Model-information-embedded active-disturbance-rejection control method for two-level digital switching power amplifier of electromagnetic bearing

Abstract

The invention provides an active-disturbance-rejection control method for an electromagnetic bearing two-level digital switch power amplifier embedded with model information so as to improve the response speed and precision of a current inner ring. Firstly, based on the Fourier series theory and coil current characteristics, a mathematical model suitable for controller design is established. Secondly, performing modelable disturbance term feed-forward compensation on a direct current component in the model; parameter perturbation and an unmodeled part are used as unknown disturbance terms, and an extended state observer is used for real-time estimation. Meanwhile, known information such as a current item is embedded into an observer, and a feedback control law is designed to compensate various items in real time. And finally, discretizing a controller by using a zero-order retainer and a current observer, and implementing on a DSP (Digital Signal Processor) digital control platform. The control performance is excellent, compared with PI and active-disturbance-rejection control, the current response is faster, the precision is higher, and the method is of great significance to stable operation of the magnetic suspension rotor.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic bearing two-level digital switching power amplifier control, and more particularly to an electromagnetic bearing two-level digital switching power amplifier self-disturbance rejection control method with embedded model information. Background Technology

[0002] The switching power amplifier and the electromagnet coil together form the actuator of a magnetically levitated rotor system. Belonging to the inner current loop, its control performance directly affects the levitation accuracy and stability of the rotor system. Two-level digital switching power amplifiers offer advantages such as high portability, simple control logic, and ease of engineering implementation, and are widely used in electromagnetic bearing rotor systems.

[0003] The prior art CN120742668A discloses an active disturbance rejection control method for an electromagnetic bearing two-level digital switching power amplifier with embedded model information. This method includes: establishing a mathematical model of the electromagnetic bearing two-level digital switching power amplifier suitable for controller design based on Fourier series theory and coil current characteristics; defining the DC component in the mathematical model as a modelable disturbance term and directly compensating it in the control law via feedforward; defining parameter perturbations and unmodeled parts in the mathematical model as unknown disturbance terms and estimating them in real time using an extended state observer; embedding the current term and control input term in the mathematical model as known model information into the design of the extended state observer; designing a feedback control law to compensate for the current term, modelable disturbance term, and unknown disturbance term in real time; discretizing the controller using a zero-order hold and a current observer, and implementing it on a DSP-based digital control platform.

[0004] However, there are still issues with the need to further improve the current response speed and control accuracy. Summary of the Invention

[0005] To address the issues of slow current response and low control accuracy, the inventors, based on their understanding of the controlled object and by fully utilizing known information, established an active disturbance rejection control strategy for an electromagnetic bearing two-level digital switching power amplifier with embedded model information. This strategy improves the current response speed and control accuracy of the system, ensuring the stable operation of the magnetic levitation rotor system.

[0006] This invention designs an active disturbance rejection control method for an electromagnetic bearing two-level digital switching power amplifier with embedded model information.

[0007] The technical solution adopted by this invention to solve its technical problem is: to provide an active disturbance rejection control method for an electromagnetic bearing two-level digital switching power amplifier with embedded model information, comprising the following steps:

[0008] Step 1: Based on Fourier series theory and coil current characteristics, establish a mathematical model of an electromagnetic bearing two-level digital switching power amplifier suitable for controller design;

[0009] Step 2: Define the DC component in the mathematical model as a modelable disturbance term and directly feedforward compensate it in the control law;

[0010] Step 3: Define the parameter perturbations and unmodeled parts in the mathematical model as unknown disturbance terms, and estimate them in real time using an extended state observer;

[0011] Step 4: Embed the current term and control input term in the mathematical model as known model information into the design of the extended state observer;

[0012] Step 5: Design a feedback control law to compensate for the current term, modelable disturbance term, and unknown disturbance term in real time;

[0013] Step 6: Discretize the controller using a zero-order hold and a current observer, and implement it on a DSP-based digital control platform.

[0014] Step 1 establishes a mathematical model for an electromagnetic bearing two-level digital switching power amplifier suitable for controller design based on Fourier series theory and coil current characteristics. Specifically:

[0015] Based on Fourier series theory and coil current characteristics, a mathematical model for an electromagnetic bearing two-level digital switching power amplifier suitable for controller design is established as follows:

[0016]

[0017] In the formula: i L U is the current in the electromagnetic bearing coil, i.e., the system output; u is the controller output, i.e., the system input; L and R are the inductance and resistance of the electromagnetic bearing coil, respectively; U in c is the DC bus power supply voltage; pwm The value of the PWM module period register in the DSP; m is the harmonic order; T s This is the switching cycle of the power transistor.

[0018] Step 2 defines the DC component in the mathematical model as a modelable disturbance term, and directly compensates for it in the control law via feedforward, specifically as follows:

[0019] Considering that harmonic components in the mathematical model only affect current ripple and not closed-loop control performance, they are not processed. The DC component -U in the mathematical model... in / L is defined as a modelable perturbation term, denoted by f0:

[0020]

[0021] Step 3 defines the parameter perturbations and unmodeled parts in the mathematical model as unknown disturbance terms, and estimates them in real time using an extended state observer. Specifically:

[0022] The inductance L and resistance R of the electromagnetic bearing coil, and the DC bus power supply voltage U are considered. in The effects of isoparameter perturbations and the unmodeled parts are defined as unknown perturbation terms, denoted by f1.

[0023] Step 4 involves embedding the current term and control input term from the mathematical model as known model information into the design of the extended state observer.

[0024] Step 4 specifically includes the following sub-steps:

[0025] Step 4.1: Expand the unknown disturbance term f1 into a new state variable, and write the expanded state equation of the system as follows:

[0026]

[0027] In the formula: x1=i L ;x2=f1; a0=R / L; b0=2U in / (Lc pwm ).

[0028] Step 4.2: For the above system, design the extended state observer as follows:

[0029]

[0030] In the formula: z1 and z2 are the observed values ​​of system state variables x1 and x2, respectively; l1 and l2 are the gains of the extended state observer.

[0031] Step 4.3: Define ω o To determine the observer bandwidth, a bandwidth parameterization method is used, where the eigenvalues ​​of the system matrix in the extended state observer are all configured at -ω. o At that point, the gains l1 and l2 of the extended state observer are solved as follows:

[0032]

[0033] Step 5 involves designing a feedback control law to provide real-time compensation for the current term, modelable disturbance term, and unknown disturbance term.

[0034] Step 5 specifically includes the following sub-steps:

[0035] Step 5.1: To achieve real-time compensation for the current term, modelable disturbance term, and unknown disturbance term, the feedback control law is designed as follows:

[0036]

[0037] In the formula: u0 is an intermediate control variable.

[0038] Step 5.2: After real-time estimation and compensation of the disturbance, design the intermediate control variables as follows:

[0039] u0=k1(i ref -z1)

[0040] In the formula: i ref k1 is the current setpoint; k1 is the controller gain, which is usually defined as the controller bandwidth ω. c .

[0041] Step 6 uses a zero-order hold and a current observer to discretize the controller, and implements it on a DSP-based digital control platform.

[0042] Step 6 specifically includes the following sub-steps:

[0043] Step 6.1: Discretize the extended state observer using a zero-order hold:

[0044]

[0045] In the formula: I is the second-order identity matrix; i represents the number of terms in the series; A, B, and D are the extended state observer matrices before discretization; A d B d D d C d L d These are the discretized extended state observer matrices; l 1d l 2d These represent the gains of the extended state observer after discretization.

[0046] Step 6.2: Further process the discretized result of the zero-order hold based on the current observer as follows:

[0047]

[0048] In the formula: A eso B eso D eso L d These are the system matrix, input matrix, perturbation input matrix, and observer gain matrix of the discretized extended state observer, respectively.

[0049] Step 6.3: Define z o For the observer poles in the discrete domain, the bandwidth parameterization method is used to define the observer system matrix A in the z-domain. eso The eigenvalues ​​are all configured at the same position z. o At this point, the solution is:

[0050]

[0051] Step 6.4: Replacing time t in the continuous system with time k yields the discretized form of the feedback control law:

[0052]

[0053] In the formula: k 1d For the discrete form of the controller gain, the bandwidth parameterization method can be used to obtain:

[0054]

[0055] The beneficial effects of this invention are:

[0056] This invention proposes an active disturbance rejection control (ADRC) method for an electromagnetic bearing two-level digital switching power amplifier with embedded model information to improve the current response speed and control accuracy of the inner current loop. First, a mathematical model of the electromagnetic bearing two-level digital switching power amplifier suitable for controller design is established based on Fourier series theory and coil current characteristics. Then, the DC component in the mathematical model is defined as a modelable disturbance term and directly compensated for in the control law via feedforward. Parameter perturbations and unmodeled parts are defined as unknown disturbance terms and estimated in real time using an extended state observer. The current term and control input term are embedded as known model information into the design of the extended state observer, and a feedback control law is designed to compensate for the current term, modelable disturbance term, and unknown disturbance term in real time. Finally, a zero-order hold and a current observer are used to discretize the controller, which is then implemented on a DSP-based digital control platform. Experimental results show that this control strategy has excellent control performance, exhibiting faster current response and higher control accuracy compared to PI control and ADRC. This is of great significance for ensuring the stable and reliable operation of magnetic levitation rotor systems. Attached Figure Description

[0057] Figure 1 This is a flowchart of an active disturbance rejection control method for an electromagnetic bearing two-level digital switching power amplifier with embedded model information, according to the present invention.

[0058] Figure 2 The constant current tracking curves and control quantity curves of the system under three control strategies—PI control, active disturbance rejection control, and the proposed controller—are shown in Example 1 of the present invention, which describes an electromagnetic bearing two-level digital switching power amplifier with embedded model information.

[0059] Figure 3 The sinusoidal current tracking curves and control quantity curves of the system under three control strategies—PI control, active disturbance rejection control, and the proposed controller—are presented in Example 1 of the present invention, which describes an electromagnetic bearing two-level digital switching power amplifier with embedded model information. Detailed Implementation

[0060] The technical solution of the present invention will be further described below with reference to the accompanying drawings and Embodiment 1.

[0061] like Figure 1 The diagram shows a flowchart of an active disturbance rejection control method for an electromagnetic bearing two-level digital switching power amplifier with embedded model information, which specifically includes the following steps:

[0062] Step 1 establishes a mathematical model for an electromagnetic bearing two-level digital switching power amplifier suitable for controller design based on Fourier series theory and coil current characteristics. Specifically:

[0063] Based on Fourier series theory and coil current characteristics, a mathematical model for an electromagnetic bearing two-level digital switching power amplifier suitable for controller design is established as follows:

[0064]

[0065] In the formula: i L U is the current in the electromagnetic bearing coil, i.e., the system output; u is the controller output, i.e., the system input; L and R are the inductance and resistance of the electromagnetic bearing coil, respectively; U in c is the DC bus power supply voltage; pwm The value of the PWM module period register in the DSP; m is the harmonic order; T s This is the switching cycle of the power transistor.

[0066] Step 2 defines the DC component in the mathematical model as a modelable disturbance term, and directly compensates for it in the control law via feedforward, specifically as follows:

[0067] Considering that harmonic components in the mathematical model only affect current ripple and not closed-loop control performance, they are not processed. The DC component -U in the mathematical model... in / L is defined as a modelable perturbation term, denoted by f0:

[0068]

[0069] Step 3 defines the parameter perturbations and unmodeled parts in the mathematical model as unknown disturbance terms, and estimates them in real time using an extended state observer. Specifically:

[0070] The inductance L and resistance R of the electromagnetic bearing coil, and the DC bus power supply voltage U are considered. in The effects of isoparameter perturbations and the unmodeled parts are defined as unknown perturbation terms, denoted by f1.

[0071] Step 4 involves embedding the current term and control input term from the mathematical model as known model information into the design of the extended state observer.

[0072] Step 4 specifically includes the following sub-steps:

[0073] Step 4.1: Expand the unknown disturbance term f1 into a new state variable, and write the expanded state equation of the system as follows:

[0074]

[0075] In the formula: x1=i L ;x2=f1; a0=R / L; b0=2U in / (Lc pwm ).

[0076] Step 4.2: For the above system, design the extended state observer as follows:

[0077]

[0078] In the formula: z1 and z2 are the observed values ​​of system state variables x1 and x2, respectively; l1 and l2 are the gains of the extended state observer.

[0079] Step 4.3: Define ω o To determine the observer bandwidth, a bandwidth parameterization method is used, where the eigenvalues ​​of the system matrix in the extended state observer are all configured at -ω. o At that point, the gains l1 and l2 of the extended state observer are solved as follows:

[0080]

[0081] Step 5 involves designing a feedback control law to provide real-time compensation for the current term, modelable disturbance term, and unknown disturbance term.

[0082] Step 5 specifically includes the following sub-steps:

[0083] Step 5.1: To achieve real-time compensation for the current term, modelable disturbance term, and unknown disturbance term, the feedback control law is designed as follows:

[0084]

[0085] In the formula: u0 is an intermediate control variable.

[0086] Step 5.2: After real-time estimation and compensation of the disturbance, design the intermediate control variables as follows:

[0087] u0=k1(i ref -z1)

[0088] In the formula: i ref k1 is the current setpoint; k1 is the controller gain, which is usually defined as the controller bandwidth ω. c .

[0089] Step 6 uses a zero-order hold and a current observer to discretize the controller, and implements it on a DSP-based digital control platform.

[0090] Step 6 specifically includes the following sub-steps:

[0091] Step 6.1: Discretize the extended state observer using a zero-order hold:

[0092]

[0093] In the formula: I is the second-order identity matrix; i represents the number of terms in the series; A, B, and D are the extended state observer matrices before discretization; A d B d D d C d L d These are the discretized extended state observer matrices; l 1d l 2d These represent the gains of the extended state observer after discretization.

[0094] Step 6.2: Further process the discretized result of the zero-order hold based on the current observer as follows:

[0095]

[0096] In the formula: A eso B eso D eso L d These are the system matrix, input matrix, perturbation input matrix, and observer gain matrix of the discretized extended state observer, respectively.

[0097] Step 6.3: Define z o For the observer poles in the discrete domain, the bandwidth parameterization method is used to define the observer system matrix A in the z-domain. eso The eigenvalues ​​are all configured at the same position z. o At this point, the solution is:

[0098]

[0099] Step 6.4: Replacing time t in the continuous system with time k yields the discretized form of the feedback control law:

[0100]

[0101] In the formula: k 1d For the discrete form of the controller gain, the bandwidth parameterization method can be used to obtain:

[0102]

[0103] like Figure 2 The figure shows the constant current response curves of the PI controller, the active disturbance rejection controller, and the controller proposed in this invention in Embodiment 1 of the electromagnetic bearing two-level digital switching power amplifier active disturbance rejection control method with embedded model information. (a) is the sinusoidal current response curve, and (b) is the control quantity curve. In the figure, PI represents the PI controller, LADRC represents the active disturbance rejection controller, and PLADRC represents the controller proposed in this invention. Figure 3 This representation is also used. (By...) Figure 2 (a) The settling time of the PI controller can be calculated to be 1.95 ms with an overshoot of 39.5%; the settling time of the active disturbance rejection controller is 2.3 ms with no overshoot; the settling time of the proposed controller is 0.7 ms with no overshoot. Therefore, the method proposed in this invention has good dynamic performance, fast response, and no overshoot. Figure 2 (b) It can be concluded that the control quantity under all three controllers eventually stabilizes around 2594, corresponding to a PWM drive signal duty cycle of 51.88%. Ideally, when the current command is a constant current, the duty cycle of the two-level switching power amplifier is 50%. However, due to the inconsistency in the on-state voltage drop of the MOSFET and the freewheeling diode, and the presence of coil resistance, the actual duty cycle will be slightly greater than 50%. Therefore, the experimental results are consistent with the theoretical analysis. Furthermore, from... Figure 2 (a) and Figure 2 (b) It can be seen that the method proposed in this invention has the smallest current fluctuation and control quantity fluctuation, and has good noise suppression performance.

[0104] The Active Disturbance Rejection Control (PLADRC) method with embedded model information proposed in this invention demonstrates significant advantages compared to traditional PI controllers and conventional Active Disturbance Rejection Control (LADRC). While the PI controller is a classic and widely used control strategy, in this application scenario, its settling time reaches 1.95 ms, and it exhibits a 39.5% overshoot. This means that when the current command changes, the PI controller requires a relatively long time to bring the current to a stable value, and significant fluctuations occur before reaching stability, which may adversely affect the stability and accuracy of the electromagnetic bearing system.

[0105] Conventional Active Disturbance Rejection Controllers (LADRCs) have a settling time extended to 2.3 ms, but they do not have overshoot. While LADRCs improve the system's anti-interference capability to some extent by estimating and compensating for internal and external disturbances through an extended state observer, the longer settling time indicates a certain deficiency in rapid response.

[0106] In comparison, the PLADC controller proposed in this invention exhibits superior performance, with a settling time of only 0.7ms and no overshoot. This is thanks to the embedded model information, which enables the controller to more accurately understand the dynamic characteristics of the system and respond more effectively to changes in the system in advance, thereby achieving fast and smooth current regulation and greatly improving the dynamic performance of the system.

[0107] from Figure 2 (a) and Figure 2 As clearly seen in (b), the PLADRC method proposed in this invention exhibits minimal current and control fluctuations, demonstrating its excellent noise suppression performance. In practical electromagnetic bearing systems, various interference and noise sources exist, such as power supply noise and electromagnetic interference. Smaller current and control fluctuations mean more stable system operation, reducing errors and instabilities caused by noise, and improving system accuracy and reliability.

[0108] Figure 3 The figures shown are sinusoidal current response curves under the PI controller, the active disturbance rejection controller, and the controller proposed in this invention, in Embodiment 1 of the electromagnetic bearing two-level digital switching power amplifier active disturbance rejection control method with embedded model information. (a) is the sinusoidal current response curve, and (b) is the control quantity curve. The current command is a sinusoidal current with an amplitude of 0.5A, a bias of 1A, and a frequency of 100Hz. Figure 3 (a) It can be seen that when the PI controller and the active disturbance rejection controller track a sinusoidal current signal, the current and control quantity will oscillate to a certain extent at the initial moment, while the proposed control strategy does not exhibit oscillation and has better control performance. Furthermore, from Figure 3 (b) It can be seen that when the current tracking is stable, the control quantity varies between 2457 and 2734, and the duty cycle of the corresponding PWM drive signal fluctuates between 49.14% and 54.68%, with an average value of 51.91%, which is slightly greater than 50%. It is only 0.03% different from the duty cycle of 51.88% after the constant current tracking is stable. The experimental results are in agreement with the theoretical analysis.

[0109] In summary, the PLADC controller proposed in this invention demonstrates superior performance in sinusoidal current tracking tasks. It not only avoids oscillations at the initial moment, achieving a fast and stable response, but also accurately tracks the current command in the steady state, maintaining a stable output of the control quantity. Compared with traditional PI controllers and active disturbance rejection controllers, it has significant advantages, providing a more effective and reliable control strategy for current control of electromagnetic bearing systems, and contributing to improving the overall performance and stability of electromagnetic bearing systems.

[0110] Those skilled in the art will understand that although some embodiments described herein include certain features but not others included in other embodiments, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the following claims, any of the claimed embodiments can be used in any combination.

Claims

1. A method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information, characterized in that, Includes the following steps: Step 1: Based on Fourier series theory and coil current characteristics, establish a mathematical model of an electromagnetic bearing two-level digital switching power amplifier suitable for controller design; Step 2: Define the DC component in the mathematical model as a modelable disturbance term and directly feedforward compensate it in the control law; Step 3: Define the parameter perturbations and unmodeled parts in the mathematical model as unknown disturbance terms f1; Step 4: Embed the current term and control input term in the mathematical model as known model information into the extended state observer; Step 5: Design a feedback control law to compensate for the current term, modelable disturbance term, and unknown disturbance term in real time; Step 6: Discretize the controller using a zero-order hold and a current observer, and implement it on a DSP-based digital control platform.

2. The method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information according to claim 1, characterized in that, Step 1 specifically includes: The mathematical model of a two-level digital switching power amplifier is: In the formula: i L U is the current in the electromagnetic bearing coil, i.e., the system output; u is the controller output, i.e., the system input; L and R are the inductance and resistance of the electromagnetic bearing coil, respectively; U in c is the DC bus power supply voltage; pwm The value of the PWM module period register in the DSP; m is the harmonic order; T s This is the switching cycle of the power transistor.

3. The method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information according to claim 1, characterized in that, Step 2 specifically includes: The DC component -U in the mathematical model in / L is defined as a modelable perturbation term, denoted by f0:

4. The method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information according to claim 1, characterized in that, Step 3 specifically includes: The inductance L and resistance R of the electromagnetic bearing coil, and the DC bus power supply voltage U are considered. in The effects of isoparameter perturbations and the unmodeled parts are defined as unknown perturbation terms, denoted by f1.

5. The method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information according to claim 1, characterized in that, Step 4 specifically includes: Step 4.1: Expand the unknown disturbance term f1 into a new state variable, and construct the extended state equation of the system as follows: In the formula: x1=i L ;x2=f1; a0=R / L; b0=2U in / (Lc pwm ); Step 4.2: For the above system, construct the extended state observer as follows: In the formula: z1 and z2 are the observed values ​​of system state variables x1 and x2, respectively; l1 and l2 are the gains of the extended state observer; Step 4.3: Define ω o To determine the observer bandwidth, the eigenvalues ​​of the system matrix in the extended state observer are all configured at -ω. o At that point, the gains l1 and l2 of the extended state observer are solved as follows:

6. The method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information according to claim 1, characterized in that, Step 5 specifically includes: Step 5.1: Construct the feedback control law as follows: In the formula: u0 is an intermediate control variable; Step 5.2: After real-time estimation and compensation of the disturbance, design the intermediate control variables as follows: u0=k1(i ref -z1) In the formula: i ref k1 is the current setpoint; k1 is the controller gain, which is usually defined as the controller bandwidth ω. c .

7. The method for active disturbance rejection control of an electromagnetic bearing two-level digital switching power amplifier with embedded model information according to claim 1, characterized in that, Step 6 specifically includes: Step 6.1: Discretize the extended state observer using a zero-order hold: In the formula: I is the second-order identity matrix; i represents the number of terms in the series; A, B, and D are the extended state observer matrices before discretization; A d B d D d C d L d These are the discretized extended state observer matrices; l 1d l 2d These are the gains of the discretized extended state observer; Step 6.2: Further process the discretized result of the zero-order hold based on the current observer as follows: In the formula: A eso B eso D eso L d These are the system matrix, input matrix, perturbation input matrix, and observer gain matrix of the discretized extended state observer, respectively. Step 6.3: Define z o For the observer poles in the discrete domain, the bandwidth parameterization method is used to define the observer system matrix A in the z-domain. eso The eigenvalues ​​are all configured at the same position z. o At this point, the solution is: Step 6.4: Replacing time t in the continuous system with time k yields the discretized form of the feedback control law: In the formula: k 1d For the discrete form of the controller gain, the bandwidth parameterization method can be used to obtain:

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