Improved sliding mode observer based on back electromotive force disturbance compensation

Abstract

The invention discloses an improved sliding-mode observer based on back electromotive force disturbance compensation, which comprises a current observation module, a control law module and a back electromotive force observation module, and is characterized in that the input end of the current observation module is divided into two parts, one part is stator voltage U alpha beta on an Alpha axis and a Beta axis output by a current inner loop PI controller, and the other part is stator voltage U alpha beta on a Beta axis; the other part is stator current I alpha beta on an Alpha axis and a Beta axis sampled by a current sensor, an output signal of the current observation module is estimated current I * alpha beta on the Alpha axis and the Beta axis, counter electromotive force is considered to serve as disturbance quantity of a current observer for modeling, and a corresponding counter electromotive force disturbance equation is established. Compared with a traditional sliding-mode observer, the method can effectively expand the observation range of the sliding mode, and improves the convergence of the whole speed domain of the sliding-mode observer.

Description

Technical Field

[0001] The invention relates to the technical field of power grids, in particular to an improved sliding mode observer based on back electromotive force disturbance compensation. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) usually uses position sensors to detect the rotor position, but the use of sensors not only increases system cost and complexity, but is also sensitive to extreme environments. Among position sensorless technologies, the sliding mode observer is the most widely used, which is based on sliding mode control theory and has strong robustness and adaptability.

[0003] In the latest research, on the one hand, by establishing a disturbance observer model, the sliding mode has increased its resistance to heavy loads, speed mutations, etc., but this scheme does not fundamentally increase the observation accuracy of the sliding mode in the steady state, and the disturbance observation has high requirements on the model parameters; on the other hand, by designing a piecewise square root function as the control law of the observer to replace the original sign function, the chattering problem of the sliding mode can be effectively reduced, but the observation effect in the full speed domain needs to be studied.

[0004] At present, the research focus and difficulties of sliding mode control theory are mainly concentrated in two aspects. First, the convergence problem of the sliding mode observer within a limited time range, that is, the reachability condition of the sliding mode, has become the core research topic. The reachability condition involves the arrival time of the system state on the sliding surface and the stability within the sliding surface, ensuring that the system can reach the expected state within the specified time. The complexity of this problem stems from the diversity and uncertainty of nonlinear systems, making it particularly difficult to design a suitable sliding mode control law to meet the convergence requirements. Therefore, in-depth exploration of the reachability conditions of sliding mode control, especially its performance under different working environments and system dynamics, is an important direction of current research. Secondly, due to the existence of the switching function in the observer, the inherent chattering problem of the sliding mode control system has also become a challenge that is difficult to eliminate. The mutation of the switching function leads to rapid changes in the control input, which triggers high-frequency oscillations in the system response. This chattering not only affects the stability and control accuracy of the system, but may also damage the long-term operation of the system. Therefore, researchers need to explore smoother switching function design schemes to reduce the chattering effect while maintaining the robustness and response speed of the system. By optimizing the shape and parameter settings of the switching function, the chattering problem can be alleviated to a certain extent, thereby improving the performance of the sliding mode control system in practical applications. Summary of the invention

[0005] In order to improve the applicability of sliding mode in different scenarios, further improve system stability and reduce the impact of sliding mode observer jitter problems, and solve the above-mentioned key and difficult problems, the present invention first establishes a disturbance observer based on back-electromotive force, which can improve the global convergence of the sliding mode and accurately observe the electrical angle at no-load of 0.03pu; then, an improved piecewise square root switching function is designed, which can reduce the position error in steady state to an electrical angle of ±0.0005pu.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] An improved sliding mode observer based on back-electromotive force disturbance compensation includes a current observation module, a control law module and a back-electromotive force observation module. The input end of the current observation module is divided into two parts. One part is the stator voltage U on the Alpha and Beta axes output by the current inner loop PI controller. αβ The other part is the stator current I on the Alpha and Beta axes obtained by sampling the current sensor. αβ The output signal of the current observation module is the estimated current I* on the stator shafts Alpha and Beta. αβ The back-EMF prediction module monitors the back-EMF in the system and outputs a disturbance signal e* αβ , used for subsequent control; the control law module generates a control signal based on the results of current monitoring and back-EMF monitoring to adjust the operating state of the system.

[0008] As a further technical solution of the present invention: the improved sliding mode observer is connected to the sensorless control system of the permanent magnet synchronous motor, and its input signal is the stator voltage on the Alpha and Beta axes output by the current inner loop PI controller and the stator current on the Alpha and Beta axes obtained by sampling the current sensor, and its output signal is the estimated back electromotive force of the Alpha and Beta axes, which contains the rotor position information, and the rotor electrical angle is obtained by the inverse tangent method.

[0009] As a further technical solution of the present invention: the permanent magnet synchronous motor sensorless control system includes a speed calculation module, a PI controller, a subtractor, an inverse tangent module, a Park inverse transformation module, a Clarke transformation module, a three-phase inverter, a sensor and a permanent magnet synchronous motor.

[0010] As a further technical solution of the present invention: the speed calculation module is used to perform integration processing on the position, and the calculation formula is:

[0011] w e =∫θdt

[0012]

[0013] Among them, θ is the angular velocity, n is the rotational speed, and np is the number of motor pole pairs.

[0014] As a further technical solution of the present invention: the parameters of the improved sliding mode observer are as follows:

[0015] Correlation coefficient B = (1-exp(-R s T s / L q )) / R s ;

[0016] Perturbation upper bound: m = (2*pi*N_base*2*p / 60)*V_base*T s ;

[0017] Back EMF disturbance observer gain: Back Emf Gain = 0.9;

[0018] Current observer gain: Current Gain = 1.1*B*m / Back Emf Gain;

[0019] Low-pass filter cutoff frequency: Cutoff Freq = 3*N_base*p / 60;

[0020] In the formula, R s is the stator resistance of the permanent magnet synchronous motor; L q is the stator resistance of the permanent magnet synchronous motor; T s is the sampling frequency of the system; N_base is the rated speed of the motor; V_base is the maximum back electromotive force of the motor; p is the number of pole pairs.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. The present invention considers the back electromotive force as the disturbance quantity of the current observer to model and establishes the corresponding back electromotive force disturbance equation. Compared with the traditional sliding mode observer, this method can effectively expand the observation range of the sliding mode and improve the convergence of the sliding mode observer in the full speed domain.

[0023] 2. In addition, the present invention designs an improved piecewise square root switching function. Compared with the traditional piecewise function, the new switching function has a smoother characteristic. By reasonably setting the boundary layer, small error amplification and large error saturation are achieved. This design can not only improve the convergence speed of the observer, but also significantly reduce the position error in the steady state.

[0024] 3. The present invention relies on fewer sliding mode parameters and does not require high accuracy of the parameters of the motor model. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1It is the sensorless control block diagram of permanent magnet synchronous motor.

[0026] Figure 2 It is a schematic diagram of the disturbance sliding mode observer of the present invention.

[0027] Figure 3 It is a schematic diagram of the switching function. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] In order to improve the convergence of the sliding mode observer and its adaptability in complex environments, the present invention considers modeling the back electromotive force as a disturbance in the current observer. By accurately modeling the system back electromotive force disturbance, the back electromotive force disturbance equation can be established to better characterize the relationship between the system dynamic behavior and the model uncertainty. In the traditional sliding mode observer design, it is often assumed that the system model is known and the disturbance has a limited impact on the performance of the observer. However, in practical applications, the back electromotive force in nonlinear systems such as motors will produce significant disturbances due to factors such as load changes and temperature fluctuations.

[0030] By introducing back-EMF as a disturbance factor, not only can the dynamic characteristics of the system be characterized more accurately, but also the robustness of the sliding mode observer to various uncertainties can be enhanced. Compared with the traditional sliding mode observer, this method significantly expands the observation range and applicability of the observer, and can achieve accurate estimation of the system state under a wider range of working conditions. In addition, this method can effectively reduce the observation error caused by model simplification, thereby improving the accuracy and reliability of system control.

[0031] In order to improve the performance of the sliding mode observer, the present invention proposes an improved piecewise square root switching function. Compared with the traditional piecewise switching function, the new switching function shows a smoother characteristic in the transition region, which not only reduces the jitter phenomenon in the switching process, but also effectively reduces the continuity error of the system.

[0032] The improved switching function achieves a differentiated response to the system error by reasonably setting the boundary layer, which is specifically manifested in the "amplification effect under small error conditions" and the "saturation effect in the large error stage". In the case of small errors, the switching function will moderately amplify the error, thereby accelerating the convergence of the system to the target state; in the case of large errors, the switching function will adopt a saturation strategy to avoid overreaction of the control input. This design not only effectively improves the convergence speed of the observer, but also significantly reduces the position error in steady state.

[0033] By applying this new switching function, the dynamic and steady-state performance of the observer has been significantly improved, so that the robustness and accuracy of the system can be maintained in a more complex and changing environment. In general, this improvement provides a more flexible and efficient tool for the design of control systems, which helps to fundamentally improve the performance of sliding mode observers in various application scenarios.

[0034] like Figure 1 As shown, the present invention is based on the fact that the DC current is zero (I d =0) is designed to control the surface-mounted permanent magnet synchronous motor. The design of the control scheme includes two key components: the current inner loop and the speed outer loop. In the current inner loop control, the key coordinate transformation process involves the accurate estimation of the electrical angle. To this end, this scheme adopts the disturbance sliding mode observer (DSMO) to obtain the electrical angle in real time. The sliding mode observer can effectively deal with the uncertainty and external disturbances in the system, provide a fast and reliable estimation of the electrical angle, ensure that the current loop can respond quickly under dynamic operation, and then accurately control the current regulation. In the speed outer loop control, in order to achieve effective feedback on the motor speed, the scheme integrates the estimated electrical angle to obtain accurate speed information. This speed feedback mechanism not only improves the stability of the control system, but also enhances the adaptability to external load changes. Through the integral calculation of the electrical angle, more accurate speed tracking can be achieved, and the speed outer loop and the current inner loop are organically combined to achieve coordinated control.

[0035] Figure 1 middle, is the stator current value estimated by the current observer; is the back-EMF disturbance variable value estimated by the disturbance observer model; A and B are the correlation coefficients of the observer discrete model; u αβ is the voltage of stator axis Alpha and Beta; sgn(k) is different from the sign function and is the designed improved piecewise square root switching function; η is the current observer gain; g is the back electromotive force observer gain; w e is the electrical angular velocity of the rotor; w cis the cutoff frequency of the low-pass filter.

[0036] The input of the sliding mode observer is divided into two parts, one is the stator voltage on the Alpha and Beta axes output by the current inner loop PI controller, and the other is the stator current on the Alpha and Beta axes sampled by the current sensor. Its output is the estimated back electromotive force of the Alpha and Beta axes, which contains the rotor position information. The rotor electrical angle can be obtained by the inverse tangent method, that is, the synchronous rotation angle used in the Park transform and the inverse Park transform.

[0037] The speed calculation module in the figure is used to perform integral processing on the position. The calculation formula is:

[0038] w e =∫θdt

[0039]

[0040] Among them, θ is the angular velocity, n is the rotation speed, and n p is the number of motor pole pairs.

[0041] PI is the speed loop PI controller, which is an abbreviated form of the common PID controller. PI is used for adjustment. qref It is the torque given current, which is the output of the speed loop;

[0042] The inverse tangent is a trigonometric calculation process;

[0043] In the formula,

[0044]

[0045] in, is the back electromotive force of the aβ-axis stationary coordinate system, which comes from the perturbation sliding mode observer calculation w, is the observed synchronous velocity, which is the integral of the observed position angle;

[0046] w is the low-pass filter cutoff frequency, which is generally twice the rated frequency of the motor.

[0047] Park transformation is a coordinate axis conversion calculation, and Clark transformation is also a common conversion.

[0048]

[0049] Alfa and beta axis calculations are converted to dq axis calculations.

[0050]

[0051] SVPWM means space vector modulation wave.

[0052] The back EMF and current difference in the disturbance sliding mode observer are calculated as follows:

[0053] Observation current:

[0054]

[0055] Observe the back EMF:

[0056]

[0057] Observe the back EMF difference:

[0058]

[0059] Observe the current difference:

[0060]

[0061] like Figure 2 As shown in the figure, the disturbance sliding mode observer is a complex monitoring and control system. Through the coordinated work of multiple modules, it realizes real-time monitoring and regulation of current and electromotive force to ensure efficient and stable operation of the system. αβ is the estimated current on stator axes Alpha and Beta, e* αβ is the estimated back EMF. The back EMF prediction module monitors the back EMF in the system and outputs a disturbance signal e* αβ , which is used for subsequent control; the control law module generates a control signal based on the results of current monitoring and back-EMF monitoring to adjust the operating state of the system and ensure that the current error converges to 0; the current prediction module can monitor the current in real time, and according to the feedback back-EMF disturbance signal, it can accelerate convergence and improve the stability of the system. The specific formula part is Figure 1 As shown in I αβ and U αβ Equivalent to Figure 1 The feedback current i αβ , and calculate the output voltage u αβ .

[0062] like Figure 3 As shown in the figure, the boundary layer is the upper bound of the control law output. Reasonable setting of the boundary layer can speed up the convergence of the system. The larger the boundary layer, the higher the slope of the switching function, the larger the switching amplitude of the control law, and the faster the system converges; the smaller the boundary layer, the flatter the slope of the switching function, the smaller the switching amplitude of the control law, and the smaller the position deviation of the system in steady state. The system achieves a differentiated response to the error, which is manifested in two extreme effects: the amplification effect under small errors and the saturation effect under large errors. Compared with the compliance function, it can significantly smooth the chattering effect of the system.

[0063] Observer parameter tuning:

[0064] Observer correlation coefficient: B = (1-exp(-R s T s / L q )) / R s ;

[0065] Perturbation upper bound: m = (2*pi*N_base*2*p / 60)*V_base*T s ;

[0066] Back EMF disturbance observer gain: Back Emf Gain = 0.9;

[0067] Current observer gain: Current Gain = 1.1*B*m / Back Emf Gain;

[0068] Low-pass filter cutoff frequency: Cutoff Freq = 3*N_base*p / 60;

[0069] In the formula, R s is the stator resistance of the permanent magnet synchronous motor; L q is the stator resistance of the permanent magnet synchronous motor; T s is the sampling frequency of the system; N_base is the rated speed of the motor; V_base is the maximum back electromotive force of the motor; p is the number of pole pairs;

[0070] As shown in the above formula, when the back-EMF observer gain g∈(0,1) is selected, the convergence of the back-EMF error can be guaranteed. The larger the value, the higher the observation accuracy, but the convergence speed will decrease. It is recommended to take a value of about 0.9. Assuming that the back-EMF disturbance has an upper bound m, there is That is, for all k, we have The value of the upper bound m needs to be selected based on the module sampling time and the maximum slope of the back EMF. In order for the current observer to converge, When there is disturbance in the system, a smaller boundary layer m and a relatively smaller gain value η (η is slightly larger than B*m / g) are selected. It will gradually approach 0. When it is estimated that the current estimation error is close to 0, it can be determined that the established sliding mode disturbance model is close to the current actual voltage model, and the electrical angle is calculated by the inverse tangent according to the current estimated back electromotive force, and fed back to the speed loop and current loop.

[0071] Embodiment 2, based on embodiment 1, in order to improve the stability and accuracy of sliding mode full-speed domain observation, a high-order observer such as a super-torsion sliding mode observer can also be adopted, but the selection of switching gain always requires a trade-off, and the sliding mode parameter tuning is more difficult.

[0072] Embodiment 3, based on embodiment 1, the sliding mode observer can also be modeled based on the DQ axis voltage coordinate system. In this case, the rotor position can be extracted through a phase-locked loop. However, when there is an error between the actual speed and the estimated speed of this scheme, a large position estimation error will be caused.

[0073] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0074] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. An improved sliding mode observer based on back electromotive force disturbance compensation, characterized in that: It includes current observation module, control law module and back electromotive force observation module. The input end of the current observation module is divided into two parts. One part is the stator voltage U on the Alpha and Beta axes output by the current inner loop PI controller. αβ The other part is the stator current I on the Alpha and Beta axes obtained by sampling the current sensor. αβ The output signal of the current observation module is the estimated current I* on the stator shafts Alpha and Beta. αβ The back-EMF prediction module monitors the back-EMF in the system and outputs a disturbance signal e* αβ , used for subsequent control; the control law module generates a control signal based on the results of current monitoring and back-EMF monitoring to adjust the operating state of the system.

2. The improved sliding mode observer based on back electromotive force disturbance compensation according to claim 1, characterized in that: The improved sliding mode observer is connected to the sensorless control system of the permanent magnet synchronous motor. Its input signals are the stator voltages on the Alpha and Beta axes output by the current inner loop PI controller and the stator currents on the Alpha and Beta axes obtained by sampling the current sensor. Its output signal is the estimated back electromotive force of the Alpha and Beta axes. The back electromotive force contains rotor position information, and the rotor electrical angle is obtained by the inverse tangent method.

3. The improved sliding mode observer based on back electromotive force disturbance compensation according to claim 2 is characterized in that: The permanent magnet synchronous motor sensorless control system comprises a speed calculation module, a PI controller, a subtractor, an inverse tangent module, a Park inverse transformation module, a Clarke transformation module, a three-phase inverter, a sensor and a permanent magnet synchronous motor.

4. The improved sliding mode observer based on back electromotive force disturbance compensation according to claim 3 is characterized in that: The speed calculation module is used to perform integration processing on the position, and the calculation formula is: In e =∫θdt Among them, θ is the angular velocity, n is the rotational speed, and np is the number of motor pole pairs.

5. The improved sliding mode observer based on back electromotive force disturbance compensation according to claim 4, characterized in that: The parameters of the improved sliding mode observer are as follows: Correlation coefficient B = (1-exp(-R s T s / L q )) / R s ; Perturbation upper bound: m = (2*pi*N_base*2*p / 60)*V_base*T s ; Back EMF disturbance observer gain: Back Emf Gain = 0.9; Current observer gain: Current Gain = 1.1*B*m / Back Emf Gain; Low-pass filter cutoff frequency: Cutoff Freq = 3*N_base*p / 60; In the formula, R s is the stator resistance of the permanent magnet synchronous motor; L q is the stator resistance of the permanent magnet synchronous motor; T s is the sampling frequency of the system; N_base is the rated speed of the motor; V_base is the maximum back electromotive force of the motor; p is the number of pole pairs.

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