A surge disturbance suppression method for a magnetic suspension centrifugal compressor

Abstract

The application discloses a kind of surge interference suppression methods of magnetic suspension centrifugal compressor, steps include: the single-channel magnetic suspension rotor system dynamics model is constructed by analyzing magnetic suspension rotor system;Surge disturbance characteristic analysis is carried out, and surge interference dynamic subsystem model is constructed;Based on single-channel magnetic suspension rotor system dynamics model and surge interference dynamic subsystem model, interference observer is constructed, and interference estimation error dynamic law is obtained;Based on interference estimation error dynamic law, the pole of interference observer is configured using pole placement method, and observer gain is obtained;Gain after interference observer is embedded in PID controller, and controller output design is carried out;The differential equation of the motion of magnetic suspension rotor system is substituted into controller output, and surge suppression is carried out.The application can effectively reduce the rotor vibration caused by pressure fluctuation during surge, reduce the possibility of structural damage caused by magnetic suspension rotor instability, and improve the system disturbance suppression capability and reliability.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of magnetic bearing control, and particularly relates to a surge interference suppression method for a magnetic suspension centrifugal compressor. BACKGROUND

[0002] A centrifugal compressor is an energy-saving device that can realize high rotation speed and continuous transportation, and is widely used in various industrial fields. The centrifugal compressor relies on a high-speed rotating impeller to drive the gas medium to generate centrifugal force and complete the work on the gas. Surge is a global instability phenomenon that occurs in a centrifugal compressor at low working flow rate, which threatens the stable operation of the compressor and shortens its safe service life. The main feature of surge is low-frequency pressure oscillation in the compressor and pipeline system. Mild surge can affect the working efficiency of the compressor. With further development of instability, gas backflow occurs in deep surge, which causes strong vibration in the compressor body, pipeline network and bearing, thereby causing severe wear of the seal and even collision between the stator and rotor in the compressor, resulting in irreversible structural damage.

[0003] A magnetic suspension centrifugal compressor uses active magnetic bearings to replace traditional mechanical bearings, has no mechanical contact and friction, and can realize oil-free pollution and longer service life. In addition, the magnetic suspension centrifugal compressor can achieve higher rotation speed, thereby realizing higher pressure ratio and efficiency. The magnetic suspension centrifugal compressor also faces the threat of surge. The magnetic suspension bearing can accurately adjust the axial position of the rotor to accurately control the gap between the impeller and the volute. In other words, adjusting the axial gap can change the working curve of the compressor to a certain extent, thereby realizing active surge control.

[0004] However, the stiffness of the magnetic bearing, which is a non-contact bearing, is much smaller than that of the traditional mechanical bearing, which means that the magnetic bearing has poorer resistance when surge instability occurs. Moreover, the rotation speed of the centrifugal compressor supported by the magnetic bearing is usually higher than that of the traditional mechanical bearing. If the surge resistance fails, the damage to the magnetic bearing will be greater. Therefore, the magnetic bearing system needs to be able to resist surge disturbance force when surge occurs to ensure that the rotor can still be stably suspended, thereby realizing stable operation of the magnetic suspension centrifugal compressor. SUMMARY

[0005] The purpose of the present application is to provide a surge interference suppression method for a magnetic suspension centrifugal compressor to solve the problems existing in the prior art.

[0006] To achieve the above purpose, the present application provides a surge interference suppression method for a magnetic suspension centrifugal compressor, comprising the following steps:

[0007] A single-channel magnetic suspension rotor system dynamics model is constructed by analyzing the magnetic suspension rotor system in the magnetic suspension centrifugal compressor.

[0008] The surge disturbance characteristics of the magnetic suspension centrifugal compressor are analyzed, and a surge disturbance dynamic subsystem model is constructed.

[0009] Based on the single-channel magnetic suspension rotor system dynamic model and the surge disturbance dynamic subsystem model, an interference observer is constructed, and a disturbance estimation error dynamic law is obtained.

[0010] Based on the disturbance estimation error dynamic law, the pole placement method is used to configure the poles of the disturbance observer, and the observer gain is obtained.

[0011] The gain of the disturbance observer is embedded in the PID controller, and the controller output is designed.

[0012] The controller output is substituted into the differential equation of the magnetic suspension rotor system motion, and the surge suppression is performed.

[0013] Optionally, the process of constructing a single-channel magnetic suspension rotor system dynamic model includes:

[0014] The differential equation of the motion of each module in the magnetic suspension rotor system is obtained.

[0015] Based on the differential equation, a dynamic equation is obtained.

[0016] The dynamic equation is converted into a state space equation form:

[0017]

[0018] where the state variable contains the rotor displacement h s and its differential, u is the controller output control quantity, f d is the surge disturbance, C=[1 0],k h and k i are the displacement stiffness and current stiffness of the magnetic bearing, respectively, k w and k s are the gains of the power amplifier and the sensor link, respectively, m is the rotor mass, and a1 and a2 are known quantities related to the structural parameters of the compressor.

[0019] Optionally, the process of constructing a surge disturbance dynamic subsystem model includes:

[0020] The composition of the surge disturbance is analyzed, and the surge disturbance frequency in the composition is regarded as a known quantity, and the surge disturbance dynamic subsystem model is constructed:

[0021]

[0022] where w(t) is a vector containing the surge disturbance component, W and V are known weighting matrices, and fd This is a surge disturbance.

[0023] Optionally, the surge disturbance includes:

[0024] f d =A1 sin(ω) h t+θ1)+A2 sin(2ω h t+θ2)

[0025] Where, ω h Let A1 and A2 be the Helmholtz frequency of the compressor system, A1 and A2 be the unknown component amplitudes, θ1 and θ2 be the unknown component phase angles, and t represent time.

[0026] Optionally, the interference observer is as follows:

[0027]

[0028] in, Here, K represents the estimated surge disturbance value, and K is the gain matrix of the disturbance observer. Let w(t) be the estimated value, and z(t) be the auxiliary variables, A, B, and B'. d Let be the known matrix of the state-space equation of the rotor system, W and V be the weighting matrices of the disturbance subsystem, u′(t) be the controller output after disturbance feedforward compensation, and x(t) represent the time-domain form of the state variable x.

[0029] Optionally, the dynamic law of the interference estimation error is as follows:

[0030]

[0031] Where e w (t) represents the estimation error of w(t). For e w The derivative of (t), K is the gain matrix of the disturbance observer, B d Let W be a known matrix of the state-space equations of the rotor system, and let W and V be weighting matrices of the disturbance subsystems.

[0032] Optionally, the process of designing the controller output includes:

[0033] The parameters of the PID controller are tuned to ensure that the magnetic levitation rotor system is in a undisturbed environment.

[0034] The surge disturbance estimate is introduced into the tuned PID controller to obtain the compensated controller output.

[0035] Optionally, the compensated controller output is as follows:

[0036]

[0037] wherein u is the PID controller output, u' is the controller output after disturbance feedforward compensation, is the surge disturbance estimation, h s is the rotor displacement, k h and k i are the displacement stiffness and current stiffness of the magnetic bearing, respectively, k w and k s are the gain of the power amplifier and sensor element, respectively, m is the rotor mass, and a1 and a2 are known quantities related to the compressor body structure parameters.

[0038] The technical effects of the present application are:

[0039] 1. The present application makes full use of the known condition that the surge disturbance frequency is the Helmholtz frequency of the system, and establishes a disturbance sub-model of harmonic disturbance according to this condition. Compared with the existing observation technology of observing lumped disturbance such as the extended state observer, the present application uses known disturbance information, so that the surge disturbance components at this frequency and its double frequency can be accurately suppressed.

[0040] 2. In order to facilitate the setting of the observer gain, the present application uses a pole placement method to place the observer poles at the same position on the negative real axis which is relatively far from the imaginary axis, so as to ensure that the observer converges quickly while having good damping characteristics, which helps to reduce the oscillation in the transient process of the observer.

[0041] 3. The present application first designs a PID controller according to the control requirements to ensure the stability of the closed loop system, and then uses a disturbance observer (DOBC) to estimate the surge harmonic disturbance in real time and embed it in the controller to realize disturbance attenuation. The use of the present application can effectively reduce the vibration of the rotor caused by pressure fluctuations during surge, thereby reducing the possibility of structural damage due to instability of the magnetic suspension rotor, and effectively improving the disturbance suppression capability and reliability of the system. At the same time, the two-degree-of-freedom control system structure combining the disturbance observer and the PID controller has weak coupling, and the introduction of the disturbance observer does not require changing the originally set controller parameters, so it is convenient for engineering application. BRIEF DESCRIPTION OF DRAWINGS

[0042] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of the present application illustrated in the drawings and their descriptions are used to explain the present application and are not intended to limit the present application. In the drawings:

[0043] Figure 1 is a surge disturbance suppression method flowchart of the magnetic suspension centrifugal compressor in the embodiment of the present application;

[0044] Figure 2 is a magnetic suspension rotor control system block diagram in the embodiment of the present application;

[0045] Figure 3 The control strategy block diagram of the magnetic suspension rotor system with the disturbance observer added in the embodiment of the application is shown in the figure;

[0046] Figure 4 The time domain and frequency domain waveform diagram of rotor displacement simulation before surge disturbance suppression in the embodiment of the application is shown in the figure;

[0047] Figure 5 The time domain and frequency domain waveform diagram of rotor displacement simulation after surge disturbance suppression in the embodiment of the application is shown in the figure. DETAILED DESCRIPTION

[0048] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0049] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0050] Embodiment one

[0051] As shown in the figure, the present embodiment provides a surge disturbance suppression method for a magnetic suspension centrifugal compressor, as shown in the figure, comprising the following steps: Figures 1-5 Figure 1 1. Establishing a single-channel magnetic suspension rotor system dynamics model

[0052] 1. Establishing a single-channel magnetic suspension rotor system dynamics model

[0053] The control block diagram of the magnetic suspension rotor system is shown in the figure. The magnetic suspension rotor system mainly includes a controller, a power amplifier, a magnetic bearing-rotor actuator, and a sensor. The power amplifier receives the output of the controller and converts it into the current of the magnetic bearing, which has a fixed gain k w in the low frequency; the sensor converts the actual displacement of the rotor into a digital quantity received by the controller, and the gain can be represented as k s ; the magnetic bearing-rotor actuator can be regarded as four independent channels under the condition that the coupling between the four channels in the radial direction is weak, and each channel has the same system motion differential equation: Figure 2

[0054]

[0055] where h s is the rotor displacement, u is the control quantity output by the controller, k h and k i are the displacement stiffness and current stiffness of the magnetic bearing respectively, k w and k​​s Gain of power amplifier and sensor element respectively, m is rotor mass, a1 and a2 are known quantities related to compressor body structure parameters, f d Is the surge disturbance.

[0056] According to the differential equation of the system motion, the state space equation form of the dynamic model of the single-channel magnetic suspension rotor system is established

[0057]

[0058] Wherein the state variable Contains rotor displacement h s And its differential, A, B and B d Are known matrices of the state space equation, C = [1 0].

[0059] 2, Establish the surge disturbance dynamic subsystem model

[0060] Since the pressure fluctuation frequency in the slight surge stage is the Helmholtz resonance frequency of the compressor system, the surge disturbance is a harmonic disturbance, and the main components are the Helmholtz frequency fundamental and double frequency components, that is, the surge disturbance can be expressed as:

[0061] f d = A1 sin(ω h t+θ1)+A2sin(2ω h t+θ2) (3)

[0062] Where ω h Is the Helmholtz frequency of the compressor system, A1 and A2 are unknown component amplitudes, θ1 and θ2 are unknown component phase angles, and t represents time.

[0063] On the basis of analyzing the composition of the surge disturbance, the surge disturbance frequency, that is, the Helmholtz frequency related to the structure of the compressor system, is regarded as a known quantity, and the disturbance dynamic subsystem is obtained:

[0064]

[0065] Where w(t) is a vector containing the surge disturbance components, W and V are known weighting matrices, and are respectively

[0066]

[0067] 3, Design disturbance observer

[0068] According to the dynamic model of the magnetic suspension rotor system and the surge disturbance dynamic subsystem model, the disturbance observer of the following form is designed:

[0069]

[0070] wherein is the surge disturbance estimation value, K is the gain matrix of the disturbance observer, is the estimation value of w(t), z(t) is an auxiliary variable, A, B and B d are known matrices of the above rotor system state space equation, W and V are weighting matrices of the above disturbance subsystem, u'(t) is the controller output after disturbance feedforward compensation, x(t) represents the time domain form of state variable x. The control strategy block diagram of the magnetic suspension rotor system with disturbance observer is shown in Figure 3 .

[0071] According to the system dynamics model and the disturbance observer model, the dynamic law of disturbance estimation error is:

[0072]

[0073] wherein e w (t) is the estimation error of w(t), is the differential of e w (t). According to the disturbance estimation error dynamics, e w (t) is closely related to the disturbance observer gain K, and K determines the convergence performance of the observer. The pole placement method is adopted in the present application to place the observer poles at the same position on the negative real axis which is relatively far from the imaginary axis, and then to select a suitable observer gain to ensure that the observer converges quickly while having good damping characteristics. The above configuration process can be represented as:

[0074] |sI-(W+KB d V)|=(s+ω o ) 4 (8)

[0075] wherein s represents the complex frequency in Laplace transform, I is the unit matrix, ω o is the bandwidth of the observer. The larger ω o is, the larger the corresponding observer gain K is, the smaller the observation error is, and thus the higher the accuracy of the observer is. However, in practical applications, the value of K is limited by the sensor noise and system sampling delay. In terms of surge disturbance, the disturbance frequency is low, and K can be taken as a small value.

[0076] 4. Design and implementation of feedforward compensation for estimating disturbance

[0077] The main feedback controller selects a PID controller, and the expression is as follows:

[0078]

[0079] wherein u(s) is the transfer function of the PID controller, kP , k I and k D are proportional, integral and differential coefficients respectively, T f is the time constant of incomplete differentiation, and s is the complex frequency in Laplace transform. By tuning the PID parameters, the magnetic suspension rotor system has good dynamic and steady-state performance without disturbance

[0080] The surge disturbance estimator is introduced into the tuned PID controller to obtain a compensated controller output, thereby realizing feedforward compensation and accurate suppression of the surge disturbance. The compensated controller output is designed as:

[0081]

[0082] wherein u is the PID controller output, u' is the controller output after disturbance feedforward compensation, is the surge disturbance estimation value, h s is the rotor displacement, k h and k i are the displacement stiffness and current stiffness of the magnetic bearing respectively, k w and k s are the gains of the power amplifier and the sensor link respectively, and m is the rotor mass. a1 and a2 are known quantities related to the structural parameters of the compressor body. The controller output u' is introduced into the differential equation of the rotor system motion, and if the estimation error of is approximately 0, the rotor motion is not affected by the surge disturbance, and the influence of the displacement negative stiffness k h is also offset, thereby realizing attenuation and suppression of the surge disturbance.

[0083] Rotor displacement simulation waveform diagrams before and after surge disturbance suppression are shown in Figure 4 and Figure 5 , wherein the harmonic disturbance at the surge frequency ω h and its double frequency is added, and a certain white noise is also added to simulate the real system. The disturbance observer bandwidth ω o is set to 3 times the surge disturbance frequency. As shown in Figure 4 , when only the PID controller is used before disturbance compensation, the rotor displacement peak-to-peak value is about 68 μm, and the main component of the displacement spectrum is the surge frequency 42 Hz and its double frequency 84 Hz. At this time, the high-speed rotor displacement fluctuation is large, and severe rotor impact on the protection bearing may occur, thereby causing system instability and serious decline in system reliability. As shown in Figure 5 , after disturbance compensation, the rotor displacement peak-to-peak value is reduced to 1.6 μm, and the spectrum does not contain the surge component, but mainly contains noise. The simulation verifies that the method of the present application can effectively suppress the rotor vibration caused by pressure fluctuation during surge, and ensure reliable operation of the compressor system.

[0084] Embodiment two

[0085] The embodiment provides another implementation of a surge interference suppression method of a magnetic suspension centrifugal compressor, and comprises the following steps:

[0086] A dynamic model of a single-channel magnetic suspension rotor system is established by analyzing input and output relations of each sub-module of the magnetic suspension rotor system; the sub-modules comprise a power amplifier, a magnetic bearing-rotor actuator and a sensor;

[0087] An external dynamic subsystem model of surge interference is established by analyzing surge disturbance characteristics;

[0088] Based on the dynamic model of the single-channel magnetic suspension rotor system and the surge interference subsystem model, an interference observer is constructed, poles of the observer are configured by a pole configuration method, and then appropriate observer gains are selected to ensure convergence of the observer;

[0089] The interference observer is embedded into a PID controller, a compensated controller output is designed, and attenuation and suppression of the surge disturbance are realized.

[0090] As a preferred embodiment of the application, the process of establishing the dynamic model of the single-channel magnetic suspension rotor system comprises:

[0091] A model of the power amplifier and the sensor is established;

[0092] A rotor system dynamic equation containing surge disturbance is obtained according to a differential equation of rotor motion;

[0093] The dynamic equation is converted into a state space equation form:

[0094]

[0095] Wherein state variables are A rotor displacement h s and a differential thereof, u is a controller output control quantity, f d is the surge disturbance, C=[1 0], k h and k i are displacement stiffness and current stiffness of the magnetic bearing respectively, k w and k s are gains of the power amplifier and the sensor respectively, m is a rotor mass, and a1 and a2 are known quantities related to structural parameters of the compressor body.

[0096] As a preferred embodiment of the present application, the process of establishing the surge disturbance subsystem model is based on analyzing the composition of the surge disturbance components, taking the surge disturbance frequency, i.e. the Helmholtz frequency related to the structure of the compressor system, as a known quantity, and obtaining the disturbance dynamic subsystem:

[0097]

[0098] where w(t) is a vector containing the surge disturbance components, and W and V are known weighting matrices.

[0099] As a preferred embodiment of the present application, the surge disturbance components are mainly the Helmholtz frequency and its double frequency components, i.e. the surge disturbance can be expressed as:

[0100] f d = A1 sin(ω h t + θ1) + A2 sin(2ω h t + θ2)

[0101] where ω h is the Helmholtz frequency of the compressor system, A1 and A2 are unknown component amplitudes, θ1 and θ2 are unknown component phase angles, and t represents time.

[0102] As a preferred embodiment of the present application, the disturbance observer is designed as:

[0103]

[0104] where is the surge disturbance estimate, K is the gain matrix of the disturbance observer, is the estimate of w(t), z(t) is an auxiliary variable, A, B and B d are known matrices of the above rotor system state space equation, W and V are the weighting matrices of the disturbance subsystem, u'(t) is the controller output after disturbance feedforward compensation, and x(t) represents the time domain form of the state variable x.

[0105] The gain K of the disturbance observer determines the convergence performance of the observer, and an appropriate solution of K can be obtained by configuring the observer poles.

[0106] As a preferred embodiment of the present application, the process of designing the controller output after compensation includes:

[0107] Tuning the PID controller to make the magnetic levitation rotor system have good dynamic and steady-state performance under undisturbed conditions;

[0108] The surge disturbance estimate The PID controller with tuning is introduced to obtain the compensated controller output, and the feedforward compensation and accurate suppression of surge disturbance are realized.

[0109] As a preferred embodiment of the present application, the compensated controller output is:

[0110]

[0111] where u is the PID controller output, u' is the controller output after disturbance feedforward compensation, is the surge disturbance estimation, h s is the rotor displacement, k h and k i are the displacement stiffness and current stiffness of the magnetic bearing, respectively, k w and k s are the gain of the power amplifier and the sensor link, respectively, m is the rotor mass, and a1 and a2 are known quantities related to the structural parameters of the compressor body.

[0112] The above merely describes a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any change or replacement within the technical scope disclosed by the present application can be easily thought of by those skilled in the art, which should be encompassed within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A surge disturbance suppression method for a magnetic levitation centrifugal compressor, characterized by, The method comprises the following steps: A magnetic suspension rotor system in a magnetic suspension centrifugal compressor is analyzed, and a single-channel magnetic suspension rotor system dynamics model is constructed; A surge disturbance characteristic of the magnetic suspension centrifugal compressor is analyzed, and a surge interference dynamic subsystem model is constructed; Based on the single-channel magnetic suspension rotor system dynamics model and the surge interference dynamic subsystem model, an interference observer is constructed, and an interference estimation error dynamic law is obtained; Based on the interference estimation error dynamic law, a pole placement method is used to place poles of the interference observer, and an observer gain is obtained; The gain-based interference observer is embedded into a PID controller, and a controller output is designed; The controller output is substituted into a differential equation of motion of the magnetic suspension rotor system, and surge suppression is performed; The process of constructing the surge interference dynamic subsystem model comprises: Components of the surge disturbance are analyzed, and a surge disturbance frequency in the component composition is regarded as a known quantity, and the surge interference dynamic subsystem model is constructed: where w(t) is a vector containing surge disturbance components, W and V are known weighting matrices, f d is the surge disturbance; The surge disturbance comprises: f d = A1 sin(ω h t + θ1) + A2 sin(2ω h t + θ2) where ω h is the Helmholtz frequency of the compressor system, A1and A2are unknown component amplitudes, θ1and θ2are unknown component phase angles, and t represents time. The process of designing the controller output comprises: Parameters of the PID controller are tuned, and the magnetic suspension rotor system is placed in a disturbance-free environment; A surge disturbance estimation is introduced into the tuned PID controller, and a compensated controller output is obtained; The compensated controller output is as follows: where u is the PID controller output, u' is the controller output after disturbance feedforward compensation, is the surge disturbance estimate, h s is the rotor displacement, k h and k i are the displacement stiffness and current stiffness of the magnetic bearing, respectively, k w and k s are the gain of the power amplifier and sensor link, respectively, m is the rotor mass, and a1 and a2 are known quantities related to the compressor body structure parameters.

2. The surge disturbance suppression method of a magnetic levitation centrifugal compressor according to claim 1, characterized by, The process of constructing the single-channel magnetic suspension rotor system dynamics model comprises: Differential equations of motion of various modules in the magnetic suspension rotor system are obtained; Based on the differential equations, dynamics equations are obtained; The dynamics equations are converted into a state space equation form: where the state variables including rotor displacement h s and its differential, u is the controller output control quantity, f d is the surge disturbance, C = [1 0], k h and k i are the displacement stiffness and current stiffness of the magnetic bearing, respectively, k w and k s are the gains of the power amplifier and sensor link, respectively, m is the rotor mass, and a1 and a2 are known quantities related to the compressor body structure parameters.

3. The surge disturbance suppression method of a magnetic levitation centrifugal compressor according to claim 1, characterized by, The interference observer is as follows: wherein is a surge disturbance estimate, K is a gain matrix of the disturbance observer, is an estimate of w(t), z(t) is an auxiliary variable, A, B and B d are known matrices of the state space equation of the rotor system, W and V are weighting matrices of the disturbance subsystem, u'(t) is the controller output after disturbance feedforward compensation, x(t) represents the time domain form of the state variable x.

4. The surge disturbance suppression method of a magnetic levitation centrifugal compressor according to claim 1, characterized by, The interference estimation error dynamic law is as follows: where e w (t) is the estimation error of w(t), is e w (t), K is the gain matrix of the disturbance observer, B d is a known matrix of the rotor system state space equation, and W and V are weighting matrices of the disturbance subsystem.

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