A segmented linear induction motor position sensorless control method based on extended state observer phase-locked loop
By introducing an extended state observer phase-locked loop and an integral sliding mode surface combined with an exponentially approaching sliding mode observer, the problems of sliding mode chattering and fluctuations in phase-locked loop speed observations in piecewise linear induction motors are solved, enabling accurate position and speed estimation under high dynamic conditions and improving the reliability and robustness of the system.
Patent Information
- Application Number
- CN202610594674.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-04-30
- Publication Date
- 2026-06-30
AI Technical Summary
Existing sensorless control methods for segmented linear induction motors suffer from problems such as large chattering of the sliding mode observer, large fluctuations in the phase-locked loop speed observation value, and slow response speed, making it difficult to meet the application requirements under short-term high-acceleration conditions.
A control method based on an extended state observer phase-locked loop (ESO-PLL) is adopted. By combining an integral sliding mode surface and an exponential reaching law sliding mode observer, back electromotive force observations are constructed. Synchronous angular velocity and synchronous electrical angle are extracted through the extended state observer phase-locked loop (ESO-PLL) to achieve accurate estimation of secondary velocity and displacement.
It effectively suppresses sliding mode chattering, improves the response speed of the phase-locked loop, enhances the observation accuracy and robustness of the system under high dynamic operating conditions, and ensures accurate estimation of secondary position and velocity.
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Figure CN122316149A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of motor control technology, and more specifically, relates to a sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop. Background Technology
[0002] The secondary winding of the segmented linear induction motor is composed of lightweight aluminum plates, which has the advantages of simple structure and high thrust-to-weight ratio. It has good application prospects in short-term high-acceleration scenarios such as electromagnetic propulsion systems and automobile crash tests.
[0003] Because segmented linear induction motors have a segmented primary structure, multiple inverters connected in parallel are typically used in practical applications. In this configuration, accurate secondary position signals are crucial for determining the switching timing of each inverter. Inaccurate secondary position signals can cause premature or delayed inverter switching, leading to reduced thrust and potentially system instability or even loss of control.
[0004] Sensorless control, as a control strategy to improve system reliability and robustness, has been widely applied in various motor systems. Among them, the sliding mode observer, as a nonlinear observer, has advantages such as fast response speed and good parameter robustness, and is a commonly used method in sensorless control. However, traditional sliding mode observers are usually based on linear sliding surfaces, which have shortcomings such as large sliding mode chattering and slow convergence speed. At the same time, traditional phase-locked loops usually use PI controllers to correct angle errors, and their fixed parameters are difficult to meet the requirements of accurate speed observation under wide speed range and high dynamic conditions, resulting in large fluctuations in speed observation values and slow response speed, which is difficult to meet the application requirements of segmented linear induction motors under short-term high acceleration conditions. Therefore, it is urgent to propose a sensorless control method suitable for the high dynamic operating conditions of segmented linear induction motors. Summary of the Invention
[0005] The purpose of this invention is to provide a sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop, which solves the problems of large sliding mode observer chattering, large fluctuations in phase-locked loop speed observations, and slow response speed in existing sensorless control methods for segmented linear induction motors.
[0006] To achieve the above objectives, this invention provides a sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop (PLL). The method includes: Step S1, constructing an equivalent mathematical model of the segmented linear induction motor without coupling coefficient terms based on the unit motor mathematical model of the segmented linear induction motor; Step S2, constructing a sliding mode observer based on an integral sliding surface combined with an exponential reaching law based on the equivalent mathematical model of the segmented linear induction motor to obtain the back electromotive force (EMF) observation value required by the PLL; Step S3, inputting the back EMF observation value into the PLL based on the extended state observer to extract the synchronous angular velocity and synchronous electrical angle, thereby calculating the secondary speed estimate and secondary displacement estimate; Step S4, feeding back the synchronous angular velocity, secondary speed estimate, and secondary displacement estimate to a closed-loop control system to achieve sensorless operation of the segmented linear induction motor. The closed-loop control system is used for segmented power supply switching control based on the secondary displacement estimate and for closed-loop adjustment of the motor's operating state based on the synchronous angular velocity and secondary speed estimate.
[0007] The beneficial effects of this invention are as follows:
[0008] This invention introduces a sliding mode observer based on an integral sliding surface combined with an exponential reaching law to suppress sliding mode chattering, and uses an extended state observer-based phase-locked loop (ESO-PLL) to reduce speed observation jitter and improve the PLL response speed, thereby achieving accurate estimation of secondary position and speed and improving system reliability and robustness. Specifically, it includes: (1) Introducing an integral sliding surface combined with an exponential reaching law can effectively suppress sliding mode chattering and improve the back EMF observation accuracy, thereby improving the observation performance of the system under high dynamic operating conditions; (2) Using ESO-PLL, compared with the traditional PI (Proportional-Integral) type PLL, there is no need to tune the PI parameters and it does not depend on the motor parameters, which can improve the convergence speed of speed observation and reduce speed observation jitter, thereby improving the accuracy of secondary speed and position estimation. Attached Figure Description
[0009] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:
[0010] Figure 1 This is a flowchart of the sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop provided by the present invention;
[0011] Figure 2This is a structural diagram of the sliding mode observer based on the integral sliding surface combined with the exponential reaching law provided by the present invention;
[0012] Figure 3 This is a structural diagram of the phase-locked loop based on the extended state observer provided by the present invention;
[0013] Figure 4 This is a speed observation result diagram of the segmented linear induction motor sensorless control method based on an extended state observer phase-locked loop provided by the present invention;
[0014] Figure 5 This is a displacement observation result diagram of the segmented linear induction motor sensorless control method based on the extended state observer phase-locked loop provided by the present invention. Detailed Implementation
[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.
[0016] Figure 1 This is a flowchart of a sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop, as provided in an embodiment of the present invention. Figure 1 As shown, the method includes:
[0017] Step S1: Based on the unit motor mathematical model of the piecewise linear induction motor, construct an equivalent mathematical model of the piecewise linear induction motor without coupling coefficient terms.
[0018] Step S2: Based on the equivalent mathematical model of the piecewise linear induction motor, construct a sliding mode observer based on the integral sliding mode surface combined with the exponential reaching law to obtain the back electromotive force observation value required by the phase-locked loop.
[0019] Step S3: Input the back EMF observation value into the phase-locked loop based on the extended state observer, extract the synchronous angular velocity and synchronous electrical angle, and calculate the secondary velocity estimate and secondary displacement estimate.
[0020] Step S4: The estimated values of synchronous angular velocity, secondary velocity, and secondary displacement are fed back to the closed-loop control system to realize the sensorless operation of the segmented linear induction motor. The closed-loop control system is used to perform segmented power supply switching control based on the estimated value of secondary displacement, and to perform closed-loop adjustment of the motor operating status based on the estimated values of synchronous angular velocity and secondary velocity.
[0021] The equivalent mathematical model of the piecewise linear induction motor without coupling coefficient terms is as follows:
[0022] ;
[0023] in, For the primary voltage vector sum, For the primary current vector sum, To divide the primary flux linkage vector sum, For the vector sum of secondary currents, For the sum of virtual secondary flux linkage vectors, For synchronous angular velocity, The difference angular frequency, For primary resistors, For secondary resistors, This is a primary level of self-perception. For secondary self-induction, For differential operators, The number of unit motors, For the primary length, For secondary length, This is primary mutual induction.
[0024] Specifically, the mathematical model of the unit motor of the piecewise linear induction motor is as follows:
[0025] ;
[0026] in, For the first The primary voltage vector of each unit motor For the first The flux linkage vector of each unit motor, For the first Virtual secondary voltage vector of each unit motor For the first Virtual secondary flux linkage vector of each unit motor For the first The actual secondary flux linkage vector of each unit motor For the first The proportional coefficient for coupling between the primary and secondary windings of the motor. For the first The primary current vector of each unit motor For the first The secondary current vector of each unit motor This is the serial number of the unit motor.
[0027] Considering In a piecewise linear induction motor system where the secondary winding is simultaneously coupled to n unit motors, assuming the set of unit motors coupled to the secondary winding is (the following is a list of unit motors coupled to the secondary winding at any given time),... For the primary and secondary voltages, currents, and flux linkages of n individually powered unit motors, the vector superposition method is used to calculate the vector parameters of the coupled system, and its expression is:
[0028] ;
[0029] in, For the primary voltage vector sum, For the primary current vector sum, Divide into primary magnetic flux vectors, For the vector sum of secondary currents, For the sum of virtual secondary flux linkage vectors, It is an integer from 1 to n, where n is the number of unit motors.
[0030] Step S2 includes: obtaining the state equation of the equivalent mathematical model in the stationary coordinate system based on the piecewise linear induction motor equivalent mathematical model; and constructing the following expression for the sliding mode observer based on the integral sliding surface combined with the exponential reaching law, according to the state equation of the equivalent mathematical model in the stationary coordinate system:
[0031] ;
[0032] in, These are primary current observations. For sliding mode control law, , , , .
[0033] The state equation of the equivalent mathematical model in the stationary coordinate system is:
[0034] ;
[0035] in, It is the back electromotive force. This is the secondary time constant.
[0036] Figure 2 This is a structural diagram of the sliding mode observer based on the integral sliding surface combined with the exponential reaching law provided by the present invention, as shown in the figure. Figure 2 As shown, the primary current vector sum of the segmented long primary double-sided linear induction motor (LP-DSLIM) is obtained. and primary current observations obtained based on equivalent mathematical models Then, the back electromotive force observation is obtained by combining the integral sliding surface and the exponential reaching law. Below is Figure 2 To elaborate further.
[0037] In step S2, the expression for the integral sliding surface of the sliding mode observer is:
[0038] ;
[0039] Where z is the integral sliding surface, For primary current error, , Let t be the integral sliding surface gain matrix, and t be time.
[0040] The expression for the exponential reaching law is:
[0041] ;
[0042] in, It is the derivative of the integral sliding surface z. It is the switching term coefficient. These are the coefficients of the linear term. It is a symbolic function.
[0043] Differentiating the expression for the integral sliding surface, and based on the expression for the sliding observer and the state equations of the equivalent mathematical model in the stationary coordinate system, combined with the exponential reaching law, we obtain the following intermediate expression:
[0044] ;
[0045] in, It is the back electromotive force.
[0046] Primary current error As the value approaches 0, the sliding mode control law and back electromotive force observations of the sliding mode observer Equal, that is And the sliding mode control law is constructed through the intermediate expression as follows:
[0047] .
[0048] Figure 3 This is a structural diagram of the phase-locked loop based on the extended state observer provided by the present invention. The following is in conjunction with... Figure 3 Step S3 of the present invention will be described in detail below.
[0049] In step S3, the time-domain expression of the phase-locked loop (ESO-PLL) based on the extended state observer is:
[0050] ;
[0051] in, For angular error, This is an estimated value for the synchronous electrical angle. For synchronous electrical angle, This is an estimate of the synchronous angular velocity. This is an estimate of the angular acceleration. The derivative of the estimated synchronous electrical angle is... The derivative of the estimated synchronous angular velocity. The derivative of the estimated angular acceleration is... For the position feedback gain of the extended state observer, For speed feedback gain, For acceleration feedback gain;
[0052] If we define the secondary acceleration as an extended state variable, then we have the following relational expression:
[0053] ;
[0054] in, For synchronous angular velocity, Angular acceleration, Angular acceleration, The differential of the synchronous electrical angle, The derivative of the synchronous angular velocity, It is the differential of angular acceleration.
[0055] Angular error The expression is as follows:
[0056] ;
[0057] in, and The back electromotive force in the stationary coordinate system are respectively shaft and Observations on the axis This represents the amplitude of the observed back electromotive force.
[0058] Step S3 further includes: performing a Laplace transform on the time-domain expression of the phase-locked loop based on the extended state observer to obtain the complex frequency-domain expression and the corresponding transfer function expression of the phase-locked loop based on the extended state observer; and placing the three poles of the phase-locked loop based on the extended state observer at the same point in the left half-plane of the complex plane to obtain the position feedback gain of the extended state observer. Speed feedback gain and acceleration feedback gain .
[0059] Specifically, for the time-domain expression of a phase-locked loop (ESO-PLL) based on an extended state observer, using... express ,use express ,use express By performing a Laplace transform on the time-domain expression of the extended state observer-based phase-locked loop (ESO-PLL), the complex frequency-domain expression is obtained as follows:
[0060] ;
[0061] in, For the Laplace operator.
[0062] The transfer function expression for ESO-PLL is:
[0063] ;
[0064] in, For ESO-PLL pass functions.
[0065] Based on the pole placement method, the three poles of the ESO-PLL are placed at the same point in the left half-plane of the complex plane, as expressed by:
[0066] ;
[0067] in, Configure parameters for the poles.
[0068] Thus, the position feedback gain of the extended state observer is obtained. Speed feedback gain Acceleration feedback gain as follows:
[0069] .
[0070] Step S3 further includes: calculating the secondary speed estimate based on the synchronous angular velocity estimate, slip angular frequency, and motor pole pitch; and calculating the secondary displacement estimate based on the secondary speed estimate. The slip angular frequency is calculated based on the primary current d-axis reference value, the primary current q-axis reference value, the secondary resistance, and the secondary self-inductance, using the following formula:
[0071] ;
[0072] in, The secondary speed estimate for the segmented long primary double-sided linear induction motor LP-DSLIM is given. The estimated secondary displacement values are for the segmented long primary double-sided linear induction motor LP-DSLIM. The slip angular frequency, The pole pitch of the motor. This is the primary current d-axis reference value. This is the q-axis reference value for the primary current.
[0073] Figure 4 This is a speed observation result diagram of the segmented linear induction motor sensorless control method based on an extended state observer phase-locked loop provided by the present invention, as shown in the figure. Figure 4 As shown, the secondary velocity estimate obtained through the technical solution provided by this invention (i.e. Figure 4 The observed velocity shown is very close to the actual velocity.
[0074] Figure 5 This is a displacement observation result diagram of the segmented linear induction motor sensorless control method based on an extended state observer phase-locked loop provided by the present invention, as shown in the figure. Figure 5 As shown, the secondary displacement estimate obtained through the technical solution provided by this invention (i.e. Figure 5 The observed displacement shown is basically consistent with the actual displacement.
[0075] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.
[0076] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.
[0077] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.
Claims
1. A sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop, characterized in that, The method includes: Step S1: Based on the unit motor mathematical model of the piecewise linear induction motor, construct an equivalent mathematical model of the piecewise linear induction motor without coupling coefficient terms. Step S2: Based on the equivalent mathematical model of the piecewise linear induction motor, construct a sliding mode observer based on the integral sliding mode surface combined with the exponential reaching law to obtain the back electromotive force observation value required by the phase-locked loop. Step S3: Input the back EMF observation value into the phase-locked loop based on the extended state observer, extract the synchronous angular velocity and synchronous electrical angle, and calculate the secondary velocity estimate and secondary displacement estimate. Step S4: The synchronous angular velocity, secondary velocity estimate, and secondary displacement estimate are fed back to the closed-loop control system to realize the sensorless operation of the segmented linear induction motor. The closed-loop control system is used to perform segmented power supply switching control based on the secondary displacement estimate and to perform closed-loop adjustment of the motor operating status based on the synchronous angular velocity and secondary velocity estimate.
2. The method for sensorless control of a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 1, characterized in that, The equivalent mathematical model of the piecewise linear induction motor without coupling coefficient terms is as follows: ； in, For the primary voltage vector sum, For the primary current vector sum, To divide the primary flux linkage vector sum, For the vector sum of secondary currents, For the sum of virtual secondary flux linkage vectors, For synchronous angular velocity, The difference angular frequency, For primary resistors, For secondary resistors, This is a primary level of self-perception. For secondary self-induction, For differential operators, The number of unit motors, For the primary length, For secondary length, This is primary mutual induction.
3. The method for sensorless control of a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 2, characterized in that, Step S2 includes: Based on the equivalent mathematical model of the piecewise linear induction motor, the state equation of the equivalent mathematical model in the stationary coordinate system is obtained. Based on the state equation of the equivalent mathematical model in the stationary coordinate system, the expression for the sliding observer based on the integral sliding surface combined with the exponential reaching law is constructed as follows: ； in, These are primary current observations. For sliding mode control law, , , , .
4. The sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 3, characterized in that, In step S2, the expression for the integral sliding surface of the sliding mode observer is: ； Where z is the integral sliding surface, For primary current error, , Let t be the integral sliding surface gain matrix, and t be time. The expression for the exponential reaching law is: ； in, It is the derivative of the integral sliding surface z. It is the switching term coefficient. These are the coefficients of the linear term. It is a symbolic function; Differentiating the expression for the integral sliding surface, and based on the expression for the sliding observer and the state equations of the equivalent mathematical model in the stationary coordinate system, combined with the exponential reaching law, we obtain the following intermediate expression: ； in, It is the back electromotive force.
5. The sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 4, characterized in that, Primary current error As the value approaches 0, the sliding mode control law and back electromotive force observations of the sliding mode observer Equal to each other, and combined with the intermediate expression, the sliding mode control law is constructed as follows: 。 6. The method for sensorless control of a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 5, characterized in that, In step S3, the time-domain expression of the phase-locked loop based on the extended state observer is: ； in, For angular error, This is an estimated value for the synchronous electrical angle. For synchronous electrical angle, This is an estimate of the synchronous angular velocity. This is an estimate of the angular acceleration. The derivative of the estimated synchronous electrical angle is... The derivative of the estimated synchronous angular velocity. The derivative of the estimated angular acceleration is... For the position feedback gain of the extended state observer, For speed feedback gain, This is the acceleration feedback gain.
7. The method for sensorless control of a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 6, characterized in that, If we define the secondary acceleration as an extended state variable, then we have the following relational expression: ； in, For synchronous angular velocity, Angular acceleration, Angular acceleration, The differential of the synchronous electrical angle, The derivative of the synchronous angular velocity, It is the differential of angular acceleration.
8. The sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 7, characterized in that, Angular error The expression is as follows: ； in, and The back electromotive force in the two-phase stationary coordinate system are respectively shaft and Observations on the axis This represents the amplitude of the observed back electromotive force.
9. The sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 7, characterized in that, Step S3 further includes: By performing a Laplace transform on the time-domain expression of the phase-locked loop based on the extended state observer, we obtain the complex frequency-domain expression and the corresponding transfer function expression of the phase-locked loop based on the extended state observer. By placing the three poles of the phase-locked loop based on the extended state observer at the same point in the left half of the complex plane, the position feedback gain of the extended state observer can be obtained. Speed feedback gain and acceleration feedback gain .
10. The sensorless control method for a segmented linear induction motor based on an extended state observer phase-locked loop according to claim 7, characterized in that, Step S3 further includes: The estimated secondary speed is calculated based on the synchronous angular velocity estimate, slip angular frequency, and motor pole pitch. The estimated value of the secondary displacement is calculated based on the estimated value of the secondary velocity. The slip angular frequency is calculated based on the primary current d-axis reference value, the primary current q-axis reference value, the secondary resistance, and the secondary self-inductance.