A Current Control Method for a Permanent Magnet Synchronous Motor with a Sinusoidal Filter

Abstract

The present invention belongs to the field of permanent magnet motor control, and discloses a current control method for a permanent magnet synchronous motor with a sine filter, which includes a non-delay full state feedback controller and a delay compensation controller connected in series. The non-delay full state feedback controller includes a state feedback matrix and an integrator. The state feedback provides damping for the non-delay system and weakens the LC oscillation; the input of the integrator is the difference between the current reference value and the actual current to eliminate the steady-state error of the current control. The gains of the state feedback matrix and the integrator can be calculated by pole placement through an augmented mathematical model with an integral term. The delay compensator controller is used to compensate for the error between the voltage reference value and the actual output voltage caused by digital control delay, and can be equivalent to a low-pass filter after reasonable design, which can greatly weaken the influence of sampling noise and pulse width modulation harmonics on the current control system.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet motor control, and particularly relates to a current control method for a permanent magnet synchronous motor with a sine filter. Background Art

[0002] In traditional permanent magnet synchronous motor drives, the motor is usually directly driven by a voltage source inverter based on Pulse Width Modulation (PWM). For permanent magnet motors with relatively small inductance, the switching chopping action of the inverter will cause harmonic currents near the relatively high switching frequency, resulting in a significant increase in the harmonic losses of the motor, serious heating, and a decrease in efficiency.

[0003] To solve the above problems, a sine filter is introduced into the motor drive system. The sine filter can be of the LCL (inductor - capacitor - inductor) structure or the LC (inductor - capacitor) structure, and is installed between the inverter and the motor. It can basically filter out the harmonic currents caused by chopping and improve the sinusoidality of the motor current. However, after the introduction of the sine filter, unstable resonance occurs in the motor current control system, making the traditional current controller difficult to apply. Full - state feedback control is an effective method to suppress resonance and achieve stable current control. However, affected by sampling noise and PWM harmonic noise, the control effect of the current controller based on full - state feedback is not good, and the current ripple is large. Therefore, a current control method for a permanent magnet synchronous motor with a sine filter is needed. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the purpose of the present invention is to provide a current control method for a permanent magnet synchronous motor with a sine filter, which solves the problem of current ripple in full - state feedback current control in the prior art.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A current control method for a permanent magnet synchronous motor with a sine filter includes a delay - free full - state feedback controller and an adaptive delay compensation controller. The delay - free full - state feedback controller and the delay compensation controller are in series control; after being in series, a modulation voltage is generated and directly acts on the motor through a PWM inverter; the delay - free full - state feedback controller, the delay compensator, and the motor are in a series relationship in sequence.

[0007] Further, the delay - free full - state feedback controller is composed of a state feedback matrix and an integrator in parallel, and the output of the delay - free full - state feedback controller is the sum of the inverses of the calculation results of two parts added together.

[0008] Further, the delay - free full - state feedback controller is designed through the following mathematical model;

[0009] First, establish the continuous-domain mathematical model of a permanent magnet motor with a sine filter as follows:

[0010]

[0011] Among them, i 1s (t) is the inverter output current; i 2s (t) is the motor current; u cs (t) is the capacitor voltage; u s (t) is the inverter output voltage; e s (t) is the motor back electromotive force;

[0012] After adopting zero-order hold discretization, the continuous-domain mathematical model of the permanent magnet motor with a sine filter in the discrete domain is obtained as follows:

[0013]

[0014] Among them, T s is the system control period;

[0015] Further use the rotating coordinate transformation to obtain the discrete mathematical model in the rotating coordinate system as follows:

[0016]

[0017]

[0018] Among them, i 1r is the inverter output current in the rotating coordinate system; i 2r (t) is the motor current in the rotating coordinate system; u cr (t) is the capacitor voltage in the rotating coordinate system; u r (t) is the inverter output voltage in the rotating coordinate system; e r (t) is the motor back electromotive force in the rotating coordinate system;

[0019] Considering the one-beat delay of the digital control system, the discrete mathematical model with digital delay in the rotating coordinate system is obtained as follows:

[0020]

[0021]

[0022] Among them, is the voltage given value in the rotating coordinate system;

[0023] For the system feedback controller, in order to eliminate the steady-state error, the integral term of the current error is introduced as follows,

[0024]

[0025] Therefore, the delay-free full-state feedback controller is designed as follows:

[0026] u r (k) = -K3x r (k) - K i x i (k) (9)

[0027] where K3 and K i are the gains of the state feedback and the integrator respectively, and their selection is equivalent to pole placement for the subsystem A - BK.

[0028] Furthermore, A s and B s are defined as follows:

[0029]

[0030] where R is the motor resistance; L1 is the inductor on the inverter side of the filter; L2 = L 1o + L s , L 1o is the inductor on the motor side of the filter, and L s is the motor winding inductance.

[0031] Furthermore, the selection is equivalent to pole placement for the subsystem A - BK, where A, B, and K are defined as shown in the following equations.

[0032]

[0033] Furthermore, the delay compensation controller is designed through the following mathematical model;

[0034] Reconsidering the digital control delay, according to the matrix transformation theory, an augmented model with a delay and an error integral term can be obtained as follows:

[0035]

[0036] Based on the above augmented model, by introducing a linear transformation, an extended mathematical model containing the dynamic expression of the voltage reference value in the rotating coordinate system is obtained as follows:

[0037]

[0038] According to the above linear transformation, an extended mathematical model containing the dynamic expression of the voltage reference value in the rotating coordinate system is obtained as follows:

[0039]

[0040] where G i , G r and Gζ They are the state transition coefficient matrices respectively, which can be directly obtained by linear transformation and are both constant matrices;

[0041] In summary, the final dynamic expression of the voltage reference value in the rotating coordinate system is obtained as follows:

[0042]

[0043] It can be seen from the above formula that G i x i (k), G r x r (k) and are all known disturbances, and K3Γ e e r (k) is an unknown disturbance; based on the mathematical model (14), a delay compensation controller is designed as follows:

[0044]

[0045] where λ is a positive constant less than 1, and ω c is the filtering constant of the disturbance observer.

[0046] Advantages of the present invention:

[0047] 1. The present invention discloses a current control method for a permanent magnet synchronous motor with a sine filter, which is composed of a non-delay full-state feedback controller and a delay compensation controller connected in series. The non-delay full-state feedback controller consists of a state feedback matrix and an integrator. The state feedback provides damping for the non-delay system and weakens the LC oscillation; the input of the integrator is the difference between the current reference value and the actual current to eliminate the steady-state error of the current control. The delay compensation controller is used to compensate for the error between the voltage reference value and the actual output voltage caused by digital control delay, and can be equivalent to a low-pass filter after reasonable design, which can greatly weaken the influence of sampling noise and pulse width modulation harmonics on the current control system, and can solve the problems that the full-state feedback current controller in the permanent magnet motor drive with a sine filter is vulnerable to sampling noise and has large ripple.

[0048] 2. The full-state feedback control of the present invention is for a digital-delay-free control system, which simplifies the calculation of the state feedback gain matrix to a certain extent.

[0049] 3. After reasonable design, the delay compensation controller can be equivalent to a low-pass filter, which can greatly weaken the influence of sampling noise and pulse width modulation harmonics on the current control system, improve the robustness of the system, and reduce the current control ripple. Description of the Drawings

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0051] Figure 1 is the block diagram of the current control structure of the permanent magnet motor with a sine filter according to the present invention;

[0052] Figure 2 is the schematic diagram of the drive equivalent circuit and control of the permanent magnet motor with a sine filter according to the present invention. Detailed implementation manners

[0053] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0054] The present invention provides a current control method for a permanent magnet synchronous motor with a sine filter, including a delay-free full-state feedback controller and a delay compensation controller. The delay-free full-state feedback controller and the adaptive delay compensation controller are in a series control structure. After being connected in series, a modulation voltage is generated and directly acts on the motor through a PWM inverter; the delay-free full-state feedback controller, the delay compensator and the motor are in a series relationship in sequence.

[0055] The delay-free full-state feedback controller is composed of a state feedback matrix and an integrator in parallel. The output of the delay-free full-state feedback controller is the sum of the negated results of two parts of calculations.

[0056] The object of action of the full-state feedback controller is a digital control delay-free system, that is, the digital control delay does not need to be considered when calculating its state feedback matrix, which can reduce the matrix order. The state feedback matrix provides damping for the delay-free system and weakens the LC oscillation; the input of the integrator is the difference between the current reference value and the actual current to eliminate the steady-state error of the current control. The gains of the state feedback matrix and the integrator can be calculated by pole placement through an augmented mathematical model with an integral term.

[0057] The delay compensation controller is used to compensate for the error between the voltage reference value and the actual output voltage caused by digital control delay, and can be equivalent to a low-pass filter after reasonable design, which can greatly weaken the influence of sampling noise and pulse width modulation harmonics on the current control system.

[0058] Whether it is the LCL (inductor-capacitor-inductor) structure or the LC (inductor-capacitor) structure, due to the existence of the motor inductance, the equivalent circuit of the permanent magnet motor control system with a sinusoidal filter can always be simplified to an inductor-capacitor-inductor-resistor-back electromotive force structure.

[0059] Based on this, the continuous-domain mathematical model of the permanent magnet motor with a sinusoidal filter is established as follows:

[0060]

[0061] Among them, i 1s (t) is the inverter output current; i 2s (t) is the motor current; u cs (t) is the capacitor voltage; u s (t) is the inverter output voltage; e s (t) is the motor back electromotive force.

[0062] A s 、B s are defined as follows,

[0063]

[0064] Among them, R is the motor resistance; L1 is the inductor on the inverter side of the filter; L2 = L 1o +L s , L 1o is the inductor on the motor side of the filter, and L s is the motor winding inductance.

[0065] After discretization using zero-order hold, the discrete-domain mathematical model of the permanent magnet motor with a sinusoidal filter in the continuous domain is obtained as follows:

[0066]

[0067] Among them, T s is the system control period.

[0068] Furthermore, by using the rotating coordinate transformation, the discrete mathematical model in the rotating coordinate system is obtained as follows:

[0069]

[0070]

[0071] Among them, i 1r is the inverter output current in the rotating coordinate system; i 2r (t) is the motor current in the rotating coordinate system; u cr (t) is the capacitor voltage in the rotating coordinate system; u r (t) is the inverter output voltage in the rotating coordinate system; er (t) is the back electromotive force of the motor in the rotating coordinate system.

[0072] Considering the one-beat delay of the digital control system, the discrete mathematical model with digital delay in the rotating coordinate system is obtained as follows:

[0073]

[0074]

[0075] Among them, is the voltage reference value in the rotating coordinate system.

[0076] For the system feedback controller, in order to eliminate the steady-state error, the integral term of the current error is introduced as follows.

[0077]

[0078] Therefore, the non-delay full-state feedback controller is designed as follows:

[0079] u r (k)=-K3x r (k)-K i x i (k) (9)

[0080] Among them, K3 and K i are the gains of the state feedback and the integrator respectively. Their selection can be equivalently regarded as pole placement for the subsystem A - BK, where A, B, and K are defined as shown in the following equations.

[0081]

[0082] Therefore, reconsidering the digital control delay, according to the matrix transformation theory, the augmented model with error integral term and delay can be obtained as follows:

[0083]

[0084] Based on the above augmented model, a linear transformation formula is introduced. The purpose is to obtain an extended mathematical model containing the dynamic expression of the voltage reference value in the rotating coordinate system for subsequent design of the adaptive delay compensator. As follows:

[0085]

[0086] According to the above linear transformation, an extended mathematical model containing the dynamic expression of the voltage reference value in the rotating coordinate system is obtained for subsequent design of the adaptive delay compensator. As follows:

[0087]

[0088] Among them, G i , G r and G ζ are respectively the state transition coefficient matrices, which can be directly obtained by linear transformation and are both constant matrices.

[0089] In summary, the final dynamic expression of the voltage reference value in the rotating coordinate system is obtained. The expression is the dynamic equation of the voltage reference value in the rotating coordinate system, which is used to describe its variation characteristics and facilitate digital control.

[0090] As follows:

[0091]

[0092] It can be seen from the above formula that G i x i (k), G r x r (k) and are all known disturbances, and K3Γ e e r (k) is an unknown disturbance. Based on the mathematical model (14), according to the control theory, an adaptive delay compensation controller is designed, and its function is to compensate for the voltage error caused by digital delay. Specifically, it is shown as follows:

[0093]

[0094] Among them, λ is a positive constant less than 1, and ω c is the filtering constant of the disturbance observer.

[0095] Based on the above-designed delay-free full-state feedback controller and delay compensation controller, a software algorithm is provided. The software calculation process steps of this algorithm are as follows:

[0096] S1: The interruption starts, enters the main program of the algorithm, and the interruption frequency is the same as the inner-loop control frequency of the capacitor voltage.

[0097] S2: The delay-free full-state feedback controller works.

[0098] S21: The integrator works, and the input is the difference between the motor current reference value and the motor current feedback value.

[0099] S22: The state feedback matrix calculates the feedback voltage, which is summed with the output voltage of the integrator to become the output voltage of the delay-free full-state feedback controller.

[0100] S3: The delay compensation controller works, the input is the output voltage of the delay full-state feedback controller, and the output is the inverter modulation voltage.

[0101] S4: Enter the PWM modulator, update the PWM duty cycle, and the debugging method can be SPWM (Sinusoidal Pulse Width Modulation) or SVPWM (Space Vector Pulse Width Modulation);

[0102] S5: The interruption ends, and wait for the next interruption trigger.

[0103] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements fall within the scope of the present invention claimed.

Claims

1. A current control method for a permanent magnet synchronous motor with a sine filter, characterized in that, It includes a non-delay full-state feedback controller and a delay compensation controller. The non-delay full-state feedback controller and the delay compensation controller are in series control. After being connected in series, a modulation voltage is generated and directly acts on the motor through a PWM inverter. The non-delay full-state feedback controller, the delay compensation controller, and the motor are in a sequential series relationship. Based on the non-delay full-state feedback controller and the delay compensation controller, a software algorithm is provided. The software calculation process of this algorithm is as follows: S1: The interruption starts, and the algorithm main program is entered. The interruption frequency is the same as the inner-loop control frequency of the capacitor voltage. S2: The non-delay full-state feedback controller works. S21: The integrator works, and the input is the difference between the motor current given value and the motor current feedback value. S22: The state feedback matrix calculates the feedback voltage, which is summed with the output voltage of the integrator to become the output voltage of the non-delay full-state feedback controller. S3: The delay compensator controller works. The input is the output voltage of the delay full-state feedback controller, and the output is the inverter modulation voltage. S4: Enter the PWM modulator to update the PWM duty cycle. The modulation method can be SPWM or SVPWM. S5: The interruption ends, and it waits for the next interruption trigger.

2. A permanent magnet synchronous motor current control method for a sine filter according to claim 1, characterized in that, The non-delay full-state feedback controller is composed of a state feedback matrix and an integrator in parallel. The output of the non-delay full-state feedback controller is the sum of the two calculation results after taking the inverse and adding them together.

3. A method for controlling the current of a permanent magnet synchronous motor with a sine filter according to claim 2, characterized in that, The non-delay full-state feedback controller is designed through the following mathematical model; First, establish the continuous-domain mathematical model of a permanent magnet motor with a sine filter as follows: where, i 1s (t) is the inverter output current; i 2s (t) is the motor current; u cs (t) is the capacitor voltage; u s (t) is the inverter output voltage; e s (t) is the motor back electromotive force; After discretization using zero-order hold, the discrete-domain continuous-domain mathematical model of a permanent magnet motor with a sine filter is obtained as follows: Among them, T s is the system control period; Further, using the rotation coordinate transformation, the discrete mathematical model in the rotating coordinate system is obtained as follows: where \(i\) 1r is the inverter output current in the rotating coordinate system; \(i\) 2r (t) is the motor current in the rotating coordinate system; \(u\) cr (t) is the capacitor voltage in the rotating coordinate system; \(u\) r (t) is the inverter output voltage in the rotating coordinate system; \(e\) r (t) is the motor back electromotive force in the rotating coordinate system; Considering the one-beat delay of the digital control system, the discrete mathematical model with digital delay in the rotating coordinate system is obtained as follows: Among them, is the voltage reference value in the rotating coordinate system; For the system feedback controller, in order to eliminate the steady-state error, an integral term of the current error is introduced as follows. Therefore, the non-delay full-state feedback controller is designed as follows: u r u(k)=-K3x r u(k)-K i x i u(k) (9) where K3 and K i are the gains of the state feedback and the integrator respectively, and their selection can be equivalent to pole placement for the subsystem A - BK.

4. A method for controlling the current of a permanent magnet synchronous motor with a sine filter according to claim 3, characterized in that A s and B s are defined as follows; Among them, R is the motor resistance; L1 is the inductor on the inverter side of the filter; L2 = L 1o + L s , L 1o is the inductor on the motor side of the filter, and L s is the motor winding inductance.

5. A method for controlling the current of a permanent magnet synchronous motor with a sine filter according to claim 3, characterized in that, Selecting can be equivalently configured as pole placement for the subsystem A - BK, where A, B, and K are defined as shown in the following formula: where K3 and K i are the gains of the state feedback and the integrator, respectively.

6. A method for controlling the current of a permanent magnet synchronous motor with a sine filter according to claim 1, characterized in that The delay compensation controller is designed through the following mathematical model; Reconsidering the digital control delay, according to the matrix transformation theory, an augmented model with a delay and an error integral term can be obtained as follows: Based on the above augmented model, introducing a linear transformation formula, an extended mathematical model including the dynamic expression of the voltage given value in the rotating coordinate system is obtained as follows: According to the above linear transformation, an extended mathematical model including the dynamic expression of the voltage given value in the rotating coordinate system is obtained as follows: Among them, G i , G r and G ζ are respectively the state transition coefficient matrices, which can be directly obtained by linear transformation and are both constant matrices; In summary, the final dynamic expression using the voltage given value in the rotating coordinate system is obtained as follows: As can be seen from the above formula, G i x i (k), G r x r (k) and are all known disturbances, and K3Γ e e r (k) is an unknown disturbance; based on the mathematical model (14), a delay compensation controller is designed as shown in the following formula: where λ is a positive constant less than 1, and ω c is the filtering constant of the disturbance observer.

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