Improved second-order super-local model-based speed and current model-free control method for permanent magnet synchronous motor

Abstract

The application discloses a permanent magnet synchronous motor speed and current model-free control method based on an improved second-order hyperlocal model, collects three-phase currents of the permanent magnet synchronous motor, constructs a second-order sliding mode observer on a mechanical angular velocity and total disturbance of the system based on an improved second-order hyperlocal model model-free sliding mode speed controller MFSMSC, observes the mechanical angular velocity and the total disturbance of the system, designs an adaptive approach law of a variable boundary layer and a second-order integral sliding mode surface, and obtains a q-axis current reference signal; the q-axis current reference signal is output to a model-free predictive current controller MFPCC based on the improved second-order hyperlocal model, dq-axis reference voltages are obtained, after inverse Park conversion, alpha-beta-axis stator voltage reference vectors are obtained, three-phase inverter switching driving signals are obtained through SVPWM operation, six switching tubes of the three-phase inverter are driven to be turned on and turned off, and then the three-phase winding currents of the permanent magnet synchronous motor are adjusted. The application adopts a classical cascade control architecture with a speed loop outer loop and a current loop inner loop, the improved second-order hyperlocal model improves disturbance estimation accuracy, and the improved second-order hyperlocal model enhances the suppression performance on high-frequency noise, and the MFPCC based on the improved second-order hyperlocal model improves the robustness of the system to motor parameter perturbation.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, specifically relating to a model-free control method for speed and current of permanent magnet synchronous motors based on an improved second-order hyperlocal model. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in new energy vehicles, aerospace, and industrial robotics due to their simple structure, high power density, and high efficiency. However, the PMSM control system is a highly coupled, nonlinear, and multivariable system, susceptible to parameter variations and unknown disturbances, which can degrade the performance of the speed and current loops. Therefore, it is necessary to study advanced control strategies to maintain the robustness of the PMSM drive system and achieve satisfactory overall control performance.

[0003] In recent years, an increasing number of control methods have been studied and implemented in permanent magnet synchronous motor drive systems, achieving satisfactory performance. These methods include traditional PI control, active disturbance rejection control (ADRC), sliding mode control (SMC), and model predictive control (MPC). Among them, MPC has become a research hotspot due to its excellent dynamic response performance and compatibility with nonlinear factors. However, MPC largely depends on an accurate model of the controlled object. In the presence of parameter variations and external disturbances, the control performance of MPC inevitably degrades. To improve the anti-disturbance capability of MPC and avoid its sensitivity to parameter changes, researchers have proposed several methods to improve MPC.

[0004] The first approach is parameter-identified MPC, which updates motor parameters in real time using parameter identification technology to ensure the accuracy of the established model. Since the motor parameters need to be updated in each cycle, this method requires a high-performance processor. The second approach introduces a disturbance observer, which can compensate for disturbances caused by parameter mismatch and unmodeled disturbances. In existing technology, a stator current and disturbance observer (SCDO) based on sliding mode exponential reaching law has been proposed. This observer can predict the future value of the stator current and system disturbances caused by parameter mismatch in real time. However, the traditional exponential reaching law may produce a certain degree of jitter during high-frequency switching, which may reduce the observer's estimation accuracy of disturbances.

[0005] Meanwhile, Model-Free Predictive Control (MFPC) has become a research hotspot due to its low parameter dependence. It constructs a data-driven model through input and output to replace the physical model. However, existing model-free control schemes generally adopt first-order hyperlocal models, which only simplify the total uncertainty of the system to a single lumped disturbance term. Essentially, this model can only describe the first-order dynamic characteristics of the system and cannot characterize higher-order information such as the rate of change of the disturbance. The matching Extended State Observer (ESO) is limited by the structure of the first-order model and can only estimate a single disturbance term. It is difficult to accurately track high-frequency and rapidly changing system disturbances. Under strong disturbance conditions such as load changes and parameter perturbations, observation lag and estimation errors will directly lead to the deterioration of control performance. In addition, most Model-Free Predictive Current Control (MFPCC) still uses traditional PI controllers to regulate speed, and its speed regulation performance is limited when facing parameter changes and unmodeled disturbances. Existing control methods that replace PI, such as Model Predictive Direct Speed ​​Control (MPDSC), have improved control performance, but the complexity of the cost function leads to a sharp increase in computational burden, while adaptive speed tracking schemes suffer from the problem of doubling the number of unknown parameters. Although sliding mode control (SMC) is highly robust, its inherent chattering problem can cause oscillations in the control signal.

[0006] Compared with the first-order hyperlocal model, the second-order hyperlocal model can decompose the total uncertainty of the system into linear coupling terms and purely unknown nonlinear disturbance terms. It can not only describe the first-order dynamics of the system, but also characterize second-order information such as the first-order derivative of the disturbance. From the model structure, it realizes a more complete characterization of the system dynamics and provides a theoretical basis for high-precision disturbance estimation. Summary of the Invention

[0007] Summary of the Invention: This invention proposes a model-free control method for the speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model. The method utilizes a composite control architecture that cascades model-free sliding mode speed control and current control based on the improved second-order hyperlocal model. By reconstructing the hyperlocal model, designing a novel sliding mode observer, and optimizing the sliding mode reaching law, the method improves the robustness, steady-state accuracy, and dynamic response speed of the system under parameter mismatch and external disturbances, and significantly suppresses control chattering.

[0008] Technical Solution: This invention discloses a model-free control method for the speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model. It employs a classic cascaded control architecture with an outer speed loop and an inner current loop, specifically including:

[0009] The three-phase current of a permanent magnet synchronous motor is collected. The model-free sliding mode speed controller MFSMSC based on the improved second-order hyperlocal model is used to reconstruct the mechanical motion relationship of the motor. A second-order sliding mode observer is constructed to observe the mechanical angular velocity and the total disturbance of the system. An adaptive reaching law of variable boundary layer and a second-order integral sliding mode surface are designed to output the q-axis reference current.

[0010] A model-free predictive current controller (MFPCC) based on an improved second-order hyperlocal model is established. An improved second-order hyperlocal model of the current loop is constructed, decomposing the total uncertainty of the system into linear coupling terms and purely unknown nonlinear disturbance terms. An improved second-order sliding mode observer is then built to observe the disturbances, obtaining the dq-axis reference voltage and the αβ-axis stator voltage reference vector u. αβ ;

[0011] The three-phase inverter switching drive signal S is obtained through SVPWM calculation. abc Drive the three-phase inverter to adjust the current of the three-phase stator windings of the permanent magnet synchronous motor.

[0012] Furthermore, the control process of the model-free sliding mode speed controller (MFSMSC) includes the following steps:

[0013] The mechanical motion equations are reconstructed into a form that includes unknown disturbances. Based on the design idea of ​​a second-order hyperlocal model, the reconstructed mechanical motion equations are then reconstructed without a model.

[0014] Based on the reconstructed model-free formula, a sliding mode observer specifically for real-time estimation of motor speed and system disturbance is constructed, and a sliding mode control function is designed.

[0015] Design an adaptive sliding mode reaching law for a hyperbolic tangent function with a variable boundary layer and a sliding surface with an integral term;

[0016] The q-axis reference current is obtained based on the adaptive reaching law and the integral sliding surface.

[0017] Furthermore, the reconstructed hyperlocal model of the velocity loop controller is as follows:

[0018] ;

[0019] Where, ω m It is mechanical angular velocity. For speed loop control gain, n p For the extreme logarithm, ψ f The flux linkage of a permanent magnet, where J is the moment of inertia. For the velocity loop lumped disturbance F ω The first derivative, B is the coefficient of friction, T L For the load torque, f ω To integrate unknown disturbances, e ω = -ω m For mechanical angular velocity tracking error, Let ω be the reference mechanical angular velocity of the motor, and ζ be the error integral compensation gain.

[0020] Furthermore, the sliding mode observer and sliding mode control function are specifically as follows:

[0021] ;

[0022] in, Estimated mechanical angular velocity The derivative, For speed loop control gain, Estimated values ​​of mechanical angular velocity observations The second derivative, i.e., the observed estimate of the mechanical angular acceleration, The derivative of the total perturbation of the velocity loop The observed estimate, u σm1 u σm2 For the dual control input of the velocity loop slip mode observer, k obs1 k obs2 k obs3 For the observer fuzzy gain, given by |e ω | Adaptive adjustment, tanh(·) is the hyperbolic tangent function, e ω For mechanical angular velocity tracking error, ε1 and ε2 are the hyperbolic tangent function boundary layer coefficients, a1 and a2 are the gain coefficients of the perturbation observer, and i q This represents the q-axis stator current.

[0023] Furthermore, the adaptive sliding mode reaching law and the second-order integral sliding mode surface of the velocity loop controller design are as follows:

[0024] ;

[0025] ;

[0026] ;

[0027] Where υ is the positive gain of the design. This refers to the mechanical angular velocity estimation error, i.e., the estimated angular velocity value. Compared with actual value The difference, Here, is the boundary layer coefficient of the velocity loop, and s is the second-order integral sliding surface. Let ε represent the mechanical angular velocity tracking error, c1 and c2 be the sliding mode surface integral gains, ε3 be the boundary layer coefficients of the hyperbolic tangent function of the sliding mode surface, τ be the intermediate variable of the integral, and M1, M2, and M3 be the adaptive gains of the reaching law. , , 0.05 < λ < 0.4, k1, k2, k3 are the basic gain of the reaching law, δ1, δ2 are the exponential decay coefficients, ε4, ε5 are the boundary layer coefficients of the hyperbolic tangent function of the reaching law, and ρ1 is the denominator gain coefficient. This is the first derivative of the mechanical angular velocity tracking error.

[0028] Furthermore, the core calculation formula for the q-axis reference current is:

[0029] ;

[0030] Furthermore, the control process of the model predictive current loop controller (MFPCC) includes the following steps:

[0031] The continuous domain voltage equation of the current loop of permanent magnet synchronous motor is discretized, and then a traditional modelless one-step prediction formula for the current loop is constructed based on the second-order hyperlocal model. A modelless prediction formula for the current loop with two-step delay compensation is also constructed.

[0032] An improved second-order hyperlocal model of the current loop is designed by reconstructing and optimizing the traditional hyperlocal model.

[0033] An improved second-order sliding mode observer (ISMO) specifically designed for current loops is constructed based on an improved second-order hyperlocal model of the current loop.

[0034] Design an exponential adaptive sliding mode reaching law containing a hyperbolic tangent term;

[0035] By combining the current estimate and disturbance estimate output by the improved second-order sliding mode observer, the dq-axis reference voltage is derived.

[0036] Furthermore, the improved second-order hyperlocal model of the current loop is as follows:

[0037] ;

[0038] Among them, u dq This refers to the dq-axis stator voltage. = W is a matrix related to motor parameters, expressed as: R s L is the stator resistance. s For stator inductance, ω e F is the electric angular velocity of the motor rotor. dq Let dq be the unknown perturbation along the dq axis, and β be the rate of change of the perturbation. For dq axis current tracking error, , For dq axis current, This is the reference value for the dq axis current.

[0039] Furthermore, the improved second-order sliding mode observer is as follows:

[0040] ;

[0041] in, This represents the observed estimate of the dq-axis stator current. u is the observed estimate of the unknown perturbation along the dq axis. dqsmo This is the sliding mode control function for the improved second-order sliding mode observer ISMO with dq-axis current loop, serving as the control input for ISMO and enabling rapid convergence of observation errors. k obs4 Here, b1 and b2 are the current observation error compensation gain, b6 is the current observation boundary layer coefficient, and ε6 is the current observation error compensation gain. This is the error in the dq-axis current observation. .

[0042] Furthermore, the formula for solving the dq-axis reference voltage considering the control delay is as follows:

[0043] ;

[0044] Among them, T pwm Given the PWM switching period, the predicted current value at time k+2 is... , , These are the predicted values ​​of the dq-axis current at times k+2 and k+1. i is the reference value for the dq axis voltage. dq (k+1) is the predicted value of the dq-axis stator current at time k+1.

[0045] Beneficial effects:

[0046] 1. This invention adopts a classic cascaded control architecture with an outer speed loop and an inner current loop. It includes the design of an improved second-order hyperlocal model, the construction of a sliding mode observer (ISMO) based on the improved second-order hyperlocal model, the design of a model-free sliding mode speed controller (MFSMSC) based on the improved second-order hyperlocal model, and the design of a model-free predictive current controller (MFPCC) based on the improved second-order hyperlocal model. The functional modules cooperate with each other and communicate data in real time to form a complete closed-loop control system.

[0047] 2. This invention proposes a second-order hyperlocal model by reconstructing and optimizing the traditional first-order hyperlocal model. This breaks away from the original model's design approach of estimating the total unknowns of the system as a whole. It accurately decomposes the total unknowns of the system into linear terms containing system state variables and independent unknown nonlinear terms, thereby achieving accurate decoupling and hierarchical estimation of the unknowns. This avoids mutual interference in disturbance estimation, significantly improves the accuracy of disturbance estimation, and lays the foundation for precise controller design.

[0048] 3. This invention relies on an improved second-order sliding mode observer to replace the traditional extended state observer (ESO). It utilizes the strong robustness of the sliding mode observer to improve the system's ability to suppress high-frequency noise and the accuracy of disturbance estimation. At the same time, it specifically designs an adaptive sliding mode reaching law containing a variable boundary layer hyperbolic tangent function to replace the sign function in the traditional reaching law. This fundamentally eliminates the chattering problem inherent in sliding mode control from the design level and ensures the smoothness of the control signal.

[0049] 4. This invention abandons the PI control strategy commonly used in traditional speed loops and designs a brand-new model-free sliding mode speed controller. It combines a second-order sliding mode surface to achieve overshoot-free tracking of speed step response, solving the pain points of insufficient robustness and difficulty in balancing dynamic and steady-state performance of PI control. This allows the speed loop to have both fast dynamic response capability and steady-state control effect with zero steady-state error, achieving overshoot-free tracking of speed step response.

[0050] 5. The model-free cascaded control system of speed and current loops constructed in this invention completely eliminates the dependence of the entire control system on the precise mathematical model of the permanent magnet synchronous motor, fundamentally solving the industry pain point of performance degradation caused by parameter mismatch in traditional first-order model predictive control. It achieves high-precision and robust control of the speed and stator current of the permanent magnet synchronous motor, effectively suppressing the control performance degradation caused by motor parameter mismatch, external unknown disturbances, and high-frequency noise. Simultaneously, the feasibility of engineering implementation is fully considered in the controller design process, and the computational load of the algorithm is reasonably controlled to ensure that the proposed method can adapt to the real-time control requirements of conventional digital controllers without the need for additional high-performance processors, thus possessing both excellent control performance and good engineering practicality. Attached Figure Description

[0051] Figure 1 The flowchart shows the model-free sliding mode velocity loop control based on the improved second-order hyperlocal model.

[0052] Figure 2 The flowchart shows the model-free predictive current loop control based on an improved second-order hyperlocal model; where (a) the dq-axis reference voltage solution considering two-step delay (k+2-step prediction + integral compensation) and (b) the structure of the improved second-order sliding mode observer (ISMO).

[0053] Figure 3 This is a block diagram of the model-free sliding mode-predictive current cascade control of permanent magnet synchronous motor based on a second-order hyperlocal model, according to the present invention.

[0054] Figure 4 The experimental results are for the analysis of d-axis and q-axis currents, phase currents and harmonics under the nominal motor parameters of this invention.

[0055] Figure 5 The results are experimental findings on the d-axis and q-axis currents and actual speeds under the nominal motor parameters of this invention. Detailed Implementation

[0056] The following, in conjunction with the accompanying drawings and specific experimental parameters, provides a more detailed and complete explanation of the specific implementation process, controller design details, core formula derivation, parameter tuning principles, and experimental verification results of this invention.

[0057] The core control object of this invention is a surface-mounted permanent magnet synchronous motor (SPMSM). The stator inductance parameters of this type of motor are equal on the d-axis and q-axis. The control method proposed in this invention can also be adapted to other types of permanent magnet synchronous motors according to actual application requirements. Only a small amount of adaptation adjustment to the core formula is needed according to the specific parameters of the motor body.

[0058] Both the experimental verification and actual engineering implementation of this invention are based on the RTUBOX-206 dedicated motor control experimental platform. This platform is a dedicated platform for industrial-grade motor control experiments. Its core main control chip is the TMS28377, which is an industrial-grade dedicated motor control chip with the characteristics of fast computing speed, high control accuracy, and rich peripheral interfaces, fully meeting the real-time computing requirements of the control method proposed in this invention. The dead time of PWM modulation in the experimental platform is set to 2μs. This parameter setting can effectively avoid the shoot-through problem of the upper and lower bridge arms of the inverter, improving the safety and stability of system operation. The sampling frequency of stator current and speed is set to 10kHz. This sampling frequency takes into account both sampling accuracy and the real-time control requirements of the system, ensuring that the controller can obtain the motor's operating status parameters in a timely and accurate manner. The surface-mount permanent magnet synchronous motor used in this experiment is a commonly used medium-power motor in industry. Its core parameters are: 4 pole pairs, stator phase inductance 0.84mH, stator phase resistance 0.245Ω, permanent magnet flux linkage 0.13Wb, rated speed 2500rpm, rated torque 15N·m, and rotor moment of inertia 0.028kg·m². The method proposed in this invention can flexibly adapt the parameters in the core formula to permanent magnet synchronous motors with different power and parameters, and has strong adaptability and wide application range.

[0059] (I) System Dynamics Modeling

[0060] Before designing the controller, it is necessary to first establish a basic mathematical model of the surface-mounted permanent magnet synchronous motor (SPMSM). This provides a solid theoretical basis for subsequent controller design, model reconstruction, and observer setup. During the modeling process, to ensure the model's practicality and simplicity, and considering the characteristics of actual industrial applications, iron losses, hysteresis losses, and eddy current losses during motor operation are ignored. Only the core electromagnetic coupling and mechanical motion relationships of the motor are considered. Three core equations are established for the SPMSM in the dq rotating coordinate system: voltage equation, mechanical motion equation, and electromagnetic torque equation. The core formulas are as follows:

[0061] 1. dq-axis voltage equation:

[0062]

[0063] Among them, u d u q For the dq-axis stator voltage, i d i q R is the dq-axis stator current. s L is the stator phase resistance. s For stator phase inductance, ψ f For rotor permanent magnet flux linkage, ω e This is the electric angular velocity of the motor rotor.

[0064] 2. Equations of motion for machines:

[0065]

[0066] Where, ω m Let ω be the mechanical angular velocity of the motor rotor, satisfying the conversion relationship between mechanical angular velocity and electrical angular velocity. m =ω e / n p n p Where is the number of pole pairs of the motor, J is the rotor moment of inertia, B is the motor friction coefficient, and T is... e T is the electromagnetic torque of the motor. L This represents the motor load torque.

[0067] 3. Electromagnetic torque equation:

[0068]

[0069] The three core equations mentioned above clarify the electrical and mechanical dynamic characteristics of the permanent magnet synchronous motor. The voltage equation mainly describes the electromagnetic coupling relationship between stator voltage, current and core motor parameters, reflecting the electrical dynamic characteristics of the motor. The mechanical motion equation mainly reflects the dynamic relationship between the mechanical angular velocity of the motor rotor and electromagnetic torque, load torque and friction coefficient, and is the core theoretical basis for the design of the speed loop controller. The electromagnetic torque equation establishes the direct correlation between the q-axis stator current and electromagnetic torque, which is the key to realizing the control of motor torque and speed. By constructing the above three basic equations, a solid theoretical foundation is laid for the subsequent design of the improved hyperlocal model and the construction of the modelless controller.

[0070] (II) Design of a Model-Free Sliding Mode Velocity Controller (MFSMSC) Based on an Improved Second-Order Hyperlocal Model:

[0071] Figure 1The diagram shows the block diagram of the model-free sliding mode speed loop control algorithm based on an improved second-order hyperlocal model, clearly illustrating the signal interaction logic of the two core modules: the construction of the speed loop sliding mode observer and the design of the sliding mode speed control law. As the outer loop of the control system, the speed loop's control performance directly determines the accuracy of motor speed control. Compared to traditional sliding mode speed controllers, which rely on precise motor parameters, are prone to chattering, and suffer from steady-state errors, this invention's speed loop adopts a model-free design approach, completely reducing dependence on the motor's intrinsic parameters. Subsequent steps will focus on the innovative design of the sliding mode observer and the sliding mode speed control law, providing detailed derivations. Through optimization and reconstruction of the core formulas, the controller's robustness, control accuracy, and chattering suppression effects will be simultaneously improved, ensuring design rationality and engineering practicality.

[0072] 1. Construction of Sliding Mode Observer

[0073] First, taking into full account the parameter changes and the influence of unknown external disturbances during motor operation, the original mechanical motion equations are reconstructed to include the unknown disturbances. The core formula is:

[0074]

[0075] Where f ω This includes comprehensive unknown disturbances such as motor parameter mismatch and unmodeled dynamics.

[0076] Based on the classic design concept of the second-order hyperlocal model, the reconstructed mechanical motion equations are reconstructed without a model to obtain the core formula:

[0077]

[0078] in, To control the input gain, The total unknown disturbance of the system includes all uncertainties affecting the motor speed, n. p For the extreme logarithm, ψ f Permanent magnet flux chain, For the velocity loop lumped disturbance F ω The first derivative, f ω To integrate unknown disturbances, e ω = -ω m For mechanical angular velocity tracking error, Let ζ be the reference mechanical angular velocity and ζ be the error integral compensation gain. Based on the above model-free formula, an improved second-order sliding mode observer is constructed specifically for real-time estimation of motor mechanical angular velocity and system lumped disturbance. Its core formula is:

[0079]

[0080] in, Estimated mechanical angular velocity The derivative of reflects rate of change Estimated values ​​of mechanical angular velocity observations The second derivative, i.e., the observed estimate of the mechanical angular acceleration, The derivative of the total perturbation of the velocity loop The observed estimate, u σm1 u σm2 For the dual control input of the velocity loop slip mode observer, k obs1 k obs2 k obs3 For the observer fuzzy gain, given by |e ω | Adaptive adjustment, tanh(·) is the hyperbolic tangent function, ε1, ε2 are the boundary layer coefficients of the hyperbolic tangent function, a1, a2 are the gain coefficients of the perturbation observer, i q This represents the q-axis stator current.

[0081] To achieve rapid and stable convergence of observation errors, a core formula for the sliding mode control function was specifically designed:

[0082]

[0083] Where υ is the positive gain of the design. This refers to the mechanical angular velocity estimation error, which is the difference between the estimated and actual angular velocity values. υ represents the velocity loop boundary layer coefficient. In the parameter design of the sliding mode observer, the positive gain υ is a positive value. The value of this parameter directly affects the convergence speed of the observer. It needs to be reasonably tuned according to the actual control requirements and motor characteristics to ensure that the observation error can converge to zero quickly, thereby achieving unbiased and accurate tracking of motor speed and system disturbances.

[0084] 2. Sliding mode speed control law design

[0085] To completely solve the chattering problem in traditional sliding mode control, this invention abandons the traditional exponential reaching law and innovatively designs an adaptive sliding mode reaching law containing a hyperbolic tangent function of a variable boundary layer. Its core formula is:

[0086]

[0087] Where s is the second-order integral sliding mode surface, and M1, M2, and M3 are the reaching law adaptive gains. , , 0.05 < λ < 0.4, k1, k2, k3 are the basic gain of the reaching law, δ1, δ2 are the exponential decay coefficients, ε4, ε5 are the boundary layer coefficients of the hyperbolic tangent function of the reaching law, and ρ1 is the denominator gain coefficient. This is the first derivative of the mechanical angular velocity tracking error.

[0088] The core characteristic of this adaptive reaching law is that when the state variable moves far away from the sliding surface ( When the state variable approaches and enters the preset boundary layer, the gain of the reaching law will automatically increase, achieving rapid convergence of the system state and significantly improving the dynamic response speed of the velocity loop; When the sliding mode trajectory is continuous, it automatically switches to hyperbolic tangent function control to ensure the continuity of the sliding mode trajectory, fundamentally eliminate chattering problems, and ensure the smoothness of the control signal.

[0089] Define the motor mechanical angular velocity tracking error:

[0090]

[0091] in, ω is the reference mechanical angular velocity of the motor. m The actual mechanical angular velocity of the motor

[0092] Design the core formula for sliding surfaces containing integral terms:

[0093]

[0094] in, ε is the mechanical angular velocity tracking error, c1 and c2 are the sliding mode surface integral gain, ε3 is the boundary layer coefficient of the hyperbolic tangent function of the sliding mode surface, and τ is the intermediate variable of the integral.

[0095] Based on the adaptive reaching law and second-order integral sliding surface of the above design, through rigorous mathematical derivation and formula transformation, the core calculation formula for the q-axis reference current is finally obtained:

[0096]

[0097] The q-axis reference current serves as the core output of the speed loop controller and is directly transmitted to the inner current loop as the core reference signal, thereby enabling the speed loop to achieve model-free precise control of the motor speed.

[0098] Through extensive simulation analysis and actual experimental debugging, combined with the specific characteristics of the motor on the experimental platform, the optimal parameter tuning value of the speed loop controller was finally determined to be: k obs1 =800, k obs2 =400, k obs3=200, ε1=0.1, ε2=0.1, a1=50, a2=20, υ=2000, ε7=0.1, c1=10, c2=10, ε3=0.1, k1=100, k2=500, k3=100, λ=0.1, ε4=0.1, ε5=0.1, δ1=1.0, δ2=1.0, ρ1=2.0, ζ=15. The above parameters are the optimal values ​​for the motor adapted to this experimental platform. In actual engineering applications, the parameters in the core formula can be flexibly fine-tuned according to the actual parameters of the motor and specific control requirements to achieve the optimal control effect.

[0099] (III) Model-Free Predictive Current Controller (MFPCC) Based on Improved Second-Order Hyperlocal Model (Please refer to...) Figure 2 In the figure, (a) shows the solution of the dq-axis reference voltage considering two-step delay, and (b) shows the structure of the improved second-order sliding mode observer (ISMO).

[0100] (a) Model-free predictive current controller (MFPCC) based on an improved second-order hyperlocal model

[0101] This module is divided into a basic control branch and a delay compensation control branch:

[0102] The upper branch is a basic MFPCC control path without digital delay compensation: the current i is sampled at time k. dq (k) and reference current This constitutes a current deviation, after gain 1 / (α) c T pwm After the operation, it is compared with the decoupling matrix W and the perturbation estimate. and gain α c The processed compensation term is used for difference calculation, and the base reference voltage u is output. dq ref(base) This is a traditional uncompensated control scheme.

[0103] The lower branch is an improved MFPCC control path that considers the two-step delay of digital control: it uses current prediction at time k+2. Construct current deviation and synchronously introduce decoupling term at time k+1. With disturbance estimation The compensation calculation is completed, and the final output is an optimized reference voltage u with two-step delay compensation. dq ref(final) This is the core control output of this study, which can effectively offset the inherent two-step delay error of the digital control system and improve the current tracking accuracy and dynamic response performance. dq ref (final) Essentially, it is the actual dq-axis reference voltage output by the system. It is used for subsequent SVPWM modulation and inverter drive control.

[0104] The flowchart includes subtractors, adders, fixed-gain modules, and time-varying decoupling matrix multipliers, and is connected to the ISMO disturbance observation stage. It clearly shows the complete signal flow of current deviation calculation, coupling and decoupling, disturbance feedforward compensation, and reference voltage solution, and is the core visual representation of the MFPCC algorithm implementation.

[0105] (b) Improved Second-Order Sliding Mode Observer (ISMO)

[0106] This module uses the actual motor current i dq The actual dq-axis stator voltage u output by the inverter dq Using this as input, observation and disturbance estimation are achieved through the following process:

[0107] With actual current i dq With observed current Constructing current error It is directly used as the sliding surface S dq The hyperbolic tangent function tanh(∗ / ε6) and the gain k obs4 After processing, one signal is integrated to output disturbance estimation. The signal is fed into the MFPCC for disturbance feedforward compensation, and another signal is fed into the control voltage u. dq Damping term R s Coupling term ω e L and disturbance compensation item− Superimposed and updated by integration of observed currents And feeds back to the error calculation node to form a closed loop.

[0108] This module is based on a second-order hyperlocal model and uses a second-order sliding mode observation mechanism to achieve current observation and disturbance estimation, providing key feedback and compensation signals for the MFPCC and improving the robustness and anti-interference capability of the control system.

[0109] 1. Design of a novel hyperlocal model

[0110] First, the continuous-domain voltage equation of the current loop of the permanent magnet synchronous motor is discretized to obtain a discrete-domain model suitable for digital controller implementation. Then, based on the design idea of ​​the second-order hyperlocal model, a model-free one-step prediction formula for the traditional current loop is constructed.

[0111]

[0112] Where, α c =1 / L s To control the gain, T pwm For the PWM switching period, F d F qThe total unknown disturbance along the dq axis of the current loop;

[0113] Based on the one-step prediction formula described above, and by recursively predicting the current value at time k+2, a two-step delay-compensated model-free prediction formula for the current loop is constructed:

[0114]

[0115] in, This represents the predicted dq-axis current at time k+2. This is the estimated total unknown disturbance value of the dq axis at time k+1, which is used for the subsequent two steps of delay compensation calculation.

[0116] Traditional hyperlocal models suffer from low estimation accuracy and weak anti-interference capabilities due to integrating all unknowns into a single unit for estimation. This invention reconstructs and optimizes the traditional hyperlocal model, designing a novel hyperlocal model with the following core formula:

[0117]

[0118] Among them, u dq Let α be the dq-axis stator voltage. c = W is a matrix related to motor parameters, expressed as: R s L is the stator resistance. s For stator inductance, ω e F is the electric angular velocity of the motor rotor. dq Let dq be an unknown perturbation, β be the rate of change of the perturbation, and e be the unknown perturbation. idq tr For dq axis current tracking error, .

[0119] 2. Construction of an Improved Second-Order Sliding Mode Observer (ISMO)

[0120] Based on the novel hyperlocal model designed above, an improved second-order sliding mode observer (ISMO) specifically for current loops is constructed, with the core formula as follows:

[0121]

[0122] in For the observed estimate of the dq-axis stator current, α c α is the gain coefficient of the current observer. c = u dq This refers to the dq-axis stator voltage. u is the observed estimate of the unknown perturbation along the dq axis. dqsmoThis is the sliding mode control function for the improved second-order sliding mode observer (ISMO) on the dq-axis of the current loop. It serves as the control input for the ISMO and is used to achieve rapid convergence of observation errors. k obs4 Here, b1 and b2 are the current observation error compensation gain, b6 is the current observation boundary layer coefficient, and ε6 is the current observation error compensation gain. This is the error in the dq-axis current observation. .

[0123] To address the chattering problem in traditional sliding mode observers, a core formula for the sliding mode reaching law, incorporating an exponential adaptive sliding mode reaching law with a hyperbolic tangent term, is designed:

[0124]

[0125] Where n and m are the positive gains to be designed, the approach law can adaptively adjust the approach speed according to the state of the sliding surface, effectively suppressing the chattering phenomenon of the observer while ensuring fast convergence, and taking into account both convergence speed and system stability.

[0126] To ensure the stability of the improved second-order sliding mode observer, this invention employs Lyapunov stability theory to rigorously prove the observer's stability by constructing a suitable Lyapunov function. The derivation yields When n>0 and m>0, , ,therefore The condition ≤0 always holds true, proving that the observer's error system can asymptotically converge to zero, ensuring the observer's stability and reliability. After extensive simulations and experimental debugging, the optimal parameters of the improved second-order sliding mode observer were finally set as: n=10000, m=0.8, which can achieve accurate and real-time estimation of the dq-axis stator current and unknown nonlinear disturbances of the system.

[0127] 3. Reference Voltage Calculation

[0128] Based on the core principle of current loop model-free predictive control, and combined with the current estimate and disturbance estimate output by the improved second-order sliding mode observer, the preliminary calculation formula for the dq-axis reference voltage is derived:

[0129]

[0130] Simultaneously, the inherent two-step delay problem in digital control systems—namely, the controller calculation delay and the PWM output delay—is fully considered. This delay is an inherent characteristic of digital controllers, and without precise compensation, it will severely reduce control accuracy. Therefore, a dedicated delay compensation is performed on the preliminary calculation formula to obtain the final core formula for the reference voltage:

[0131]

[0132] The predicted current value at time k+2 is , Let u be the predicted value of the dq-axis current at time k+2. dq ref(final) For the preliminary calculated value of the dq-axis voltage, u dq ref(final) The final output reference value for the dq-axis voltage is essentially the actual dq-axis reference voltage u output by the system. dq ref i dq ref This is the reference value for the dq axis current. This is the predicted value of the dq-axis stator current at time k+1. The final calculated dq-axis reference voltage is transmitted to the Space Vector Pulse Width Modulation (SVPWM) module. The SVPWM modulation algorithm converts the reference voltage into a drive signal for the inverter, driving the inverter to output the corresponding voltage to the stator windings of the permanent magnet synchronous motor, thereby achieving closed-loop precise control of the stator dq-axis current.

[0133] (iv) Cascaded control architecture construction and hierarchical parameter tuning

[0134] Figure 3 This invention presents a modelless sliding mode-predictive current cascaded control block diagram for a permanent magnet synchronous motor based on an improved second-order hyperlocal model. The overall architecture adopts a classic cascaded control architecture with an inner current loop and an outer speed loop. This architecture conforms to the electromagnetic and mechanical characteristics of permanent magnet synchronous motors and can achieve precise hierarchical control of speed and current. The output of the modelless sliding mode speed controller in the speed loop serves as the reference signal for the q-axis stator current in the current loop, while the reference signal for the d-axis stator current is directly set to 0. This is a classic control strategy for surface-mounted permanent magnet synchronous motors, which can achieve maximum torque-to-current ratio (MTPA) control of the motor and effectively improve the motor's operating efficiency.

[0135] The complete workflow of the cascaded control system is as follows: First, the actual mechanical angular velocity ω of the motor is collected through various sensors. m and stator three-phase current i a i b i c The collected three-phase currents are converted into current i in a synchronously rotating coordinate system along the dq axis using Clark and Park transformations. d i q The actual mechanical angular velocity ω m With reference mechanical angular velocity The mechanical angular velocity tracking error e is obtained by real-time comparison. ω The mechanical angular velocity tracking error e ωThe input is fed into an improved second-order model-free sliding mode speed controller, and the output q-axis reference current is calculated using the core formula. Combined with the zero reference current on the d-axis =0, thus obtaining the reference value of the dq-axis stator current. ; Set the dq-axis stator reference current With the actual dq axis current i dq The difference is input to a model-free predictive current controller based on an improved second-order hyperlocal model, combined with the current estimate output by an improved second-order sliding mode observer. and disturbance estimates The dq-axis stator reference voltage is calculated using the core formula for the reference voltage. Finally, the dq axis reference voltage is converted into the inverter's PWM drive signal through SVPWM modulation, which drives the inverter to provide the corresponding stator voltage for the permanent magnet synchronous motor. At the same time, the actual operating parameters of the motor (speed and current) are fed back to the input of the controller in real time, forming a complete closed-loop cascaded control system.

[0136] In the controller parameter tuning process of this invention, a layered tuning strategy is specifically adopted to reduce the complexity of parameter tuning and improve tuning efficiency and accuracy. The specific tuning principle is as follows: First, the sliding mode observer and model-free predictive current controller parameters of the current loop are tuned. When tuning the current loop parameters, the speed loop is temporarily controlled by a traditional PI controller to ensure that the current loop can achieve fast and accurate tracking of the reference current, thus guaranteeing the dynamic and steady-state performance of the current loop. This is the foundation for the stable operation of the entire cascaded control system. After the current loop parameters are tuned and the optimal control effect is achieved, the sliding mode observer and model-free sliding mode speed controller parameters of the speed loop are tuned. When tuning the speed loop parameters, the core objective is to achieve speed tracking without overshoot, fast dynamic response, and steady-state control without steady-state error, while also taking into account the need for chatter suppression, balancing various control performance indicators, and achieving optimal overall system performance. All controller parameters were initially tuned using the Matlab / Simulink simulation platform to obtain a parameter range close to the optimal value. Then, they were finely tuned using the actual experimental platform to finally determine the optimal parameter tuning values ​​for the specific motor, ensuring that the control performance of the proposed control method reaches the best. At the same time, all parameters are positive gain or conventional coefficients, without complicated calculation requirements, which facilitates the actual operation and debugging of engineering technicians.

[0137] (V) Multi-condition experimental verification and control effect analysis

[0138] To verify the core advantages of the model-free velocity and current cascaded control architecture based on an improved second-order hyperlocal model proposed in this invention, this experiment comprehensively and systematically compares it with commonly used control methods in industrial and academic research, such as traditional model-free predictive current control combined with extended state observer (MFPCC-ESO), direct predictive current control (DPCC), and traditional PI velocity control. The experiment comprehensively analyzes and verifies the performance from multiple dimensions, including current loop control performance, velocity loop control performance, system robustness, and engineering feasibility. The experimental results fully demonstrate the superiority and practicality of this invention.

[0139] To fully and comprehensively verify the effectiveness, superiority, and robustness of the control method proposed in this invention, comparative experiments were conducted based on the RTUBOX-206 experimental platform and the determined optimal parameter settings. These experiments were performed under various typical operating conditions, including nominal motor parameters, stator inductance parameter mismatch, permanent magnet flux linkage parameter mismatch, and rotor moment of inertia parameter mismatch. The stator inductance parameter mismatch was set to two conditions: 50% and 150% of the nominal value. The permanent magnet flux linkage and rotor moment of inertia parameter mismatches were both set to 60% of the nominal value. These mismatch conditions are typical conditions that may occur after long-term operation of the motor in actual industrial applications, and can fully and realistically verify the controller's resistance to parameter mismatch.

[0140] Figure 4 To compare the performance of three different control strategies in a permanent magnet synchronous motor (PMSM) drive system, the evaluation was conducted from three dimensions: dq-axis current tracking, A-phase current waveform, and total harmonic distortion (THD). (a) is the traditional MFPCC (without delay compensation), (b) is the MFPCC with one-step delay compensation, and (c) is the MFPCC-ISMO composite control (k+2-step prediction + integral compensation) based on an improved second-order hyperlocal model proposed in this invention. The traditional MFPCC (without delay compensation) is a model-free predictive current control that does not consider the two-step delay of digital control. Its dq-axis current tracking exhibits significant lag and fluctuations, and the A-phase current waveform distortion is severe, with a THD of 9.42%, reflecting the limitations of this method in dynamic response and current quality. The MFPCC with one-step delay compensation, based on the traditional MFPCC, predicts the current at the next moment... An improved scheme to compensate for digital control delay is proposed. This method effectively improves current tracking accuracy, improves the sinusoidal nature of the A-phase current waveform, and reduces THD to 8.00%, verifying the effectiveness of the delay compensation strategy. Based on the improved hyperlocal model, the MFPCC-ISMO composite control (k+2-step prediction + integral compensation) uses ISMO to observe and feedforward compensate for the total system disturbance in real time, further suppressing current chattering and harmonics, making the A-phase current waveform smoother. The THD is 8.57%, which is slightly higher than that of MFPCC with one-step delay compensation (8.00%). However, the method of this invention prioritizes chattering suppression and parameter robustness through the hyperbolic tangent function and the second-order sliding mode observer, sacrificing small harmonic performance for overall system control stability, resulting in the best comprehensive control quality.

[0141] Figure 5 The graph shows the steady-state experimental results of the dq-axis current and actual mechanical angular velocity of the motor under three control methods with nominal motor parameters. The horizontal axis represents time (scale 100ms / div), and the vertical axis represents the dq-axis current (unit: A) and the actual mechanical angular velocity of the motor (unit: rpm), respectively. ref This is the reference current. Figure 5 In the middle (a), the measured waveform of traditional PI speed control is shown, which is characterized by large steady-state speed fluctuation (13.31 rpm), significant tracking deviation of dq axis current, obvious lag and oscillation in the waveform, and poor steady-state control accuracy. Figure 5 (b) shows the measured waveform of Direct Predictive Current Control (DPCC). The steady-state speed fluctuation is slightly improved (12 rpm), but the current tracking still has a small error. The dynamic response speed and anti-interference ability have not been substantially improved. Figure 5 Image (c) shows the measured waveform of the model-free sliding mode speed control (MFSMSC) based on a second-order hyperlocal model according to this invention. The steady-state speed fluctuation is only 2.49 rpm, which is the best among the three schemes. Moreover, the dq-axis current can accurately follow the reference current, the tracking error is smooth and oscillating, and the dynamic response is fast and the steady-state performance is excellent. The comparison of the three sets of experiments intuitively demonstrates the core innovative advantages of the model-free cascaded control architecture of this invention in improving the steady-state speed accuracy, optimizing the current tracking characteristics, and enhancing the dynamic response of the system. At the same time, it verifies the engineering feasibility of the method of this invention under conventional digital controller hardware conditions. The algorithm execution time of 10.24 μs is much smaller than the 100 μs sampling period of stator current and mechanical angular velocity, without the need for additional hardware costs.

[0142] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any parameter adjustments to the core formula, simple optimizations of the controller structure, or reasonable improvements to the control process made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A model-free control method for speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model, characterized in that, The classic cascaded control architecture, consisting of an outer speed loop and an inner current loop, is adopted, specifically including: The three-phase current of a permanent magnet synchronous motor is collected. The model-free sliding mode speed controller MFSMSC based on the improved second-order hyperlocal model is used to reconstruct the mechanical motion relationship of the motor. A second-order sliding mode observer is constructed to observe the mechanical angular velocity and the total disturbance of the system. An adaptive reaching law of variable boundary layer and a second-order integral sliding mode surface are designed to output the q-axis reference current. A model-free predictive current controller (MFPCC) based on an improved second-order hyperlocal model is established. An improved second-order hyperlocal model of the current loop is constructed, decomposing the total uncertainty of the system into linear coupling terms and purely unknown nonlinear disturbance terms. An improved second-order sliding mode observer is then built to observe the disturbances, obtaining the dq-axis reference voltage and the αβ-axis stator voltage reference vector u. αβ ; The three-phase inverter switching drive signal S is obtained through SVPWM calculation. abc Drive the three-phase inverter to adjust the current of the three-phase stator windings of the permanent magnet synchronous motor.

2. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 1, characterized in that, The control process of the model-free sliding mode speed controller (MFSMSC) includes the following steps: The mechanical motion equations are reconstructed into a form that includes unknown disturbances. Based on the design idea of ​​a second-order hyperlocal model, the reconstructed mechanical motion equations are then reconstructed without a model. Based on the reconstructed model-free formula, a sliding mode observer specifically for real-time estimation of motor speed and system disturbance is constructed, and a sliding mode control function is designed. Design an adaptive sliding mode reaching law for a hyperbolic tangent function with a variable boundary layer and a sliding surface with an integral term; The q-axis reference current is obtained based on the adaptive reaching law and the integral sliding surface.

3. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 2, characterized in that, The reconstructed hyperlocal model of the velocity loop controller is as follows: ； Where, ω m It is mechanical angular velocity. For speed loop control gain, n p For the extreme logarithm, ψ f The flux linkage of a permanent magnet, where J is the moment of inertia. For the velocity loop lumped disturbance F ω The first derivative, B is the coefficient of friction, T L For the load torque, f ω To integrate unknown disturbances, e ω = -ω m For mechanical angular velocity tracking error, Let ω be the reference mechanical angular velocity of the motor, and ζ be the error integral compensation gain.

4. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 2, characterized in that, The sliding mode observer and sliding mode control function are specifically as follows: ； in, Estimated mechanical angular velocity The derivative of For speed loop control gain, Estimated values ​​of mechanical angular velocity observations The second derivative, i.e., the observed estimate of the mechanical angular acceleration, The derivative of the total perturbation of the velocity loop The observed estimate, u σm1 u σm2 k is the dual-channel control input for the velocity loop sliding mode observer. obs1 k obs2 k obs3 For the observer fuzzy gain, given by |e ω | Adaptive adjustment, tanh(·) is the hyperbolic tangent function, e ω For mechanical angular velocity tracking error, ε1 and ε2 are the hyperbolic tangent function boundary layer coefficients, a1 and a2 are the gain coefficients of the perturbation observer, and i q This represents the q-axis stator current.

5. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 2, characterized in that, The adaptive sliding mode reaching law and the second-order integral sliding surface of the speed loop controller design are as follows: ； ； ； Where υ is the designed positive gain. This refers to the mechanical angular velocity estimation error, i.e., the estimated angular velocity value. Compared with actual value The difference, Here, is the boundary layer coefficient of the velocity loop, and s is the second-order integral sliding surface. Let ε represent the mechanical angular velocity tracking error, c1 and c2 be the sliding mode surface integral gains, ε3 be the boundary layer coefficients of the hyperbolic tangent function of the sliding mode surface, τ be the intermediate variable of the integral, and M1, M2, and M3 be the adaptive gains of the reaching law. , , 0.05 < λ < 0.4, k1, k2, k3 are the basic gain of the reaching law, δ1, δ2 are the exponential decay coefficients, ε4, ε5 are the boundary layer coefficients of the hyperbolic tangent function of the reaching law, and ρ1 is the denominator gain coefficient. This is the first derivative of the mechanical angular velocity tracking error.

6. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 5, characterized in that, The core formula for calculating the q-axis reference current is: ； 7. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 1, characterized in that, The control process of the Model Predictive Current Loop Controller (MFPCC) includes the following steps: The continuous domain voltage equation of the current loop of permanent magnet synchronous motor is discretized, and then a traditional modelless one-step prediction formula for the current loop is constructed based on the second-order hyperlocal model. A modelless prediction formula for the current loop with two-step delay compensation is also constructed. An improved second-order hyperlocal model of the current loop is designed by reconstructing and optimizing the traditional hyperlocal model. An improved second-order sliding mode observer (ISMO) specifically designed for current loops is constructed based on an improved second-order hyperlocal model of the current loop. Design an exponential adaptive sliding mode reaching law containing a hyperbolic tangent term; By combining the current estimate and disturbance estimate output by the improved second-order sliding mode observer, the dq-axis reference voltage is derived.

8. The method for model-free control of speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model according to claim 7, characterized in that, The improved second-order hyperlocal model of the current loop is as follows: ； Among them, u dq This refers to the dq-axis stator voltage. = W is a matrix related to motor parameters, expressed as: R s L is the stator resistance. s For stator inductance, ω e F is the electric angular velocity of the motor rotor. dq Let dq be the unknown perturbation along the dq axis, and β be the rate of change of the perturbation. For dq axis current tracking error, , For dq axis current, This is the reference value for the dq axis current.

9. A model-free control method for speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model, as described in claim 8, is characterized in that... The improved second-order sliding mode observer is: ； in, This represents the observed estimate of the dq-axis stator current. u is the observed estimate of the unknown perturbation along the dq axis. dqsmo This is the sliding mode control function for the improved second-order sliding mode observer ISMO with dq-axis current loop, serving as the control input for ISMO and enabling rapid convergence of observation errors. k obs4 Here, b1 and b2 are the current observation error compensation gain, b6 is the current observation boundary layer coefficient, and ε6 is the current observation error compensation gain. This is the error in the observation of the dq-axis current. .

10. A model-free control method for speed and current of a permanent magnet synchronous motor based on an improved second-order hyperlocal model, as described in claim 9, is characterized in that... The formula for solving the dq-axis reference voltage considering control delay is: ； Among them, T pwm Given the PWM switching period, the predicted current value at time k+2 is... , , These are the predicted values ​​of the dq-axis current at times k+2 and k+1. i is the reference value for the dq axis voltage. dq (k+1) is the predicted value of the dq-axis stator current at time k+1.

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