A control method of a permanent magnet synchronous motor based on a quasi-z-source inverter

Abstract

The application discloses a control method of a permanent magnet synchronous motor based on a quasi-Z-source inverter, and belongs to the technical field of permanent magnet synchronous motor control. In order to solve the problem of insufficient response speed of a linear sliding mode control strategy in a variable bus control system of a permanent magnet synchronous motor, the application constructs a mathematical model of a quasi-Z-source inverter in a pass-through state and a mathematical model of the quasi-Z-source inverter in a non-pass-through state; a pass-through vector is introduced on the basis of a voltage vector synthesized by a four-vector SVPWM to obtain a new synthesized voltage vector, and the minimum value of a zero vector duty cycle in a cycle is calculated; a variable bus voltage control is performed on a direct current bus with the lowest direct current bus voltage requirement as a benchmark to obtain a variable bus voltage mathematical model; a variable bus control strategy based on a reduced-order fast non-singular terminal sliding mode is constructed to solve the pass-through duty cycle of the quasi-Z-source inverter; and the system state of the permanent magnet synchronous motor is analyzed based on a Lyapunov stable function to determine the stability of the reduced-order non-singular terminal sliding mode control strategy.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control technology, specifically relating to a control method for a permanent magnet synchronous motor based on a quasi-Z source inverter. Background Technology

[0002] Traditional motor control systems often use a constant bus voltage, but this increases switching losses at low and medium speeds. While setting the DC bus voltage of the motor drive system to a constant value is simple, it is not the optimal solution. Due to the unique buck-boost capability of the quasi-Z-source inverter, the bus voltage can be adjusted dynamically according to the motor's operating conditions without adjusting the inverter and power supply. The quasi-Z-source inverter is a fourth-order nonlinear system. As a strongly nonlinear system, using a linear sliding surface in certain extreme conditions, such as sudden heavy loads, may result in insufficient response speed to changes in the bus voltage. Linear sliding surfaces are only suitable for a certain range of external disturbances and are not ideal for resisting stronger nonlinear disturbances. Nonlinear sliding surfaces, on the other hand, can adaptively adjust the convergence rate and have stronger error correction capabilities. To address the problem that linear sliding surface errors cannot converge quickly within a finite time, terminal sliding mode uses a nonlinear sliding surface to replace the linear sliding surface, allowing the system state to converge to the sliding surface within a finite time. However, traditional terminal sliding mode is only suitable for systems with high-order derivatives, and cannot be directly used for systems like the quasi-Z-source inverter where high-order derivatives are difficult to represent. Summary of the Invention

[0003] This invention aims to address the problem of insufficient response speed of linear sliding mode control strategy in the variable bus control system of permanent magnet synchronous motor, and proposes a permanent magnet synchronous motor control method based on quasi-Z source inverter.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A control method for a permanent magnet synchronous motor based on a quasi-Z-source inverter includes the following steps:

[0006] S1. Based on the quasi-Z source inverter permanent magnet synchronous motor system, construct the mathematical model of the quasi-Z source inverter in the shoot-through state and the mathematical model of the quasi-Z source inverter in the non-shoot-through state. Then, apply a small external disturbance to the quasi-Z source inverter to obtain the steady-state and transient models of the quasi-Z source inverter, which are the relationship between the input voltage and the shoot-through duty cycle and the output voltage.

[0007] S2. Based on the voltage vector synthesized by the four-vector SVPWM, a pass-through vector is introduced to obtain a new synthesized voltage vector, and then the minimum value of the zero vector duty cycle within one cycle is calculated;

[0008] S3. Based on the minimum DC bus voltage requirement, the DC bus is controlled by variable bus voltage to obtain a variable bus voltage mathematical model, including the DC bus voltage under variable bus voltage control and the synthesized voltage vector under steady-state conditions under variable bus voltage control.

[0009] S4. Construct a variable bus control strategy based on reduced-order fast non-singular terminal sliding mode and solve for the shoot-through duty cycle of the quasi-Z source inverter;

[0010] S5. Collect the phase current of the permanent magnet synchronous motor at time k, and obtain the d-axis current i at time k through coordinate transformation. d (k) and q-axis current i q (k), the electrical angle w at time k is calculated based on the acquired rotor position angle θ. e (k), then substitute it into the variable bus voltage mathematical model to calculate the minimum bus voltage setpoint at time k. Add the minimum bus voltage setpoint to the input voltage and divide by 2 to obtain the setpoint voltage of capacitor C1. ;

[0011] S6. Apply the given voltage to capacitor C1. The voltage U fed back from the actual capacitor C1 C1 The given current of inductor L1 is obtained through the PI controller. Then the given current of inductor L1 With the actual current i of inductor L1 L1 Substitute the difference into the variable bus control strategy based on reduced-order fast non-singular terminal sliding mode in step S4 to output the direct-current duty cycle of the quasi-Z source inverter.

[0012] S7. The obtained direct-on duty cycle of the quasi-Z source inverter is inserted into the four-vector SVPWM to control the switching state of the switching transistors, thereby controlling the permanent magnet synchronous motor and the bus voltage U. o ;

[0013] S8. Analyze the system state of the permanent magnet synchronous motor obtained in step S7 based on the Lyapunov stability function, determine the stability of the reduced-order non-singular terminal sliding mode control strategy, and optimize the convergence time of the reduced-order fast non-singular terminal sliding mode.

[0014] Furthermore, the specific implementation method of step S1 includes the following steps:

[0015] S1.1. Setting up a quasi-Z source inverter permanent magnet synchronous motor system and The first and second capacitors of the quasi-Z source inverter. and For the first and second inductors of the quasi-Z source inverter, R1 and R2 are respectively and The corresponding equivalent resistances, r1 and r2 are respectively and The corresponding equivalent resistance of the quasi-Z source inverter adopts symmetrical parameter settings, that is, let L1=L2=L, C1=C2=C, R1=R2=R, r1=r2=r, where L is the symmetrical inductor, C is the symmetrical capacitor, R is the equivalent resistance of the inductor, and r is the symmetrical resistance of the capacitor.

[0016] u C1 u C2 They are respectively and Voltage across terminals, u L1 u L2 They are respectively and Voltage at both ends, They are respectively and The inductor current, u in DC input power supply To output DC voltage, To output DC current;

[0017] S1.2. Construct the mathematical model of the quasi-Z source inverter in the shoot-through state, the expression of which is:

[0018]

[0019] in, for The first derivative of the inductor current, for The first derivative of the inductor current, for The first derivative of the voltage across the terminals, for The first derivative of the voltage across the terminals;

[0020] Then, converting it to matrix form in the direct-through state, we get:

[0021]

[0022] in, This is the inductor-capacitor parameter matrix. Let be the derivative matrix of the state variables. This is the coefficient matrix of the state variables in the direct-flow state. This is the coefficient matrix of the input variables in the pass-through state. For the state variable matrix, The input matrix;

[0023] S1.3. Construct the mathematical model of the quasi-Z source inverter in the non-shoo-through state, the expression of which is:

[0024]

[0025] Then, converting it to matrix form under non-straight-through conditions, we get:

[0026]

[0027] in, This is the coefficient matrix of the state variables in the non-direct-through state. This is the coefficient matrix of the input variables in the non-pass-through state;

[0028] S1.4. In one carrier cycle, apply the state-space averaging method to the matrix forms obtained in steps S1.2 and S1.3, assuming the cut-through duty cycle is... The non-through duty cycle is The system equations are obtained as follows:

[0029]

[0030] Then, disturbance signals are applied to the system's state variables, output variables, and control variables. ,get:

[0031]

[0032] in, To control variables, For state variables, For output variables;

[0033] Substituting these values ​​into the system equations, we obtain the steady-state equation and small-signal model of the system as follows:

[0034] .

[0035] Furthermore, the specific implementation method of step S2 includes the following steps:

[0036] S2.1. As can be seen from vector modulation technology, after adding the pass-through time, the synthesized voltage vector is:

[0037]

[0038] in, The first duty cycle of the effective vector, The second duty cycle of the effective vector. The third duty cycle of the effective vector. The fourth duty cycle for the effective vector; As the first fundamental vector, As the second fundamental vector, As the third fundamental vector, It is the fourth fundamental vector. It is a zero vector. It is a through vector. Zero vector duty cycle, For direct duty cycle;

[0039] Then we get:

[0040]

[0041] in, The DC bus voltage under steady state. It is a zero vector. The angle between the composite vector and the α-axis;

[0042] Then calculate the minimum zero vector duty cycle within one period. for:

[0043] .

[0044] Furthermore, the specific implementation method of step S3 includes the following steps:

[0045] S3.1. Construct a steady-state mathematical model of the quasi-Z-source inverter, simplifying the DC bus voltage as follows:

[0046]

[0047] in, For steady-state input power supply, The capacitor voltage under steady state. This is the capacitor voltage under steady state;

[0048] S3.2. Substitute the minimum zero vector duty cycle value obtained in step S2 into the formula in step S3.1, and... When the value is 0, we get:

[0049]

[0050] in, for The minimum value;

[0051] Then to Correcting the minimum value, we get:

[0052]

[0053] in, This is the margin coefficient;

[0054] S3.3. Calculate the DC bus voltage under variable bus voltage control, the expression is:

[0055]

[0056] S3.4. Considering the dq-axis components in the control strategy for permanent magnet synchronous motors, the voltage equation of the motor in steady state is obtained as follows:

[0057]

[0058] in, The voltage along the d-axis. This is the q-axis voltage. For stator resistance, For d-axis current, For q-axis current, For d-axis inductance, It is the q-axis inductance. The angular velocity of the motor. For motor magnetic flux;

[0059] Then, based on the voltage equation of the motor in steady state, the synthesized voltage vector under the steady-state condition of variable bus voltage control is obtained. for:

[0060] .

[0061] Furthermore, the specific implementation method of step S4 includes the following steps:

[0062] S4.1. Utilizing the condition where the state variables of the permanent magnet synchronous motor control system move onto the sliding surface and stabilize, there exists... A reduced-order fast nonsingular terminal sliding surface is constructed as follows:

[0063]

[0064] in, Let be the value of the state variable at time t. For switching functions, , , They are the first coefficient, the second coefficient, and the third coefficient, respectively. , , ;

[0065] S4.2. The error in the design current is a state variable, obtained by establishing a large-signal model:

[0066]

[0067] in, Let L1 be the expected value of the inductor current. This is the actual value of the inductor current. Let be the derivative of the state variable, and A and B be the parameter matrices of the large-signal model, respectively. It originates from uncertainty and external interference, and is the sum of matched and mismatched interferences. Mismatched interference is not included. In the column space;

[0068] S4.3. Design Control Rate Composed of the equivalent control law and the approach law, we obtain:

[0069]

[0070] in, For equivalent control rate, For the rate of convergence;

[0071] S4.4. When the system is stable, there is ,get:

[0072]

[0073] Then the equivalent control rate is obtained as follows:

[0074]

[0075] S4.5. Set the convergence rate Using the exponential approach rate, the final equivalent control rate is obtained as follows:

[0076]

[0077] based on The global control law of the sliding mode system is equivalent to the direct-on duty cycle D of the quasi-Z source inverter.

[0078] Furthermore, the specific implementation method for determining the stability of the reduced-order non-singular terminal sliding mode control strategy based on the Lyapunov stability function in step S8 includes the following steps:

[0079] S8.1. Based on the consideration of state error, after passing through a controller combining a non-singular terminal sliding surface and a control law, the current error should eventually converge to 0 within a finite time. This is achieved by constructing... Functions verify the stability of the system;

[0080] set up The function is:

[0081]

[0082] in, for function;

[0083] S8.2. Base pairs Taking the derivative and substituting it into the corresponding formula in step S4.4, we get:

[0084]

[0085] in, >0, Let be the disturbance error value, and be a bounded function, when: When satisfied:

[0086]

[0087] This proves that the system is stable, demonstrating that the system error will converge to 0 within a finite time.

[0088] S8.3. When the system converges to the sliding surface, we have Then we have:

[0089]

[0090] According to the terminal sliding mode principle, the state variables should converge to 0 along the sliding surface at any position within a finite time. Solving the above differential equation yields the convergence time. for:

[0091]

[0092] This verifies that the RFNTSM system state error converges to 0 within a finite time.

[0093] The beneficial effects of this invention are:

[0094] This invention discloses a control method for permanent magnet synchronous motors based on a quasi-Z-source inverter. It proposes a reduced-order non-singular terminal sliding mode control strategy for the permanent magnet synchronous motor based on a quasi-Z-source. Under steady-state conditions, the fluctuations and glitches of the direct-current duty cycle are smaller than those of linear sliding mode, indicating that the reduced-order non-singular terminal sliding mode control strategy provides stronger bus voltage stability in steady-state time. Furthermore, compared to linear sliding mode control, it offers faster response and smoother voltage control when handling complex dynamic changes, exhibiting superior robustness and stability. It can ensure that the motor quickly tracks voltage changes when the speed changes, thus achieving variable bus voltage control.

[0095] The response speed and stability of the nonlinear sliding mode system are superior to those of the linear sliding mode system. It can ensure that the motor can quickly track the voltage change when the speed changes to achieve variable bus voltage control. Next, the linear sliding mode and RFNTSM are used to realize the variable bus control of the permanent magnet synchronous motor, which significantly improves the dynamic response capability of the system.

[0096] The present invention discloses a control method for permanent magnet synchronous motor based on quasi-Z source inverter. The proposed reduced-order non-singular terminal sliding mode control strategy can converge quickly within a finite time and respond quickly to and change the bus voltage value according to the motor operating state. Attached Figure Description

[0097] Figure 1 This is a flowchart of a permanent magnet synchronous motor control method based on a quasi-Z source inverter according to the present invention;

[0098] Figure 2 This is a topology diagram of the permanent magnet synchronous motor system based on the quasi-Z source inverter of this invention;

[0099] Figure 3 The present invention defines the through and non-through states of the quasi-Z source inverter, wherein (a) is the through state of the quasi-Z source inverter and (b) is the non-through state of the quasi-Z source inverter.

[0100] Figure 4 This is a block diagram of the variable busbar control based on sliding mode of the present invention;

[0101] Figure 5 The response waveforms of the control strategy of the present invention are shown below, where (a) is the inductor current ripple of the quasi-Z source inverter, (b) is the voltage and current magnification diagram of the quasi-Z source inverter, (c) is the phase current of the permanent magnet synchronous motor, and (d) is the torque pulsation of the permanent magnet synchronous motor.

[0102] Figure 6 The diagram shows the control strategy of the quasi-Z source inverter based on linear sliding mode according to the present invention, where (a) is linear sliding mode and (b) is the direct duty cycle.

[0103] Figure 7 This is a control strategy diagram for the quasi-Z source inverter based on RFNTSM according to the present invention, where (a) is RFNTSM and (b) is the direct duty cycle;

[0104] Figure 8 The diagram shows the bus voltage during linear sliding mode and RFNTSM variable speed operation according to the present invention, where (a) is linear sliding mode and (b) is RFNTSM.

[0105] Figure 9 The capacitor voltage is defined as the linear sliding mode and the RFNTSM variable speed in this invention, where (a) is the linear sliding mode and (b) is the RFNTSM.

[0106] Figure 10 The diagram shows a comparison of the q-axis current of the linear sliding mode and the RFNTSM variable load in this invention, where (a) is the linear sliding mode and (b) is the RFNTSM. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0108] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0109] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 - Appendix Figure 10 Detailed explanation is as follows:

[0110] Example 1:

[0111] A control method for a permanent magnet synchronous motor based on a quasi-Z-source inverter includes the following steps:

[0112] S1. Based on the quasi-Z source inverter permanent magnet synchronous motor system, construct the mathematical model of the quasi-Z source inverter in the shoot-through state and the mathematical model of the quasi-Z source inverter in the non-shoot-through state. Then, apply a small external disturbance to the quasi-Z source inverter to obtain the steady-state and transient models of the quasi-Z source inverter, which are the relationship between the input voltage and the shoot-through duty cycle and the output voltage.

[0113] Compared to traditional two-stage converters, quasi-Z-source inverters, as single-stage converters, simplify circuit design and make the entire system more compact. Due to their unique topology, the DC bus step-up / step-down voltage can be achieved by adjusting the shoot-through duty cycle. To understand the operating characteristics of quasi-Z-source inverters, it is necessary to establish average state equations and perform small-signal modeling analysis. The average state-space equations can be constructed based on the shoot-through and non-shoot-through states of the quasi-Z-source inverter, as shown in the following figures: Figure 3 As shown;

[0114] Furthermore, the specific implementation method of step S1 includes the following steps:

[0115] S1.1. Setting up a quasi-Z source inverter permanent magnet synchronous motor system and The first and second capacitors of the quasi-Z source inverter. and For the first and second inductors of the quasi-Z source inverter, R1 and R2 are respectively and The corresponding equivalent resistances, r1 and r2 are respectively and The corresponding equivalent resistance of the quasi-Z source inverter adopts symmetrical parameter settings, that is, let L1=L2=L, C1=C2=C, R1=R2=R, r1=r2=r, where L is the symmetrical inductor, C is the symmetrical capacitor, R is the equivalent resistance of the inductor, and r is the symmetrical resistance of the capacitor.

[0116] u C1 u C2 They are respectively and Voltage across terminals, u L1 u L2 They are respectively and Voltage at both ends, They are respectively and The inductor current, u in DC input power supply To output DC voltage, To output DC current;

[0117] S1.2. Construct the mathematical model of the quasi-Z source inverter in the shoot-through state, the expression of which is:

[0118]

[0119] in, for The first derivative of the inductor current, for The first derivative of the inductor current, for The first derivative of the voltage across the terminals, for The first derivative of the voltage across the terminals;

[0120] Furthermore,

[0121] In shoot-through mode, the diodes are turned off due to reverse voltage across their terminals, ensuring at least one path in the six-phase inverter is shoot-through. Figure 3 (a) shows the current direction as the reference positive direction. The inductor current and capacitor voltage are chosen as state variables, denoted as... With output current and output voltage as input variables, denoted as Construct the state equations. Then express them using matrix equations as follows:

[0122]

[0123] make ;

[0124] Then, converting it to matrix form in the direct-through state, we get:

[0125]

[0126] in, This is the inductor-capacitor parameter matrix. Let be the derivative matrix of the state variables. This is the coefficient matrix of the state variables in the direct-flow state. This is the coefficient matrix of the input variables in the pass-through state. For the state variable matrix, The input matrix;

[0127] S1.3. Construct the mathematical model of the quasi-Z source inverter in the non-shoo-through state, the expression of which is:

[0128]

[0129] In the non-straight-through state, since the permanent magnet synchronous motor is a large inertial system, the current change within one carrier cycle is very small. Therefore, it can be regarded as a constant current source. At this time, the diode conducts under the forward voltage drop. Figure 3 (b), and then expressed using matrix equations as:

[0130]

[0131] make ;

[0132] Then, converting it to matrix form under non-straight-through conditions, we get:

[0133]

[0134] in, This is the coefficient matrix of the state variables in the non-direct-through state. This is the coefficient matrix of the input variables in the non-pass-through state;

[0135] S1.4. In one carrier cycle, apply the state-space averaging method to the matrix forms obtained in steps S1.2 and S1.3, assuming the cut-through duty cycle is... The non-through duty cycle is The system equations are obtained as follows:

[0136]

[0137] The expanded expression is:

[0138] ;

[0139] Since the quasi-Z source inverter network is a typical nonlinear time-varying system, a linearization method is needed to analyze the quasi-Z source inverter network.

[0140] Then, disturbance signals are applied to the system's state variables, output variables, and control variables. ,get:

[0141]

[0142] in, To control variables, For state variables, For output variables;

[0143] Substituting these values ​​into the system equations, we obtain the steady-state equation and small-signal model of the system as follows:

[0144] .

[0145] Furthermore, a steady-state mathematical model of the quasi-Z-source inverter is constructed:

[0146] When the system is in steady state, the time derivative of the state variables is zero. Substituting the expanded expression into the steady-state equations of the system, we can solve the state equations to obtain:

[0147] ;

[0148] If we ignore the effect of the equivalent resistance of the inductors and capacitors in the quasi-Z source inverter network, that is, let Then the above formula can be simplified to:

[0149]

[0150] Considering the non-straight-through state Therefore, the DC bus voltage can be simplified as follows:

[0151]

[0152] Define boost factor Voltage gain M is the modulation index. We have:

[0153]

[0154] in, This represents the peak value of the inverter's output phase voltage.

[0155] S2. Based on the voltage vector synthesized by the four-vector SVPWM, a pass-through vector is introduced to obtain a new synthesized voltage vector, and then the minimum value of the zero vector duty cycle within one cycle is calculated;

[0156] Furthermore, the specific implementation method of step S2 includes the following steps:

[0157] S2.1. As can be seen from vector modulation technology, after adding the pass-through time, the synthesized voltage vector is:

[0158]

[0159] in, The first duty cycle of the effective vector, The second duty cycle of the effective vector. The third duty cycle of the effective vector. The fourth duty cycle for the effective vector; As the first fundamental vector, As the second fundamental vector, As the third fundamental vector, It is the fourth fundamental vector. It is a zero vector. It is a through vector. Zero vector duty cycle, For direct duty cycle;

[0160] Then we get:

[0161]

[0162] in, The DC bus voltage under steady state. It is a zero vector. The angle between the composite vector and the α-axis;

[0163] Then calculate the minimum zero vector duty cycle within one period. for:

[0164] .

[0165] S3. Based on the minimum DC bus voltage requirement, the DC bus is controlled by variable bus voltage to obtain a variable bus voltage mathematical model, including the DC bus voltage under variable bus voltage control and the synthesized voltage vector under steady-state conditions under variable bus voltage control.

[0166] Furthermore, the specific implementation method of step S3 includes the following steps:

[0167] S3.1. Construct a steady-state mathematical model of the quasi-Z-source inverter, simplifying the DC bus voltage as follows:

[0168]

[0169] in, For steady-state input power supply, The capacitor voltage under steady state. This is the capacitor voltage under steady state;

[0170] S3.2. Substitute the minimum zero vector duty cycle value obtained in step S2 into the formula in step S3.1, and... When the value is 0, we get:

[0171]

[0172] in, for The minimum value;

[0173] Then to Correcting the minimum value, we get:

[0174]

[0175] in, This is the margin coefficient;

[0176] S3.3. Calculate the DC bus voltage under variable bus voltage control, the expression is:

[0177]

[0178] S3.4. Considering the dq-axis components in the control strategy for permanent magnet synchronous motors, the voltage equation of the motor in steady state is obtained as follows:

[0179]

[0180] in, The voltage along the d-axis. This is the q-axis voltage. For stator resistance, For d-axis current, For q-axis current, For d-axis inductance, It is the q-axis inductance. The angular velocity of the motor. For motor magnetic flux;

[0181] Then, based on the voltage equation of the motor in steady state, the synthesized voltage vector under the steady-state condition of variable bus voltage control is obtained. for:

[0182] .

[0183] S4. Construct a variable bus control strategy based on reduced-order fast non-singular terminal sliding mode and solve for the shoot-through duty cycle of the quasi-Z source inverter;

[0184] Furthermore, the specific implementation method of step S4 includes the following steps:

[0185] S4.1. Utilizing the condition where the state variables of the permanent magnet synchronous motor control system move onto the sliding surface and stabilize, there exists... A reduced-order fast nonsingular terminal sliding surface is constructed as follows:

[0186]

[0187] in, Let be the value of the state variable at time t. For switching functions, , , They are the first coefficient, the second coefficient, and the third coefficient, respectively. , , ;

[0188] S4.2. The error in the design current is a state variable, obtained by establishing a large-signal model:

[0189]

[0190] in, Let L1 be the expected value of the inductor current. This is the actual value of the inductor current. Let be the derivative of the state variable, and A and B be the parameter matrices of the large-signal model, respectively. It originates from uncertainty and external interference, and is the sum of matched and mismatched interferences. Mismatched interference is not included. In the column space;

[0191] S4.3. Design Control Rate Composed of the equivalent control law and the approach law, we obtain:

[0192]

[0193] in, For equivalent control rate, For the rate of convergence;

[0194] S4.4. When the system is stable, there is ,get:

[0195]

[0196] Then the equivalent control rate is obtained as follows:

[0197]

[0198] S4.5. Set the convergence rate Using the exponential approach rate, the final equivalent control rate is obtained as follows:

[0199]

[0200] based on The global control law of the sliding mode system is equivalent to the direct-on duty cycle D of the quasi-Z source inverter.

[0201] S5. Collect the phase current of the permanent magnet synchronous motor at time k, and obtain the d-axis current i at time k through coordinate transformation. d (k) and q-axis current i q (k), the electrical angle w at time k is calculated based on the acquired rotor position angle θ. e (k), then substitute it into the variable bus voltage mathematical model to calculate the minimum bus voltage setpoint at time k. Add the minimum bus voltage setpoint to the input voltage and divide by 2 to obtain the setpoint voltage of capacitor C1. ;

[0202] S6. Apply the given voltage to capacitor C1. The voltage U fed back from the actual capacitor C1 C1 The given current of inductor L1 is obtained through the PI controller. Then the given current of inductor L1 With the actual current i of inductor L1 L1 Substitute the difference into the variable bus control strategy based on reduced-order fast non-singular terminal sliding mode in step S4 to output the direct-current duty cycle of the quasi-Z source inverter.

[0203] S7. The obtained direct-on duty cycle of the quasi-Z source inverter is inserted into the four-vector SVPWM to control the switching state of the switching transistors, thereby controlling the permanent magnet synchronous motor and the bus voltage U. o ;

[0204] S8. Analyze the system state of the permanent magnet synchronous motor obtained in step S7 based on the Lyapunov stability function, determine the stability of the reduced-order non-singular terminal sliding mode control strategy, and optimize the convergence time of the reduced-order fast non-singular terminal sliding mode.

[0205] Furthermore, the specific implementation method for determining the stability of the reduced-order non-singular terminal sliding mode control strategy based on the Lyapunov stability function in step S8 includes the following steps:

[0206] S8.1. Based on the consideration of state error, after passing through a controller combining a non-singular terminal sliding surface and a control law, the current error should eventually converge to 0 within a finite time. This is achieved by constructing... Functions verify the stability of the system;

[0207] set up The function is:

[0208]

[0209] in, for function;

[0210] S8.2. Base pairs Taking the derivative and substituting it into the corresponding formula in step S4.4, we get:

[0211]

[0212] in, >0, Let be the disturbance error value, and be a bounded function, when: When satisfied:

[0213]

[0214] This proves that the system is stable, demonstrating that the system error will converge to 0 within a finite time.

[0215] S8.3. When the system converges to the sliding surface, we have Then we have:

[0216]

[0217] According to the terminal sliding mode principle, the state variables should converge to 0 along the sliding surface at any position within a finite time. Solving the above differential equation yields the convergence time. for:

[0218]

[0219] This verifies that the RFNTSM system state error converges to 0 within a finite time.

[0220] The experimental verification of this embodiment is as follows:

[0221] Given a DC bus voltage of 400V, from Figure 6(a) It can be seen that during the voltage rise, the linear sliding mode control exhibited an overshoot of approximately 40V, which stabilized after about 50ms. Although the DC bus voltage eventually stabilized at 400V, the instability of the shoot-through duty cycle caused significant fluctuations and glitches in the DC bus voltage during the stabilization process, which affected the accuracy and stability of the system. Figure 7 (a) shows the DC bus voltage response under the RFNTSM control strategy. It can be seen that the RFNTSM response speed is superior to that of linear control, stabilizing in just 20ms with virtually no overshoot and minimal fluctuations during the system's steady-state period. Figure 7 (b) It can be seen that the duty cycle fluctuation of RFNTSM after using adaptive approach rate is reduced by half compared to linear sliding mode. Figure 6 , Figure 7 The comparison shows that for a highly nonlinear system like a quasi-Z source inverter, the response speed and stability of the nonlinear sliding mode system are better than those of the linear sliding mode system. This ensures that the motor can quickly track voltage changes when the speed changes, thus achieving variable bus voltage control. Next, we will use linear sliding mode and RFNTSM to achieve variable bus control of the permanent magnet synchronous motor. Figure 8 The response graph of the DC bus voltage to changes in rotational speed is shown. From Figure 8 (a) and Figure 8 In comparison (b), it is evident that under linear sliding mode control, a significant overshoot phenomenon occurs in the DC bus voltage as the rotational speed increases. In contrast, the DC bus voltage change is smoother during the speed increase with RFNTSM, without overshoot, indicating that RFNTSM can more effectively track speed changes. When the rotational speed begins to decrease, the DC bus voltage under linear sliding mode control stabilizes within approximately 50 ms. RFNTSM, however, exhibits a superior response speed, stabilizing within only 50 ms as the rotational speed begins to decrease and reaches stability. This indicates that RFNTSM can adjust the voltage more quickly during speed changes and rapidly reach a steady state. Comparative results show that, compared to linear sliding mode control, RFNTSM provides faster response and smoother voltage control when handling complex dynamic changes, exhibiting superior robustness and stability. Figure 9 For linear sliding mode and RFNTSM, the capacitor voltage response is given. From Figure 9 (a) It can be seen that the capacitor voltage ripple in linear sliding mode is relatively large, with a peak-to-peak value reaching 3V. Figure 9 (b) It can be seen that the capacitor voltage ripple of RFNTSM is significantly lower than that of linear sliding mode, with a peak-to-peak value of less than 1V. From Figure 10 (a) It can be seen that the linear sliding mode exhibits an overshoot of approximately 0.2A in the q-axis current when a sudden load is applied, but the overshoot is larger, approximately 1.5A, when the load is suddenly removed. Figure 10(b) It can be seen that the q-axis current of RFNTSM does not fluctuate significantly when the load is suddenly applied or dropped, and the q-axis current control effect is better than that of linear sliding mode.

[0222] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0223] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A control method for a permanent magnet synchronous motor based on a quasi-Z source inverter, characterized in that, Includes the following steps: S1. Based on the quasi-Z source inverter permanent magnet synchronous motor system, construct the mathematical model of the quasi-Z source inverter in the shoot-through state and the mathematical model of the quasi-Z source inverter in the non-shoot-through state. Then, apply a small external disturbance to the quasi-Z source inverter to obtain the steady-state and transient models of the quasi-Z source inverter, which are the relationship between the input voltage and the shoot-through duty cycle and the output voltage. The specific implementation method of step S1 includes the following steps: S1.

1. Setting up a quasi-Z source inverter permanent magnet synchronous motor system and The first and second capacitors of the quasi-Z source inverter. and For the first and second inductors of the quasi-Z source inverter, R1 and R2 are respectively and The corresponding equivalent resistances, r1 and r2 are respectively and The corresponding equivalent resistance of the quasi-Z source inverter adopts symmetrical parameter settings, that is, let L1=L2=L, C1=C2=C, R1=R2=R, r1=r2=r, where L is the symmetrical inductor, C is the symmetrical capacitor, R is the equivalent resistance of the inductor, and r is the symmetrical resistance of the capacitor. u C1 u C2 They are respectively and Voltage across terminals, u L1 u L2 They are respectively and Voltage at both ends, They are respectively and The inductor current, u in DC input power supply To output DC voltage, To output DC current; S1.

2. Construct the mathematical model of the quasi-Z source inverter in the shoot-through state, the expression of which is: ； in, for The first derivative of the inductor current, for The first derivative of the inductor current, for The first derivative of the voltage across the terminals, for The first derivative of the voltage across the terminals; Then, converting it to matrix form in the direct-through state, we get: ； in, This is the inductor-capacitor parameter matrix. Let be the derivative matrix of the state variables. This is the coefficient matrix of the state variables in the direct-flow state. This is the coefficient matrix of the input variables in the pass-through state. For the state variable matrix, The input matrix; S1.

3. Construct the mathematical model of the quasi-Z source inverter in the non-shoo-through state, the expression of which is: ； Then, converting it to matrix form under non-straight-through conditions, we get: ； in, This is the coefficient matrix of the state variables in the non-direct-through state. This is the coefficient matrix of the input variables in the non-pass-through state; S1.

4. In one carrier cycle, apply the state-space averaging method to the matrix forms obtained in steps S1.2 and S1.3, assuming the cut-through duty cycle is... The non-through duty cycle is The system equations are obtained as follows: ； Then, disturbance signals are applied to the system's state variables, output variables, and control variables. ,get: ； in, To control variables, For state variables, For output variables; Substituting these values ​​into the system equations, we obtain the steady-state equation and small-signal model of the system as follows: ； S2. Based on the voltage vector synthesized by the four-vector SVPWM, a pass-through vector is introduced to obtain a new synthesized voltage vector, and then the minimum value of the zero vector duty cycle within one cycle is calculated; S3. Based on the minimum DC bus voltage requirement, the DC bus is controlled by variable bus voltage to obtain a variable bus voltage mathematical model, including the DC bus voltage under variable bus voltage control and the synthesized voltage vector under steady-state conditions under variable bus voltage control. S4. Construct a variable bus control strategy based on reduced-order fast non-singular terminal sliding mode and solve for the shoot-through duty cycle of the quasi-Z source inverter; S5. Collect the phase current of the permanent magnet synchronous motor at time k, and obtain the d-axis current i at time k through coordinate transformation. d (k) and q-axis current i q (k), the electrical angle w at time k is calculated based on the acquired rotor position angle θ. e (k), then substitute it into the variable bus voltage mathematical model to calculate the minimum bus voltage setpoint at time k. Add the minimum bus voltage setpoint to the input voltage and divide by 2 to obtain the setpoint voltage U of capacitor C1. C1 * ; S6. Apply the given voltage U to capacitor C1. C1 * The voltage U fed back from the actual capacitor C1 C1 After passing through the PI controller, the given current i of inductor L1 is obtained. L1 * Then the given current i of inductor L1 L1 * With the actual current i of inductor L1 L1 The difference is substituted into the variable bus control strategy based on reduced-order fast non-singular terminal sliding mode in step S4 to output the direct-current duty cycle of the quasi-Z source inverter. S7. The obtained direct-on duty cycle of the quasi-Z source inverter is inserted into the four-vector SVPWM to control the switching state of the switching transistors, thereby controlling the permanent magnet synchronous motor and the bus voltage U. o ; S8. Analyze the system state of the permanent magnet synchronous motor obtained in step S7 based on the Lyapunov stability function, determine the stability of the reduced-order non-singular terminal sliding mode control strategy, and optimize the convergence time of the reduced-order fast non-singular terminal sliding mode.

2. The control method for a permanent magnet synchronous motor based on a quasi-Z source inverter according to claim 1, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. As can be seen from vector modulation technology, after adding the pass-through time, the synthesized voltage vector is: ； in, The first duty cycle of the effective vector, The second duty cycle of the effective vector. The third duty cycle of the effective vector. The fourth duty cycle for the effective vector; As the first fundamental vector, As the second fundamental vector, As the third fundamental vector, It is the fourth fundamental vector. It is a zero vector. It is a through vector. Zero vector duty cycle, For direct duty cycle; Then we get: ； in, The DC bus voltage under steady state. It is a zero vector. The angle between the composite vector and the α-axis; Then calculate the minimum zero vector duty cycle within one period. for: 。 3. The control method for a permanent magnet synchronous motor based on a quasi-Z source inverter according to claim 2, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Construct a steady-state mathematical model of the quasi-Z-source inverter, simplifying the DC bus voltage as follows: ； in, For steady-state input power supply, The capacitor voltage under steady state. This is the capacitor voltage under steady state; S3.

2. Substitute the minimum zero vector duty cycle value obtained in step S2 into the formula in step S3.1, and... When the value is 0, we get: ； in, for The minimum value; Then to Correcting the minimum value, we get: ； in, This is the margin coefficient; S3.

3. Calculate the DC bus voltage under variable bus voltage control, the expression is: ； S3.

4. Considering the dq-axis components in the control strategy for the permanent magnet synchronous motor, the voltage equation of the motor in steady state is obtained as follows: ； in, The voltage along the d-axis. This is the q-axis voltage. For stator resistance, For d-axis current, For q-axis current, For d-axis inductance, It is the q-axis inductance. The angular velocity of the motor. For motor magnetic flux; Then, based on the voltage equation of the motor in steady state, the synthesized voltage vector under the steady-state condition of variable bus voltage control is obtained. for: 。 4. The control method for a permanent magnet synchronous motor based on a quasi-Z source inverter according to claim 3, characterized in that, The specific implementation method of step S4 includes the following steps: S4.

1. Utilizing the condition where the state variables of the permanent magnet synchronous motor control system move onto the sliding surface and stabilize, there exists... A reduced-order fast nonsingular terminal sliding surface is constructed as follows: ； in, Let be the value of the state variable at time t. For switching functions, , , They are the first coefficient, the second coefficient, and the third coefficient, respectively. , , ; S4.

2. The error in the design current is a state variable, obtained by establishing a large-signal model: ； in, Let L1 be the expected value of the inductor current. This is the actual value of the inductor current. Let be the derivative of the state variable, and A and B be the parameter matrices of the large-signal model, respectively. It originates from uncertainty and external interference, and is the sum of matched and mismatched interferences. Mismatched interference is not included. In the column space; S4.

3. Design Control Rate Composed of the equivalent control law and the approach law, we obtain: ； in, For equivalent control rate, For the rate of convergence; S4.

4. When the system is stable, there is ,get: ； Then the equivalent control rate is obtained as follows: ； S4.

5. Set the convergence rate Using the exponential approach rate, the final equivalent control rate is obtained as follows: ； based on The global control law of the sliding mode system is equivalent to the direct-on duty cycle D of the quasi-Z source inverter.

5. The control method for a permanent magnet synchronous motor based on a quasi-Z source inverter according to claim 4, characterized in that, Step S8 involves analyzing the stability of the reduced-order non-singular terminal sliding mode control strategy based on the Lyapunov stability function. The specific implementation method includes the following steps: S8.

1. Based on the consideration of state error, after passing through a controller combining a non-singular terminal sliding surface and a control law, the current error should eventually converge to 0 within a finite time. This is achieved by constructing... Functions verify the stability of the system; set up The function is: ； in, for function; S8.

2. Base pairs Taking the derivative and substituting it into the corresponding formula in step S4.4, we get: ； in, >0, Let be the disturbance error value, and be a bounded function, when: When satisfied: ； This proves that the system is stable, demonstrating that the system error will converge to 0 within a finite time. S8.

3. When the system converges to the sliding surface, we have Then we have: ； According to the terminal sliding mode principle, the state variables should converge to 0 along the sliding surface at any position within a finite time. Solving the above differential equation yields the convergence time. for: ； This verifies that the RFNTSM system state error converges to 0 within a finite time.

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