CN108828951B - Magnetic suspension bearing multi-model robust undisturbed switching control method - Google Patents
Magnetic suspension bearing multi-model robust undisturbed switching control method Download PDFInfo
- Publication number
- CN108828951B CN108828951B CN201810817851.3A CN201810817851A CN108828951B CN 108828951 B CN108828951 B CN 108828951B CN 201810817851 A CN201810817851 A CN 201810817851A CN 108828951 B CN108828951 B CN 108828951B
- Authority
- CN
- China
- Prior art keywords
- controller
- model
- matrix
- rotor
- magnetic suspension
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000000725 suspension Substances 0.000 title claims abstract description 67
- 238000000034 method Methods 0.000 title claims abstract description 48
- 238000013507 mapping Methods 0.000 claims abstract description 21
- 230000008569 process Effects 0.000 claims abstract description 13
- 239000011159 matrix material Substances 0.000 claims description 75
- 238000012546 transfer Methods 0.000 claims description 44
- 238000006073 displacement reaction Methods 0.000 claims description 18
- 230000000694 effects Effects 0.000 claims description 11
- 238000005259 measurement Methods 0.000 claims description 10
- 230000001133 acceleration Effects 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 claims description 5
- 230000010354 integration Effects 0.000 claims description 5
- 238000013016 damping Methods 0.000 claims description 4
- 238000005457 optimization Methods 0.000 claims description 3
- 238000006243 chemical reaction Methods 0.000 claims description 2
- 238000012360 testing method Methods 0.000 description 7
- 238000010586 diagram Methods 0.000 description 5
- 238000011217 control strategy Methods 0.000 description 4
- 230000008859 change Effects 0.000 description 2
- 238000005034 decoration Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000013178 mathematical model Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000009467 reduction Effects 0.000 description 2
- 239000000126 substance Substances 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000012937 correction Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000013076 uncertainty analysis Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
Abstract
The invention discloses a magnetic suspension bearing multi-model robust undisturbed switching control method, which comprises the following three steps: measuring uncertainty of an interval to obtain an uncertainty mapping metric value in a rotating speed range; designing an interval robust controller, designing robust controllers under different rotating speeds based on a robust control theory according to the obtained uncertainty mapping metric values in different rotating speed ranges, and converting the robust controllers into a state space equation expression form; and step three, performing undisturbed switching control through the switching control device. The invention discloses a magnetic suspension bearing multi-model robust undisturbed switching control method which can effectively solve the problems of instability and buffeting in the switching process of different controllers.
Description
Technical Field
The invention discloses a magnetic suspension bearing multi-model robust undisturbed switching control method, and belongs to the technical field of magnetic suspension bearings.
Background
Along with the forward development of the magnetic suspension bearing rotating machinery in high rotating speed, light structure, large span and flexible direction, the magnetic suspension bearing rotating machinery has higher and higher requirements on the performance indexes of the whole machine. The magnetic suspension bearing as a core supporting component has the requirement that the working rotating speed of the magnetic suspension bearing is changed within the range of thousands of revolutions per minute to hundreds of thousands of revolutions per minute. Therefore, in the whole speed increasing and reducing process, the rotor system has to span a plurality of modal frequencies, the gyro moment influence is continuously increased along with the increase of the rotating speed, and the dynamic characteristic of the rotor system is changed rapidly in the change process in a large rotating speed range. In the design of the existing magnetic suspension shaft controller, a time-varying gyro matrix is mostly ignored, and a corresponding controller is designed according to the assumption of a linear time-invariant system.
The robust control strategy considers a linear time-varying gyro matrix as the uncertainty of the system, and the method is effective and feasible when the gyro effect does not change sharply. However, in the whole acceleration process from low speed to ultra high speed, a single robust control designed according to a single model has great conservatism, and therefore, the practical challenges are faced. The multi-model multi-controller switching control strategy is to utilize a plurality of models to approximate the dynamic characteristics of the system and design a plurality of controllers based on the plurality of models. The controller can achieve better control precision, tracking speed and stability for a complex system, but the phenomena of instability and buffeting exist in the switching process of different controllers.
Disclosure of Invention
The purpose of the invention is as follows: the single robust control designed for the single model has the defects of a plurality of challenges in practice due to greater conservation; the method has the advantages that the defects of instability and buffeting in the switching process of the multiple models and the multiple controllers are overcome, the method for controlling the robust undisturbed switching of the multiple models of the magnetic suspension bearing is provided, and the instability and the buffeting in the switching process of different controllers can be effectively solved.
The technical scheme is as follows:
a magnetic suspension bearing multi-model robust undisturbed switching control method comprises the following three steps:
step one, measuring the uncertainty of the interval,
(a) establishing a dynamic equation of the flexible rotor of the magnetic suspension bearing in a suspension state,
(b) obtaining the state space of the rotor model, correspondingly obtaining the transfer function of the rotor model,
(c) establishing a transfer function of an electric control system, establishing a transfer function of a rotor model simultaneously to obtain a transfer function of an electromechanical integrated model of the flexible rotor magnetic suspension bearing,
(d) setting a rotating speed range according to the operating condition of the flexible rotor magnetic suspension bearing system, taking a system model at the corresponding lower limit of the rotating speed in different rotating speed ranges as a nominal model,
(e) calculating the mapping measurement of the two models on a Nyquist curve by taking the rotating speed as a variable to obtain an uncertainty mapping measurement value in a rotating speed range;
designing an interval robust controller, designing robust controllers under different rotating speeds based on a robust control theory according to the obtained uncertainty mapping metric values in different rotating speed ranges, and converting the robust controllers into a state space equation expression form;
and step three, performing undisturbed switching control through the switching control device.
Further, in the step one (a), the dynamic equation of the flexible rotor of the magnetic bearing is as follows:
in the formula, MR，CR，GR，KRRespectively representing a rotor mass matrix, a rotor structure damping matrix, a gyroscopic effect matrix and a rotor rigidity matrix, wherein omega represents the working rotating speed of the rotor;q is the motion acceleration, speed and displacement of the rotor respectively; k is a radical ofxAnd k isiThe coefficient of the magnetic suspension bearing is self-coefficient.
Further, in the step one (b), the rotor model state space is:
order to
Gr＝[C11 04×216]
In the above formula, I216An identity matrix of order 216; c11Selecting a matrix for the node, obtained in the model state space conversion process, and the simplified formula (5) is as follows:
equation (6) A in the State space equation of the rotor modelrRelating to the rotating speed omega, writing the state space equation of the rotor model obtained by the formula (6) into a transfer function form Gamb。
Further, in step one (c), the transfer function of the electronic control system includes a sensor transfer function G of the electronic control systems(s) power amplifier transfer function Ga(s), DSP delay transfer function GD(s) a transfer function of the magnetic suspension bearing rotor and the electric control system is combined, the transfer function of the electromechanical integrated model of the magnetic suspension bearing of the flexible rotor is as follows,
G(s)＝Gamb(s)Gs(s)Ga(s)GD(s) (7)
wherein, the transfer function of the sensor in the electric control system adopts a proportional link for modeling and fitting, and the transfer function of the power amplifier adopts a first-order inertia link for fitting, specifically speaking, the transfer function of the power amplifier adopts a first-order inertia link for modeling and fittingThe DSP time delay transfer function adopts a 2-order Pade model to carry out approximate fitting, specificallya. b and c are coefficients; ts is the DSP sample time, A is the current, and V is the voltage.
Further, in the step one (d), the set rotation speed ranges are respectively Ω0～Ω1，Ω1～Ω2，Ω2～Ω3，...，Ωn-1～Ωn。
Further, in the step one (e), the rotating speed is taken as a variable, the mapping metric of the two models on the Nyquist curve is calculated, the uncertainty mapping metric value in the rotating speed range is obtained,
……
wherein the content of the first and second substances,expressed in the speed range omegan-1～ΩnInner and lower rotation speed limit omegan-1The rotor model of (a), i.e. the nominal model in the current rotational speed range,represents the nth rotation speed range omegan-1～ΩnAnd mapping the uncertainty of the model and the nominal model at the current rotating speed.
Further, in step two, the robust controller is converted into a state space equation expression form as follows:
……
in the state space, Ai，Bi，Ci，DiFor each controller matrix.
Further, in step three, the switching control device includes n controllers, and the controller i includes a controller matrix Ai，Bi，Ci，DiThe controller input signal Ini is multiplied by a Bi matrix and enters the accumulator ia; the value of the accumulator ia passes through an integrator 1/s, and then is multiplied by a matrix Ci to enter an accumulator ib; multiplying the input signal Ini of the controller by a matrix Di, and entering an accumulator ib; multiplying the output signal of the Ci matrix by an Ai matrix, and positively and negatively feeding the output signal of the Ci matrix into an accumulator ia; the K1 matrix output signal is fed back and forth to the accumulator ia; the output value Outi of the accumulator ib is the output value of the controller i, when the controller 2m-1 works on line, the Kalman gain matrix K2m-1 has no input signal, the controller inputs a signal In2m-1, the output signal Out2m-1 of the controller is connected to the controlled system, the output signal of the controlled system is input to the displacement sensor, the output signal of the displacement sensor is differed with the reference signal r to form an error signal, and the error signal is input to the controller 2m-1In, the input In2m of the offline controller 2m does not access the displacement sensor signal, the output Out2m does not access the controlled system, and the state of the kalman gain matrix K2m at this time is 0; when the controller 2m is ready to enter switching, an offline controller 2m is started, an input In2m of the offline controller 2m is accessed to a displacement sensor signal, but an output Out2m is not accessed to a controlled system, an input end of a Kalman gain matrix K2m of the offline controller 2m is accessed to an output Out2m-1 of the online controller 2m-1, the Kalman gain matrix K2m continuously carries Out gain optimization calculation on a difference value and a difference first-order derivative between Out2m-1 and Out2m, and when the output Out2m-1 of the controller 2m-1 is the same as an output Out2m of the controller 2m and the first-order derivatives of the two output values are the same, switching is carried Out; during switching, the output Out2m-1 of the controller 2m-1 is disconnected with the controlled system, and simultaneously, the output Out2m of the controller 2m is connected to the controlled system; after switching, the input end of the controller 2m-1 disconnects the accessed error signal; the input of the Kalman gain matrix K2m-1 of the controller 2m-1 is accessed to the output signal Out2m of the controller 2m to wait for the subsequent switching requirement; after switching, the input In2m of the controller 2m is switched In to the sensor signal, the kalman gain matrix K2m of the controller 2m is switched off from the input signal, the output value of the kalman gain matrix K2m of the controller 2m is slowly and continuously reduced to zero, the controller 2m-1 becomes an offline controller, and the controller 2m becomes an online controller
Has the advantages that:
the invention has the following beneficial effects
(1) Aiming at different working conditions, a robust controller corresponding to the working conditions is established;
(2) the undisturbed switching among different controllers of the magnetic suspension bearing is realized, and the performance and the stability of the magnetic suspension bearing are improved;
(3) the Kalman gain matrix is high in calculation efficiency, and the calculation amount is not increased along with the increase of recursion.
Drawings
FIG. 1: designing a schematic diagram of a robust controller at different rotating speeds.
FIG. 2: the on-line controller 1 and the off-line controller 2 before switching are schematically shown in structure.
FIG. 3: the switched off-line controller 1 and on-line controller 2 are schematically shown in structure.
FIG. 4: embodiment 1 does not adopt the method of the present invention and directly switches the effect diagram.
FIG. 5: the method of the invention is adopted in the specific embodiment 1, and a disturbance-free switching effect graph is obtained.
FIG. 6: the specific embodiment 2 directly switches the effect diagram without adopting the method of the invention.
FIG. 7: the method of the invention is adopted in the specific embodiment 2, and a disturbance-free switching effect graph is obtained.
Detailed Description
The invention is further explained below with reference to the drawings.
The technical scheme is divided into three steps: and (3) carrying out interval uncertainty analysis, designing an interval robust controller and realizing a disturbance-free switching control strategy.
Step one, measuring uncertainty of interval
(a) Establishing a dynamic equation of the flexible rotor of the magnetic suspension bearing in a suspension state,
(b) obtaining the state space of the rotor model, correspondingly obtaining the transfer function of the rotor model,
(c) establishing a transfer function of an electric control system, establishing a transfer function of a rotor model simultaneously to obtain a transfer function of an electromechanical integrated model of the flexible rotor magnetic suspension bearing,
(d) setting a rotating speed range according to the operating condition of the flexible rotor magnetic suspension bearing system, taking a system model at the corresponding lower limit of the rotating speed in different rotating speed ranges as a nominal model,
(e) and calculating the mapping measurement of the two models on a Nyquist curve by taking the rotating speed as a variable to obtain an uncertainty mapping measurement value in a rotating speed range.
In a suspension state, modeling the supporting electromagnetic force provided by the magnetic suspension bearing to reflect the current rigidity and the displacement rigidity of the electric control system, and establishing a dynamic equation of the flexible rotor of the magnetic suspension bearing:
in the formula, MR，CR，GR，KRRespectively representing a rotor mass matrix, a rotor structure damping matrix, a gyroscopic effect matrix and a rotor rigidity matrix, wherein omega represents the working rotating speed of the rotor;q is the motion acceleration, speed and displacement of the rotor respectively; k is a radical ofxAnd k isiThe coefficient of the magnetic suspension bearing is self-coefficient.
K in the formula (1)xMoving to the left of the equation:
formula (2) left multiplicationThe following can be obtained:
taking the state quantity:
obtaining a rotor model state space:
order to
Cr＝[C11 04×216]
The simplified formula (5) is:
equation (6) A in the State space equation of the rotor modelrIs related to the rotational speed omega. Writing the state space equation of the rotor model obtained by the formula (6) into a transfer function form GambIf the rotor speed is omega1Then the corresponding rotor model transfer function is recorded as
Based on the test frequency characteristic, the transfer function G of the sensor in the electric control system is respectively established by utilizing the model correction technologys(s) power amplifier model Ga(s), DSP delay model GD(s), establishing a transfer function of the magnetic suspension bearing rotor and an electric control system simultaneously to obtain a transfer function of an electromechanical integrated model of the magnetic suspension bearing of the flexible rotor:
G(s)＝Gamb(s)Gs(s)Ga(s)GD(s) (7)
setting the rotating speed ranges to be omega respectively according to the running condition of the flexible rotor magnetic suspension bearing system0～Ω1，Ω1～Ω2，Ω2～Ω3，...，Ωn-1～ΩnAnd taking the system model at the corresponding lower rotation speed limit in different rotation speed ranges as a nominal model.
Transfer function G defining two system models1、G2The mapping metric on the Nyquist curve is:
and calculating the mapping measurement of the two models on the Nyquist curve by taking the rotating speed as a variable to obtain an uncertainty mapping measurement value in a rotating speed range.
From equation (8), the uncertainty in the speed range is obtained:
……
wherein the content of the first and second substances,expressed in the speed range omegan-1～ΩnInner and lower rotation speed limit omegan-1The rotor model is a nominal model in the current rotating speed range.Represents the nth rotation speed range omegan-1～ΩnAnd mapping the uncertainty of the model and the nominal model at the current rotating speed.
And step two, designing an interval robust controller.
And designing robust controllers at different rotating speeds based on a robust control theory according to the obtained uncertainty mapping metric values in different rotating speed ranges, as shown in figure 1. The designed controllers are respectively marked as G1, G2... GN, and then converted into a state space equation expression form:
……
in the state space, Ai，Bi，Ci，DiAre the respective corresponding matrices of the controllers.
And step three, realizing a disturbance-free switching control strategy.
To implement a bumpless switching process, a switching architecture as shown in fig. 2 is constructed. Controllers each Ai，Bi，Ci，DiThe matrix connection form is shown in the dotted line box of FIG. 2, all controllers Ai，Bi，Ci，DiThe matrix coupling is the same.
Taking controllers 1 and 2 as an example, as shown in fig. 2, 1/s in the figure is an integrator of the controller, Σ 1a is an accumulator 1a of the controller 1, and Σ 1b is an accumulator 1b of the controller 1; k1 is the kalman gain matrix of controller 1;
when the controller 1 works, an input signal In1 is multiplied by a B1 matrix and enters an accumulator 1 a; multiplying the input signal by a D1 matrix, and entering an accumulator 1 b; the output signal of the C1 matrix enters an accumulator 1 b; the output signal of the C1 matrix is multiplied by the A1 matrix and fed to the accumulator 1a in positive and negative mode; the K1 matrix output signal is fed back and forth to accumulator 1 a; the value of the accumulator 1a passes through an integrator 1/s and is multiplied by a C1 matrix to enter an accumulator 1 b; the value of accumulator 1b, Out1, is the controller 1 output value.
As shown in fig. 2, the controller 1 is an online operation controller in the figure; the controller 2 is in the figure an off-line controller, i.e. a controller waiting for a handover.
As shown in fig. 2, the controller 1 is operating on-line, when there is no input signal to the kalman gain matrix K1. The input signal of the controller is In1, the output signal Out1 of the controller is connected to the controlled system, the output signal of the controlled system is input to the displacement sensor, the output signal of the displacement sensor is different from the reference signal r to form an error signal which is input to the controller 1, the input In2 of the offline controller 2 is not connected to the sensor signal, and the output Out2 is not connected to the controlled system.
When the switching is ready to be carried Out, the off-line controller 2 is started, the input In2 of the off-line controller 2 is accessed to a displacement sensor signal, but the output Out2 is not accessed to a controlled system, the input end of the Kalman gain matrix K2 of the off-line controller 2 is accessed to the output Out1 of the on-line controller 1, and the controller 2 synchronously inputs the output value of Out2 to the Kalman gain matrix K2. The Kalman gain matrix K2 continues to perform gain optimization calculations on the difference between Out1 and Out2 and the first derivative of the difference. Switching occurs when the output Out1 of controller 1 is the same value as the output Out2 of controller 2 and the first derivative of the two output values is the same.
During switching, the output Out1 of the controller 1 is disconnected from the controlled system; at the same time, the output Out2 of controller 2 is accessed into the controlled system.
After the handover, as shown in fig. 3: input In1 of controller 1 disconnects the switched-In error signal; the input of the kalman gain matrix K1 of controller 1 is connected to the output Out2 of controller 2, waiting for a subsequent switching demand. The input In2 of the controller 2 receives a sensor signal; the kalman gain matrix K2 of the controller 2 disconnects the input signal; the kalman gain matrix K2 output values of the controller 2 slowly decrease continuously to zero. After switching, the controller 1 becomes an offline controller; the controller 2 becomes an online controller.
The switching process is realized in the controller through an algorithm without mechanical operation, and the switching process takes the switching between the controller 1 and the controller 2 as an example; the switching process between every two other controllers is consistent with the switching method.
Example 1
(1) Under the suspension state, modeling the supporting electromagnetic force provided by the magnetic suspension bearing into the current rigidity and the displacement rigidity of an electric control system, and establishing a transfer function G of the flexible rotor of the magnetic suspension bearingamb。
(2) And (3) obtaining an electromechanical integration model transfer function of the flexible rotor magnetic suspension bearing by taking the test frequency characteristic as a basis:
G(s)＝Gamb(s)Gs(s)Ga(s)GD(s)
(2) and respectively calculating the uncertainty of the flexible rotor magnetic suspension bearing electromechanical integration model in the corresponding rotating speed interval based on an interval uncertainty measuring method in the rotating speed range of 0-3000rpm and 3000-6000rpm by taking the rotating speed as a variable.
(3) Based on a mathematical model and the uncertainty of a controlled system in two working rotating speed intervals, respectively designing a controller 1 suitable for a rotating speed interval of 0-3000rpm and a controller 2 suitable for a rotating speed interval of 3000-6000 rpm;
(4) with the form of fig. 2, a controller and a kalman gain matrix are constructed.
(5) The magnetic suspension bearing rotor system starts suspension, and the rotating speed is increased from 0rpm to 3000 rpm;
(6) starting a non-disturbance switching program, and switching at the rotating speed of 3000rpm, wherein the specific switching method is consistent with the third step in the technical scheme;
(7) FIG. 4 is a test data chart of direct switching without using the method of the present invention, and it can be seen that the vibration of the rotor system of the magnetic suspension bearing at the moment of switching is more obvious without using the method of the present invention; fig. 5 is a test data diagram of undisturbed switching by using the method of the present invention, and it can be seen from the figure that the vibration reduction of the rotor system of the magnetic suspension bearing at the moment of switching is very obvious and the effect is good by using the method of the present invention.
Example 2
(1) Under the suspension state, modeling the supporting electromagnetic force provided by the magnetic suspension bearing into the current rigidity and the displacement rigidity of an electric control system, and establishing a transfer function G of the flexible rotor of the magnetic suspension bearingamb。
(2) And (3) obtaining an electromechanical integration model transfer function of the flexible rotor magnetic suspension bearing by taking the test frequency characteristic as a basis:
G(s)＝Gamb(s)Gs(s)Ga(s)GD(s)
(2) and respectively calculating the uncertainty of the flexible rotor magnetic suspension bearing electromechanical integration model in the corresponding rotating speed interval based on an interval uncertainty measuring method in the rotating speed range of 0-6000rpm and the range of 6000-9000rpm by taking the rotating speed as a variable.
(3) Respectively designing a controller 1 suitable for a rotating speed interval of 0-6000rpm and a controller 2 suitable for a rotating speed interval of 6000-9000rpm based on a mathematical model and the uncertainty of a controlled system in two working rotating speed intervals;
(4) with the form of fig. 2, a controller and a kalman gain matrix are constructed.
(5) The magnetic suspension bearing rotor system starts suspension, and the rotating speed is increased from 0rpm to 6000 rpm;
(6) starting a non-disturbance switching program, and switching at the rotating speed of 6000rpm, wherein the specific switching method is consistent with the third step in the technical scheme;
(7) FIG. 6 is a test data chart of direct switching without using the method of the present invention, and it can be seen that the vibration of the rotor system of the magnetic suspension bearing at the moment of switching is more obvious without using the method of the present invention; fig. 7 is a test data diagram of undisturbed switching by using the method of the present invention, and it can be seen from the figure that the vibration reduction of the rotor system of the magnetic suspension bearing at the moment of switching is very obvious and the effect is good by using the method of the present invention.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (8)
1. A magnetic suspension bearing multi-model robust undisturbed switching control method is characterized by comprising the following three steps:
step one, measuring the uncertainty of the interval,
(a) establishing a dynamic equation of the flexible rotor of the magnetic suspension bearing in a suspension state,
(b) obtaining the state space of the rotor model, correspondingly obtaining the transfer function of the rotor model,
(c) establishing a transfer function of an electric control system, establishing a transfer function of a rotor model simultaneously to obtain a transfer function of an electromechanical integrated model of the flexible rotor magnetic suspension bearing,
(d) setting a rotating speed range according to the operating condition of the flexible rotor magnetic suspension bearing system, taking a system model at the corresponding lower limit of the rotating speed in different rotating speed ranges as a nominal model,
(e) calculating the mapping measurement of the two models on a Nyquist curve by taking the rotating speed as a variable to obtain an uncertainty mapping measurement value in a rotating speed range;
designing an interval robust controller, designing robust controllers under different rotating speeds based on a robust control theory according to the obtained uncertainty mapping metric values in different rotating speed ranges, and converting the robust controllers into a state space equation expression form;
and step three, performing undisturbed switching control through the switching control device.
2. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in the first step (a), the dynamic equation of the flexible rotor of the magnetic suspension bearing is as follows:
in the formula, MR，CR，GR，KRRespectively representing a rotor mass matrix, a rotor structure damping matrix, a gyroscopic effect matrix and a rotor rigidity matrix, wherein omega represents the working rotating speed of the rotor;q is the motion acceleration, speed and displacement of the rotor respectively; k is a radical ofxAnd k isiThe coefficient of the magnetic suspension bearing is self-coefficient; and i is the control current of the magnetic bearing.
3. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in the step one (b), the rotor model state space is:
in the formulaq is the motion acceleration, speed and displacement of the rotor respectively;is the inverse of the rotor mass matrix; cR，GR，KRRespectively representing a rotor structure damping matrix, a gyro effect matrix, a rotor rigidity matrix, kxAnd k isiThe coefficient of the magnetic suspension bearing is self-coefficient;
order to
Cr＝[C11 04×216]
In the above formula, I216An identity matrix of order 216; c11Selecting a matrix for the node, obtained in the model state space conversion process, and the simplified formula (5) is as follows:
equation (6) A in the State space equation of the rotor modelrRelating to the rotating speed omega, writing the state space equation of the rotor model obtained by the formula (6) into a transfer function form Gamb。
4. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in the step one (c), the transfer function of the electric control system comprises a sensor transfer function G in the electric control systems(s) power amplifier transfer function Ga(s), DSP delay transfer function GD(s) simultaneous magnetic bearing rotor transfer function Gamb(s) and an electric control system transfer function, and the flexible rotor magnetic suspension bearing electromechanical integration model transfer function is as follows,
G(s)＝Gamb(s)Gs(s)Ga(s)GD(s) (7)
wherein, the transfer function of the sensor in the electric control systemThe method adopts a proportional link for modeling and fitting, and a power amplifier transfer function adopts a first-order inertia link for fitting, specificallyThe DSP time delay transfer function adopts a 2-order Pade model to carry out approximate fitting, specificallya. b and c are coefficients; t issFor DSP sample time, A is the current and V is the voltage.
5. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in the step one (d), the set rotation speed ranges are respectively omega0～Ω1，Ω1～Ω2，Ω2～Ω3，…，Ωn-1～Ωn。
6. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in the first step (e), the mapping measurement of the two models on the Nyquist curve is calculated by taking the rotating speed as a variable, the uncertainty mapping measurement value in the rotating speed range is obtained,
……
wherein, G (e)jw) A nominal model of the rotor is represented,expressed in the speed range omegan-1～ΩnInner and lower rotation speed limit omegan-1The rotor model of (a), i.e. the nominal model in the current rotational speed range,represents the nth rotation speed range omegan-1～ΩnAnd mapping the uncertainty of the model and the nominal model at the current rotating speed.
7. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in the second step, the robust controller is converted into a state space equation expression form as follows:
……
in the state space, Ai，Bi，Ci，DiThe number of control signals for each controller matrix, x,and y are the state quantity, the state quantity 1 derivative and the output quantity, respectively.
8. The magnetic suspension bearing multi-model robust undisturbed switching control method as claimed in claim 1, wherein: in step three, the switching control device comprises n controllers, and the controller i comprises a controller matrix Ai，Bi，Ci，DiProduct of qi and bloodSeparator 1/s, accumulator ia, accumulator ib, kalman gain matrix Ki, i ═ 1, 2, 3. um. et seq. 2m-1, 2m. et seq. natural number, m. et seq. the controller input signal Ini is multiplied by the Bi matrix, and enters accumulator ia; the value of the accumulator ia passes through an integrator 1/s, and then is multiplied by a matrix Ci to enter an accumulator ib; multiplying the input signal Ini of the controller by a matrix Di, and entering an accumulator ib; multiplying the output signal of the Ci matrix by an Ai matrix, and positively and negatively feeding the output signal of the Ci matrix into an accumulator ia; the K1 matrix output signal is fed back and forth to the accumulator ia; the output value Outi of the accumulator ib is the output value of the controller i, when the controller 2m-1 works online, the Kalman gain matrix K2m-1 has no input signal, the controller inputs a signal In2m-1, the output signal Out2m-1 of the controller is accessed to the controlled system, the output signal of the controlled system is input to the displacement sensor, the output signal of the displacement sensor is differed from the reference signal r to form an error signal which is input to the controller 2m-1, the input In2m of the offline controller 2m is not accessed to the signal of the displacement sensor, the output Out2m is not accessed to the controlled system, and the state of the Kalman gain matrix K2m at the moment is 0; when the controller 2m is ready to enter switching, an offline controller 2m is started, an input In2m of the offline controller 2m is accessed to a displacement sensor signal, but an output Out2m is not accessed to a controlled system, an input end of a Kalman gain matrix K2m of the offline controller 2m is accessed to an output Out2m-1 of the online controller 2m-1, the Kalman gain matrix K2m continuously carries Out gain optimization calculation on a difference value and a difference first-order derivative between Out2m-1 and Out2m, and when the output Out2m-1 of the controller 2m-1 is the same as an output Out2m of the controller 2m and the first-order derivatives of the two output values are the same, switching is carried Out; during switching, the output Out2m-1 of the controller 2m-1 is disconnected with the controlled system, and simultaneously, the output Out2m of the controller 2m is connected to the controlled system; after switching, the input end of the controller 2m-1 disconnects the accessed error signal; the input of the Kalman gain matrix K2m-1 of the controller 2m-1 is accessed to the output signal Out2m of the controller 2m to wait for the subsequent switching requirement; after switching, the input In2m of the controller 2m is switched In to the sensor signal, the kalman gain matrix K2m of the controller 2m disconnects the input signal, the output value of the kalman gain matrix K2m of the controller 2m is slowly and continuously reduced to zero, the controller 2m-1 becomes an offline controller, and the controller 2m becomes an online controller.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810817851.3A CN108828951B (en) | 2018-07-20 | 2018-07-20 | Magnetic suspension bearing multi-model robust undisturbed switching control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810817851.3A CN108828951B (en) | 2018-07-20 | 2018-07-20 | Magnetic suspension bearing multi-model robust undisturbed switching control method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108828951A CN108828951A (en) | 2018-11-16 |
| CN108828951B true CN108828951B (en) | 2019-12-24 |
Family
ID=64139993
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810817851.3A Active CN108828951B (en) | 2018-07-20 | 2018-07-20 | Magnetic suspension bearing multi-model robust undisturbed switching control method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108828951B (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113741181A (en) * | 2021-01-18 | 2021-12-03 | 南京航空航天大学 | Rotating speed self-adaptive magnetic suspension rotor system odd harmonic current suppression method |
Family Cites Families (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN100587633C (en) * | 2007-12-17 | 2010-02-03 | 北京航空航天大学 | Method for designing precession cross parameter of magnetic levitation high speed rotor |
| CN102425559B (en) * | 2011-11-02 | 2014-06-25 | 北京中科科仪股份有限公司 | Smooth control method in speed-down process of magnetic suspension molecular pump |
| CN102868352A (en) * | 2012-10-12 | 2013-01-09 | 三弘重工科技有限公司 | Induction motor vector control system with rotor resistance robustness and induction motor vector control system method |
| CN104503238B (en) * | 2014-12-15 | 2017-03-22 | 北京航空航天大学 | Current harmonic suppression method for magnetic suspension rotor system based on self-adaptive repetitive controller |
| CN104697525B (en) * | 2015-01-06 | 2018-09-21 | 中国人民解放军装备学院 | A kind of attitude angular velocity measurement method based on magnetic suspension control sensitivity gyro configuration |
| CN105549393B (en) * | 2015-12-26 | 2018-06-12 | 曲阜师范大学 | A kind of control method of magnetic suspension system floating and descent |
| CN107656437B (en) * | 2017-08-14 | 2019-07-09 | 南京航空航天大学 | Magnetic suspension rotor system based on disturbance observer mismatches the control method of disturbance |
| CN107727088A (en) * | 2017-10-13 | 2018-02-23 | 河南工业大学 | A kind of full active magnet bearing systems axes of inertia discrimination method based on nonlinear autoregressive |
-
2018
- 2018-07-20 CN CN201810817851.3A patent/CN108828951B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN108828951A (en) | 2018-11-16 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| JP6774637B2 (en) | Control device and control method | |
| CN111360830B (en) | Vibration control method of flexible mechanical arm based on cooperative tracking | |
| CN110018638B (en) | Neural network active disturbance rejection controller for alternating-current radial magnetic bearing and construction method thereof | |
| CN107612445B (en) | Control method of follow-up speed regulation system with load acceleration feedback | |
| CN105867136A (en) | Parameter identification based multi-motor servo system synchronization and tracking control method | |
| CN108303885A (en) | A kind of motor position servo system self-adaptation control method based on interference observer | |
| CN109495050B (en) | Double-motor torque synchronous model prediction control method based on quadratic value function | |
| CN108181813A (en) | A kind of fractional order sliding-mode control of flexible joint mechanical arm | |
| CN107193211B (en) | Single-arm manipulator controller based on active disturbance rejection and inversion technology and design method thereof | |
| CN109067274A (en) | The integral sliding mode control method of PMSM Speed based on interference compensation | |
| CN105680746A (en) | Method for designing current of permanent-magnet synchronous motor and parameter of speed controller PI by using online particle swarm optimization algorithm | |
| CN111103792B (en) | Robot control method, device, electronic equipment and readable storage medium | |
| CN108828951B (en) | Magnetic suspension bearing multi-model robust undisturbed switching control method | |
| CN110287505B (en) | Aircraft stability analysis method | |
| CN108415253B (en) | Control method of flywheel battery magnetic bearing system based on Markov jump theory | |
| CN111404432B (en) | Finite set model prediction direct speed control method of permanent magnet synchronous motor | |
| WO2021237910A1 (en) | Active magnetic bearing controller construction method based on table lookup method | |
| CN110649845A (en) | Photoelectric turntable position tracking control method based on robust generalized predictive control | |
| CN107528514B (en) | Approximate discrete fast terminal sliding mode control method of PMSM speed regulation system | |
| CN103631281B (en) | A kind of oil motor angular velocity servo system | |
| CN109189075B (en) | Model-free adaptive course control method for ship by using fuzzy forgetting factor | |
| CN113014167A (en) | Permanent magnet motor nonsingular terminal sliding mode control method based on disturbance observer | |
| Xun et al. | An exoskeleton joint output force control technology based on improved ADRC | |
| CN116442223A (en) | Nonlinear dynamic controller design method for track tracking of manipulator system | |
| CN110932609B (en) | Self-adaptive recursion control method and system for multi-motor servo system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |