CN114048594A - Online adjusting method, system and terminal for blade top gap of magnetic suspension compressor - Google Patents
Online adjusting method, system and terminal for blade top gap of magnetic suspension compressor Download PDFInfo
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Abstract
According to the online adjustment method, the online adjustment system and the online adjustment terminal for the blade top clearance of the magnetic suspension compressor, firstly, a mathematical model of a magnetic suspension bearing is established, then the adaptive PID controller is obtained according to the balance position, when the balance position is changed, parameters of the adaptive PID controller are automatically changed, manual parameter debugging is not needed, the stability and good response performance of the system can still be guaranteed, and the blade top clearance can be adjusted in real time when the compressor normally operates.
Description
Technical Field
The application relates to the technical field of compressors, in particular to an online adjusting method, system, terminal and storage medium for blade top clearance of a magnetic suspension compressor.
Background
At present, a centrifugal cold compressor is generally adopted internationally to reduce the pressure and the temperature of a supercooling groove to obtain high-flow super-flow helium. The grease lubrication bearing and the gas bearing are difficult to meet the running conditions of low temperature, negative pressure and high speed of the cold compressor. The active magnetic suspension bearing utilizes electromagnetic force to suspend the rotor in a space without friction and lubrication, and has the general advantages of no abrasion, high rotating speed, long service life and the like. The active magnetic suspension bearing can also achieve expected performance by designing a control algorithm, realizes stable and efficient operation of the compressor, and is the best choice for a rotor supporting component of a cold compressor in the current super-flow helium refrigeration system.
Fig. 1 shows a schematic diagram of a blade top gap of a magnetic suspension compressor in the prior art, and the adjustment of the blade top gap of the compressor can be realized by actively controlling the axial position of a rotor thrust disc, so that specific performance under different operating conditions is obtained. The smaller blade top clearance is beneficial to improving the pressure ratio and the efficiency; however, when the flow rate is increased, the blade tip clearance needs to be increased in time, and the stable operation area of the compressor is widened to achieve the effect of preventing surging. In addition, the compressor needs a larger blade top clearance in the shutdown stage to prevent the adhesion damage caused by thermal deformation of the impeller with fast re-heating and the volute with slow re-heating from influencing the next normal startup. Therefore, in the tip clearance range, it is important to deal with the above problem that the rotor can be robustly and smoothly balanced at a specified position.
Currently, the technology for positioning the controlled object by means of the active magnetic levitation technology mostly focuses on micron-scale tracking of the processing props of the machine tool. The goal of this technique is to improve positioning accuracy, speed and shape, with less requirements on the range over which it can be positioned. However, the positioning technique is difficult to be directly applied because the tip clearance of the rotating machine is large and reaches hundreds of micrometers. If the balance position is forcibly modified in a large range, the actual model and the theoretical model generate deviation, and the originally applicable controller can cause the dynamic response, the steady-state tracking and the anti-interference capability of a new system to be poor, and even can influence the stability of the rotor.
In addition, in the top clearance pressure regulating model and experiment of the existing magnetic suspension compressor, the axial positioning of the rotor is not completed on line. This means that when changing different equilibrium positions, the compressor needs to be shut down and the parameters of the controller are debugged off-line to ensure that the magnetic levitation system starts the compressor after the equilibrium position can be stabilized. Therefore, there is no guarantee of a fast adjustment of the tip clearance in real time during the operation of the compressor in order to achieve a fast switching between efficiency improvement and surge prevention.
Disclosure of Invention
In view of the above, there is a need to provide an online adjustment method, system, terminal and storage medium for blade tip clearance of a magnetic levitation compressor, which can achieve real-time adjustment of the blade tip clearance when the compressor is normally operated.
In order to solve the above problems, the following technical solutions are adopted in the present application:
the application provides an online adjusting method for a blade top gap of a magnetic suspension compressor, which comprises the following steps:
step S110: constructing a mathematical model of the magnetic suspension bearing;
step S120: acquiring a PID controller according to the balance position of a rotor of the magnetic suspension bearing;
step S130: the PID controller carries out simulation test on the dynamic and static response capability of the magnetic suspension bearing;
step S140: judging whether the simulation result meets the requirements; if yes, ending; if not, the process returns to step S130.
In some embodiments, in step S110, a mathematical model of the magnetic bearing is constructed, specifically:
the mathematical model of the magnetic suspension bearing is as follows:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x and the instantaneous current of the coil is marked i, mu0Is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
In some embodiments, in step S120, acquiring a PID controller based on the equilibrium position specifically includes:
step S121: self-defining a relative stiffness coefficient mu, a relative damping coefficient xi and a relative integral coefficient eta required by the balance position;
step S122: and acquiring the PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta.
In some embodiments, the relative stiffness coefficient μ ranges from 1 to 3, the relative damping coefficient ξ ranges from 20% to 80%, and the relative integral coefficient η is selected empirically.
In some embodiments, in step S122, a PID controller is obtained according to the relative stiffness coefficient μ, the relative damping coefficient ξ, and the relative integral coefficient η, specifically:
obtaining a PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta, wherein the PID controller is
Wherein:
Kpis a proportionality coefficient, KdIs a differential coefficient, KiFor the integral coefficient, the following three formulas are respectively used for solving the following problems:
in the formula, GaIs the gain of the power amplifier, GsIs the gain of the sensor.
Another technical scheme adopted by the embodiment of the application is as follows: an on-line adjusting system for the blade top gap of a magnetic suspension compressor comprises:
a model construction unit: the method is used for constructing a mathematical model of the magnetic suspension bearing;
a controller unit: the PID controller is obtained according to the balance position of the rotor of the magnetic suspension bearing;
a simulation unit: the PID controller is used for realizing the simulation test of the dynamic and static response capability of the magnetic suspension bearing;
a judging unit: and the simulation result is used for judging whether the simulation result meets the requirement or not.
In some of these embodiments, the mathematical model of the magnetic bearing system is:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x and the instantaneous current of the coil is marked i, mu0Is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
In some of these embodiments, the controller unit comprises:
a parameter setting module: the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta which are required by self-defining the balance position;
a calculation module: and acquiring the PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta.
In some embodiments, the relative stiffness coefficient μ ranges from 1 to 3, the relative damping coefficient ξ ranges from 20% to 80%, and the relative integral coefficient η is selected empirically.
In some of these embodiments, the PID controller is
Wherein:
Kpis a proportionality coefficient, KdIs a differential coefficient, KiFor the integral coefficient, the following three formulas are respectively used for solving the following problems:
the embodiment of the application adopts another technical scheme that: a terminal comprising a processor, a memory coupled to the processor, wherein,
the memory stores program instructions for implementing the online adjustment method of the blade top gap of the magnetic suspension compressor;
the processor is configured to execute the program instructions stored by the memory to control online adjustment of a maglev compressor tip clearance.
The embodiment of the application adopts another technical scheme that: a storage medium storing program instructions executable by a processor to perform a method of online adjustment of a blade tip clearance of a magnetically levitated compressor.
Compared with the prior art, the embodiment of the application has the advantages that: according to the online adjusting method, the online adjusting system, the online adjusting terminal and the storage medium for the blade top clearance of the magnetic suspension compressor, firstly, a mathematical model of a magnetic suspension bearing is established, then the adaptive PID controller is obtained according to the balance position, when the balance position is changed, parameters of the adaptive PID controller are automatically changed, manual parameter debugging is not needed, the stability and good response performance of the system can still be guaranteed, and the blade top clearance can be adjusted in real time when the compressor normally operates.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the description of the embodiments of the present application or the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic view of a prior art magnetic levitation compressor blade tip clearance;
FIG. 2 is a flowchart illustrating the steps of an online adjustment method for the blade tip clearance of a magnetic levitation compressor according to embodiment 1 of the present invention;
FIG. 3 is a schematic structural diagram of an online adjustment system for the blade tip clearance of a magnetic levitation compressor provided in embodiment 2 of the present invention;
fig. 4 is a schematic structural diagram of a terminal provided in embodiment 3 of the present application;
FIG. 5 is a schematic structural diagram of a storage medium provided in embodiment 4 of the present application;
FIG. 6 is a schematic view of an axial magnetic bearing provided by an embodiment of the present application;
FIG. 7 is a simulation plot of the step response of a fixed-parameter PID controller according to an embodiment of the application;
FIG. 8 is a simulation plot of a step response of an adaptive PID controller provided in an embodiment of the application;
fig. 9 is a graph of an experimental result of a step response provided in the embodiment of the present application.
Detailed Description
Reference will now be made in detail to embodiments of the present application, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining the present application and should not be construed as limiting the present application.
In the description of the present application, it is to be understood that the terms "upper", "lower", "horizontal", "inner", "outer", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are only for convenience in describing the present application and simplifying the description, and do not indicate or imply that the referred devices or elements must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present application.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present application, "a plurality" means two or more unless specifically limited otherwise.
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments.
Example 1
Referring to fig. 2, a flowchart of steps of an online adjusting method for a blade tip gap of a magnetic levitation compressor according to embodiment 1 of the present application includes the following steps:
step S110: and (5) constructing a mathematical model of the magnetic suspension bearing.
In this embodiment, the mathematical model of the magnetic suspension bearing is:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x and the instantaneous current of the coil is marked i, mu0Is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
It can be understood that under the condition that the rotor system is completely assembled in the magnetic suspension bearing, the axial magnetic suspension bearing is not powered, the rotor is given vertical downward acting force, the rotor completely falls on the auxiliary bearing, the axial position at the moment is calibrated to be 0, and the air gap centers of the axial magnetic bearing and the protective bearing are overlapped by continuously adjusting the gaskets of the axial magnetic bearing and the protective bearing.
Step S120: and acquiring a PID controller according to the balance position of the rotor of the magnetic suspension bearing.
In this embodiment, obtaining the PID controller according to the equilibrium position of the rotor of the magnetic suspension bearing specifically includes:
step S121: and self-defining a relative rigidity coefficient mu, a relative damping coefficient xi and a relative integral coefficient eta required by the balance position.
In particular, μ is the relative stiffness, the magnetic bearing is inherently negative, and therefore to stabilize the magnetic levitation rotor, the stiffness provided by the control system needs to be greater than the intrinsic negative stiffness of the magnetic bearing, i.e. the displacement stiffness. But excessive stiffness requirements may cause magnetic field saturation. Therefore, the value range is (1-3). When the overshoot of the system is expected to be small, a low-rigidity control strategy is adopted; when a relatively fast response speed of the system is desired, a high stiffness strategy is employed.
In particular, xi is a relative damping coefficient, and in order to obtain better static and dynamic response performance, the relative damping coefficient of the magnetic suspension bearing in a working range is required to be not less than 20%. And the relative damping coefficient is not higher than 80% to avoid saturation of the saturation magnetic field of the power amplifier caused by noise signal amplification, and the value range is (20% -80%).
Specifically, the relative integral coefficient η may be obtained according to an empirical value, that is, the performance (such as sampling frequency, bandwidth, etc.) of actually adopted electronic control hardware (such as NI PXIe-8840, power amplifier, sensor, etc.) and an actual test experience are selected, and the value of the relative integral coefficient η is 400 here.
Step S122: and acquiring the PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta.
In some embodiments, in obtaining the PID controller according to the relative stiffness coefficient μ, the relative damping coefficient ξ and the relative integral coefficient η, the PID controller is
Wherein:
KpIs a proportionality coefficient, KdIs a differential coefficient, KiFor the integral coefficient, the following three formulas are respectively used for solving the following problems:
where Ga is the gain of the power amplifier and Gs is the gain of the sensor.
Step S130: and the PID controller carries out simulation test on the dynamic and static response capability of the magnetic suspension bearing.
It will be appreciated that the scaling factor K will be based on the setting of μ, ξ and η in the above stepspCoefficient of differentiation KdIntegral coefficient KiAnd substituting the calculated values into a PID controller and a mathematical model of the magnetic suspension bearing to construct a closed-loop control system.
The other parameters remain unchanged at (0,2 ×)p) Range change equilibrium position x0And the tracking condition of the closed-loop system on the step reference signal and the anti-interference capability on the sinusoidal signal are examined.
Step S140: judging whether the simulation result meets the requirements; if yes, ending; if not, the process returns to step S130.
It will be appreciated that if the dynamic and static response capabilities of the system do not meet the user requirements, then the second step is returned to alter μ, ξ and η until satisfactory performance is achieved.
It can be understood that, this application designs rotor balanced position's self-adaptation PID controller based on magnetic suspension bearing, according to the location demand of difference, control parameter automatic adjustment, when having avoided adjusting balanced position, need manual adjustment control parameter again loaded down with trivial details, even in any position balance within a large range of 200 microns, PID controller can both satisfy the stable demand of rotor, also can guarantee rigidity and damping that magnetic suspension closed-loop system corresponds, the dynamic and static performance of rotor response has been guaranteed promptly, automatic control's reliability improves greatly.
It should be noted that: the magnetic suspension bearing related in the application not only can be a rotor supported by an active magnetic suspension bearing, but also can be a magnetic suspension ball, a magnetic suspension rack, a machine tool cutter, a magnetic suspension train and the like; the bearing is not only suitable for magnetic suspension bearings, but also suitable for radial magnetic suspension bearings; the magnetic suspension bearing is not only suitable for a magnetic suspension bearing which is vertically arranged, but also suitable for a magnetic suspension bearing which is horizontally arranged; the magnetic suspension bearing is not only suitable for asymmetric magnetic suspension bearings, but also suitable for symmetric magnetic suspension bearings.
In the method for online adjusting the blade top gap of the magnetic suspension compressor provided by the above embodiment 1 of the present application, a mathematical model of the magnetic suspension bearing is firstly established, then the adaptive PID controller is obtained according to the balance position, when the balance position is changed, the parameters of the adaptive PID controller are automatically changed without manually debugging the parameters, the stability and good response performance of the system can still be ensured, and the real-time adjustment of the blade top gap can be realized when the compressor normally operates.
Example 2
Referring to fig. 3, a schematic structural diagram of an online adjusting system for a blade tip gap of a magnetic levitation compressor according to embodiment 2 of the present application includes: the model construction unit 110 is used for constructing a mathematical model of the magnetic suspension bearing; the controller unit 120 is configured to obtain a PID controller according to a balance position of a rotor of the magnetic bearing; the simulation unit 130 is used for implementing the PID controller to perform simulation test on the dynamic and static response capability of the magnetic suspension bearing, and the judgment unit 140 is used for judging whether the simulation result meets the requirement.
Specifically, the model construction unit 110 constructs a mathematical model of the magnetic bearing as follows:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x and the instantaneous current of the coil is marked i, mu0Is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
It can be understood that under the condition that the rotor system is completely assembled in the magnetic suspension bearing, the axial magnetic suspension bearing is not powered, the rotor is given vertical downward acting force, the rotor completely falls on the auxiliary bearing, the axial position at the moment is calibrated to be 0, and the air gap centers of the axial magnetic bearing and the protective bearing are overlapped by continuously adjusting the gaskets of the axial magnetic bearing and the protective bearing.
In some of these embodiments, the controller unit 120 includes: a parameter setting module 121 and a calculating module 122. Wherein:
the parameter setting module 121 is configured to self-define a relative stiffness coefficient μ, a relative damping coefficient ξ, and a relative integral coefficient η, which are required by the equilibrium position.
In particular, μ is the relative stiffness, the magnetic bearing is inherently negative, and therefore to stabilize the magnetic levitation rotor, the stiffness provided by the control system needs to be greater than the intrinsic negative stiffness of the magnetic bearing, i.e. the displacement stiffness. But excessive stiffness requirements may cause magnetic field saturation. Therefore, the value range is (1-3). When the overshoot of the system is expected to be small, a low-rigidity control strategy is adopted; when a relatively fast response speed of the system is desired, a high stiffness strategy is employed.
In particular, xi is a relative damping coefficient, and in order to obtain better static and dynamic response performance, the relative damping coefficient of the magnetic suspension bearing in a working range is required to be not less than 20%. And the relative damping coefficient is not higher than 80% to avoid saturation of the saturation magnetic field of the power amplifier caused by noise signal amplification, and the value range is (20% -80%).
Specifically, the relative integral coefficient η may be empirically selected, that is, the performance (e.g., sampling frequency, bandwidth, etc.) of the actually adopted electronic control hardware (e.g., NI PXIe-8840, power amplifier, sensor, etc.) and the actual test experience are selected, and the value of the relative integral coefficient η is 400 here.
The calculation module 122 obtains the PID controller according to the relative stiffness coefficient μ, the relative damping coefficient ξ and the relative integral coefficient η.
In some of these embodiments, the PID controller is
Wherein:
Kpis a proportionality coefficient, KdIs a differential coefficient, KiFor the integral coefficient, the following three formulas are respectively used for solving the following problems:
where Ga is the gain of the power amplifier and Gs is the gain of the sensor.
It is understood that in the simulation unit 130, the scaling factor K may be set according to μ, ξ and η set in the above stepspSystem of differentialNumber KdIntegral coefficient KiAnd substituting the calculated values into a PID controller and a mathematical model of the magnetic suspension bearing to construct a closed-loop control system.
The other parameters remain unchanged at (0,2 ×)p) Range change equilibrium position x0And the tracking condition of the closed-loop system on the step reference signal and the anti-interference capability on the sinusoidal signal are examined.
It will be appreciated that when the decision unit 140 determines that the dynamic and static response capabilities of the system do not meet the user requirements, it returns to the controller unit 120 and alters μ, ξ and η until satisfactory performance is achieved.
It can be understood that, this application designs rotor balanced position's self-adaptation PID controller based on magnetic suspension bearing, according to the location demand of difference, control parameter automatic adjustment, when having avoided adjusting balanced position, need manual adjustment control parameter again loaded down with trivial details, even in any position balance within a large range of 200 microns, PID controller can both satisfy the stable demand of rotor, also can guarantee rigidity and damping that magnetic suspension closed-loop system corresponds, the dynamic and static performance of rotor response has been guaranteed promptly, automatic control's reliability improves greatly.
It should be noted that: the magnetic suspension bearing related in the application not only can be a rotor supported by an active magnetic suspension bearing, but also can be a magnetic suspension ball, a magnetic suspension rack, a machine tool cutter, a magnetic suspension train and the like; the bearing is not only suitable for magnetic suspension bearings, but also suitable for radial magnetic suspension bearings; the magnetic suspension bearing is not only suitable for a magnetic suspension bearing which is vertically arranged, but also suitable for a magnetic suspension bearing which is horizontally arranged; the magnetic suspension bearing is not only suitable for asymmetric magnetic suspension bearings, but also suitable for symmetric magnetic suspension bearings.
The online adjusting system for the blade top clearance of the magnetic suspension compressor provided by the embodiment 2 of the application firstly establishes the mathematical model of the magnetic suspension bearing, then obtains the adaptive PID controller according to the balance position, and when the balance position is changed, the parameters of the adaptive PID controller are automatically changed without manually debugging the parameters, so that the stability and good response performance of the system can be still ensured, and the real-time adjustment of the blade top clearance is realized when the compressor normally operates.
Example 3
Please refer to fig. 4, which is a schematic diagram of a terminal structure according to embodiment 3 of the present application. The terminal 50 comprises a processor 51, a memory 52 coupled to the processor 51.
The memory 52 stores program instructions for implementing the method for online adjustment of the blade tip clearance of a magnetic levitation compressor as described.
The processor 51 is operable to execute program instructions stored in the memory 52 to control the on-line adjustment of the blade tip clearance of the maglev compressor.
The processor 51 may also be referred to as a CPU (Central Processing Unit). The processor 51 may be an integrated circuit chip having signal processing capabilities. The processor 51 may also be a general purpose processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), an off-the-shelf programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
Example 4
Please refer to fig. 5, which is a schematic structural diagram of a storage medium according to an embodiment of the present application. The storage medium of the embodiment of the present application stores a program file 61 capable of implementing all the methods described above, where the program file 61 may be stored in the storage medium in the form of a software product, and includes several instructions to enable a computer device (which may be a personal computer, a server, or a network device) or a processor (processor) to execute all or part of the steps of the methods of the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a mobile hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, or terminal devices, such as a computer, a server, a mobile phone, and a tablet.
The above technical solution is described in detail with reference to specific embodiments below.
And (4) carrying out blade top gap self-adaptive adjustment on a certain vertically-arranged magnetic suspension compressor.
(1) Mathematical model for constructing magnetic suspension bearing
The mathematical model of the magnetic bearing system is shown in the following formula:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x and the instantaneous current of the coil is marked i, mu0Is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
Referring to fig. 6, the structural diagram of the axial magnetic bearing is shown, and the structural parameters of the axial magnetic bearing are shown in the following table:
(2) and acquiring a PID controller according to the balance position of the rotor of the magnetic suspension bearing.
In this embodiment, the value range of the relative stiffness coefficient μ required by self-defining the balance position is (1-3); the relative damping coefficient ξ is 75% and the relative integral coefficient η is 400.
In this embodiment, a PID controller is obtained according to the relative stiffness coefficient μ, the relative damping coefficient ξ and the relative integral coefficient η, and the PID controller is a PID controller
Wherein:
(3) And the PID controller carries out simulation test on the dynamic and static response capability of the magnetic suspension bearing.
And obtaining a mathematical model of the PID controller and the magnetic suspension bearing to construct a closed-loop control system according to the set mu, xi and eta. The other parameters remain unchanged at (0,2 ×)p) Range change equilibrium position x0And the tracking condition of the closed-loop system on the step reference signal and the anti-interference capability on the sinusoidal signal are examined. If the dynamic and static response capability of the system does not meet the requirements of the user, the second step is returned to change mu, xi and eta until the satisfactory performance is achieved.
(4) Analysis of simulation results
Firstly, analyzing simulation result of PID controller with fixed parameters
And comparing the parameters and giving out a PID control simulation result under the condition of fixed parameters.
When a fixed constant PID controller is used, the controller parameters are shown in the following table.
TABLE 1 PID controller with fixed parameters
| Name (R) | Numerical value |
| Coefficient of proportionality Kp | 0.32 |
| |
40 |
| Differential coefficient Kd | 7.5e-4 |
| Differential time |
1/400 Pi |
When respectively stepping from the zero initial position to the equilibrium position x0At 50 μm,100 μm,200 μm,300 μm,400 μm and 500 μm, the rotor displacement and control current responses were recorded as shown in FIG. 7. Step response simulation of the fixed-parameter PID controller of fig. 7, (a) x0 ═ 50 μm; (b) x0 ═ 100 μm; (c) x0 ═ 200 μm; (d) x0 ═ 300 μm; (e) x0 ═ 400 μm; (f) x0 ═ 500 μm.
It can be seen from figure 7 that a system with a fixed parameter controller can only maintain satisfactory performance in a particular narrow region. For example, the equilibrium position responds well at 200-300 μm, while it does not perform well in other areas. When less than 100 μm or more than 400 μm, the overshoot has exceeded the limit of the auxiliary bearing (0-600 μm). If less than 50 μm or greater than 500 μm, the system will be unstable because the controller cannot provide sufficient stiffness and damping.
② self-adaptive PID controller
Through iterative verification, the system can obtain satisfactory performance when the relative rigidity mu is 1.5, the relative damping coefficient xi is 0.75 and the relative integral coefficient eta is 400. When respectively stepping from the zero initial position to the equilibrium position x050 μm,100 μm,200 μm,300 μm,400 μm and 5At 00 μm, the rotor displacement and control current response are recorded as shown in FIG. 8. Step response simulation of the adaptive PID controller of FIG. 8 (a) x0＝50μm；(b)x0＝100μm；(c)x0＝200μm；(d)x0＝300μm；(e)x0＝400μm；(f)x0＝500μm。
The above results show that the adaptive controller can ensure that the rotor remains stable in any equilibrium position in the range of 50 to 500 μm. Within the range of 50-400 mu m, the good response performance of the rotor at any balance position is ensured. The range of 50-400 μm is recommended for practical debugging.
It should be noted that the response performance of the rotor at different equilibrium positions is not symmetrical about the central position of 300 μm, but the response performance is better at the position downward from the central position because the geometry of the upper and lower axial magnetic bearings in this embodiment is not symmetrical.
(4) Experiment of
Keeping the same control parameters and control strategies as the simulation adaptive controller and combining the formula
And writing the discrete data into the controller by a bilinear transformation method.
The monitoring and control of the experiment are completed based on the NI PXIe-8840 high-performance embedded product. The results of experiments are shown in FIG. 9 when the steps from the zero initial position to the equilibrium position x0 are 50 μm,100 μm,150 μm,200 μm,250 μm,300 μm and 350 μm, respectively. Experimental results of the step response in fig. 9, (a) x0 ═ 50 μm; (b) x0 ═ 100 μm; (c) x0 ═ 150 μm; (d) x0 ═ 200 μm; (e) x0 ═ 250 μm; (f) x0 ═ 300 μm; (f) x0 ═ 350 μm.
Experimental results show that the self-adaptive control strategy provided by the application ensures the stability of the rotor within the range of 50-350 mu m. However, when the equilibrium position is 50 μm, the settling time is longest and a large amount of noise is introduced. The reason may be that the rotor is too far from the upper AMB, and the nonlinear characteristics of the excited electromagnetic force are more prominent than those of the rotor at a closer distance. When the rotor is balanced at 350 μm, both the response time and the current overshoot are significant due to the large step size. In summary, the debugging range of the compressor in actual operation is recommended to be within 100-300 μm.
The foregoing is considered as illustrative only of the preferred embodiments of the invention, and is presented only for the purpose of illustrating the principles of the invention and not in any way to limit its scope. Any modifications, equivalents and improvements made within the spirit and principles of the present application and other embodiments of the present application without the exercise of inventive faculty will occur to those skilled in the art and are intended to be included within the scope of the present application.
Claims (12)
1. An online adjusting method for a blade top gap of a magnetic suspension compressor is characterized by comprising the following steps:
step S110: constructing a mathematical model of the magnetic suspension bearing;
step S120: acquiring a PID controller according to the rotor balance position of the magnetic suspension bearing;
step S130: the PID controller carries out simulation test on the dynamic and static response capability of the magnetic suspension bearing;
step S140: judging whether the simulation result meets the requirements; if yes, ending; if not, the process returns to step S120.
2. The method for online adjustment of the blade tip clearance of a magnetic levitation compressor as claimed in claim 1, wherein in step S110, a mathematical model of the magnetic levitation bearing is constructed, specifically:
the mathematical model of the magnetic suspension bearing is as follows:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x, the instantaneous current of the coil is marked i,μ0is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
3. The method for on-line adjustment of the blade tip clearance of the magnetic levitation compressor as claimed in claim 2, wherein in step S120, a PID controller is obtained according to the equilibrium position of the rotor of the magnetic levitation bearing, specifically comprising:
step S121: self-defining a relative stiffness coefficient mu, a relative damping coefficient xi and a relative integral coefficient eta required by the balance position;
step S122: and acquiring the PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta.
4. The on-line adjusting method for the blade top gap of the magnetic suspension compressor as claimed in claim 3, characterized in that the value range of the relative stiffness coefficient μ is 1-3, the value range of the relative damping coefficient ξ is 20% -80%, and the relative integral coefficient η is selected empirically.
5. The on-line adjusting method for the blade tip clearance of the magnetic levitation compressor as claimed in claim 4, wherein in step S122, a PID controller is obtained according to the relative stiffness coefficient μ, the relative damping coefficient ξ and the relative integral coefficient η, specifically:
obtaining a PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta, wherein the PID controller is
Wherein:
Kpis a proportionality coefficient, KdIs a differential coefficient, KiFor the integral coefficient, the following three formulas are respectively used for solving the following problems:
in the formula, GaIs the gain of the power amplifier, GsIs the gain of the sensor.
6. An on-line adjustment system for the blade tip clearance of a magnetic levitation compressor, comprising:
a model construction unit: the method is used for constructing a mathematical model of the magnetic suspension bearing;
a controller unit: the PID controller is obtained according to the balance position of the rotor of the magnetic suspension bearing;
a simulation unit: the PID controller is used for realizing the simulation test of the dynamic and static response capability of the magnetic suspension bearing;
a judging unit: and the simulation result is used for judging whether the simulation result meets the requirement or not.
7. The system for the on-line adjustment of the blade tip clearance of a magnetic levitation compressor as recited in claim 6, wherein the mathematical model of the magnetic levitation bearing system is:
in the formula, the equilibrium position of the rotor is marked as x0Bias current of winding coil is i0The instantaneous displacement of the rotor is marked x and the instantaneous current of the coil is marked i, mu0Is the magnetic permeability of vacuum, kiAnd kxCurrent stiffness and displacement stiffness, k, of the axial magnetic bearing, respectivelyuAnd kdRespectively the bearing parameters of the upper and lower axial magnetic bearings, the magnetic pole area of the upper axial magnetic suspension bearing and the magnetic pole area of the lower axial magnetic suspension bearing are respectively marked as AuAnd AdThe number of turns of the coil of the upper axial magnetic suspension bearing and the number of turns of the coil of the lower axial magnetic suspension bearing are respectively marked as NuAnd NdThe mass of the rotor is denoted m, the single-sided air gap of the magnetic bearing and the protective bearing is equal to x respectivelymAnd xp；
8. The system for the online adjustment of the blade tip clearance of a magnetic levitation compressor as recited in claim 7, wherein the controller unit comprises:
a parameter setting module: the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta which are required by self-defining the balance position;
a calculation module: and acquiring the PID controller according to the relative stiffness coefficient mu, the relative damping coefficient xi and the relative integral coefficient eta.
9. The system for on-line adjustment of the blade tip clearance of the magnetic levitation compressor as claimed in claim 8, wherein the relative stiffness coefficient μ ranges from 1 to 3, the relative damping coefficient ξ ranges from 20% to 80%, and the relative integral coefficient η is empirically selected.
10. The system for the on-line adjustment of the blade tip clearance of a magnetic levitation compressor as recited in claim 9, wherein the PID controller is
Wherein:
Kpis a proportionality coefficient, KdIs a differential coefficient, KiFor the integral coefficient, the following three formulas are respectively used for solving the following problems:
in the formula, GaIs the gain of the power amplifier, GsIs the gain of the sensor.
11. A terminal, comprising a processor, a memory coupled to the processor, wherein,
the memory stores program instructions for implementing the online adjustment method of the blade tip clearance of the magnetic levitation compressor as set forth in any one of claims 1-5;
the processor is configured to execute the program instructions stored by the memory to control online adjustment of a maglev compressor tip clearance.
12. A storage medium, characterized in that a program instructions executable by a processor for performing the method for online adjustment of the blade tip clearance of a magnetic levitation compressor as claimed in any one of claims 1 to 5 is stored.
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