Centrifugal compressor anti-surge prediction control method based on mechanism and data fusion

Abstract

A centrifugal compressor anti-surge prediction control method based on mechanism and data fusion belongs to the field of information technology. The anti-surge controller is designed based on the mechanism description of the Moore-Greitzer model of the centrifugal compressor, and the anti-surge response speed and stability of the centrifugal compressor are improved. On this basis, a disturbance compensation scheme based on the fusion of the predictive controller and the active disturbance rejection controller is designed to further improve the anti-disturbance performance of the centrifugal compressor. The actual case of the centrifugal compressor is verified, which shows that the method has obvious advantages in anti-disturbance performance and response speed.

Description

TECHNICAL FIELD

[0001] The method belongs to the field of information technology, relates to Moore-Greitzer-based mechanism description, characteristic curve modeling and application of a data-driven predictive control algorithm, and is a centrifugal compressor anti-surge control method based on mechanism and data fusion. Based on the Moore-Greitzer-based compressor mechanism description, a compressor anti-surge controller is designed, so as to improve the anti-surge response speed and stability of the compressor; on this basis, a disturbance compensation scheme based on the fusion of a predictive controller and a disturbance rejection controller is designed, so as to further improve the anti-disturbance performance of the compressor. Verification is carried out in combination with an actual compressor case, and it is shown that the method has obvious advantages in terms of anti-disturbance performance and response speed. BACKGROUND

[0002] As the core power equipment in the modern industrial system, the stable operation of the compressor has important strategic significance for key fields such as energy, chemical industry and national defense. With the intelligent transformation and upgrading of the manufacturing industry, the country has put forward higher requirements for the operation reliability, energy utilization efficiency and intelligent control level of high-end compressors.

[0003] Compressor surge is a kind of instability phenomenon caused by severe flow separation in impeller, which leads to a sudden decrease in flow rate and a dramatic fluctuation in pressure. Once surge occurs, it will cause severe vibration of the unit, damage to key components, and even system shutdown, which poses a serious threat to industrial production safety. The dynamic characteristics of compressor surge involve gas-solid coupled vibration, and have complex mechanisms such as nonlinearity and time-varying, which are difficult to completely suppress by conventional control methods. At present, scholars at home and abroad have carried out extensive research on compressor surge control and proposed various solutions. Cortinovis, A., Pareschi, D., Mercangoez, M., Besselmann, T., 2012. Model Predictive Anti-Surge Control of Centrifugal Compressors with Variable-Speed Drives. IFAC Proceedings Volumes 45, 251–256 proposed a model predictive control method named torque auxiliary surge control (TASC) for the anti-surge control of centrifugal compressors, but did not study the control performance when the model does not match the actual compressor dynamics. Roudsari, N.R., Ataei, M., Koofigar, H.R., Montazeri, A., 2024. A nonlinear disturbance observer for sliding mode control of surge in centrifugal compressors via TCV actuator. Journal of Process Control 139, 10322. proposed a sliding mode control method based on a nonlinear disturbance observer, but only considered the first-order Moore-Greitzer model, ignoring the rotating stall dynamic characteristics, which may not be suitable for high-order dynamic scenarios.(Sheng, H., Chen, Q., Li, J., Li, Z., Wang, Z., Zhang, T., 2020. Robust adaptive backstepping active control of compressor surge based on wavelet neural network. Aerospace Science and Technology 106, 106139. https: / / doi.org / 10.1016 / j.ast.2020.106139.) proposed a robust adaptive backstepping control method based on wavelet neural network, the article only verified through simulation, lack of experimental data support of actual compressor platform, these existing methods in model precision, dynamic adaptability or engineering practicability and so on still have obvious limitation. Therefore, the mechanism model of high-order Moore-Greitzer is established, the characteristic curve modeling of mechanism and data fusion is proposed, and the effectiveness of the proposed controller is verified combined with the actual case of compressor. SUMMARY

[0004] The technical goal to be achieved by the method is a surge control strategy with strong adaptability, fast response speed and certain anti-disturbance ability.

[0005] The overall control of the technical scheme of the method is shown in the accompanying Figure 1 The specific steps are as follows:

[0006] A centrifugal compressor anti-surge predictive control method based on mechanism and data fusion, the steps are as follows:

[0007] Step one: Moore-Greitzer model derivation: combining mass, momentum and energy conservation law, the physical quantity is dimensionless processed, the centrifugal compressor Moore-Greitzer model is established by introducing disturbance and linearization processing;

[0008] Step two: mechanism and data combined characteristic curve modeling: according to the centrifugal compressor Moore-Greitzer model combined with actual data, the performance curve of centrifugal compressor is drawn, and then the surge line and surge control line are obtained;

[0009] Step three: design of self-disturbance anti-surge controller: according to the performance curve of centrifugal compressor, the distance from working point to surge control line is regarded as deviation, the self-disturbance anti-surge controller is designed, and compared with PID surge control;

[0010] Step four: design of model predictive controller with disturbance compensation: estimate the disturbance value by using sliding mode observer, so as to compensate to the model, avoid the centrifugal compressor into surge due to external disturbance.

[0011] Further, the step one is specifically:

[0012] The centrifugal compressor Moore-Greitzer model is a nonlinear partial differential equation set, which is set as follows:

[0013] 1) the rotor speed is constant;

[0014] 2) high hub ratio;

[0015] 3) uniform inlet flow;

[0016] 4) incompressible flow in centrifugal compressor;

[0017] 5) gas compressibility in the cavity;

[0018] 6) spatially uniform cavity pressure;

[0019] 7) the number of stages of centrifugal compressor is simulated as half impeller;

[0020] Under the conditions of 1) ~ 7), the centrifugal compressor is set to operate in axisymmetric flow, and the deviation amount of the off-stable axisymmetric flow and the flow-pressure relationship are used to establish the following nonlinear partial differential equation set of Moore-Greitzer model:

[0021] (1)

[0022] wherein, is a dimensionless throttling coefficient parameter, is the tip speed, is the sound speed, is the centrifugal compressor outlet cross-sectional area, is the volume between the centrifugal compressor outlet and the outlet throttle valve, is the characteristic length of the centrifugal compressor; is the circumferential direction coordinate, is the dimensionless time, is the dimensionless pressure rise, denoted as ; is the dimensionless flow, denoted as ; is the centrifugal compressor characteristic curve function, represents the deviation amount of the off-stable axisymmetric flow, reflects the distribution of non-uniform disturbance in different directions, and the subscript combination represents the partial derivative in the corresponding direction, is the dimensionless delay length, is a dimensionless mass parameter, is a dimensionless half-chord length, is the inverse of the outlet throttle valve characteristic equation; where The following cubic equation is selected:

[0023] (2)

[0024] The following third-order ordinary differential equation set is taken:

[0025] (3)

[0026] where, and represent the half-height and half-width of the cubic axisymmetric characteristic line, is the dimensionless pressure rise through the centrifugal compressor when no flow exists, represents a dimensionless function of the disturbance intensity, denoted as , is a constant choke coefficient;

[0027] Take , and according to the relationship between the centrifugal compressor speed and the pressure rise, we get:

[0028] (4)

[0029] where, respectively represent the centrifugal compressor speed and the initial speed; represents the dimensionless pressure rise coefficient at the current speed; represents the proportional coefficient, which reflects the scaling factor of speed and pressure rise;

[0030] From the law of conservation of energy, we get:

[0031] (5)

[0032] Further, we get:

[0033] (6)

[0034] From the electrical drive theory, we get:

[0035] (7)

[0036] where, is the output torque of the synchronous motor, is the centrifugal compressor rotation torque, is the inertia coefficient of the rotating shaft, is the angular velocity of the centrifugal compressor, represents the time factor;

[0037] The rotating torque of centrifugal compressor is equal to the change of angular momentum of gas flow, which is: , is the tangential velocity of gas flow, is the radius of centrifugal compressor, is the slip coefficient, is the dimensionless peripheral velocity of centrifugal compressor;

[0038] The formula (7) is rearranged as:

[0039] (8)

[0040] wherein, is the expected speed of centrifugal compressor under steady state, is the density of fluid, is the blade installation angle of impeller;

[0041] Thus, the rotating speed dynamic equation of centrifugal compressor is:

[0042] (9)

[0043] wherein, is the rotating speed regulation instruction;

[0044] The mass balance analysis is carried out on the chamber and the outlet throttle valve of centrifugal compressor. The mass flow in the chamber is , the mass flow through the outlet throttle valve of centrifugal compressor is , the density and pressure change of gas in the chamber is caused by the change of opening degree of outlet throttle valve; the mass balance equation in the chamber is:

[0045] (10)

[0046] wherein, is the density of gas in the chamber, the gas in the chamber is set to be isentropic, the density change of gas in the chamber is proportional to the pressure change, which has:

[0047] (11)

[0048] wherein, is the pressure of gas in the chamber;

[0049] The momentum conservation equation of centrifugal compressor at the outlet throttle valve is:

[0050] (12)

[0051] wherein, is the dimensionless mass flow at the outlet of outlet throttle valve, The length of the outlet pipe of the outlet throttle valve is ignored, and the pipe loss of the outlet throttle valve is ignored.

[0052] The linear process is used to describe the regulation process of the outlet throttle valve.

[0053] (13)

[0054] wherein, is the time constant, indicating the steady state value to which the system needs to be adjusted; is the relative opening of the outlet throttle valve; is the regulation instruction of the outlet throttle valve;

[0055] The dynamic equation of the outlet pressure of the centrifugal compressor:

[0056] (14)

[0057] wherein, indicates the characteristic flow rate;

[0058] By using the mass flow of the centrifugal compressor is dimensionless, and by using the pressure difference of the fluid in the centrifugal compressor is dimensionless, and the following equation is obtained:

[0059] (15)

[0060] Through the analysis of the internal mechanism of the centrifugal compressor, combined with equation (15), the following equation is obtained:

[0061] (16)

[0062] (17)

[0063] (18)

[0064] (19)

[0065] Finally, the Moore-Greitzer model of the centrifugal compressor with three inputs and two outputs is constructed, wherein the relative opening of the outlet throttle valve , the opening of the anti-surge valve and the rotating speed of the centrifugal compressor are taken as inputs, and the pressure rise and the flow rate are taken as outputs.

[0066] Further, the step two is specifically:

[0067] The centrifugal compressor has different performance curves under different working conditions, and the working condition is determined by the centrifugal compressor speed. For the Moore-Greitzer model of the centrifugal compressor, after selecting appropriate parameters, the working point of a certain working condition can be determined by fixing the centrifugal compressor speed coefficient and changing the outlet throttle valve opening degree, wherein the centrifugal compressor speed coefficient is The performance curve of the centrifugal compressor can be obtained by fitting different working points. The quadratic curve shown in formula (20) is used to fit the pressure rise-flow rate performance curve under different speeds:

[0068] (20)

[0069] wherein, is the pressure rise coefficient of the centrifugal compressor at different working points, is the flow rate coefficient of the centrifugal compressor at different working points, is a constant obtained by quadratic curve fitting, and the fitting result corresponds to the curve coefficient under different centrifugal compressor speeds;

[0070] Each pressure rise-flow rate performance curve has a surge limit point, that is, once the anti-surge valve opening degree is further reduced, the pressure and flow rate will oscillate, and surge phenomenon will occur. These surge limit points form a surge limit line. In order to suppress surge and avoid the centrifugal compressor approaching the deep surge region, a surge control line is set. The surge control line is set by moving the surge line to the right by 5% to 10%. The surge control line makes it unnecessary to wait for the working point to cross the surge line before taking control measures during anti-surge control, but starts adjusting when the working point reaches the left side of the surge line, so as to more timely prevent surge from occurring.

[0071] Further, the step three is specifically:

[0072] The distance between the working point and the surge control line is taken as the deviation, when the current working point is defined as , combining formula (20) and experimental data, the deviation amount is obtained:

[0073] (21)

[0074] wherein, represents the flow rate coefficient of the current working point, represents the pressure rise coefficient of the current working point, which is the coefficient representation of the pressure rise and the flow rate in the Moore-Greitzer model of the centrifugal compressor;

[0075] PID surge control:

[0076] When the working point is outside the surge control line, no control is needed, and when the working point enters the surge control line, the anti-surge valve opening needs to be adjusted; definition:

[0077] (22)

[0078] For the surge problem, the PID surge control avoids the system from entering the surge area by adjusting the feedback signal of the system, which is as follows:

[0079] (23)

[0080] Where: is the control input, are the proportional, integral, and derivative gains, respectively;

[0081] Design of active disturbance rejection anti-surge controller:

[0082] The active disturbance rejection anti-surge controller consists of the following three parts: tracking-differentiator TD, which is used to obtain the differential signal and configure the transition process; extended state observer ESO, which is used to observe the total disturbance; nonlinear state error feedback control law NLSEF, which is used to generate the control amount;

[0083] Since the signal to be tracked is the deviation, the target value of the deviation is always zero, at this time the tracking-differentiator TD is ignored, and the surge control of the active disturbance rejection anti-surge controller is composed of the extended state observer and the nonlinear state error feedback control law;

[0084] The following relationship is obtained by combining equations (16)-(19) and equation (21):

[0085] (24)

[0086] Where, two dots above the character represent the second derivative of the corresponding parameter, and one dot above the character represents the first derivative of the corresponding parameter;

[0087] Therefore, the deviation is constructed into a second-order nonlinear equation, unknown, which is treated as a disturbance, and let is also an unknown function, so we have:

[0088] (25)

[0089] Where, is the control input, is the actual output, is the gain coefficient of the control input;

[0090] The extended state observer is set as:

[0091] (26)

[0092] where, is the output estimation error, is the estimation of the system output, is the estimation of the system first derivative, is the estimation of the total disturbance; represents the tuning gain of the extended state observer, tunes the convergence speed of, tunes the convergence speed of, tunes the estimation speed of;

[0093] is a nonlinear function:

[0094] (27)

[0095] where, is a nonlinear index to control the smoothness of the function; is a linear interval threshold to avoid the sudden change of the function value when the error is small;

[0096] Through the extended state observer, the error signal and the error differential signal can be obtained, and the total disturbance of the system can also be estimated and directly offset as a feedforward compensation term, thereby reducing the dependence on error integration, simplifying the control structure, and improving the response speed. The nonlinear state error feedback control law is designed as:

[0097] (28)

[0098] where, is the original control amount, is a nonlinear index, is a control gain coefficient to adjust the weight of the nonlinear term.

[0099] Further, the step four is specifically:

[0100] Let the relative opening degree of the outlet throttle valve be fixed, the control input of the centrifugal compressor be the centrifugal compressor speed , the anti-surge valve opening degree , the output be and , the state vector be , the control vector be , and the output vector be , then the state vector and the output vector equations of the centrifugal compressor are expressed as:

[0101] (29)

[0102] where, is the dimensionless and , is the state and the state parameter coefficient;

[0103] In order to obtain the linearization of the state vector and output vector equation of the centrifugal compressor, let:

[0104] (30)

[0105] Combined with the actual parameters of the centrifugal compressor, the state vector and output vector equation of the system is converted to:

[0106] (31)

[0107] where, is the intermediate control quantity obtained by state feedback linearization, and the state vector and output vector equation of formula (31) is rewritten as an incremental model:

[0108] (32)

[0109] where, is the incremental form of , which has the following relationship with , , ;

[0110] The optimization problem of model predictive control is as follows:

[0111] (33)

[0112] where, is the objective function, is the control time domain parameter, is the prediction time domain parameter;

[0113] and according to the actual situation to meet the constraints:

[0114] (34)

[0115] where, is the maximum and minimum of , is the maximum and minimum of , is the maximum and minimum of , The maximum and minimum values ​​need to be determined by equation (30). The constraints are the operating range of the centrifugal compressor, and should be selected according to the actual situation;

[0116] The above constraints are then reduced to inequality constraints:

[0117] (35)

[0118] in, Inequality constraints;

[0119] The optimization objective is specifically expressed as follows:

[0120] (36)

[0121] The weighting matrix is:

[0122] (37)

[0123] The reference sequence is:

[0124] (38)

[0125] in, In order to be in Time prediction Output value at time; For the future The reference trajectory sequence of the step, For each step, a reference trajectory, To output the weighted diagonal matrix of tracking error and control increment penalty, For each input tracking error weight value and control increment penalty weight value;

[0126] If there is a disturbance at the input, it may cause the centrifugal compressor to malfunction or even surge. Therefore, it is necessary to compensate for the disturbance and re-estimate the anti-surge valve opening signal.

[0127] Using a sliding mode observer to estimate disturbance values ​​has the advantages of strong robustness to external disturbances and ease of engineering implementation;

[0128] We obtain the following from the first term in equation (30):

[0129] (39)

[0130] To estimate the anti-surge valve opening, let:

[0131] (40)

[0132] in, This represents the estimated value of the synovial membrane.

[0133] Thus, the error equation is obtained, and the error is the sliding mode surface:

[0134] (41)

[0135] The sliding mode control law is designed as:

[0136] (42)

[0137] where, is the sliding mode gain, is a saturation function, when is large enough, that is, the Lyapunov stability is satisfied: the sliding mode convergence condition is established; when the control amount decays to zero, the state variable of the sliding mode observer reaches the sliding mode surface , the state of the sliding mode observer is always kept on the sliding mode surface, so the observed value of the anti-surge valve opening converges to the true value; the same method can also be used to estimate the input disturbance error caused by the speed regulation.

[0138] The beneficial effects of the present application: through mechanism and data fusion, hybrid control and disturbance compensation, the complexity problem of centrifugal compressor surge control is solved, which is superior to the traditional method in response speed, anti-interference performance and running efficiency, and is suitable for the high reliability demand of industrial scene. BRIEF DESCRIPTION OF DRAWINGS

[0139] Figure 1 is the flowchart of the present control method;

[0140] Figure 2 is the compressor surge line and surge control line combined with data fitting;

[0141] Figure 3 is the flow surge phenomenon of the centrifugal compressor;

[0142] Figure 4 is the pressure rise surge phenomenon of the centrifugal compressor;

[0143] Figure 5 is the anti-surge effect of the active disturbance rejection controller on the flow;

[0144] Figure 6 is the anti-surge effect of the active disturbance rejection controller on the pressure rise;

[0145] Figure 7 is the anti-surge effect of the PID controller on the flow;

[0146] Figure 8 is the anti-surge effect of the PID controller on the pressure rise;

[0147] Figure 9 is the tracking effect of the model predictive control on the flow;

[0148] Figure 10 For model predictive control to track the pressure rise;

[0149] Figure 11 For flow curve without disturbance controller;

[0150] Figure 12 For pressure rise curve without disturbance controller;

[0151] Figure 13 For flow curve with disturbance controller;

[0152] Figure 14 For pressure rise curve with disturbance controller;

[0153] Figure 15 For centrifugal compressor pressure rise-flow curve. DETAILED DESCRIPTION

[0154] The control flow of the method is shown in the accompanying Figure 1 The specific implementation steps are as follows:

[0155] Step 1: Moore-Greitzer model derivation;

[0156] The Moore-Greitzer model of the centrifugal compressor is a set of nonlinear partial differential equations (PDE), which has the following settings:

[0157] 1) The rotor speed is constant;

[0158] 2) High hub ratio;

[0159] 3) Uniform inlet flow;

[0160] 4) Incompressible flow in the centrifugal compressor;

[0161] 5) Compressibility of the cavity gas;

[0162] 6) Spatially uniform cavity pressure;

[0163] 7) The number of stages (rotor and stator) of the centrifugal compressor is simulated as a half-disk.

[0164] Under the conditions of 1) ~ 7), the centrifugal compressor is set to operate in axisymmetric flow, and the deviation amount of the off-stable axisymmetric flow and the flow-pressure relationship are used to establish the following nonlinear partial differential equations of the Moore-Greitzer model:

[0165] (1)

[0166] where, is a dimensionless throttling coefficient parameter, is the tip speed, is the sound speed, is the centrifugal compressor outlet cross-sectional area, is the centrifugal compressor outlet to outlet throttle volume, is the centrifugal compressor characteristic length; is the circumferential direction coordinate, is the dimensionless time, is the dimensionless pressure rise, denoted as ; is the dimensionless flow rate, denoted as ; is the centrifugal compressor characteristic curve function, represents the deviation from the steady axisymmetric flow, reflecting the distribution of non-uniform perturbations in different directions, and the subscript combination represents the partial derivative in the corresponding direction, is the dimensionless delay length, is the dimensionless mass parameter, is the dimensionless half-perimeter, is the inverse of the outlet throttle characteristic equation. Where the following cubic equation is selected:

[0167] (2)

[0168] Take the third-order ordinary differential equation set:

[0169] (3)

[0170] where, represents the half-height and half-width of the cubic axisymmetric characteristic line, is the dimensionless pressure rise through the centrifugal compressor when no flow exists, represents the dimensionless function of perturbation intensity, denoted as , is the constant choke coefficient.

[0171] Take , and according to the relationship between the centrifugal compressor speed and the pressure rise, we get:

[0172] (4)

[0173] where, respectively represent the centrifugal compressor speed and the initial speed; represents the dimensionless pressure rise coefficient at the current speed; represents the proportional coefficient, which reflects the scaling factor of speed and pressure rise.

[0174] From the law of conservation of energy, we get:

[0175] (5)

[0176] Further obtained:

[0177] (6)

[0178] From the electric drive theory:

[0179] (7)

[0180] Wherein, is the output torque of the synchronous motor, is the rotating torque of the centrifugal compressor, is the inertia coefficient of the rotating shaft, is the angular velocity of the centrifugal compressor, represents the time factor.

[0181] The rotating torque of the centrifugal compressor is equal to the change of angular momentum of the gas flow, and has: , represents the tangential velocity of the gas flow, represents the radius of the centrifugal compressor, represents the slip coefficient, represents the dimensionless blade speed of the centrifugal compressor.

[0182] The formula (7) is arranged to obtain:

[0183] (8)

[0184] Wherein, is the expected speed of the centrifugal compressor under steady state, is the density of the fluid, is the blade installation angle.

[0185] Thus, the centrifugal compressor speed dynamic equation is:

[0186] (9)

[0187] Wherein, is the speed regulation instruction.

[0188] The mass balance analysis is carried out on the cavity and the outlet throttle valve, the mass flow in the cavity is , the mass flow through the outlet throttle valve of the centrifugal compressor is , and the change of gas density and pressure in the cavity is caused by the change of the opening degree of the outlet throttle valve. The mass balance equation in the cavity is:

[0189] (10)

[0190] where, is the gas density in the volume, the gas in the volume is set to be isentropic, the gas density change is proportional to the pressure change, and there is:

[0191] (11)

[0192] where, is the gas pressure in the volume.

[0193] The momentum conservation equation at the outlet throttle valve of the centrifugal compressor is:

[0194] (12)

[0195] where, is the dimensionless outlet throttle valve outlet mass flow, is the outlet throttle valve outlet pipe length, considering the actual outlet throttle valve pipe situation, the outlet throttle valve pipe length is set to be 5m~30m, and the outlet throttle valve pipe loss is ignored because the distance is short enough.

[0196] At the same time, a linear process is used to describe the outlet throttle valve regulation process:

[0197] (13)

[0198] where, is the time constant, indicating the steady state value to which the system needs to be adjusted; is the relative opening of the outlet throttle valve; is the outlet throttle valve regulation instruction.

[0199] The dynamic equation of the centrifugal compressor outlet pressure is:

[0200] (14)

[0201] where, indicates the characteristic flow velocity.

[0202] By using the centrifugal compressor mass flow is dimensionless, and by using the fluid pressure difference in the centrifugal compressor is dimensionless, and:

[0203] (15)

[0204] Through the analysis of the internal mechanism of the centrifugal compressor, combined with equation (15), we get:

[0205] (16)

[0206] (17)

[0207] (18)

[0208] (19)

[0209] Final construction of a three-input two-output centrifugal compressor Moore-Greitzer model with export throttle valve relative opening , anti-surge valve opening and centrifugal compressor speed as input, and pressure rise , flow as output.

[0210] Step two: characteristic curve modeling combined with mechanism and data;

[0211] Surge is due to the load reduction of centrifugal, exhaust volume less than a certain value, the normal transport of gas is destroyed, the exhaust gas volume is more or less, in and out, strong shock occurs, and emits like asthma patients "panting" noise. At this time, we can see the gas outlet pressure, flow meter indication fluctuation; with, the body will also be severe vibration, and the export pipeline, plant vibration, centrifugal will emit periodic, intermittent roar, this phenomenon is centrifugal compressor surge.

[0212] There are different performance curves under the working condition of centrifugal compressor, which is determined by the speed of centrifugal compressor. For centrifugal compressor Moore-Greitzer model, after selecting the appropriate parameters, it can be determined by fixing the centrifugal compressor speed coefficient, changing the export throttle valve opening, to determine the working point of a certain working condition, wherein the centrifugal compressor speed coefficient is By fitting different working points, the performance curve of centrifugal compressor can be obtained. The quadratic curve shown in equation (20) is used to fit the pressure rise-flow performance curve under different speeds:

[0213] (20)

[0214] Wherein, is the pressure rise coefficient of centrifugal compressor at different working points, is the flow coefficient of centrifugal compressor at different working points, is the constant obtained by quadratic curve fitting, and the fitting result corresponds to the curve coefficient under different centrifugal compressor speeds. The specific results are shown in Table 1.

[0215] Table 1: Fitted pressure rise-flow performance curve coefficients

[0216]

[0217] Each performance curve has a surge limit point, i.e. once the valve opening is reduced further, the pressure and flow will oscillate and surge occurs. All these points form a surge limit line. Since the Moore-Greitzer model is dimensionless, no specific units are given, and the values of the flow and pressure rise coefficient at each surge limit point are given in Table 2.

[0218] Table 2. Data of each surge limit point

[0219]

[0220] The surge points in the above table are fitted by a first-order and a second-order polynomial respectively, and the root mean square error and R 2 :

[0221] Table 3. Fitting degree

[0222]

[0223] On the basis of not too much error, a first-order function is used for fitting in order to make it more convenient for control. Thus the surge line is obtained as:

[0224] (21)

[0225] In order to more effectively suppress surge and avoid the centrifugal compressor approaching the deep surge region, a surge control line is set. The surge control line makes it unnecessary to wait for the working point to cross the surge line before taking control measures in the anti-surge control process, but starts to adjust when the working point reaches the left side of the control line, so as to more timely prevent surge from occurring. The surge control line can be set by moving the surge line to the right by 5%~10% of the position. Thus the surge control line is obtained as:

[0226] (22)

[0227] The surge control line is close to the surge line and can play an early warning role, so that the anti-surge control system can open the anti-surge valve opening earlier and supplement part of the inlet flow in time to avoid the working point from moving further to the left to the surge region. The surge line and the surge control line of the performance curve of the centrifugal compressor are shown in Figure 2 .

[0228] Step three: design of the active disturbance rejection anti-surge controller;

[0229] The distance between the working point and the surge control line is taken as the deviation, and when the current working point is defined as , the deviation amount is obtained by combining formula (22) and experimental data:

[0230] (23)

[0231] where, is the flow coefficient of the current operating point, is the pressure rise coefficient of the current operating point, which is the derivative of the pressure rise with respect to the flow rate in the Moore-Greitzer model of the centrifugal compressor and the flow rate are expressed as coefficients;

[0232] PID surge control:

[0233] When the operating point is outside the surge control line, no control is needed, and when the operating point enters the surge control line, the anti-surge valve opening needs to be adjusted. Definition:

[0234] (24)

[0235] For the surge problem, the PID surge control avoids the system entering the surge region by adjusting the feedback signal of the system, which is as follows:

[0236] (25)

[0237] where: is the control input, are the proportional, integral, and derivative gains, respectively.

[0238] Design of active disturbance rejection anti-surge controller:

[0239] The active disturbance rejection anti-surge controller consists of the following three parts: a tracking-differentiator (TD) for obtaining the derivative signal and configuring the transition process; an extended state observer (ESO) for observing the total disturbance; and a nonlinear state error feedback control law (NLSEF) for generating the control amount.

[0240] Since the signal to be tracked is the deviation, the target value of the deviation is always zero, at which time the tracking-differentiator TD is ignored, and the surge control of the active disturbance rejection anti-surge controller is composed of the extended state observer and the nonlinear state error feedback control law.

[0241] Through the combination of equations (16) to (19) and equation (23), the following relationship is obtained:

[0242] (26)

[0243] where the two dots above the character represent the second derivative of the corresponding parameter, and the dot above the character represents the first derivative of the corresponding parameter;

[0244] Therefore, the deviation is constructed into a second-order nonlinear equation, is unknown, which is treated as a disturbance, and is also an unknown function, so we have:

[0245] (27)

[0246] wherein, represents the control input, represents the actual output, represents the gain coefficient of the control input.

[0247] The extended state observer is set as:

[0248] (28)

[0249] wherein, is the output estimation error, is the estimated value of the system output, is the estimated value of the first derivative of the system, is the estimated value of the total disturbance. represents the adjustment gain of the extended state observer, adjusts the convergence speed, adjusts the convergence speed, adjusts the estimation speed.

[0250] is a nonlinear function:

[0251] (29)

[0252] wherein, is a nonlinear index used to control the smoothness of the function. is a linear interval threshold value to avoid sudden changes in function values when small errors occur.

[0253] Through the extended state observer, error signals and error differential signals can be obtained, and the total disturbance of the system can also be estimated and directly offset as a feedforward compensation term, thereby reducing the dependence on error integration, simplifying the control structure, and improving the response speed. The nonlinear state error feedback control law is designed as:

[0254] (30)

[0255] wherein, is the original control amount, is a nonlinear index, is a control gain coefficient used to adjust the weight of the nonlinear term.

[0256] The above formula constructs an active disturbance rejection anti-surge controller. Simulink simulations are used to study PID surge control and the active disturbance rejection anti-surge controller. When there is no disturbance, the centrifugal compressor operates at a steady point. When a disturbance is introduced, as shown in the attached diagram... Figure 3 , Figure 4 As shown, flow and pressure oscillate, resulting in surge. Adding a surge controller at this point opens the surge valve, thus suppressing the surge. Under the same conditions, PID surge control and active disturbance rejection surge control were added respectively. The simulation results are shown in the attached figure when the appropriate parameters were adjusted. Figure 5 , Figure 6 , Figure 7 , Figure 8 As shown in the comparison, the active disturbance rejection and anti-surge controller has a faster response speed.

[0257] Although the surge problem has been effectively resolved, the goal of control is to reduce the deviation. When the deviation is zero, the operating point can only be kept on the surge control line. However, this point is not the point of highest efficiency, so it is still necessary to adjust the operating point of the centrifugal compressor.

[0258] Step 4: Design of a model predictive controller with disturbance compensation;

[0259] Assume the relative opening of the outlet throttle valve The control input for a fixed centrifugal compressor is the centrifugal compressor speed. Anti-surge valve opening The output is Let the state vector be... The control vector is The output vector is Then the state vector and output vector equations of the centrifugal compressor are expressed as:

[0260] (31)

[0261] in, Dimensionless , Representing state With state Parameter coefficients.

[0262] In order to obtain a linearized representation of the state vector and output vector equations of the centrifugal compressor, let:

[0263] (32)

[0264] Based on the actual parameters of the centrifugal compressor, the system's state vector and output vector equations are transformed into:

[0265] (33)

[0266] where, is the intermediate control quantity obtained by state feedback linearization, the state vector and output vector equations of formula (33) are rewritten as an incremental model:

[0267] (34)

[0268] where, represents an incremental form of the following relationship , .

[0269] The optimization problem of model predictive control is as follows:

[0270] (35)

[0271] where, is the objective function, is the control time domain parameter, is the prediction time domain parameter.

[0272] And according to the actual situation to meet the constraints:

[0273] (36)

[0274] where, represents the maximum and minimum values, represents the maximum and minimum values, represents the maximum and minimum values, the maximum and minimum values need to be determined by formula (32), the constraint condition of

[0275] The above constraints are further converted into inequality constraints:

[0276] (37)

[0277] where, is the inequality constraint.

[0278] The optimization objective is specifically represented as:

[0279] (38)

[0280] The weighting matrix is:

[0281] (39)

[0282] The reference sequence is:

[0283] (40)

[0284] wherein, is the output value at time t predicted at time t; is the reference trajectory sequence of future n steps, is the reference trajectory of each step, is the weight diagonal matrix of output tracking error and control increment penalty, is each input tracking error weight value and control increment penalty weight value. As ,

[0285] The control method is established on the condition that the model can work stably, that is, the working point is outside the surge line. When the system is disturbed and surges occur, the output cannot track the reference signal, and at this time the control method fails, so while tracking control is performed, hybrid control needs to be combined with anti-surge control. At the same time, in order to improve the anti-interference ability. Figure 9 Figure 10 Suppose there is a disturbance in the input, which will cause the centrifugal compressor to run inaccurately, or even cause surging phenomenon, so the disturbance needs to be compensated and the anti-surge valve opening signal needs to be re-estimated.

[0286] The disturbance value is estimated by using a sliding mode observer, which has the advantages of strong external disturbance robustness and easy engineering implementation.

[0287] The first term in equation (32) is:

[0288]

[0289] (41)

[0290] In order to estimate the anti-surge valve opening, let:

[0291] (42)

[0292] wherein, represents the sliding film estimation value.

[0293] Thus the error equation is obtained, and the error is the sliding surface:

[0294] (43)

[0295] The sliding mode control law is designed as:

[0296] (44) ​​​

[0297] where, is the sliding mode gain, is a saturation function, when is large enough, i.e. satisfying Lyapunov stability: the sliding mode convergence condition holds. When the control quantity decays to zero, the state variable of the sliding mode observer reaches the sliding surface , the sliding mode observer state remains on the sliding surface, so the observed value of the anti-surge valve opening converges to the true value. The same method can also estimate the input disturbance error caused by speed regulation.

[0298] The tracking prediction control method of centrifugal compressor with disturbance compensation is simulated in Simulink. Disturbance is added to the input, as shown in Fig. Figure 11 , Figure 12 , Figure 13 , Figure 14 The disturbance is eliminated after compensation, and the output can stably track the reference value.

[0299] The overall effect of this method is analyzed by analyzing the operating trajectory on the pressure rise-flow performance curve. The pressure rise-flow performance curve is shown in Fig. Figure 15 The working point of the centrifugal compressor runs from the original reference point to another reference point due to variable working conditions. Due to external disturbance, the working point runs to the surge area. When it runs into the surge control line, the anti-surge valve opening is opened due to the influence of the anti-surge controller, so that the working point stays on the surge control line. After stabilization, the observer observes the disturbance value and compensates it, so that the working point runs to the reference point again.

Claims

1. A predictive control method for anti-surge of centrifugal compressors based on mechanism and data fusion, characterized in that, The steps are as follows: Step 1: Derivation of the Moore-Greitzer model: Combining mass, momentum and the law of conservation of energy, the physical quantities are made dimensionless. By introducing perturbations and linearizing them, the Moore-Greitzer model of the centrifugal compressor is established. Step 2: Modeling characteristic curves by combining mechanism and data: Based on the Moore-Greitzer model of the centrifugal compressor and actual data, the performance curves of the centrifugal compressor are plotted, and the surge line and surge control line are obtained. Step 3: Design of Active Disturbance Rejection Anti-Surge Controller: Based on the performance curve of the centrifugal compressor, the distance from the operating point to the surge control line is used as the deviation. An active disturbance rejection anti-surge controller is designed and compared with PID surge control. Step 4: Design of Model Predictive Controller with Disturbance Compensation: The disturbance value is estimated using a sliding mode observer, thereby compensating the model and preventing the centrifugal compressor from entering surge due to external disturbances.

2. The anti-surge predictive control method for centrifugal compressors based on mechanism and data fusion according to claim 1, characterized in that, The first step is as follows: The Moore-Greitzer model of a centrifugal compressor is a system of nonlinear partial differential equations, with the following specifications: 1) The rotor speed is constant; 2) High wheel hub ratio; 3) Consistent import flow; 4) Incompressible flow rates in centrifugal compressors; 5) Compressibility of the gas in the cavity; 6) Consistent cavity pressure throughout the space; 7) The centrifugal compressor stage simulation is a semi-excited disk; Under the conditions set in 1) to 7), the centrifugal compressor is configured to operate in axisymmetric flow mode. The following set of nonlinear partial differential equations for the Moore-Greitzer model is established using the deviation from the steady axisymmetric flow and the flow-pressure relationship: （1） in, It is a dimensionless throttling coefficient parameter. It is the circumferential velocity of the leaf tip. It's the speed of sound. It is the outlet cross-sectional area of ​​the centrifugal compressor. It is the volume between the outlet of the centrifugal compressor and the outlet throttle valve. It is the characteristic length of a centrifugal compressor; These are circumferential coordinates. It is dimensionless time. It is a dimensionless pressure rise, denoted as ; It is a dimensionless flow rate, denoted as ; It is a characteristic curve function of a centrifugal compressor. This represents the deviation from a stable axisymmetric flow, reflecting the distribution of non-uniform disturbances in different directions. The subscript combination indicates the partial derivative in the corresponding direction. It is a dimensionless delay length. It is a dimensionless mass parameter. It is a dimensionless semi-perimeter. It is the inverse of the characteristic equation of the outlet throttle valve; where Choose the following cubic equation: （2） Take a system of third-order ordinary differential equations: （3） in, and This represents the half-height and half-width of a cubic axisymmetric characteristic line. It is the dimensionless pressure rise through the centrifugal compressor when there is no flow. The dimensionless function representing the intensity of the disturbance is denoted as . , It is a constant value for the blocking cone coefficient; Pick And based on the relationship between centrifugal compressor speed and pressure rise, we can obtain: （4） in, These represent the centrifugal compressor's rotational speed and initial rotational speed, respectively. This represents the dimensionless pressure rise coefficient at the current rotational speed; This represents the scaling factor, which reflects the scaling of speed and pressure rise. According to the law of conservation of energy: （5） Therefore, we get: （6） According to the theory of electric drive: （7） in, To provide the output torque of the synchronous motor, For the centrifugal compressor's rotational torque, Let be the coefficient of inertia of the rotating axis. The angular velocity of the centrifugal compressor. Indicates the time factor; The rotational torque of a centrifugal compressor is equal to the change in the angular momentum of the airflow, therefore: , Indicates the tangential velocity of the airflow. This indicates the radius of the centrifugal compressor. Indicates the slip coefficient. This represents the circumferential velocity of the dimensionless impeller in a centrifugal compressor. Rearranging equation (7) yields: （8） in, This represents the desired speed of the centrifugal compressor under steady-state conditions. For the density of the fluid, The installation angle of the impeller blades; Therefore, the dynamic equation for the centrifugal compressor speed is obtained as follows: （9） in, This is a speed adjustment command; Mass balance analysis was performed inside the cavity and at the outlet throttle valve: the mass flow rate inside the cavity was... The mass flow rate after passing through the outlet throttle valve of the centrifugal compressor is The changes in gas density and pressure within the cavity are caused by the change in the opening degree of the outlet throttle valve; the mass balance equation within the cavity is: （10） in, Let be the gas density inside the cavity. Assuming the gas inside the cavity is isentropic, the change in gas density is proportional to the change in pressure, as follows: （11） in, This refers to the gas pressure inside the cavity; The momentum conservation equation at the outlet throttling valve of a centrifugal compressor is: （12） in, This refers to the dimensionless outlet mass flow rate of the outlet throttle valve. The length of the outlet pipe of the outlet throttle valve is given, and pipe losses of the outlet throttle valve are ignored. The outlet throttle valve regulation process is described using a linear process: （13） in, The time constant represents the steady-state value that the system needs to be adjusted to. The relative opening of the outlet throttle valve; This is an instruction to adjust the outlet throttle valve; The dynamic equation for the outlet pressure of a centrifugal compressor: （14） in, Indicates characteristic flow velocity; use To achieve dimensionless mass flow rate of centrifugal compressors, utilizing... Dimensionless transformation of the fluid pressure difference in a centrifugal compressor yields: （15） By analyzing the internal mechanism of the centrifugal compressor and combining it with equation (15), we obtain: （16） （17） （18） （19） The final structure is based on the relative opening of the outlet throttle valve. Anti-surge valve opening and centrifugal compressor speed For input, and pressure rise ,flow The Moore-Greitzer model of a centrifugal compressor with three inputs and two outputs.

3. The anti-surge predictive control method for centrifugal compressors based on mechanism and data fusion according to claim 2, characterized in that, The second step is specifically as follows: Centrifugal compressors exhibit different performance curves under various operating conditions. The operating condition is determined by the compressor's speed. For the Moore-Greitzer model of a centrifugal compressor, after selecting appropriate parameters, the operating point for a specific condition can be determined by fixing the compressor speed coefficient and changing the outlet throttle valve opening. The compressor speed coefficient is... By fitting different operating points, the performance curve of the centrifugal compressor can be obtained. Now, the pressure rise-flow performance curve at each speed is fitted using the quadratic curve shown in equation (20): （20） in, The pressure rise coefficient of a centrifugal compressor at different operating points. The flow coefficient of the centrifugal compressor at different operating points. and It is a constant obtained by fitting a quadratic curve, and the fitting result corresponds to the curve coefficient at different centrifugal compressor speeds; Each pressure rise-flow performance curve has a surge limit point, meaning that once the anti-surge valve opening is further reduced, pressure and flow will oscillate, resulting in surge. These surge limit points constitute a surge limit line. To suppress surge and prevent the centrifugal compressor from approaching the deep surge region, a surge control line is set. The surge control line is set by shifting the surge line to the right by 5% to 10%. This surge control line allows for adjustment during anti-surge control without waiting for the operating point to cross the surge line before taking control measures. Instead, adjustment begins when the operating point reaches the left side of the surge line, thus preventing surge more promptly.

4. The anti-surge predictive control method for centrifugal compressors based on mechanism and data fusion according to claim 3, characterized in that, Step three specifically refers to: The distance between the operating point and the surge control line is used as the deviation. When the current operating point is defined as... Then, combining equation (20) and experimental data, the deviation is obtained: （21） in, This represents the flow coefficient of the current working point. The pressure rise coefficient, representing the pressure rise at the current operating point, is used in the Moore-Greitzer model of a centrifugal compressor. With traffic The coefficientized representation; PID surge control: When the operating point is outside the surge control line, no control is needed. When the operating point enters the surge control line, the anti-surge valve opening needs to be adjusted. Definition: （22） To address the surge problem, PID surge control prevents the system from entering the surge region by adjusting the system's feedback signal, as follows: （23） in: To control the input, These are proportional, integral, and differential gain, respectively. Design of a self-disturbing and surge-resistant controller: The active disturbance rejection and surge prevention controller consists of three parts: a tracking-differentiator (TD) for acquiring the differential signal and configuring the transient process; an extended state observer (ESO) for observing the total disturbance; and a nonlinear state error feedback control law (NLSEF) for generating the control input. Since the signal to be tracked is the deviation, and the target value of the deviation is always zero, the tracking-differentiator TD is ignored. The surge control of the active disturbance rejection anti-surge controller is composed of an extended state observer and a nonlinear state error feedback control law. By combining equations (16) to (19) with equation (21), the following relationship is obtained: （24） In this context, adding two dots above a character indicates the second derivative of the corresponding parameter, and adding one dot above a character indicates the first derivative of the corresponding parameter. Therefore, the deviation is constructed as a second-order nonlinear equation. The unknown is treated as a disturbance, and thus... It is also an unknown function, so we have: （25） in, Indicates control input, Indicates the actual output. This represents the gain coefficient of the control input; The extended state observer is set as follows: （26） in, To output the estimation error, This is the estimated value output by the system. This is an estimate of the system's first derivative. This is an estimate of the total disturbance; This represents the adjustment gain of the extended state observer. adjust The convergence speed, adjust The convergence speed, adjust The estimated speed; It is a nonlinear function: （27） in, It is a non-linear exponent used to control the smoothness of the function; A linear interval threshold is used to avoid sudden changes in function values ​​when there are small errors. By using an extended state observer, the error signal and the error derivative signal can be obtained, and the total disturbance of the system can be estimated. The total disturbance is then directly canceled out as a feedforward compensation term, thereby reducing the dependence on the error integral. This simplifies the control structure and improves the response speed. The nonlinear state error feedback control law is designed as follows: （28） in, This is the original control quantity. It is a non-linear exponent. The gain coefficient is used to adjust the weight of the nonlinear term.

5. The anti-surge predictive control method for centrifugal compressors based on mechanism and data fusion according to claim 4, characterized in that, The fourth step is specifically as follows: Assume the relative opening of the outlet throttle valve The control input for a fixed centrifugal compressor is the centrifugal compressor speed. Anti-surge valve opening The output is and Let the state vector be... The control vector is The output vector is Then the state vector and output vector equations of the centrifugal compressor are expressed as: （29） in, Dimensionless and , Representing state With state Parameter coefficients; In order to obtain a linearized representation of the state vector and output vector equations of the centrifugal compressor, let: （30） Based on the actual parameters of the centrifugal compressor, the system's state vector and output vector equations are transformed into: （31） in, It is the intermediate control quantity obtained by linearizing the state feedback. The state vector and output vector equations of equation (31) are rewritten as an incremental model: （32） in, express The incremental form, which is related to The following relationship , ; The optimization problem of model predictive control is as follows: （33） in, Let be the objective function. To control time-domain parameters, To predict time-domain parameters; And satisfy the constraints according to the actual situation: （34） in, express The maximum and minimum values, , express The maximum and minimum values, express The maximum and minimum values, The maximum and minimum values ​​need to be determined by equation (30). The constraints are the operating range of the centrifugal compressor, and should be selected according to the actual situation; The above constraints are then reduced to inequality constraints: （35） in, Inequality constraints; The optimization objective is specifically expressed as follows: （36） The weighting matrix is: （37） The reference sequence is: （38） in, In order to be in Time prediction Output value at time; For the future The reference trajectory sequence of the step, For each step, a reference trajectory, To output the weighted diagonal matrix of tracking error and control increment penalty, For each input tracking error weight value and control increment penalty weight value; If there is a disturbance at the input, it may cause the centrifugal compressor to malfunction or even surge. Therefore, it is necessary to compensate for the disturbance and re-estimate the anti-surge valve opening signal. The disturbance value is estimated using a sliding mode observer, obtained through the first term in equation (30): （39） To estimate the anti-surge valve opening, let: （40） in, This represents the estimated value of the synovial membrane. Therefore, the error equation is obtained, and the error is the sliding surface: （41） The sliding mode control law is designed as follows: （42） in, For sliding mode gain, For a saturation function, when Sufficiently large, i.e., satisfying Lyapunov stability: the sliding mode convergence condition holds; when the control variable decays to zero, the state variables of the sliding mode observer reach the sliding surface. Since the sliding mode observer remains on the sliding surface, the observed value of the anti-surge valve opening converges to the true value; similarly, the input disturbance error caused by speed regulation can also be estimated.

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