Dead-beat predictive control method for dual three-phase permanent magnet synchronous motor with disturbance compensation

Abstract

The invention discloses a dead-beat prediction control method for a dual three-phase permanent magnet synchronous motor with disturbance compensation. The method comprises the following steps: designing a generalized extended state observer; inputting the actual voltage and current of the motor system into the observer, and outputting estimated harmonic current and disturbance compensation; calculating a fundamental current and a harmonic current at the next moment; a voltage equation is established and discretized, a weight factor is introduced, the fundamental current, the harmonic current and disturbance compensation at the next moment are input into the voltage equation, and fundamental space and harmonic space reference voltage is calculated; the fundamental wave space reference voltage is subjected to coordinate transformation and then is input into SVPWM together with the harmonic wave space reference voltage, and output PWM waves are processed to obtain driving voltage to drive a motor to operate. According to the method, real-time observation of the system current of the dual three-phase motor under parameter change is realized, disturbance caused by counter electromotive force harmonic waves, parameter change and unmodeled dynamics is compensated, and the effect of effectively suppressing the harmonic current is achieved.

Description

Technical Field

[0001] This invention relates to the field of permanent magnet synchronous motor drive control applications, specifically to a disturbance-compensated, deadbeat-free predictive control method for dual three-phase permanent magnet synchronous motors. Background Technology

[0002] The demands for power and reliability in high-end equipment manufacturing have made the development of high-power multiphase motor drive systems a trend. Traditional three-phase motor drive systems are limited in high-power applications due to voltage and power device limitations. Multiphase drive systems, with their significant advantages such as low torque ripple, excellent fault-tolerant control performance, ability to achieve low-voltage high-power output, and high degree of control freedom, have been widely used and highly recognized in high-end equipment manufacturing fields such as new energy vehicles, ship propulsion, and aerospace. Compared with other algorithms, predictive control can simultaneously satisfy multiple constraints and nonlinear characteristics of the system, exhibiting significant advantages in handling multivariable, multi-constraint linear systems such as motors and power converters. Therefore, researching deadbeat-free predictive control methods for dual three-phase permanent magnet synchronous motors to improve motor dynamic response and control accuracy is of significant practical importance.

[0003] To achieve deadbeat predictive control of permanent magnet synchronous motors (PMSMs), scholars both domestically and internationally have conducted research on the extended state observer method. Chinese invention patent CN120034063A discloses a deadbeat predictive control method for PMSMs based on a cascaded observer. It designs a cascaded disturbance observer consisting of a Romberg observer and a sliding mode disturbance observer based on superspiral theory, enabling rapid compensation of system disturbances and one-step control delay, while reducing the switching gain of the sliding mode observer. Compared to traditional deadbeat predictive control, this method has advantages in adaptability, robustness, parameter insensitivity, and dynamic / static performance. Chinese invention patent CN114499312B discloses a model-free current predictive control method and system for dual three-phase PMSMs. This method uses a model-free current controller to obtain the corresponding voltage reference signal based on the current signals of the dq and z1-z2 subplanes and the current reference signal. Model-free current controllers include fundamental plane and harmonic plane model-free current controllers, used to obtain corresponding voltage reference signals based on the shaft current signals and current reference signals of each subplane. However, deadbeat predictive control is more sensitive to parameters, and the presence of harmonic space in dual three-phase motors makes control more complex. Therefore, how to achieve real-time observation of the system current of dual three-phase motors under parameter changes, compensate for disturbances caused by back EMF harmonics, parameter changes, and unmodeled dynamics, and effectively suppress harmonic currents is an urgent technical problem to be solved. Summary of the Invention

[0004] Summary of the Invention: The purpose of this invention is to provide a disturbance-compensated, deadbeat-free predictive control method for dual three-phase permanent magnet synchronous motors. This method enables real-time observation of the system current of the dual three-phase motor under parameter changes, and compensates for disturbances caused by back EMF harmonics, parameter changes, and unmodeled dynamics, thereby effectively suppressing harmonic currents.

[0005] Technical solution: The present invention provides a disturbance-compensated, deadbeat-free predictive control method for a dual three-phase permanent magnet synchronous motor, comprising:

[0006] Harmonic current estimation: A generalized extended state observer is designed based on the sliding mode surface and the observer function; the actual voltage and actual current of the motor system are used as the input of the generalized extended state observer, and the estimated harmonic current and disturbance compensation are used as the output of the generalized extended state observer.

[0007] Voltage vector prediction: Based on the estimated harmonic current and the fundamental current at the current moment, calculate the fundamental current and harmonic current at the next moment; establish the voltage equation of the dual three-phase permanent magnet synchronous motor under space vector decoupling, use the first-order Taylor formula to discretize the voltage equation, introduce weighting factors, input the fundamental current and harmonic current at the next moment and the disturbance compensation into the voltage equation after processing, and calculate the reference voltage of the fundamental space and the reference voltage of the harmonic space of the dual three-phase permanent magnet synchronous motor.

[0008] Speed ​​closed-loop control: The reference voltage in the fundamental space is input to SVPWM after coordinate transformation, and the reference voltage in the harmonic space is directly input to SVPWM. SVPWM outputs a PWM wave, which is processed by the inverter and outputs a drive voltage to drive the dual three-phase permanent magnet synchronous motor. The actual speed of the dual three-phase permanent magnet synchronous motor is detected by the position sensor. The difference between the actual speed and the given speed is used to output a given iq value for voltage vector prediction by PI control, thus forming a speed closed-loop control system.

[0009] Furthermore, the design of the generalized extended state observer based on the sliding modal surface and observer function, using the actual voltage and current of the motor system as inputs to the generalized extended state observer, and estimating harmonic currents and disturbance compensation as outputs, includes:

[0010] Traditional extended state observers use linear system models. An extension variable x is introduced into the traditional extended state observer model. n+1 Let x represent the uncertainty of a dual three-phase motor control system, where the expanded variable x n+1 The expression is as follows:

[0011] x n+1 =f(x,ω(t),t)

[0012] Where f(x,ω(t),t) represents the uncertainty of the dual three-phase motor control system;

[0013] And assume the expansion variable x n+1 The rate of change is a finite value system state vector Expanded to:

[0014]

[0015] The dynamic current equation of a dual three-phase permanent magnet synchronous motor, considering parameter variations, can be expressed as follows:

[0016]

[0017] Among them, u xy and i xy These represent the voltage and current in the harmonic space, respectively; D xy d is the disturbance compensation amount. xy This represents the change in disturbance compensation.

[0018] In order to simultaneously calculate the estimated harmonic current i at the next time step k+1 xy (k+1) and disturbance compensation D xy (k+1) represents the estimated harmonic current i at the current time k. xy The perturbation compensation D at the current time k xy (k) is considered as a state variable, and the discrete state space equation is derived; according to the design principle of the generalized extended state observer, the equation of the generalized extended state observer is obtained;

[0019] The estimated value of harmonic current and the true value i xy and the estimated value of the disturbance and the true value D xy Subtraction yields the following error for the generalized extended state observer:

[0020]

[0021] Among them, e ixy (k+1) represents the observation error value of the harmonic current at the next time step k+1;

[0022] e Dxy (k+1) represents the observation error value of the harmonic disturbance at the next time step k+1; The current time value represents the observation error of the k-harmonic disturbance; Δ Dxy (k) represents the disturbance D at time k. xy The rate of change of (k);

[0023] According to the generalized extended state observer theory, the sliding mode design process can be divided into two steps: first, the design of the sliding mode surface, and second, the design of the observer function; the goal of the observer is to eliminate harmonic current prediction errors, and the sliding mode surface is selected as follows:

[0024] s(k)=[s x (k)s y (k)] T =e ixy (k)

[0025] The sliding mode control function is designed using the following exponential convergence law:

[0026] s(k+1)-s(k)=-k1T s εsgn(s(k))-λT s s(k)

[0027] and

[0028]

[0029] Here, λ and ε are two different adjustable parameters, with limits of λ>0 and ε>0, and 1-λT s If the value is greater than 0, sgn() is a sign function;

[0030] An improved approach law is used to reduce sliding mode chattering, as shown in the following equation:

[0031]

[0032] Where σ and δ are adjustable parameters, and σ>0 and δ>0 are the limits of the adjustable parameters;

[0033] e Dxy (k) can be considered as a bounded perturbation of the observer function, and the nonlinear observer function can be designed as follows:

[0034]

[0035] This function can be used to reduce the harmonic current observation error e. ixy (k) converges to zero.

[0036] Furthermore, the expression for the discrete state-space equation is as follows:

[0037]

[0038] Among them, i xy (k+1) represents the estimated harmonic current at the next time step k+1; R s Nominal resistance; L z For nominal leakage inductance; i xy(k) represents the estimated harmonic current at the current time k; D xy (k) represents the disturbance compensation at the current moment; D xy (k+1) represents the disturbance compensation at the next time step k+1; D xy (k+1)Δ Dxy (k)=[Δ Dx Δ Dy ] T The disturbance compensation D at the current moment xy The rate of change of (k); T s The sampling period; u xy (k) represents the estimated harmonic voltage at the current time k.

[0039] Furthermore, the equations for the generalized extended state observer are as follows:

[0040]

[0041] in, This is an estimate of the harmonic current at the next time step k+1; This is the estimated value of the disturbance compensation at the next time step k+1; T s L is the sampling period; s Nominal stator inductance; L z Nominal leakage inductance; R s Nominal resistance; Let i be the actual current of the k motor system at the current moment. xy The estimated value of (k); The current time k disturbance compensation D xy The estimated value of (k); u xy (k) represents the actual voltage of the k motor system at the current time;

[0042] f(e ixy (k) is the extended state variable observer function to be designed; β xy This is the gain coefficient;

[0043] This represents the observation error value of the k-harmonic current at the current moment.

[0044] Furthermore, the step of estimating the harmonic current and the fundamental current at the current moment, and calculating the fundamental current and harmonic current at the next moment, includes:

[0045] Based on the deadbeat current predictive control principle, feedback variables are sampled at time k. A mathematical model is then used to predict these feedback variables, and the control voltage vector is calculated using this model. A PWM wave is then generated using a spatial modulation method and applied to the inverter, ensuring that the current follows the given current. Therefore, the voltage vector equation at time k is:

[0046]

[0047] Among them, u d (k) represents the expected value of the d-axis voltage at time k; u q (k) represents the expected value of the q-axis voltage at time k; i d (k) represents the expected value of the d-axis current at time k; i q (k) The expected value of the q-axis current at time k; i d (k+1) is the expected value of the d-axis current at time k+1; i q (k+1) is the expected value of the q-axis current at time k+1; L s For nominal stator inductance; T s L is the sampling period; z Nominal leakage inductance; R s The nominal resistance; ψ f ω is the rotor flux linkage; ω(k) is the mechanical angular velocity of the motor at time k; u x (k) and u y (k) represent the z1 and z2 harmonic subspace voltages at time k, respectively; i x (k) and i y (k) represent the z1 and z2 harmonic subspace currents at time k, respectively; i x (k+1) and i y (k+1) represent the z1 and z2 harmonic subspace currents at time k+1, respectively;

[0048] Calculate the fundamental current and harmonic current at the next time k+1 based on the voltage vector equation at time k:

[0049]

[0050] Among them, L s0 For actual stator inductance; L z0 ψ is the actual leakage inductance; ω(k) is the mechanical angular velocity of the motor at time k; f0 This refers to the actual magnetic flux linkage.

[0051] Furthermore, the step of estimating the harmonic current and the fundamental current at the current moment, and calculating the fundamental current and harmonic current at the next moment, includes:

[0052] Introducing weighting factors α and β, where α + β = 1, the relationship between the current reference and feedback with weighting factors is as follows:

[0053]

[0054] in, Let k be the reference current. The current after adding the weighting factor at time k;

[0055] The voltage vector equation after introducing the weighting factor can be obtained as follows:

[0056]

[0057] in, This is the given value of the d-axis current at time k+1; This is the given value of the q-axis current at time k+1;

[0058] The voltage vector applied in the next cycle is calculated using the voltage vector equation after introducing a weighting factor. In the next cycle, the voltage vector calculated in the previous cycle is applied to the actual system to achieve the current response. Therefore, the fundamental current and harmonic current at the next moment after introducing the weighting factor are as follows:

[0059]

[0060] in, This is the given value of the d-axis current at time k; This is the given value of the q-axis current at time k; and These are the z1 and z2 harmonic subspace reference currents at time k, respectively.

[0061] Furthermore, the voltage equations for the dual three-phase permanent magnet synchronous motor under spatial decoupling are established by discretizing the voltage equations using a first-order Taylor formula, introducing weighting factors, and inputting the fundamental current, harmonic current, and disturbance compensation at the next moment into the processed voltage equations to calculate the reference voltage in the fundamental space and the reference voltage in the harmonic space of the dual three-phase permanent magnet synchronous motor, including:

[0062] The voltage equation for a dual three-phase permanent magnet synchronous motor under spatial decoupling is established, and its expression is as follows:

[0063]

[0064] The expression for the fundamental current at the next time step is discretized using the first-order Taylor formula, resulting in the current prediction model at time k+1:

[0065]

[0066] Among them, i d (k+1) is the expected value of the d-axis current at time k+1; i q (k+1) is the expected value of the q-axis current at time k+1; L s For nominal stator inductance; T s R is the sampling period; s The nominal resistance; ψ f For rotor flux linkage; i d (k) represents the expected value of the d-axis current at time k; iq (k) The expected value of the q-axis current at time k; u d (k) represents the expected value of the d-axis voltage at time k; u q (k) represents the expected value of the q-axis voltage at time k; ω(k) represents the mechanical angular velocity of the motor at time k.

[0067] The current given value at time k is taken as the expected value at time k+1:

[0068]

[0069] in, This is the given value of the d-axis current at time k; This is the given value of the q-axis current at time k;

[0070] Since the current components in the z1-z2 subspace can be obtained from the voltage and the simplified transfer function, the reference voltage of the fundamental space of the dual three-phase permanent magnet synchronous motor is obtained:

[0071]

[0072] In the formula, The given value of the d-axis voltage vector at time k+1; ω(k) is the given value of the q-axis voltage vector at time k+1; ω(k) is the mechanical angular velocity of the motor at time k.

[0073] Considering lumped parameter disturbances, the harmonic voltage equation in the voltage equation of a dual three-phase permanent magnet synchronous motor under spatial decoupling can be rewritten as follows:

[0074]

[0075] in, The harmonic voltage reference value is given at time k+1; G = 1 - R s T s / L z H = T s / L z , and These are the per-unit values ​​for G and H, respectively; This is a reference value for harmonic current. i xy (k+1) represents the current in the harmonic space at time k+1; D xy (k+1) represents the disturbance compensation amount at time k+1;

[0076] By incorporating the estimated system disturbances and harmonic currents into the calculation formula for the reference voltage in the harmonic space, the following expression for the reference voltage in the harmonic space of a dual three-phase permanent magnet synchronous motor is obtained:

[0077]

[0078] in, and This is the harmonic space reference voltage; and This is the harmonic space reference current; and This is an estimated value for the harmonic current; and This is an estimate of the disturbance compensation; T s The sampling period.

[0079] Furthermore, in the voltage equation of the dual three-phase permanent magnet synchronous motor under spatial decoupling, the flux linkage equation of the dual three-phase PMSM is:

[0080]

[0081] Among them, L d and L q For the α-β planar inductance component; L z Nominal leakage inductance; ψ f For rotor flux linkage; i x and i y These are the z1 and z2 harmonic subspace currents, respectively.

[0082] Furthermore, the expression for the linear system model is as follows:

[0083]

[0084] in, Let A be the state vector of the linear system; u∈R be the control input; f(x,ω(t),t) be the uncertainty of the system, including unmodeled dynamics and external disturbances; y be the output of the observer; A, B u and B d These represent the system dynamic matrix, control input matrix, and disturbance effect matrix, respectively; C is the measurement output matrix.

[0085] Furthermore, during the speed closed-loop control process, the reference voltage in the fundamental space is transformed into reference voltages for the α and β axes, which are then input into SVPWM along with the reference voltage in the harmonic space.

[0086] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) The generalized extended state observer proposed in the present invention can estimate harmonic disturbances, reduce the disturbance of harmonic current to the system, and reduce the stator current ripple content; (2) The deadbeat control method improved by introducing weight factors in the present invention improves the prediction accuracy and weakens the influence of stator inductance parameter disturbances on the system; (3) The present invention dynamically corrects the voltage reference value output by the deadbeat current prediction controller, thereby improving the robust control performance of the system; (4) The generalized extended observer proposed in the present invention is not only applicable to dual three-phase motors, but can also be extended to other multi-phase motors, with similar effects. Attached Figure Description

[0087] Figure 1 This is a schematic diagram of the process of the present invention;

[0088] Figure 2 This is a schematic diagram of a generalized extended state observer.

[0089] Figure 3 Block diagram of harmonic current and disturbance observer;

[0090] Figure 4 This is a waveform diagram of the rotational speed under the condition of sudden speed change;

[0091] Figure 5 The current waveform is shown under the condition of sudden change in rotational speed.

[0092] Figure 6 This is a comparison chart of harmonic currents when the stator resistance changes;

[0093] Figure 7 This is a comparison diagram of harmonic currents when the stator leakage inductance changes. Detailed Implementation

[0094] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0095] like Figure 1 As shown, the present invention provides a disturbance-compensated, deadbeat-free predictive control method for a dual three-phase permanent magnet synchronous motor, which specifically includes the following steps:

[0096] S1. Harmonic Current Estimation: A generalized extended state observer is designed based on the sliding mode surface and the observer function. The actual voltage and actual current of the motor system are used as the input of the generalized extended state observer, and the estimated harmonic current and disturbance compensation are used as the output of the generalized extended state observer.

[0097] The specific implementation process of step S1 is as follows:

[0098] It is known that the traditional extended state observer uses a linear system model, and the expression of the linear system model is as follows:

[0099]

[0100] in, Let A be the state vector of the linear system; u∈R be the control input; f(x,ω(t),t) be the uncertainty of the system, including unmodeled dynamics and external disturbances; A, B u and B d Here, represents the system dynamics matrix, control input matrix, and disturbance effect matrix, respectively; y is the observer output; and C is the measurement output matrix. This model covers general system types where disturbances may act on the system through a different channel than the control input (i.e., B). u ≠λB d Since λ∈R), a new observer structure needs to be designed to effectively estimate the disturbance.

[0101] Since the dual three-phase motor control system is a multi-input multi-output system, an extended variable x is introduced on the basis of the traditional extended state observer. n+1 Let x represent the uncertainty of a dual three-phase motor control system, where the expanded variable x n+1 The expression is as follows:

[0102] x n+1 =f(x,ω(t),t)

[0103] Where f(x,ω(t),t) represents the uncertainty of the dual three-phase motor control system;

[0104] And assume the expansion variable x n+1 The rate of change is a finite value The system state vector is extended as follows:

[0105]

[0106] To address the disturbance of the system caused by harmonic currents from a dual three-phase motor, the actual system voltage and current are used as the input to the observer. The compensated current and disturbance compensation are used as the observer output and state variables, respectively. This yields the proposed generalized extended state observer structure diagram, as shown below. Figure 2 As shown, this structure comprises two parts: a harmonic current model and a generalized extended state observer model. Simultaneously, an interference compensation gain K is constructed. D and state feedback gain K x Adjust the system.

[0107] The dynamic current equation of a dual three-phase permanent magnet synchronous motor, considering parameter variations, can be expressed as follows:

[0108]

[0109] Among them, u xy and i xyD represents the voltage and current in the harmonic space, respectively. xy For the disturbance compensation amount, d xy This represents the change in disturbance compensation.

[0110] In order to simultaneously calculate the estimated harmonic current i at the next time step k+1 xy (k+1) and disturbance compensation D xy (k+1) represents the estimated harmonic current i at the current time k. xy The perturbation compensation D at the current time k xy (k) can be considered as a state variable, and a discrete state-space equation can be derived from it. The expression of the discrete state-space equation is as follows:

[0111]

[0112] Among them, i xy (k+1) represents the estimated harmonic current at the next time step k+1; R s Nominal resistance; L z For nominal leakage inductance; i xy (k) represents the estimated harmonic current at the current time k; D xy (k) represents the disturbance compensation at the current moment; D xy (k+1) represents the disturbance compensation at the next time step k+1; D xy (k+1)Δ Dxy (k)=[Δ Dx Δ Dy ] Ts The disturbance compensation D at the current moment xy The rate of change of (k). T s The sampling period; u xy (k) represents the estimated harmonic voltage at the current time k.

[0113] Therefore, based on the design principle of the generalized extended state observer, the equation of the generalized extended state observer is obtained, and its expression is as follows:

[0114]

[0115] in, This is an estimate of the harmonic current at the next time step k+1; This is the estimated value of the disturbance compensation at the next time step k+1; T s L is the sampling period; s Nominal stator inductance; L z Nominal leakage inductance; R s Nominal resistance; Let i be the actual current of the k motor system at the current moment. xy The estimated value of (k); The current time k disturbance compensation D xyThe estimated value of (k); u xy (k) represents the actual voltage of the k motor system at the current time;

[0116] f(e ixy (k) is the extended state variable observer function to be designed; β xy This is the gain coefficient;

[0117] This represents the observation error value of the harmonic current at the current moment.

[0118] The estimated value of harmonic current and the true value i xy and the estimated value of the disturbance D and the true value xy Subtraction yields the following error for the generalized extended state observer:

[0119]

[0120] Among them, e ixy (k+1) represents the observation error value of the harmonic current at the next time step k+1; e Dxy (k+1) represents the observation error value of the harmonic disturbance at the next time step k+1; The current time value represents the observation error of the k-harmonic disturbance; Δ Dxy (k) represents the disturbance D at time k. xy The rate of change of (k).

[0121] To effectively and stably estimate disturbance and harmonic currents, a nonlinear discrete sliding mode observer function is proposed. Based on the generalized extended state observer theory, the sliding mode design process can be divided into two steps: first, the design of the sliding mode surface, and second, the design of the observer function. The goal of the observer is to eliminate harmonic current prediction errors. The sliding mode surface is selected as follows:

[0122] s(k)=[s x (k)s y (k)] T =e ixy (k)

[0123] Traditional sliding mode control function design methods do not consider the convergence characteristics of the sliding surface. To improve the observation accuracy of the sliding mode observer, an exponential convergence law is used to design the sliding mode control function as follows:

[0124] s(k+1)-s(k)=-k1T s εsgn(s(k))-λT s s(k)

[0125] and

[0126]

[0127] Where λ and ε are adjustable parameters, with limits of λ>0, ε>0, and 1-λT s >0, sgn() is a symbolic function.

[0128] While the current reaching law satisfies the reaching condition and stabilizes the system, the sliding mode chattering caused by the sign function degrades system performance. Therefore, an improved reaching law is proposed to reduce sliding mode chattering, as shown in the following equation:

[0129]

[0130] Here, σ and δ are two different adjustable parameters, and σ>0 and δ>0 are the limits of the adjustable parameters;

[0131] e Dxy (k) can be considered as a bounded perturbation of the observer function, and the nonlinear observer function can be designed as follows:

[0132]

[0133] This function can be used to reduce the harmonic current observation error e. ixy (k) converges to zero. The final harmonic current disturbance observer is as follows: Figure 3 As shown.

[0134] S2. Voltage Vector Prediction: Based on the estimated harmonic current and the fundamental current at the current moment, calculate the fundamental current and harmonic current at the next moment; establish the voltage equation of the dual three-phase permanent magnet synchronous motor under space vector decoupling, use the first-order Taylor formula to discretize the voltage equation, introduce weighting factors, input the fundamental current and harmonic current at the next moment and the disturbance compensation into the processed voltage equation, and calculate the reference voltage of the fundamental space and the reference voltage of the harmonic space of the dual three-phase permanent magnet synchronous motor.

[0135] The specific implementation process of step S2 is as follows:

[0136] S2.1. Using the estimated harmonic current and the fundamental current at the current moment, calculate the fundamental current and harmonic current at the next moment, as follows:

[0137] Based on the deadbeat current predictive control principle, feedback variables are sampled at time k. Then, a mathematical model is predicted using these feedback variables. The control voltage vector is calculated using this mathematical model and then used to generate a PWM wave that acts on the inverter via spatial modulation, ensuring the current follows the given current. Therefore, the voltage vector equation at time k is:

[0138]

[0139] Among them, u d(k) represents the expected value of the d-axis voltage at time k; u q (k) represents the expected value of the q-axis voltage at time k; i d (k) represents the expected value of the d-axis current at time k; i q (k) The expected value of the q-axis current at time k; i d (k+1) is the expected value of the d-axis current at time k+1; i q (k+1) is the expected value of the q-axis current at time k+1; L s For nominal stator inductance; T s Sampling period L z Nominal leakage inductance; R s The nominal resistance; ψ f ω is the rotor flux linkage; ω(k) is the mechanical angular velocity of the motor at time k; u x (k) and u y (k) represent the z1 and z2 harmonic subspace voltages at time k, respectively; i x (k) and i y (k) represent the z1 and z2 harmonic subspace currents at time k, respectively; i x (k+1) and i y (k+1) represents the z1 and z2 harmonic subspace currents at time k+1, respectively.

[0140] However, in actual operation of the motor, the motor parameters change due to factors such as armature effect, resulting in an error between the actual current and the predicted current. Therefore, the fundamental current and harmonic current at the next time k+1 under the actual motor parameters can be calculated based on the voltage vector equation at time k.

[0141]

[0142] Among them, L s0 For the actual stator inductance, L z0 For actual leakage inductance, R s0 For the actual resistance, ψ f 0 represents the actual flux linkage.

[0143] To address the impact of parameter accuracy on control performance in current predictive controllers, a weighting factor is introduced to improve the deadbeat predictive control scheme for stable parameters. Since the control cycle of the current loop is typically 100 μs and the motor inductance is a few milliohms, 1-TR / L s0 With 1-TR / L z0 It can be approximated as 1. Therefore, the fundamental current and harmonic current at the next moment can be rewritten as:

[0144]

[0145] Among them, L s0For actual stator inductance; L z0 ψ is the actual leakage inductance; ω(k) is the mechanical angular velocity of the motor at time k; f0 This refers to the actual magnetic flux linkage.

[0146] Introducing weighting factors α and β, where α + β = 1, the relationship between the current reference and feedback with weighting factors is as follows:

[0147]

[0148] in, Let k be the reference current. The current after adding the weighting factor at time k.

[0149] The voltage vector equation after introducing the weighting factor can be obtained as follows:

[0150]

[0151] in, This is the estimated value of the d-axis current at time k; This is the estimated value of the q-axis current at time k; This is the estimated value of the z1 harmonic subspace current at time k; This is the estimated value of the z2 harmonic subspace current at time k; This is the given value of the d-axis current at time k+1; This is the given value of the q-axis current at time k+1; and These are the z1 and z2 harmonic subspace reference currents at time k+1, respectively.

[0152] The voltage vector applied in the next cycle is calculated using the voltage vector equation after introducing a weighting factor. In the next cycle, the voltage vector calculated in the previous cycle is applied to the actual system to achieve the current response. Therefore, the fundamental current and harmonic current at the next moment after introducing the weighting factor are as follows:

[0153]

[0154] in, This is the given value of the d-axis current at time k; This is the given value of the q-axis current at time k. and These are the z1 and z2 harmonic subspace reference currents at time k, respectively.

[0155] The voltage equations of a dual three-phase permanent magnet synchronous motor under spatial decoupling are established. The voltage equations are discretized using a first-order Taylor formula, and weighting factors are introduced. The fundamental current and harmonic current at the next moment, along with disturbance compensation, are input into the processed voltage equations to calculate the reference voltages in the fundamental and harmonic spaces of the dual three-phase permanent magnet synchronous motor. The details are as follows:

[0156] The voltage equation for a dual three-phase permanent magnet synchronous motor under spatial decoupling is established, and its expression is as follows:

[0157]

[0158] The flux linkage equation for a dual three-phase PMSM is as follows:

[0159]

[0160] Among them, L d and L q For the α-β planar inductance component; L z Nominal leakage inductance; ψ f For rotor flux linkage; i x and i y These are the z1 and z2 harmonic subspace currents, respectively.

[0161] Due to the sampling period T s Since the value is sufficiently small, the expression for the fundamental current at the next time step can be discretized using the first-order Taylor formula, resulting in the current prediction model at time k+1:

[0162]

[0163] Among them, i d (k+1) is the expected value of the d-axis current at time k+1; i q (k+1) is the expected value of the q-axis current at time k+1; L s For nominal stator inductance; T s R is the sampling period; s The nominal resistance; ψ f For rotor flux linkage; i d (k) represents the expected value of the d-axis current at time k; i q (k) The expected value of the q-axis current at time k; u d (k) represents the expected value of the d-axis voltage at time k; u q (k) represents the expected value of the q-axis voltage at time k.

[0164] The current given value at time k is taken as the expected value at time k+1:

[0165]

[0166] in, This is the given value of the d-axis current at time k; This is the given value of the q-axis current at time k.

[0167] Since the current components in the z1-z2 subspace can be obtained from the voltage and the simplified transfer function, no corresponding prediction model is required. Therefore, the reference voltage in the fundamental space of the dual three-phase permanent magnet synchronous motor is obtained as follows:

[0168]

[0169] In the formula, The given value of the d-axis voltage vector at time k+1; ω(k) is the given value of the q-axis voltage vector at time k+1; ω(k) is the mechanical angular velocity of the motor at time k.

[0170] Considering lumped parameter disturbances, the harmonic voltage equation in the voltage equation of a dual three-phase permanent magnet synchronous motor under spatial decoupling can be rewritten as follows:

[0171]

[0172] in, The harmonic voltage reference value is given at time k+1; G = 1 - R s T s / L z H = T s / L z , and These are the per-unit values ​​of constants G and H, respectively; This is a reference value for harmonic current. It is generally set to 0 to suppress harmonic currents, i xy (k+1) represents the current in the harmonic space at time k+1, D xy (k+1) represents the disturbance compensation amount at time k+1.

[0173] Finally, the estimated system disturbances Harmonic current From the calculation formula of the reference voltage compensated to the harmonic space, the following expression for the reference voltage of the harmonic space of a dual three-phase permanent magnet synchronous motor is obtained:

[0174]

[0175] in, and This is the harmonic space reference voltage; and This is the harmonic space reference current; and This is an estimated value for the harmonic current; and This is an estimate of the disturbance compensation; T s The sampling period.

[0176] S3. Speed ​​Closed-Loop Control: The reference voltage in the fundamental space is input to SVPWM after coordinate transformation, and the reference voltage in the harmonic space is directly input to SVPWM. SVPWM outputs a PWM wave, which is processed by the inverter and outputs a drive voltage. The drive voltage drives the dual three-phase permanent magnet synchronous motor to run. The actual speed of the dual three-phase permanent magnet synchronous motor is detected by the position sensor. The difference between the actual speed and the given speed is used to output a given iq value for voltage vector prediction by PI control, thus forming a speed closed-loop control system.

[0177] The reference voltage in the fundamental space is transformed by coordinates to output the reference voltage u along the α and β axes. αβ * The reference voltages of the α and β axes and the reference voltage of the harmonic space are input together into SVPWM (space vector pulse width modulation).

[0178] The six-phase current i is sampled from the inverter. abc and i def The currents i along the α and β axes are obtained through a static transformation matrix. αβ k Harmonic current i xy k .

[0179] In vector control, coordinate transformation of voltage or current in different coordinate systems is required, therefore determining the transformation matrix is ​​equally important. A double three-phase winding is a symmetrical twelve-phase winding where two sets of windings, 180° out of phase, are connected in reverse series to obtain one phase. Combining this with multiphase Clarke transformation theory, the final static transformation matrix of the double three-phase motor is:

[0180]

[0181] Therefore, all variables of a dual three-phase permanent magnet synchronous motor can be mapped to three mutually orthogonal subplanes: α-β, z1-z2, and o1-o2. The fundamental frequency and the 12k±1 (k=1,2,3,…) harmonics are mapped to the α-β subplane, which generates magnetomotive force in the motor's air gap and participates in the electromechanical energy conversion. The 6k±1 (k=1,2,3,…) harmonic components of the dual three-phase motor are mapped to the z1-z2 subplane, which is orthogonal to the α-β subplane. The corresponding current components do not generate magnetomotive force and do not participate in electromechanical energy conversion. The 6k±3 (k=1,2,3,…) harmonic components of the dual three-phase motor are mapped to the o1-o2 subplane, and similarly do not participate in electromechanical energy conversion. With neutral point isolation, the o1-o2 subplane is a zero-sequence subplane, and all variables in this subplane are zero.

[0182] By performing a rotational coordinate transformation on the α-β subplane involved in the electromechanical energy conversion, the rotational transformation matrix can be obtained as follows:

[0183]

[0184] After static and rotating coordinate transformations, a dual-phase three-phase motor forms a multi-dimensional space. For a dual-phase three-phase motor converter, to obtain a sinusoidal voltage, the α-β subspace and the z1-z2 subspace need to be controlled. To minimize the synthesized vector in the z1-z2 subspace, four non-zero vectors need to be selected for synthesis. The basic idea of ​​four-vector SVPWM is to select four adjacent large vectors in the plane, i.e., the maximum four-vector algorithm. Every three adjacent voltage vectors are synthesized into a virtual voltage vector, and the amplitude ratio of these three maximum voltage vectors is adjusted so that the voltage vectors corresponding to them in the z1-z2 plane are synthesized to 0. When the target voltage vector is located in a certain sector, the target voltage vector can be synthesized by the two virtual voltage vectors constituting that sector.

[0185] Figure 4 and Figure 5 The figures show the motor speed and current waveforms under the condition of sudden speed change. As can be seen from the figures, the proposed method exhibits high stator current sinusoidality and high steady-state speed accuracy under the condition of sudden speed change.

[0186] Figure 6 and Figure 7 The harmonic currents of the traditional method and the proposed method are compared when the stator resistance is increased by 10 times and the stator leakage inductance is reduced by 1 time, respectively. It can be seen that when the resistance increases, the proposed method maintains the harmonic current at the ideal value of 0A, with fluctuations within 0.25A, effectively suppressing harmonics under increased stator resistance. Under the condition of reduced leakage inductance, the system phase current waveform is basically consistent with the steady-state condition, the harmonic current amplitude fluctuation is controlled within 5%, and the current ripple amplitude is reduced by more than 2A compared to the traditional method.

Claims

1. A disturbance-compensated, deadbeat-free predictive control method for a dual three-phase permanent magnet synchronous motor, characterized in that, include: Harmonic current estimation: Design of a generalized extended state observer based on sliding mode surface and observer function; The actual voltage and actual current of the motor system are used as the input of the generalized extended state observer, and the estimated harmonic current and disturbance compensation are used as the output of the generalized extended state observer. Voltage vector prediction: Based on the estimated harmonic current and the fundamental current at the current moment, calculate the fundamental current and harmonic current at the next moment; establish the voltage equation of the dual three-phase permanent magnet synchronous motor under space vector decoupling, use the first-order Taylor formula to discretize the voltage equation, introduce weighting factors, input the fundamental current and harmonic current at the next moment and the disturbance compensation into the voltage equation after processing, and calculate the reference voltage of the fundamental space and the reference voltage of the harmonic space of the dual three-phase permanent magnet synchronous motor. Speed ​​closed-loop control: The reference voltage in the fundamental space is input to SVPWM after coordinate transformation, and the reference voltage in the harmonic space is directly input to SVPWM. SVPWM outputs a PWM wave, which is processed by the inverter and outputs a drive voltage to drive the dual three-phase permanent magnet synchronous motor. The actual speed of the dual three-phase permanent magnet synchronous motor is detected by the position sensor. The difference between the actual speed and the given speed is used to output a given iq value for voltage vector prediction by PI control, thus forming a speed closed-loop control system.

2. The disturbance-compensated predictive control method for dual three-phase permanent magnet synchronous motors with zero deadbeat time according to claim 1, characterized in that, The design of the generalized extended state observer is based on the sliding modal surface and the observer function; the actual voltage and current of the motor system are used as the inputs of the generalized extended state observer, and the estimated harmonic current and disturbance compensation are used as the outputs of the generalized extended state observer, including: Traditional extended state observers use linear system models. An extension variable x is introduced into the traditional extended state observer model. n+1 Let x represent the uncertainty of a dual three-phase motor control system, where the expanded variable x n+1 The expression is as follows: x n+1 =f(x,ω(t),t) Where f(x,ω(t),t) represents the uncertainty of the dual three-phase motor control system; And assume the expansion variable x n+1 The rate of change is a finite value system state vector Expanded to: The dynamic current equation of a dual three-phase permanent magnet synchronous motor, considering parameter variations, can be expressed as follows: Among them, u xy and i xy These represent the voltage and current in the harmonic space, respectively; D xy d is the disturbance compensation amount. xy This represents the change in disturbance compensation. In order to simultaneously calculate the estimated harmonic current i at the next time step k+1 xy (k+1) and disturbance compensation D xy (k+1) represents the estimated harmonic current i at the current time k. xy The perturbation compensation D at the current time k xy (k) is treated as a state variable, and the discrete state space equation is derived; according to the design principle of the generalized extended state observer, the equation of the generalized extended state observer is obtained; The estimated value of harmonic current and the true value i xy and the estimated value of the disturbance and the true value D xy Subtraction yields the following error for the generalized extended state observer: Among them, e ixy (k+1) represents the observation error value of the harmonic current at the next time step k+1; e Dxy (k+1) represents the observation error value of the harmonic disturbance at the next time step k+1; The current time value represents the observation error of the k-harmonic disturbance; Δ Dxy (k) represents the disturbance D at time k. xy The rate of change of (k); According to the generalized extended state observer theory, the sliding mode design process can be divided into two steps: first, the design of the sliding mode surface, and second, the design of the observer function; the goal of the observer is to eliminate harmonic current prediction errors, and the sliding mode surface is selected as follows: s(k)=[s x (k)s y (k)] T =e ixy (k) The sliding mode control function is designed using the following exponential convergence law: s(k+1)-s(k)=-k1T s εsgn(s(k))-λT s s(k) and Here, λ and ε are two different adjustable parameters, with limits of λ>0 and ε>0, and 1-λT s If the value is greater than 0, sgn() is a sign function; An improved approach law is used to reduce sliding mode chattering, as shown in the following equation: Where σ and δ are adjustable parameters, and σ>0 and δ>0 are the limits of the adjustable parameters; e Dxy (k) can be considered as a bounded perturbation of the observer function, and the nonlinear observer function can be designed as follows: This function can be used to reduce the harmonic current observation error e. ixy (k) converges to zero.

3. The disturbance-compensated predictive control method for dual three-phase permanent magnet synchronous motors with zero deadbeat time according to claim 2, characterized in that, The expression for the discrete state-space equation is as follows: Among them, i xy (k+1) represents the estimated harmonic current at the next time step k+1; R s Nominal resistance; L z For nominal leakage inductance; i xy (k) represents the estimated harmonic current at the current time k; D xy (k) represents the disturbance compensation at the current moment; D xy (k+1) represents the disturbance compensation at the next time step k+1; D xy (k+1)Δ Dxy (k)=[Δ Dx Δ Dy ] T The disturbance compensation D at the current moment xy The rate of change of (k); T s The sampling period; u xy (k) represents the estimated harmonic voltage at the current time k.

4. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 2, characterized in that, The equations for the generalized extended state observer are as follows: in, This is an estimate of the harmonic current at the next time step k+1; The value is the estimated value of the disturbance compensation at the next time step k+1; T is the sampling period; L s Nominal stator inductance; L z Nominal leakage inductance; R s Nominal resistance; Let i be the actual current of the k motor system at the current moment. xy The estimated value of (k); The current time k disturbance compensation D xy The estimated value of (k); u xy (k) represents the actual voltage of the k-motor system at the current time; f(e) ixy (k) is the extended state variable observer function to be designed; β xy This is the gain coefficient; This represents the observation error value of the harmonic current at the current moment.

5. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 1, characterized in that, The process of estimating the harmonic current and the fundamental current at the current moment, and calculating the fundamental current and harmonic current at the next moment, includes: Based on the deadbeat current predictive control principle, feedback variables are sampled at time k. A mathematical model is then used to predict these feedback variables, and the control voltage vector is calculated using this model. A PWM wave is then generated using a spatial modulation method and applied to the inverter, ensuring that the current follows the given current. Therefore, the voltage vector equation at time k is: Among them, u d (k) represents the expected value of the d-axis voltage at time k; u q (k) represents the expected value of the q-axis voltage at time k; i d (k) represents the expected value of the d-axis current at time k; i q (k) represents the expected value of the q-axis current at time k; i d (k+1) is the expected value of the d-axis current at time k+1; i q (k+1) is the expected value of the q-axis current at time k+1; L s For nominal stator inductance; T s L is the sampling period; z Nominal leakage inductance; R s The nominal resistance; ψ f ω is the rotor flux linkage; ω(k) is the mechanical angular velocity of the motor at time k; u x (k) and u y (k) represent the z1 and z2 harmonic subspace voltages at time k, respectively; i x (k) and i y (k) represent the z1 and z2 harmonic subspace currents at time k, respectively; i x (k+1) and i y (k+1) represent the z1 and z2 harmonic subspace currents at time k+1, respectively; Calculate the fundamental current and harmonic current at the next time k+1 based on the voltage vector equation at time k: Among them, L s0 For actual stator inductance; L z0 ψ is the actual leakage inductance; ω(k) is the mechanical angular velocity of the motor at time k; f0 This refers to the actual magnetic flux linkage.

6. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 5, characterized in that, The process of estimating the harmonic current and the fundamental current at the current moment, and calculating the fundamental current and harmonic current at the next moment, includes: Introducing weighting factors α and β, where α + β = 1, the relationship between the current reference and feedback with weighting factors is as follows: in, Let k be the reference current; The current after adding the weighting factor at time k; The voltage vector equation after introducing the weighting factor can be obtained as follows: in, This is the estimated value of the d-axis current at time k; This is the estimated value of the q-axis current at time k; This is the estimated value of the z1 harmonic subspace current at time k; This is the estimated value of the z2 harmonic subspace current at time k; This is the given value of the d-axis current at time k+1; This is the given value of the q-axis current at time k+1; and These are the z1 and z2 harmonic subspace reference currents at time k+1, respectively; The voltage vector applied in the next cycle is calculated using the voltage vector equation after introducing a weighting factor. In the next cycle, the voltage vector calculated in the previous cycle is applied to the actual system to achieve the current response. Therefore, the fundamental current and harmonic current at the next moment after introducing the weighting factor are as follows: in, This is the given value of the d-axis current at time k; This is the given value of the q-axis current at time k; and These are the z1 and z2 harmonic subspace reference currents at time k, respectively.

7. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 1, characterized in that, The voltage equations for the dual three-phase permanent magnet synchronous motor under spatial decoupling are established by discretizing the voltage equations using a first-order Taylor formula, introducing weighting factors, and inputting the fundamental current, harmonic current, and disturbance compensation at the next moment into the processed voltage equations. The reference voltages in the fundamental space and harmonic space of the dual three-phase permanent magnet synchronous motor are then calculated, including: The voltage equation for a dual three-phase permanent magnet synchronous motor under spatial decoupling is established, and its expression is as follows: The expression for the fundamental current at the next time step is discretized using the first-order Taylor formula, resulting in the current prediction model at time k+1: Among them, i d (k+1) is the expected value of the d-axis current at time k+1; i q (k+1) is the expected value of the q-axis current at time k+1; L s For nominal stator inductance; T s R is the sampling period; s The nominal resistance; ψ f For rotor flux linkage; i d (k) represents the expected value of the d-axis current at time k; i q (k) The expected value of the q-axis current at time k; u d (k) represents the expected value of the d-axis voltage at time k; u q (k) represents the expected value of the q-axis voltage at time k; ω(k) represents the mechanical angular velocity of the motor at time k. The current given value at time k is taken as the expected value at time k+1: in, This is the given value of the d-axis current at time k; This is the given value of the q-axis current at time k; Since the current components in the z1-z2 subspace can be obtained from the voltage and the simplified transfer function, the reference voltage of the fundamental space of the dual three-phase permanent magnet synchronous motor is obtained: In the formula, The given value of the d-axis voltage vector at time k+1; ω(k) is the given value of the q-axis voltage vector at time k+1; ω(k) is the mechanical angular velocity of the motor at time k. Considering lumped parameter disturbances, the harmonic voltage equation in the voltage equation of a dual three-phase permanent magnet synchronous motor under spatial decoupling can be rewritten as follows: in, The harmonic voltage reference value is given at time k+1; G = 1 - R s T s / L z H = T s / L z , and These are the per-unit values ​​of constants G and H, respectively; This is a reference value for harmonic current. D represents the current in the harmonic space at time k+1. xy (k+1) represents the disturbance compensation amount at time k+1; By incorporating the estimated system disturbances and harmonic currents into the calculation formula for the reference voltage in the harmonic space, the following expression for the reference voltage in the harmonic space of a dual three-phase permanent magnet synchronous motor is obtained: in, and This is the harmonic space reference voltage; and This is the harmonic space reference current; and This is an estimated value for the harmonic current; and T is the estimated value for disturbance compensation. s The sampling period.

8. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 7, characterized in that, In the voltage equations of the dual three-phase permanent magnet synchronous motor under spatial decoupling, the flux linkage equations of the dual three-phase PMSM are as follows: Among them, L d and L q For the α-β planar inductance component; L z Nominal leakage inductance; ψ f For rotor flux linkage; i x and i y These are the z1 and z2 harmonic subspace currents, respectively.

9. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 2, characterized in that, The expression for the linear system model is as follows: in, Let A be the state vector of the linear system; u∈R be the control input; f(x,ω(t),t) be the uncertainty of the system, including unmodeled dynamics and external disturbances; y be the output of the observer; A, B u and B d These represent the system dynamic matrix, control input matrix, and disturbance effect matrix, respectively; C is the measurement output matrix.

10. The disturbance-compensated predictive control method for a dual three-phase permanent magnet synchronous motor with zero deadbeat time according to claim 1, characterized in that, During the speed closed-loop control process, the reference voltage in the fundamental space is transformed into reference voltages for the α and β axes. The reference voltages for the α and β axes and the reference voltage in the harmonic space are input together into SVPWM.

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