights, To The first-level estimate, To The second-order precise estimate, It is a non-periodic disturbance.

[0009] Furthermore, in step S2, the perturbation estimation transfer function of the zero-point decoupled variable structure cascaded extended state observer is: ; ; in, The perturbation estimation transfer function for a zero-point decoupled variable structure cascaded extended state observer. For the Laplace operator, This is an intermediate parameter used to represent the denominator, and has no physical meaning. All are kernel gains; The perturbation estimation error transfer function of the zero-point decoupled variable structure cascaded extended state observer is: ; in, The perturbation estimation error transfer function for the zero-point decoupled variable structure cascaded extended state observer. For the Laplace operator.

[0010] Furthermore, step S3 specifically includes the following steps: S31: Input the rotor electrical angle corresponding to the current permanent magnet synchronous motor into the von Mises periodic basis radial basis function neural network: ; in, For the first The output of the von Misessky function For rotor electrical angle, For concentration parameters, For the first The node center of a von Misesky function For the number of nodes, The node number; S32: The unknown-order periodic perturbation compensation amount is obtained by orthogonal spectral compression of the compressed regression vector of the von Mises periodic basis radial basis function neural network using the following formula: ; ; ; ; in, This represents the compensation amount for periodic disturbances of unknown order. Let T be the transpose of the first weight vector. This is the compressed regression vector after removing pre-defined harmonic components through orthogonal projection. For the first The compressed basis obtained by orthogonally projecting a von Misesky function to remove pre-defined known harmonic components. To be orthogonal to the pre-defined known order harmonic subspace, K is the order, where k is either 1 or 2, and K is the total order. and All are Bessel constants. For rotor electrical angle, For concentration parameters, For the first The node center of a von Misesky function For the number of nodes, For node sequence number, Let be the derivative of the first weight vector with respect to time. It is a positive definite gain matrix. Leakage coefficient, For speed error, This is the first weight vector.

[0011] Furthermore, in step S4, the calculation formula for extracting the slowly varying envelope using the measured q-axis current of the current permanent magnet synchronous motor is as follows: ; in, To measure the slowly varying envelope of the q-axis current, For the Laplace operator, This is the cutoff angular frequency of the envelope filter. This is the measured q-axis current.

[0012] Furthermore, in step S4, the calculation formula used to calculate the known current measurement error harmonic disturbance based on the slowly varying envelope is as follows: ; ; ; ; in, Given the known harmonic disturbance quantity of the current measurement error. Let T be the transpose of the second weight vector. For the regression vector, Let k be the k-th order sine or cosine carrier wave, where k is 1 or 2. To measure the slowly varying envelope of the q-axis current, This is the second weight vector. For rotor electrical angle, For zero-biased weight pairs, For mismatched weight pairs, The time derivative of the zero-biased weight pairs For the time derivative of the mismatched weight pairs, The adaptive gain for zero-biased weight pairs. For the adaptive gain of mismatched weight pairs, The leakage coefficient for zero-biased weight pairs. For indicator functions, For speed error, This is the freeze threshold.

[0013] Furthermore, in step S5, the fixed-time nonlinear state error feedback control law is: ; in, This is the q-axis reference current. This refers to the nominal control gain of the speed loop. For the derivative of the reference mechanical angular velocity, and All are feedback gains. For the main large error range, , For the small error range of the main body, , For speed tracking error, This is the compensation amount for non-periodic disturbances. This is the periodic disturbance compensation amount, which is the sum of the unknown-order periodic disturbance compensation amount and the known harmonic disturbance amount of the current measurement error. It is a signed power-law nonlinear function. As a scalar independent variable, For powers, It is a symbolic function.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: (1) The hierarchical dual-mode active disturbance rejection tracking control method of the present invention embeds the hierarchical dual-mode active disturbance rejection algorithm into the speed loop of three coaxial PMSM drive shafts, suppresses various disturbances that are amplified by the parallel mechanism and cause pointing jitter, and transforms the advantages of high stiffness and low inertia into high-precision and stable pointing.

[0015] (2) The hierarchical dual-mode active disturbance rejection tracking control method described in this invention, the Zero-Decoupled Variable-Structure Cascaded Extended State Observer (ZD-VSCESO), through dual-mode zero-point shaping combining a fixed-pole kernel and an output synthesis layer, achieves a strong low-frequency disturbance rejection effect of +60 dB / dec in the dynamic mode and a strong disturbance rejection effect in the steady-state mode without changing the poles. It boasts a high-frequency noise reduction capability of 60 dB / dec; the quadruple poles are constant and independent of the variable structure constant, combining fast recovery and uninterrupted switching, overcoming the slow pole problem caused by the zero-core coupling and symmetric gain of the Variable-Structure ESO (VSESO).

[0016] (3) The hierarchical dual-mode active disturbance rejection tracking control method described in this invention uses the von Mises periodic-basis radial basis function neural network (vM-RBFNN) with the rotor electrical angle as input and the basis function having 2π periodicity. It can approximate unknown order periodic disturbances without relying on frequency priors, eliminate the discontinuity problem of Gaussian boundary seams, and reduce the number of nodes required. Its regression vector is compressed by the orthogonal spectrum of Bessel coefficients to remove known first and second order components, decoupled from the PP-HC spectrum, avoids competition between harmonic component identification, and ensures that the mismatch ratio is identifiable.

[0017] (4) The hierarchical dual-mode active disturbance rejection tracking control method described in this invention uses a physical parameterized harmonic compensator (PP-HC) to parameterize the known current measurement error harmonics based on physical sources: the zero-bias amplitude is learned as a constant independent of the load, and the gain mismatch amplitude is calibrated by feedforward using the measured current envelope. For load changes, it relies on envelope feedforward to track in real time, without the need for repeated iterations to learn the amplitude like ADALINE, which can more effectively suppress optical axis jitter under variable load conditions.

[0018] (5) The hierarchical dual-modal active disturbance rejection tracking control method described in this invention adopts a lightweight first-order linear weight update law in the two branches (specifically, the branch where the von Mises periodic basis radial basis function neural network is located and the branch where the physical parameterized harmonic compensator is located). Each weight only performs a multiplication and addition operation once per control cycle, without fractional exponentiation, which is convenient for low-cost DSP real-time implementation. The fixed-time NLSEF gives the algorithm fixed-time convergence independent of the initial value, which can shorten the transient process of variable speed and load and improve the stability of dynamic compensation.

[0019] (6) The layered dual-mode active disturbance rejection tracking control method described in this invention combines the multi-cycle characteristic of infinite continuous rolling in the azimuth direction to achieve continuous following of the shortest path in multiple cycles and the establishment of the three-axis synchronous zero position, avoiding the problem of non-shortest path detour and inconsistency with the initial reference, and achieving a smooth exit from external given control to achieve a seamless handover of control, thereby improving pointing efficiency and engineering availability. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic diagram of the structure of the hierarchical dual-modal active disturbance rejection tracking control method described in the embodiment of the present invention; Figure 2 The overall structural block diagram of the hierarchical dual-modal active disturbance rejection tracking control described in the embodiments of the present invention; Figure 3 The ZD-VSCESO structural block diagram described in the embodiments of the present invention; Figure 4 The Bode plots of the perturbation estimation and estimation error transfer function under different variable structure constants described in the embodiments of the present invention are shown in (a) and (b). (a) is the amplitude-frequency characteristic plot of the perturbation estimation transfer function and (b) is the amplitude-frequency characteristic plot of the estimation error transfer function. Detailed Implementation

[0021] 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 specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0023] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0024] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0025] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] like Figure 1 As shown, this invention proposes a hierarchical dual-mode active disturbance rejection tracking control method to suppress coexisting aperiodic and periodic disturbances in the permanent magnet synchronous motors of a coaxial spherical parallel tracking frame. Specifically, it includes the following steps: S1: Construct a speed loop expansion state model and use the speed loop expansion state model to decompose the total disturbance of the current permanent magnet synchronous motor into three types of components: non-periodic disturbance, unknown order periodic disturbance, and known current measurement error harmonics. S2: Construct a zero-point decoupled variable structure cascaded expansion state observer, and use the zero-point decoupled variable structure cascaded expansion state observer to process aperiodic disturbances and obtain aperiodic disturbance compensation amounts. S3: Input the rotor electrical angle corresponding to the current permanent magnet synchronous motor into the von Mises periodic basis radial basis function neural network, and perform orthogonal spectrum compression on the compressed regression vector of the von Mises periodic basis radial basis function neural network to obtain the unknown order periodic disturbance compensation amount. S4: Extract the slow-changing envelope using the measured q-axis current corresponding to the current permanent magnet synchronous motor, and calculate the known current measurement error harmonic disturbance based on the slow-changing envelope; S5: Construct a fixed-time nonlinear state error feedback control law. Input the non-periodic disturbance compensation, the unknown-order periodic disturbance compensation, and the known current measurement error harmonic disturbance into the fixed-time nonlinear state error feedback control law for processing to obtain the q-axis reference current. Replace the current permanent magnet synchronous motor with the next permanent magnet synchronous motor and repeat steps S1-S4 until the q-axis reference current corresponding to each permanent magnet synchronous motor is obtained, thereby realizing the tracking control of the moving platform.

[0027] This invention proposes a hierarchical dual-modal active disturbance rejection tracking control method. For the coexisting aperiodic and periodic disturbances in the velocity loops of the three coaxial PMSM drive shafts of the coaxial spherical parallel tracking frame, the following steps are applied to the velocity loop of each PMSM drive shaft: Step 1: Establish a velocity loop extended state model, decomposing the total disturbance of the current velocity loop into three components: aperiodic disturbance, unknown-order periodic disturbance, and known current measurement error harmonics. The unknown-order periodic disturbance and the known current measurement error harmonics are considered periodic disturbances. Step 2: Design a Zero-Decoupled Variable-Structure Cascaded Extended State Observer (ZD-VSCESO) to observe and compensate for the aperiodic components, achieving dual-mode zero-point shaping and disturbance-free switching with "dynamic strong disturbance suppression and steady-state strong noise reduction" under fixed poles. Step 3: Design a von Mises periodic-basis radial basis function neural network (vM-RBFNN) branch for the rotor electrical angle input, and perform orthogonal spectrum compression on its regression vector to remove known-order components, approximating the unknown-order periodic disturbance without frequency prior. Step 4: Design a Physics-Parameterized Harmonic Compensator. The Compensator (PP-HC) branch uses the slowly varying envelope of the measured q-axis current of this drive axis as a feedforward quantity, and together with the online adaptive weights, constitutes the known current measurement error harmonic compensation quantity. Step 5: Using each compensation quantity as a feedforward, a q-axis reference current is generated through a fixed-time nonlinear state error feedback (NLSEF) control law; the three axes are processed simultaneously, and the kinematic mapping of the parallel mechanism achieves high-precision and stable pointing and continuous tracking of the moving platform.

[0028] like Figure 2As shown, the control system includes a controller, an EtherCAT real-time communication bus, three servo drives, and three PMSM drive axes. Each PMSM drive axis is equipped with an encoder at its tail to provide position and speed feedback. Each PMSM drive axis employs a cascaded speed loop-current loop vector control, with the d-axis current set to zero. The speed loop is implemented by the controller of this invention, using ZD-VSCESO to compensate for aperiodic disturbances and vM-RBFNN and PP-HC in parallel to compensate for periodic disturbances, outputting the q-axis reference current via a fixed-time NLSEF control law. The current loop outputs the drive signal via Space Vector Pulse Width Modulation (SVPWM). The three axes operate independently using the same algorithm; a single-axis example is used for illustration.

[0029] Step 1: Modeling the velocity loop expansion state model In the rotor dq coordinate system, the equations of motion for the PMSM electromagnetic torque are: (1); (2); In the formula, , These are the d-axis and q-axis stator currents, respectively. , These are the d-axis and q-axis inductances, respectively. It is a permanent magnet flux chain. For extreme logarithms, For rotational inertia, The viscous damping coefficient is... For mechanical angular velocity, For load torque, For electromagnetic torque, For time. Surface-mount motors or conventional vector control. Under the operating conditions, equation (1) simplifies to In the formula The torque coefficient, The equation of motion for the machine is written as Considering the uncertainty of actual parameters , , ,in , , These are the nominal values ​​of moment of inertia, damping coefficient, and torque coefficient, respectively. , , The corresponding perturbation amount; then consider the current loop tracking error. , The q-axis reference current is used. The disturbance is decomposed into aperiodic disturbances. With periodic disturbances ,have to: (3); in, Composed of slowly varying factors such as load, wind load, inertial perturbation, friction, bus fluctuation, and current loop mismatch, it can be represented as: , For unknown internal and external disturbances; This is the nominal control gain for the speed loop. Changes in the attitude of the moving platform cause load and inertia perturbations, which are... A significant source. Periodic disturbances. The factors originating from cogging torque, inverter dead zone, flux harmonics, current harmonics, and current measurement errors are characterized by finite-order Fourier series. In the formula, For harmonic orders, , They are respectively The amplitude and initial phase of the second harmonic. The rotor's electrical angular velocity. The current measurement error harmonics have a known physical structure: the DC zero bias of the current sampling generates a first-order electrical angular harmonic, the amplitude of which is independent of the load; phase-to-phase gain mismatch generates a second-order electrical angular harmonic, the amplitude of which is proportional to the stator current amplitude and the mismatch ratio is a hardware constant. This prior knowledge will be utilized in steps 3 and 4. The total disturbance... Expanding to the system state, we obtain For input, with The output velocity loop expansion state model. The periodic disturbance is decomposed into unknown-order periodic disturbances based on the degree of prior knowledge. Harmonic components of known measurement error ,Right now The compensation is made by steps 3 and 4, respectively. During low-speed precision tracking... Prominent, therefore for and Stratified suppression.

[0030] Step 2: Design of ZD-VSCESO like Figure 3 As shown, this is to enhance the resistance to aperiodic disturbances without changing the fixed poles. To improve estimation capabilities, this invention constructs ZD-VSCESO, which consists of a fixed-pole kernel and an output synthesis layer. The kernel is as follows: First-level observer: (4); Second-level observer: (5); In the formula, For speed estimation error, This is an estimated value for the rotational speed. To The first-level estimate, To The second-order precise estimate, This is an estimate of the perturbation derivative term. The difference between the two-level disturbance estimates. This represents the kernel gain; the dot above the variable indicates the derivative of that variable with respect to time. This invention introduces an output synthesis layer at the output end to estimate the residual perturbation. Write it as a linear integration of two-level estimates and apply unbiased constraints: (6); In the formula, and For switching variables with binary values The changed output is a comprehensive weight. Therefore... The compensated output is linearly integrated from two levels of estimation, so the kernel state matrix and poles remain unchanged, and only the output synthesis parameters are adjusted. The estimated channel zeros can then be reconstructed. The disturbance estimation transfer function is obtained from equations (3) to (6). With the perturbation estimation error transfer function In the formula For the Laplace operator, the denominator is... To balance low-frequency disturbance suppression during the dynamic phase and high-frequency noise reduction during the steady-state phase, the variable structure constant is taken as... And with a full-pole configuration using four core gains, Solving for: (7); in, The bandwidth of the zero-point decoupled variable structure cascaded expansion state observer is given. Substituting equation (7) into the equation, we get... , .like Figure 4 As shown, regardless For what value should the poles of the zero-point decoupled variable structure cascaded extended state observer be constant? (Quadruple) (critical damping), only the zero point follows Reconstruction. The speed error is large in the dynamic stage; therefore, [the following is taken]. , coefficient of the quadratic term Therefore The low-frequency slope increases from +40dB / dec to +60dB / dec. At this point, The system has a triple zero at the origin, which causes the steady-state estimation errors of step-type, ramp-type, and acceleration-type aperiodic disturbances to converge to zero, thereby enhancing the disturbance resistance in the dynamic stage; correspondingly, The high-frequency slope is 40dB / dec. The velocity error is small in the steady-state phase; therefore, we take... , , High frequency roll-off reaches 60 dB / dec, which can enhance noise suppression to reduce optical axis jitter, while Low-frequency recovery +40dB / dec. Both modes share the same gain group, and the poles remain constant. Modality switching only changes the downstream weights. Without changing the pole configuration, perturbationless bimodal zero-point shaping is achieved. A binary switching law is introduced: when... season ;when season In the formula To switch thresholds, For speed error, The ZD-VSCESO output is used as a reference mechanical angular velocity. That is to The amount of compensation.

[0031] Step 3: Design of Spectral Compression vM-RBFNN Branches Periodic disturbance Based on spectral support and a priori availability, it can be decomposed into known current measurement error harmonics. With unknown order periodic perturbation Take a set of known orders ,remember Towards Zhang Cheng's subspace orthogonal projection operator For the rotor electrical angle, then for Fourier components of a known order, The design does not contain first- or second-order components. To match this, the compensator employs a dual-branch structure: vM-RBFNN approximates the unknown-order periodic perturbation. Compact PP-HC compensates for known current measurement error harmonic components ; and with the same projection Spectral compression is applied to the regression vector of vM-RBFNN to decouple the spectra of the two branches and prevent them from competing with each other. (Approximation) The vM-RBFNN branch takes the first One of von Misessky's contributions was: (8); in, For the first The node center of a von Misesky function For concentration parameters, For the number of nodes, For node sequence number, For the first The output of the von Misesky function. Due to the periodicity of cosine, we have... Therefore, there is no discontinuity at the von Mises boundary between 0 and 2π. Concentration is determined by equivalent width. Spacing between nodes Match, take Stacking the bases yields the original regression vector. superscript Indicates transpose, its passband coverage includes In lower orders, including those mentioned above: if used directly, the two branches will compete for the same spectral line, and the fast vM-RBFNN will absorb second-order errors, causing the slow mismatch identification of PP-HC to lose its excitation. Therefore, projection is used instead. Remove the known order from the regression vector. The von Mises kernel has a Bessel expansion. In the formula As the angle independent variable, For harmonic orders, for The first-order modified Bessel function is thus a compression basis. It has a closed translation-invariant form: (9); in, and These two Bessel constants can be pre-calculated offline without any additional cost for online computation. (Compressed regression vector) Exactly orthogonal to the first and second harmonics, and The spectral support matches. Let the weight vector be... Von Mises periodic basis radial basis function neural network, neural network branch pairs The estimate is ;because Constructed without first- or second-order components, the universal approximation theorem holds directly on the contraction basis, and the ideal approximation is: In the formula, For ideal weights, To approximate the error and , Its upper bound. Considering the limited computing power of the Digital Signal Processor (DSP) and the fact that fractional power evaluation in the double power fixed-time update law accounts for the main computational overhead of the network, both branches of this invention adopt a first-order linear update law, and each weight only requires one multiplication-addition operation in each control cycle; the fixed-time convergence characteristic independent of the initial value is provided by the fixed-time NLSEF control law in step 5. The weight update law of the vM-RBFNN branch is: (10); in, express The derivative with respect to time, It is a positive definite gain matrix. Let be the leakage coefficient. The first term is the gradient learning term; the leakage term suppresses weight drift and compresses the absorption spectrum. The weight null space generated by dimensionality reduction of the spanned space of each basis is used to select the minimum norm solution. This branch approximates the unknown order periodic components without relying on frequency priors. And retain the prior knowledge of the rotor electrical angle period.

[0032] Step 4: PP-HC Branch Design Harmonics of known current measurement error , order set It has a clear physical source: the zero bias of current sampling generates a first-order harmonic, the amplitude of which is independent of the load; the phase-to-phase gain mismatch generates a second-order harmonic, the amplitude of which is proportional to the stator current amplitude, and the mismatch ratio is a hardware constant. PP-HC parameterizes the amplitudes of each order according to this physical source, rather than freely learning constant amplitudes for each order as in ADALINE. This is based on the measured q-axis current. Extracting the slow-varying envelope In the formula, Let be the cutoff angular frequency of the envelope filter and take... ,make It is approximately constant within one electrical cycle. Represents absolute value. Takes sine and cosine carrier waves of known orders. , Construct the regression vector: (11); Let the weight vector be... Its dimension , Given the number of orders, For zero-biased weight pairs, This is a mismatched weight pair. This branch pair... The estimate is Zero-biased weight pairs Learning a first-order zero-bias amplitude independent of load; mismatch weight pair Learning the dimensionless hardware mismatch ratio, the second-order amplitude load correlation is entirely determined by the slowly varying envelope of the feedforward. It offers the following advantages: load disturbances can be effectively tracked by introducing time delay only through the envelope filter; the learning targets corresponding to the two sets of weights do not shift with changes in operating conditions, which is superior to ADALINE, where the optimal second-order weights require repeated relearning as the load current shifts. Furthermore... Approximately constant within one electrical cycle, each regression term maintains a single-order pure tone form without injected sideband components. In a known-order subspace, according to the universal approximation theorem, we can obtain: In the formula, For ideal weights, To approximate the error and , Its upper bound. The two pairs of weights are updated according to the separation time scale: (12); In the formula, , They represent , The derivative with respect to time, , The adaptive gains of zero-biased weight pairs and mismatched weight pairs are respectively taken as follows: , The leakage coefficient for zero-biased weight pairs. This is an indicator function (it takes the value 1 if the condition is true, and 0 otherwise). The threshold is set to freeze. Zero-biased weight pairs suppress weight drift through leakage terms; mismatched weight pairs undergo slow adaptive adjustment towards the corresponding constant hardware target. To avoid introducing multiplicative bias into this constant target, leakage terms are omitted here. Under light load... Freeze updates in time to avoid parameter drift caused by insufficient stimulus; The regression term is ( Its amplitude is proportional to ,when hour Continuous excitation is applied, with the freezing condition matching the excitation condition. The discriminability of the mismatch ratio depends on the spectral compression mechanism in step 3: without spectral compression, the fast vM-RBFNN will absorb second-order errors, causing the slow mismatch identification to lose its effective excitation.

[0033] Step 5: Compound Cyclic Compensation and NLSEF Control Law and Triaxial Application The vM-RBFNN and PP-HC branches are connected in parallel. The estimation of the total periodic disturbance and the feedforward compensation are as follows: , To The estimation of speed tracking error. Differentiating and substituting into equation (3), we get , and They are respectively and The derivative with respect to time. To obtain convergence independent of the initial value, a double-power sign function is defined. In the formula, As a scalar independent variable, For powers, The sign function is applied to the vector component by component; let the closed-loop error take the form of a double power. and with compensate , The fixed-time nonlinear state error feedback (NLSEF) control law is obtained as follows: (13); in, , For feedback gain, Supervisor of large error range, Supervisor of small error range, This is a signed power-law nonlinear function used to maintain the positive and negative directions of the speed tracking error and to nonlinearly adjust the strength of the feedback control action based on the magnitude of the speed tracking error. As a scalar independent variable, For powers, For sign functions; when It is used to enhance the feedback correction effect in large error regions, when It is used to enhance error compression in regions with small errors. (Similar to a linear proportional term.) ( Compared to the proportional gain of the velocity loop, the fixed-time NLSEF control law has a larger equivalent gain at both ends, faster transient response, tighter steady-state response, and convergence independent of the initial value. The two branches employ a linear weight update law, where each weight undergoes only one multiplication-addition operation per control cycle, without fractional exponentiation, making it suitable for low-cost real-time DSP implementation. This control is applied to all three axes and kinematically mapped via a parallel mechanism, enabling the moving platform's attitude and angular velocity to converge rapidly to the reference, achieving high-precision and stable pointing.

[0034] Preferably, for a multi-circle position system in the azimuth direction, the target angle is processed using multi-circle shortest path analysis: first, the target angle is normalized to the range of 0° to 360°, and candidate positions are generated based on the current full-circle position. ,Compare Angular displacement difference between the current position and the current position ,when When the angle is greater than 180°, then Subtract 360°; when Less than At 180°, then Adding 360°, the final output is the equivalent target position closest to the current position. To avoid detour delays and impacts.

[0035] Preferably, the three-axis synchronous zero-position establishment is achieved by performing a synchronous scan, recording the first trigger signal of each axis with the negative edge of the encoder zero pulse, reconstructing the reference zero position, and canceling the probe. After the scan is completed, a consistent initial reference is established. When switching from tracking mode to idle mode, stop mode, or homing mode, the external position command is withdrawn, and the current position, zero velocity, and zero acceleration are fed in to avoid sudden changes in commands.

[0036] This invention also proposes a hierarchical dual-modal active disturbance rejection tracking control system for implementing the above method, comprising: a tracking frame body, three coaxial PMSM axes driving three branches, servo drivers, a real-time communication bus, and a controller. The controller operates the ZD-VSCESO, vM-RBFNN, and PP-HC branches for each drive axis speed loop, outputs the q-axis reference current through a fixed-time NLSEF control law, and then drives the motor through a current loop and SVPWM.

[0037] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0038] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A hierarchical dual-mode active disturbance rejection tracking control method for suppressing coexisting aperiodic and periodic disturbances in each permanent magnet synchronous motor of a coaxial spherical parallel tracking frame, characterized in that: Specifically, the steps include the following: S1: Construct a speed loop expansion state model and use the speed loop expansion state model to decompose the total disturbance of the current permanent magnet synchronous motor into three types of components: non-periodic disturbance, unknown order periodic disturbance, and known current measurement error harmonics. S2: Construct a zero-point decoupled variable structure cascaded expansion state observer, and use the zero-point decoupled variable structure cascaded expansion state observer to process aperiodic disturbances and obtain aperiodic disturbance compensation amounts. S3: Input the rotor electrical angle corresponding to the current permanent magnet synchronous motor into the von Mises periodic basis radial basis function neural network, and perform orthogonal spectrum compression on the compressed regression vector of the von Mises periodic basis radial basis function neural network to obtain the unknown order periodic disturbance compensation amount. S4: Extract the slow-changing envelope using the measured q-axis current corresponding to the current permanent magnet synchronous motor, and calculate the known current measurement error harmonic disturbance based on the slow-changing envelope; S5: Construct a fixed-time nonlinear state error feedback control law. Input the non-periodic disturbance compensation, the unknown-order periodic disturbance compensation, and the known current measurement error harmonic disturbance into the fixed-time nonlinear state error feedback control law for processing to obtain the q-axis reference current. Replace the current permanent magnet synchronous motor with the next permanent magnet synchronous motor and repeat steps S1-S4 until the q-axis reference current corresponding to each permanent magnet synchronous motor is obtained, thereby realizing the tracking control of the moving platform.

2. The hierarchical dual-modal active disturbance rejection tracking control method according to claim 1, characterized in that: In step S1, the expression for the velocity loop expansion state model is: ； ； ； ； in, For mechanical angular velocity, For time, This refers to the nominal control gain of the speed loop. This is the q-axis reference current. This is the nominal value of the torque coefficient. This is the nominal value of the moment of inertia. This is a non-periodic disturbance. For periodic disturbances, This is the nominal value of the damping coefficient. The viscous damping coefficient is... For rotational inertia, The torque coefficient, For load torque, For unknown internal and external disturbances. For current loop tracking error, For components of unknown order, The known measurement error harmonic components.

3. The hierarchical dual-modal active disturbance rejection tracking control method according to claim 1, characterized in that: In step S2, the expression for the zero-point decoupled variable structure cascaded expansion state observer is: ； ； in, For speed estimation error, For mechanical angular velocity, This is an estimated value for the rotational speed. To The first-level estimate, To The second-order precise estimate, This refers to the nominal control gain of the speed loop. This is the q-axis reference current. This is an estimate of the perturbation derivative term. The difference between the two-level disturbance estimates. All are kernel gains. The derivative of the estimated rotational speed. To The derivative of the first-order estimate, To The derivative of the second-order precise estimate, The derivative of the estimated value of the perturbation derivative term. It is a non-periodic disturbance.

4. The hierarchical dual-modal active disturbance rejection tracking control method according to claim 1, characterized in that: In step S2, the formula for calculating the non-periodic disturbance compensation amount is: ； ； in, This is the compensation amount for non-periodic disturbances. and All are variables that switch with binary values. The changing output composite weights, To The first-level estimate, To The second-order precise estimate, It is a non-periodic disturbance.

5. The hierarchical dual-mode active disturbance rejection tracking control method according to claim 4, characterized in that: In step S2, the perturbation estimation transfer function of the zero-point decoupled variable structure cascaded extended state observer is: ； ； in, The perturbation estimation transfer function for a zero-point decoupled variable structure cascaded extended state observer. For the Laplace operator, This is an intermediate parameter used to represent the denominator, and has no physical meaning. All are kernel gains; The perturbation estimation error transfer function of the zero-point decoupled variable structure cascaded extended state observer is: ； in, The perturbation estimation error transfer function for the zero-point decoupled variable structure cascaded extended state observer. For the Laplace operator.

6. The hierarchical dual-mode active disturbance rejection tracking control method according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31: Input the rotor electrical angle corresponding to the current permanent magnet synchronous motor into the von Mises periodic basis radial basis function neural network: ； in, For the first The output of the von Misessky function For rotor electrical angle, For concentration parameters, For the first The node center of a von Misesky function For the number of nodes, The node number; S32: The unknown-order periodic perturbation compensation amount is obtained by orthogonal spectral compression of the compressed regression vector of the von Mises periodic basis radial basis function neural network using the following formula: ； ； ； ； in, This represents the compensation amount for periodic disturbances of unknown order. Let T be the transpose of the first weight vector. This is the compressed regression vector after removing pre-defined harmonic components through orthogonal projection. For the first The compressed basis obtained by orthogonally projecting a von Misesky function to remove pre-defined known harmonic components. To be orthogonal to the pre-defined known order harmonic subspace, K is the order, where k is either 1 or 2, and K is the total order. and All are Bessel constants. For rotor electrical angle, For concentration parameters, For the first The node center of a von Misessky function For the number of nodes, For node sequence number, Let be the derivative of the first weight vector with respect to time. It is a positive definite gain matrix. Leakage coefficient, For speed error, This is the first weight vector.

7. The hierarchical dual-mode active disturbance rejection tracking control method according to claim 1, characterized in that: In step S4, the calculation formula for extracting the slowly varying envelope using the measured q-axis current of the current permanent magnet synchronous motor is as follows: ； in, To measure the slowly varying envelope of the q-axis current, For the Laplace operator, This is the cutoff angular frequency of the envelope filter. This is the measured q-axis current.

8. The hierarchical dual-modal active disturbance rejection tracking control method according to claim 1, characterized in that: In step S4, the calculation formula used to calculate the known current measurement error harmonic disturbance based on the slowly varying envelope is as follows: ； ； ； ； in, Given the known harmonic disturbance quantity of the current measurement error. Let T be the transpose of the second weight vector. For the regression vector, Let k be the k-th order sine or cosine carrier wave, where k is 1 or 2. To measure the slowly varying envelope of the q-axis current, This is the second weight vector. For rotor electrical angle, For zero-biased weight pairs, For mismatched weight pairs, The time derivative of the zero-biased weight pairs For the time derivative of the mismatched weight pairs, The adaptive gain for zero-biased weight pairs. For the adaptive gain of mismatched weight pairs, The leakage coefficient for zero-biased weight pairs. For indicator functions, For speed error, This is the freeze threshold.

9. The hierarchical dual-mode active disturbance rejection tracking control method according to claim 1, characterized in that: In step S5, the fixed-time nonlinear state error feedback control law is: ； in, This is the q-axis reference current. This refers to the nominal control gain of the speed loop. For the derivative of the reference mechanical angular velocity, and All are feedback gains. For the main large error range, , For the small error range of the main body, , For speed tracking error, This is the compensation amount for non-periodic disturbances. This is the periodic disturbance compensation amount, which is the sum of the unknown-order periodic disturbance compensation amount and the known harmonic disturbance amount of the current measurement error. It is a signed power-law nonlinear function. As a scalar independent variable, For powers, It is a symbolic function.

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