Sensorless robust prediction-backstepping double-loop control method and device for permanent magnet synchronous motor

Abstract

The invention provides a sensorless robust prediction-backstepping double-loop control method and device for a permanent magnet synchronous motor, and solves the problems that in an existing sensorless control system of the permanent magnet synchronous motor, a PI control structure is difficult to give consideration to fast dynamic response and robust stability, and a complex nonlinear algorithm is poor in real-time performance and insufficient in realizability. According to the method, a sliding-mode observer based on a Sigmoid function is constructed to estimate induced electromotive force, and a phase-locked loop is combined to extract a smooth rotor speed and position estimation value; a robust prediction controller based on a proportion-integral type error trend index is adopted in a rotating speed outer ring, an integral type backstepping controller is adopted in a current inner ring, and the motor is driven to operate through SVPWM modulation. According to the invention, through prediction-backstepping double-loop cooperative control, the dynamic response speed, anti-disturbance capability and stability of the system are substantially enhanced, the structure is simple, and engineering realization is easy.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and in particular to a sensorless robust predictive-backstepping dual-loop control method and device for permanent magnet synchronous motors. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in new energy vehicles, servo drives, and intelligent manufacturing due to their high efficiency, high power density, and excellent speed regulation performance. However, PMSMs inherently possess characteristics such as strong nonlinearity, time-varying parameters, and multivariable coupling. The system operation is susceptible to factors such as temperature rise, flux linkage changes, and load disturbances, which can lead to a decrease in control performance and a reduction in steady-state accuracy.

[0003] In traditional control systems, proportional-integral (PI) controllers are widely used in PMSM dual-loop control systems due to their simple structure and convenient parameter tuning. While this control structure can achieve basic speed regulation and current stabilization, its linear characteristics make it sensitive to changes in motor parameters, making it difficult to balance fast dynamic response and robust stability. When the system is under parameter perturbation or external disturbance conditions, PI controllers often exhibit problems such as hysteresis, large overshoot, and insufficient disturbance rejection, making it difficult to meet the high-performance control requirements under complex operating conditions.

[0004] To achieve sensorless control, sliding mode observers (SMOs) are widely used for estimating the position and speed of PMSM rotors due to their advantages such as strong anti-interference capability, simple implementation, and insensitivity to parameter changes. Traditional PI+SMO structures achieve a balance between speed regulation and state estimation performance to some extent, but a trade-off remains between estimation accuracy and control response. Specifically, the switching law of an SMO is usually implemented using a sign function, and its discontinuity easily causes high-frequency chattering near the sliding surface, resulting in unsmooth back EMF and position estimation signals, affecting the system's dynamic tracking performance. Although existing research has improved sliding mode performance by introducing saturation functions, variable gain adjustment, fuzzy logic, and filtering compensation, these improved schemes generally suffer from complex structures, difficult parameter tuning, and poor real-time algorithm performance, limiting their widespread application in engineering control systems.

[0005] Furthermore, to improve the robustness and dynamic performance of the system, researchers have proposed various improved control methods. For example, Model Predictive Control (MPC) achieves optimal control under constraints by solving the predictive model through rolling optimization, theoretically achieving good control performance. However, the algorithm has a large computational load and is significantly dependent on model accuracy and weight parameters, making it difficult to implement in real-time in embedded control systems. Model Reference Adaptive System (MRAS) control relies on adaptive laws for parameter identification and state estimation, but its stability depends on PI-type adaptive laws, resulting in poor noise resistance and insufficient robustness under non-ideal conditions. Extended Kalman Filter (EKF) methods achieve state reconstruction based on statistical estimation theory. Although they have high estimation accuracy, they require complex matrix operations, are highly sensitive to noise parameters, and have a large computational load and high implementation cost. In addition, nonlinear robust control, sliding mode variable structure control, and adaptive backstepping control based on Lyapunov stability theory can improve the dynamic performance and disturbance rejection of the system, but their control law structures are complex, parameter tuning is difficult, and algorithm implementation is cumbersome, making them unsuitable for practical applications.

[0006] Therefore, there is still a lack of a permanent magnet synchronous motor control method that can achieve high dynamic response, strong robustness, and high estimation accuracy without position sensors, while maintaining a simple structure and ease of implementation. Summary of the Invention

[0007] This invention addresses the problems of existing sensorless control systems for permanent magnet synchronous motors (PMSMs), such as the difficulty in balancing fast dynamic response and robust stability with complex nonlinear algorithms, resulting in poor real-time performance and limited feasibility. Therefore, it provides a sensorless robust predictive-backstepping dual-loop control method and device for PMSMs. While retaining the simplicity and ease of implementation of the traditional PI+SMO structure, this invention improves the inner and outer loop controller structures and control laws, and introduces a sigmoid function and a phase-locked loop structure to optimize the sliding mode observer, effectively enhancing the system's dynamic response speed, anti-interference capability, and speed and position estimation accuracy. The technical solution of this invention is as follows: based on d - q A mathematical model of a permanent magnet synchronous motor is established using a synchronous rotating coordinate system; Constructing a sliding mode observer: The sliding mode observer receives three-phase current and voltage sampling signals sampled by the VI measurement module and processed by Park transformation; The sliding mode observer uses the Sigmoid function as the switching function to calculate the induced electromotive force component in real time to obtain the estimated value of the induced electromotive force in the synchronous rotating coordinate system; The rotor position and speed are optimized and estimated using a phase-locked loop (PLL): The PLL receives the estimated value of the induced electromotive force output by the sliding mode observer, and extracts a smooth speed estimate through a PI control adjustment loop. with location estimate The estimated rotational speed The robust predictive controller feeds back to the outer loop of the speed measurement; the position estimate is then fed back to the outer loop. Feedback is sent to the coordinate transformation module to realize the current in d , q Decoupling control between axes; Constructing a robust predictive controller for the outer loop of the rotational speed: This robust predictive controller uses the target reference rotational speed as the reference speed. and the estimated rotational speed As input, the speed error is calculated, and a nonlinear robust predictive control law is constructed based on the speed error and the proportional-integral error trend index, resulting in... q Shaft reference current expression, output q Shaft reference current ; Construct an inner-loop integral backstepping controller: This integral backstepping controller receives... q Shaft current reference value and will q Shaft current reference value The control voltage is calculated by comparing the three-phase current sampling signal output by the VI measurement module after Park transformation with the signal, and by constructing an integral backstepping control law. and ; The control voltage and After being successively modulated by the inverse Park transformation and the space vector pulse width modulation module, it is applied to the three-phase bridge arm of the inverter to drive the permanent magnet synchronous motor to run, thus completing the coordinated control based on the predictive-backstep dual loop and the improved sliding mode observer.

[0008] Furthermore, in d - q In a synchronous rotating coordinate system, the stator voltage equation and electromagnetic torque equation of a permanent magnet synchronous motor are as follows:

[0009] In the formula, and They represent shaft and Stator current on the shaft; and They represent shaft and Stator voltage on the shaft; and They represent shaft and Stator inductance on the shaft; This refers to the mechanical angular velocity of the motor. R andP These are the motor's fixed resistance and the number of pole pairs, respectively. Represents permanent magnet flux linkage; Represents permanent magnet flux linkage; In a synchronous rotating coordinate system, the mechanical motion equations of a permanent magnet synchronous motor are:

[0010] In the formula, It is the moment of inertia; The damping coefficient; and These represent electromagnetic torque and load torque, respectively.

[0011] Furthermore, the VI measurement module is positioned between the inverter and the motor; The control law of the sliding mode observer is:

[0012] In the formula, k For sliding mode gain; μ This is the smoothness coefficient, used to adjust the smoothness of the switching function.

[0013] Furthermore, according to the Lyapunov stability criterion, the sliding mode gain... k The range of values ​​for is:

[0014] In the formula, for d Error in shaft current observations; for q Error in current observations; E d for d Shaft-induced electromotive force. E q for q Shaft-induced electromotive force; R This is the stator resistor for the motor; L d for q Shaft stator inductance; It represents the electric angular velocity.

[0015] Furthermore, the signal output terminal of the sliding mode observer is equipped with a low-pass filter module to suppress high-frequency noise interference and extract the smooth induced electromotive force component; the low-pass filter module is an IIR type filter.

[0016] Furthermore, the coordinate transformation module includes a Park module and an inverse Park transformation module; The PI control adjustment mechanism is as follows:

[0017] in, , These are the proportional and integral coefficients of the phase-locked loop, respectively. s For the Laplace operator; The closed-loop transfer function corresponding to the PI control structure is:

[0018] In the formula, This is a location estimate; This is the actual electrical angle; V q for q Shaft voltage command; s For the Laplace operator; The desired damping ratio; The desired bandwidth; Based on the desired damping ratio With expected bandwidth The parameters of the PI controller are:

[0019]

[0020] Speed ​​estimate with location estimate for:

[0021] In the formula, This is an estimated value for the electric angular velocity; P This represents the number of pole pairs of the motor. , These are the proportional and integral coefficients of the phase-locked loop, respectively. for d Shaft reference voltage; for d Actual shaft voltage; for d The integral term of the shaft voltage deviation; This is the integral term of the estimated electric angular velocity.

[0022] Furthermore, the speed error is:

[0023] In the formula, For the target reference speed, The estimated rotational speed for the sliding mode observer.

[0024] Furthermore, the proportional-integral error trend index is:

[0025] in, α、β The weighting coefficient is adjusted by... α、β The ability of the value adjustment controller to suppress dynamic and long-term deviations; For speed error; From the initial time to the current time t Integral over the speed error; The nonlinear robust predictive control law is:

[0026] In the formula, K p The proportional gain is used to determine the dynamic response speed of the system by responding to the current velocity error. K i The integral gain is used to eliminate steady-state error by integrating the accumulated velocity error. J It is the moment of inertia; P It is the extreme logarithm; For permanent magnet flux linkage; For speed error; The damping coefficient; The desired rotational speed; The feedback rotational speed estimated for the sliding mode observer.

[0027] Furthermore, the three-phase current sampling signal includes d Axis current components and q Axis current components; The integral backstep control law is as follows:

[0028]

[0029] In the formula, U d for d Shaft voltage command; L d for d Shaft stator inductance; R This is the stator resistor for the motor; i d for d Actual stator current of the shaft; P This represents the number of pole pairs of the motor. This refers to the mechanical angular velocity of the motor. L q for q Shaft stator inductance; i q for q Actual stator current of the shaft; for d The proportional gain of the shaft current loop; for d The proportional-integral error variable of the shaft current; for d Shaft reference current; for d Integral gain of the shaft current loop; for d The integral term of the shaft current error; U q for q Shaft voltage command; L q for q Shaft stator inductance; For permanent magnet flux linkage; for q The proportional gain of the shaft current loop; for d The proportional-integral error variable of the shaft current; for q Integral gain of the shaft current loop; for q Shaft reference current; for q The integral term of shaft current error.

[0030] The present invention also provides a sensorless robust predictive-backstep dual-loop control device for permanent magnet synchronous motors, characterized in that the device includes a memory and a processor, the memory storing a motor control program, and the processor executing the motor control program to implement the above-mentioned motor control method.

[0031] The beneficial effects of this invention are: Compared with existing technologies, this invention proposes a sensorless robust predictive-backstepping dual-loop control method for permanent magnet synchronous motors. By improving the outer loop, inner loop, and observer structure of traditional sensorless control systems, it achieves control effects with fast system response, high estimation accuracy, and strong robustness. While retaining the advantages of the PI+SMO structure's simplicity and ease of implementation, the algorithm is improved without adding extra hardware or complex computational modules, exhibiting high engineering feasibility and widespread application value. This invention has the following improvements: (1) A proportional-integral error trend prediction control law is introduced into the speed outer loop. Dynamic feedforward compensation is achieved through the coordinated adjustment of the current error and the historical error. This significantly improves the predictive ability and anti-disturbance performance of speed regulation, improves the slow response problem of traditional PI control under parameter changes and load disturbances, and reduces overshoot and response lag in the speed regulation process.

[0032] (2) The inner current loop adopts an integral-type backstepping control law based on Lyapunov stability theory, through... d , q The introduction of an integral term in shaft current regulation achieves global asymptotic stability and rapid decoupling of current, thereby effectively suppressing current and torque fluctuations. This enables the system to maintain stable operation under conditions of motor parameter changes and load disturbances, demonstrating strong robustness and adaptability.

[0033] (3) The sliding mode observer uses the Sigmoid function as the switching function and combines it with the phase-locked loop structure, which significantly suppresses the high-frequency chattering problem inherent in the traditional sliding mode observer and improves the smoothness and accuracy of back EMF and position and velocity estimation. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of the overall system control of the present invention.

[0036] Figure 2 This is a schematic diagram of the outer-loop robust predictive controller principle of the present invention.

[0037] Figure 3 This is a schematic diagram of the inner-loop integral backstepping controller of the present invention.

[0038] Figure 4 This is a schematic diagram of the improved sliding mode observer structure of the present invention.

[0039] Figure 5 This is a schematic diagram illustrating the working principle of the phase-locked loop of the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Combination Figures 1-5 This invention proposes a sensorless robust predictive-backstepping dual-loop control method for permanent magnet synchronous motors, the method comprising: based on d - qA mathematical model of a permanent magnet synchronous motor is established using a synchronous rotating coordinate system; Step 101, in the synchronous rotating coordinate system ( d - q (Coordinate system) The stator voltage equation and electromagnetic torque equation of the permanent magnet synchronous motor are:

[0042] in: and They represent shaft and Stator current on the shaft; and They represent shaft and Stator voltage on the shaft; and They represent shaft and Stator inductance on the shaft; This refers to the mechanical angular velocity of the motor. R and P These are the motor's fixed resistance and the number of pole pairs, respectively. Represents permanent magnet flux linkage; Represents permanent magnet flux linkage.

[0043] Step 102: In the synchronous rotating coordinate system, the mechanical motion equations of the permanent magnet synchronous motor are:

[0044] In the formula: It is the moment of inertia; The damping coefficient; and These represent electromagnetic torque and load torque, respectively.

[0045] A sliding mode observer based on the Sigmoid function is constructed. The sliding mode observer receives three-phase current and voltage sampling signals sampled by the VI measurement module and processed by Park transformation. The sliding mode observer uses the Sigmoid function as the switching function to calculate the induced electromotive force component in real time to obtain the estimated value of the induced electromotive force in the synchronous rotating coordinate system, thereby realizing state observation and velocity estimation. To achieve speed and position estimation of permanent magnet synchronous motors under sensorless conditions, this invention designs an improved sliding mode observer (SMO). This observer uses stator voltage and current signals to calculate the induced electromotive force component in real time, and achieves state observation and speed estimation through a nonlinear switching function.

[0046] Step 201: Based on the mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system, the dynamic system equation of the stator current can be rewritten as follows:

[0047] In the formula: The electrical angle of the permanent magnet synchronous motor; For permanent magnet flux linkage in motors; This is the equivalent induced electromotive force in a synchronously rotating coordinate system.

[0048] Step 202: Construct the following improved sliding mode observer equations in the synchronous rotating coordinate system:

[0049] in, , These are stator current observations in a synchronously rotating coordinate system. , This refers to the stator voltage in a synchronously rotating coordinate system.

[0050] Step 203: Estimate the current value using a sliding mode observer, and define the sliding surface switching function as follows:

[0051] Traditional sliding mode observers based on sign functions are prone to significant high-frequency chattering when entering the sliding surface. The impact of chattering can generally be mitigated by adding low-pass filtering or phase compensation, but this often complicates the system structure and may introduce a certain response delay.

[0052] Step 204: This invention introduces the Sigmoid function in a synchronously rotating coordinate system to replace the traditional sign function, enabling the system to achieve more continuous switching near the sliding surface. Its expression is:

[0053] In the formula, k For sliding mode gain μ This is a smoothing coefficient used to adjust the smoothness of the switching function. When μ When a suitable range is selected, a good balance can be achieved between chatter suppression and dynamic response speed, thereby improving the smoothness and stability of the observation process.

[0054] Step 205: Subtract the sliding mode observer current observation equation from sub-step 202 from the rewritten stator current equation from sub-step 201 to obtain the system current error state equation:

[0055] In the formula, , This represents the error in current observations under a synchronously rotating coordinate system.

[0056] Step 206: To ensure numerical stability and suppress high-frequency noise, the sliding mode observer current observation equation in sub-step 205 is discretized using the reverse difference method, resulting in:

[0057] In the formula T s The sampling time of the system.

[0058] Step 207: When the system enters the sliding mode, there is The system's equivalent control voltage is derived from the current error state equation based on the equivalent control principle:

[0059] Step 208: To verify the stability of the system's observer part, construct the following Lyapunov function:

[0060] Step 209: Differentiate it and substitute it into the current error dynamic equation in sub-step 205 to obtain the derivative expression of the Lyapunov function for the system observer part:

[0061] Step 210: According to the Lyapunov stability criterion, to ensure the stability of the sliding mode observer and enable the system trajectory to reach the sliding surface, the system needs to satisfy the following conditions: ,Right now:

[0062] Step 211: Therefore, the sliding mode gain can be derived from the Lyapunov function derivative expression of the system observer part in sub-step 209 and the stability criterion formula in sub-step 210. k The range of values ​​for is:

[0063] Under these conditions, the system not only remains asymptotically stable in the Lyapunov sense, but also satisfies sliding mode reachability, enabling the state trajectory to approach the sliding surface and enter the sliding motion phase within a finite time.

[0064] To suppress high-frequency noise interference, this invention incorporates a low-pass filter at the output of the estimation signal. The low-pass filter uses an IIR filter to extract a smooth induced electromotive force component. This signal is then input into a phase-locked loop (PLL) module for angle and velocity extraction, thereby obtaining the rotor position estimate. and estimated rotational speed .

[0065] A phase-locked loop (PLL) is used to optimize and estimate the rotor position and speed. The PLL receives the estimated value of the induced electromotive force output by the sliding mode observer and extracts smooth rotor speed and position estimates through a PI control adjustment loop. The estimated rotational speed The robust predictive controller feeds back to the outer loop of the speed measurement; the position estimate is then fed back to the outer loop. Feedback is sent to the coordinate transformation module to realize the current in d , q Decoupling control between axes ensures the correct execution of the inner and outer current control laws; After obtaining the back electromotive force component of the motor by the sliding mode observer, in order to further improve the accuracy and stability of speed estimation, this invention introduces a phase-locked loop (PLL) structure based on PI regulation in the synchronous rotating coordinate system.

[0066] Step 301, by It can be seen that speed estimation can be achieved by... q The shaft-induced electromotive force was calculated as follows:

[0067] Step 302, however, the rotor estimated in this way Position and speed are easily affected by flux fluctuations and integral drift, leading to deviations. Therefore, a phase-locked loop (PLL) structure based on PI control is introduced. The three-phase motor voltages are transformed to a rotating coordinate system, resulting in:

[0068] Step 303: Set the electric angular velocity estimation error to... Under ideal tracking conditions At the same time, a PI control adjustment loop is constructed to achieve speed synchronization:

[0069] in, , These are the proportional and integral coefficients of the phase-locked loop, respectively.

[0070] Step 304: Construct the closed-loop transfer function corresponding to the PI control structure as follows:

[0071] Based on the desired damping ratio Expected bandwidth The parameters of the PI controller can be obtained as follows: .

[0072] Through the aforementioned PI-based phase-locked loop (PLL) structure, the system can maintain smooth tracking of the electric angular velocity even in the presence of observation noise and parameter disturbances, effectively suppressing estimation errors caused by flux fluctuations and integral drift. Ultimately, the angular velocity output by the PLL module... With position The signal is fed back to the speed outer loop predictive controller and other modules of the system in real time, realizing high-precision closed-loop control under sensorless conditions.

[0073] The sliding mode observer of this invention, by employing a combined structure of a sigmoid smooth switching function and a phase-locked loop, significantly reduces chattering and noise sensitivity while ensuring fast response, improves estimation accuracy and system robustness, and provides reliable speed and position signal support for sensorless robust predictive-backstep dual-loop control of permanent magnet synchronous motors.

[0074] Construct a robust predictive controller for the outer loop of the rotational speed; this robust predictive controller uses the target reference rotational speed as the reference speed. and the estimated rotor speed As input, the velocity error is calculated, and a nonlinear robust predictive control law is constructed based on the proportional-integral error trend index, resulting in... q Shaft reference current expression, output q Shaft reference current ; To improve speed regulation performance while ensuring stability, this invention constructs a robust nonlinear predictive control strategy based on short-time domain prediction of speed error trends to replace the traditional PI controller, thereby achieving faster dynamic response and higher steady-state accuracy.

[0075] Step 401: Combine the electromagnetic torque expression and mechanical motion equation from sub-step 1... Then, the new mechanical motion equation expression for the permanent magnet synchronous motor can be derived:

[0076] Step 402: The spatial model of the motion equations of the permanent magnet synchronous motor based on sub-step 201 can be defined as follows:

[0077] In the formula, , , , , , , .

[0078] Step 403: In order to improve the controller's ability to respond quickly to sudden system disturbances while maintaining the accuracy of steady-state tracking, this invention improves the traditional error trend term. Based on this, the following proportional-integral error trend index is constructed:

[0079] This structure integrates current and historical error accumulation, which can enhance early-stage adjustment capabilities and steady-state tracking performance, thus contributing to improved overall controller performance and robustness. This represents the real-time rotational speed error; This is the integral of the rotational speed error, i.e., the error in angular displacement; α、β This is a weighting coefficient, and its value determines the controller's ability to suppress dynamic and long-term deviations.

[0080] Step 404: Based on the proportional-integral error trend index in sub-step 203, establish the cost function of the speed loop prediction model:

[0081] in, ,parameter τ This represents the prediction time domain, i.e., the time span of the prediction. After Taylor expansion to the second-order terms, we have...

[0082] Step 405: The error trend index can be further expressed as a matrix based on the expansion of the error trend index in sub-step 204. Therefore, the cost function of the prediction model can be expressed as:

[0083] in The specific expression is as follows:

[0084]

[0085] Step 406, let the cost function expression in sub-step 405 be... You can get q The expression for the shaft reference current is:

[0086] In the expression, the proportional gain K p By responding to the dynamic response speed of the system dominated by the current speed error, the integral gain K i Steady-state error is eliminated by accumulating the integral of the speed error; the two work together to achieve rapid speed tracking and ensure the stability of the system under parameter perturbations and external disturbances.

[0087] The proportional gain of the current reference expression in step 407 and sub-step 406K p and integral gain K i The specific representation is as follows:

[0088] Step 408, according to sub-step 406 q From the shaft reference current expression, the error dynamic equation for the outer loop of rotational speed can be derived:

[0089] Steps 409 and 408 form a standard second-order linear ordinary differential equation, and its corresponding characteristic equation is:

[0090] Step 410: According to the Routh criterion, the necessary condition for the stability of a closed-loop system is... , In conjunction with step 407, if the trend indicator's weighting direction on the error is correct, the control law can generate positive proportional and integral gains. Therefore, this invention imposes constraints on the design parameters. , , Under these conditions, the closed-loop characteristic roots of the system can be expressed as:

[0091] because , It can be seen that the real part of the eigenvalues ​​is always negative, and the root locus of the system lies entirely in the left half of the complex plane, thus ensuring closed-loop stability. This enables a robust predictive controller for the outer loop of the rotational speed, based on the target rotational speed. With estimation Calculate the speed error, construct a PI-type predictive control law, and use the trend prediction term of the current error and historical error to achieve feedforward compensation, thereby improving the dynamic response speed and disturbance rejection capability of speed regulation, and outputting... q Shaft reference current .

[0092] This current component is directly transmitted to the inner current loop backstepping controller, which then performs the actual current response. q shaft current This precise tracking allows for indirect and precise regulation of the motor's output electromagnetic torque. Through the design of the aforementioned nonlinear robust predictive controller, the outer loop can generate [data in real time]. q Shaft reference current This provides precise target instructions for the inner-loop backstepping control law, thereby forming a predictive-backstepping dual-loop control framework with fast response and strong robustness.

[0093] Construct an inner-loop integral backstepping controller; this integral backstepping controller receives... q Shaft current reference value and will q Shaft current reference value The control voltage is calculated by comparing the three-phase current sampling signal output by the VI measurement module after Park transformation with the signal, and by constructing an integral backstepping control law. and ; Because the current dynamics of a PMSM in a synchronous rotating coordinate system exhibit strong coupling and nonlinear characteristics, traditional PI controllers struggle to maintain high-quality tracking under parameter disturbances or sudden load changes. This invention, based on the current model in a synchronous rotating coordinate system, introduces a backstepping method to design the control law for the inner current loop. Its control objective is based on the reference current generated by the outer loop. ( Adjust the actual current. , This enables the system to track reference commands quickly and smoothly. Global asymptotic stability of the system is achieved through the design of dynamic equations for current error and Lyapunov stability analysis.

[0094] Step 501: From the stator voltage equation in sub-step 101, the current equation of the PMSM in the synchronous rotating coordinate system can be derived:

[0095] Step 502: To suppress steady-state deviations caused by load disturbances and parameter uncertainties, the current error in the synchronous rotating coordinate system is further defined, and an integral error variable is introduced based on the traditional backstepping method. As an extended state-embedded control law, it enhances the system's robustness and steady-state accuracy. Separately establish... d , q The corresponding error dynamic equation for the shaft:

[0096]

[0097] Step 503: Based on the error dynamic equation in sub-step 502, construct the following Lyapunov functions, satisfying the global asymptotic stability of the system in the Lyapunov sense, and derive... d , q The corresponding control law is generated to enable the dual-axis current to maintain high-precision tracking under disturbance and parameter change conditions.

[0098]

[0099] Step 504: Based on the structure constructed in sub-step 503 dThe Lyapunov function along the axis can be derived by further differentiation:

[0100] Step 505: To eliminate the magnetoresistive effect, set... d Shaft reference current Then according to sub-step 502 d The shaft error equation can be obtained as follows:

[0101] Step 506: Substitute the d-axis current error from sub-step 505 into sub-step 504. d The Lyapunov function of the axis is rearranged to obtain a new one. d The derivative of the Lyapunov function on the axis:

[0102] Step 507, due to d Lyapunov functions of axes Combined with sub-step 506 d The derivative expression of the Lyapunov function of the axis can be obtained by designing d The axis control law is as follows:

[0103] Step 508: The design of sub-step 507 d Substituting the axis control law into sub-step 507 d The derivative of the Lyapunov function along the axis, after simplification, yields:

[0104] That is when hour, The system satisfies Lyapunov stability, therefore d The axis control law setting is established.

[0105] Step 509: Similarly, based on the structure constructed in sub-step 503... q The Lyapunov function of the axis and the stator current equation in step 501 are related to this. q Differentiating the Lyapunov function of the axis yields expression:

[0106] Step 510, according to the settings established in sub-step 502 q The dynamic equation for shaft current error can be derived by subtracting and rearranging. q Shaft current expression:

[0107] Step 511, in sub-step 510 q Substituting the shaft current error expression into substep 509 q The derivative expression of the Lyapunov function of the axis is rearranged to obtain a new one. q The derivative of the Lyapunov function on the axis:

[0108] Step 512, the permanent magnet synchronous motor in sub-step 501 q Substituting the shaft current formula into sub-step 511 q The derivative of the Lyapunov function on the axis, after simplification, yields:

[0109] Step 513, due to q Lyapunov functions of axes Combined with sub-step 512 q The derivative expression of the Lyapunov function of the axis can be obtained by designing q The axis control law is as follows:

[0110] Step 514, in sub-step 513 q Substituting the axis control law into the formula in sub-step 512 and simplifying, we get:

[0111] when hour, The system satisfies Lyapunov stability, and also demonstrates q shaft current at The control law tracks the reference value generated by the speed loop. This allows for effective tracking of the reference trajectory by the rotational speed. q The axis control law setting is established.

[0112] Step 515, set in sub-step 503 d - q The Lyapunov function of the axis is derived and obtained in the synchronous rotating coordinate system. d , q The control law for the axis can be constructed by taking the Lyapunov function of the overall backstepping integral controller and differentiating it, as shown in the following formula:

[0113]

[0114] This invention utilizes Lyapunov functions to perform stability analysis on the current loop, aiming to rigorously prove that the current tracking error can achieve global asymptotic convergence under the designed control law, thus providing a theoretical guarantee for the overall closed-loop stability of the system. From the above equation, it can be obtained that when... and hour, The entire controller satisfies Lyapunov stability, and the backstepping integral current control law designed in sub-steps 507 and 513 can control the current loop respectively. d shaft and q The shaft current is stabilized at a set reference level. By adjusting the control law gain and related parameters, the robustness of the system under parameter variations and external disturbances can be enhanced, ensuring the stability of the current loop.

[0115] Through the design of the above integral backstepping controller, the inner current loop can achieve [the desired control]. , It provides rapid and stable adjustment, effectively suppressing the impact of load disturbances and parameter uncertainties on system performance, and works in conjunction with the speed outer loop predictive controller to form a dual-loop control structure with fast response and strong stability.

[0116] The control voltage and After being sequentially processed by inverse Park transform and space vector pulse width modulation module, the signal is applied to the three-phase bridge arm of the inverter to drive the permanent magnet synchronous motor, thus completing the coordinated control based on predictive-backstep dual-loop and improved sliding mode observer. The specific steps are as follows: Signal acquisition and observation: The three-phase current of the motor is obtained through sampling and coordinate transformation. , Current components, and the inner loop reference current ( The comparison generates current error. Simultaneously, the sliding mode observer and phase-locked loop use the motor stator voltage and current information to estimate the rotor position. With rotational speed This estimated value is fed back to the outer loop controller in real time.

[0117] Outer loop adjustment: The speed outer loop is adjusted to the desired speed. Compared with estimated speed As input, calculate the speed error. A torque component reference current is generated using a PI-type predictive control law. And maintain the reference current of the flux linkage component. The outer ring's predictive compensation term pre-corrects future error trends, enabling rapid dynamic response.

[0118] Inner loop control: The inner loop receives the input from the outer loop. In combination with the current situation The control voltage is calculated using an integral backstep control law. , This control law is based on Lyapunov stability theory, ensuring the global asymptotic stability of the system, and eliminating steady-state error through integral terms, thereby achieving rapid current decoupling and precise tracking.

[0119] Motor drive execution: The voltage command output from the inner loop is modulated by PWM or SVPWM and applied to the three-phase bridge arm of the inverter to drive the PMSM operation. In actual operation, current and voltage signals are continuously sampled and fed back, forming a real-time adaptive closed loop.

[0120] Dual-loop cooperative operation mechanism: Estimated velocity provided by sliding mode observer This is the outer loop feedback quantity; the outer loop generates a reference current. The inner loop adjusts the voltage based on the reference current to achieve precise control of the electromagnetic torque; the torque output reacts to the motor speed, forming a speed closed loop.

[0121] Through the aforementioned dual-loop collaborative mechanism, this invention achieves high-speed closed-loop control under sensorless conditions, enabling the system to maintain stable operation under complex working conditions such as sudden load changes and parameter variations, and significantly improving the dynamic response performance and operating accuracy of the motor control system.

[0122] Combination Figures 1-5 This invention proposes a sensorless robust predictive-backstep dual-loop control device for permanent magnet synchronous motors. The device includes a memory and a processor. The memory stores a motor control program, and when the processor executes the motor control program, it implements the aforementioned motor control method.

[0123] The three-phase current and voltage are sampled by the VI measurement module between the inverter and the motor, and then obtained through Park coordinate transformation. d , q Axis current components , The input is fed to the backstepping controller in the inner current loop for adjustment; simultaneously, the acquired voltage and current signals are input to the sliding mode observer to achieve real-time estimation of the induced electromotive force component. The electromotive force signal output from the observer is processed by the phase-locked loop module to obtain smooth speed and position signals, which are then fed back to the outer speed predictive controller and the Park transform module, respectively. The outer speed predictive controller calculates the speed error based on the feedback speed and the target speed, generating... q Shaft reference current This information is then transmitted to the backstepping controller in the inner current loop; the inner loop backstepping controller calculates the voltage command based on the reference current. , After being modulated by the space vector pulse width modulation module, it acts on the inverter bridge to drive the motor and realize the dual closed-loop operation of the system.

[0124] The sensorless robust predictive-backstep dual-loop control method and device for permanent magnet synchronous motors proposed in this invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A sensorless robust predictive-backstepping dual-loop control method for a permanent magnet synchronous motor, characterized in that, The method includes: based on d - q A mathematical model of a permanent magnet synchronous motor is established using a synchronous rotating coordinate system; Constructing a sliding mode observer: The sliding mode observer receives three-phase current and voltage sampling signals sampled by the VI measurement module and processed by Park transformation; The sliding mode observer uses the Sigmoid function as the switching function to calculate the induced electromotive force component in real time to obtain the estimated value of the induced electromotive force in the synchronous rotating coordinate system; The rotor position and speed are optimized and estimated using a phase-locked loop (PLL): The PLL receives the estimated value of the induced electromotive force output by the sliding mode observer, and extracts a smooth speed estimate through a PI control adjustment loop. With location estimate The estimated rotational speed The robust predictive controller feeds back to the outer loop of the speed measurement; the position estimate is then fed back. Feedback is sent to the coordinate transformation module to realize the current in d , q Decoupling control between axes; Constructing a robust predictive controller for the outer loop of the rotational speed: This robust predictive controller uses the target reference rotational speed as the reference speed. and the estimated rotational speed As input, the speed error is calculated, and a nonlinear robust predictive control law is constructed based on the speed error and the proportional-integral error trend index, resulting in... q Shaft reference current expression, output q Shaft reference current ; Construct an inner-loop integral backstepping controller: This integral backstepping controller receives... q Shaft current reference value and will q Shaft current reference value The control voltage is calculated by comparing the three-phase current sampling signal output by the VI measurement module after Park transformation with the signal, and by constructing an integral backstepping control law. and ; The control voltage and After being successively modulated by the inverse Park transformation and the space vector pulse width modulation module, it is applied to the three-phase bridge arm of the inverter to drive the permanent magnet synchronous motor to run, thus completing the coordinated control based on the predictive-backstep dual loop and the improved sliding mode observer.

2. The method according to claim 1, characterized in that, exist d - q In a synchronous rotating coordinate system, the stator voltage equation and electromagnetic torque equation of a permanent magnet synchronous motor are as follows: In the formula, and They represent shaft and Stator current on the shaft; and They represent shaft and Stator voltage on the shaft; and They represent shaft and Stator inductance on the shaft; This refers to the mechanical angular velocity of the motor. R and P These are the fixed resistance and the number of pole pairs of the motor, respectively. Represents permanent magnet flux linkage; Represents permanent magnet flux linkage; In a synchronous rotating coordinate system, the mechanical motion equations of a permanent magnet synchronous motor are: In the formula, It is the moment of inertia; The damping coefficient; and These represent electromagnetic torque and load torque, respectively.

3. The method according to claim 1, characterized in that: The VI measurement module is located between the inverter and the motor; The control law of the sliding mode observer is: In the formula, k For sliding mode gain; μ This is the smoothness coefficient, used to adjust the smoothness of the switching function.

4. The method according to claim 3, characterized in that: According to the Lyapunov stability criterion, the sliding mode gain k The range of values ​​for is: In the formula, for d Error in shaft current observations; for q Error in current observations; E d for d Shaft-induced electromotive force. E q for q Shaft-induced electromotive force; R This is the stator resistor for the motor; L d for q Shaft stator inductance; ω is the electric angular velocity.

5. The method according to claim 1, characterized in that: The signal output terminal of the sliding mode observer is equipped with a low-pass filter module to suppress high-frequency noise interference and extract smooth induced electromotive force components; the low-pass filter module is an IIR type filter.

6. The method according to claim 1, characterized in that: The coordinate transformation module includes a Park module and an inverse Park transformation module; The PI control adjustment mechanism is as follows: in, , These are the proportional and integral coefficients of the phase-locked loop, respectively. s For the Laplace operator; The closed-loop transfer function corresponding to the PI control structure is: In the formula, This is a location estimate; This is the actual electrical angle; V q for q Shaft voltage command; s For the Laplace operator; The desired damping ratio; The desired bandwidth; Based on the desired damping ratio With expected bandwidth The parameters of the PI controller are: Speed ​​estimate With location estimate for: In the formula, This is an estimated value for the electric angular velocity; P This represents the number of pole pairs of the motor. , These are the proportional and integral coefficients of the phase-locked loop, respectively. for d Shaft reference voltage; for d Actual shaft voltage; for d The integral term of the shaft voltage deviation; This is the integral term of the estimated electric angular velocity.

7. The method according to claim 1, characterized in that: The speed error is: In the formula, For the target reference speed, The estimated rotational speed for the sliding mode observer.

8. The method according to claim 1, characterized in that: The proportional-integral error trend index is: in, α、β The weighting coefficient is adjusted by... α、β The ability of the value adjustment controller to suppress dynamic and long-term deviations; For speed error; From the initial time to the current time t Integral over the speed error; The nonlinear robust predictive control law is: In the formula, K p The proportional gain is used to determine the dynamic response speed of the system by responding to the current velocity error. K i The integral gain is used to eliminate steady-state error by integrating the accumulated velocity error. J It is the moment of inertia; P It is the extreme logarithm; For permanent magnet flux linkage; For speed error; The damping coefficient; The desired rotational speed; The feedback rotational speed estimated for the sliding mode observer.

9. The method according to claim 1, characterized in that: The three-phase current sampling signal includes d Axis current components and q Axis current components; The integral backstep control law is as follows: In the formula, U d for d Shaft voltage command; L d for d Shaft stator inductance; R This is the stator resistor for the motor; i d for d Actual stator current of the shaft; P This represents the number of pole pairs of the motor. This refers to the mechanical angular velocity of the motor. L q for q Shaft stator inductance; i q for q Actual stator current of the shaft; for d The proportional gain of the shaft current loop; for d The proportional-integral error variable of the shaft current; for d Shaft reference current; for d Integral gain of the shaft current loop; for d The integral term of the shaft current error; U q for q Shaft voltage command; L q for q Shaft stator inductance; For permanent magnet flux linkage; for q The proportional gain of the shaft current loop; for d The proportional-integral error variable of the shaft current; for q Integral gain of the shaft current loop; for q Shaft reference current; for q The integral term of shaft current error.

10. A sensorless robust predictive-backstepping dual-loop control device for a permanent magnet synchronous motor, characterized in that, The device includes a memory and a processor. The memory stores a motor control program. When the processor executes the motor control program, it implements the motor control method according to any one of claims 1-9.

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