CN110007605B - Robust prediction control method of repelling magnetic suspension device - Google Patents

Robust prediction control method of repelling magnetic suspension device Download PDF

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CN110007605B
CN110007605B CN201910419115.7A CN201910419115A CN110007605B CN 110007605 B CN110007605 B CN 110007605B CN 201910419115 A CN201910419115 A CN 201910419115A CN 110007605 B CN110007605 B CN 110007605B
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周锋
朱培栋
谢明华
陈俊东
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Changsha University
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Abstract

The invention discloses a robust prediction control method of a repulsion type magnetic suspension device, which comprises the steps of collecting historical data N groups of input voltage and output distance of the repulsion type magnetic suspension device, and establishing a nonlinear model; establishing a convex polyhedron state space model of the repelling magnetic suspension device based on the nonlinear model; and obtaining an optimized objective function for the robust control of the repelling magnetic suspension device based on the convex polyhedron state space model, and solving the objective function to obtain an input voltage value acting on a winding of the repelling magnetic suspension device at the moment t. The invention considers the influence of system modeling error and uncertain interference in the controller design, and is a control method with stable robustness and strong applicability.

Description

Robust prediction control method of repelling magnetic suspension device
Technical Field
The invention relates to the field of automatic control, in particular to a robust prediction control method for a repulsive magnetic suspension device.
Background
The magnetic suspension technology is an electromechanical integration technology, eddy current is formed on the surface of metal by utilizing a high-frequency magnetic field, and then Lorentz magnetic force is generated to suspend metal equipment, so that the contact between the equipment is effectively avoided, the mutual friction is reduced, and the application prospect is wide. The magnetic suspension system is a complex nonlinear system integrating control of electric magnetic force, air gap, current and the like, and an accurate mathematical model of the magnetic suspension system is difficult to obtain in practical application. The identification modeling method based on data driving is a mathematical modeling method independent of system physical mechanism, only uses input and output data of an object to perform modeling, and is widely applied to modeling of a complex nonlinear system.
The PID controller has a simple control algorithm structure and does not depend on an accurate mathematical model of a controlled object, so that the PID controller is widely applied to magnetic suspension control. However, the global control characteristic of the PID controller for a complex nonlinear object is poor, and particularly for a magnetic levitation ball control system with extremely high stability requirement, the situation of instantaneous uncontrolled falling of a levitation ball is very easy to occur in a large range near a boundary. The linear quadratic regulator is a control algorithm based on a controlled object state space model, and is widely applied to control of complex systems. But the robustness and stability of the control still need to be improved because the control is highly dependent on the accuracy of the controlled object model. Model predictive control is an advanced computer control algorithm generated in industrial process control practice and is widely used in the control of complex industrial systems. Through the search of the existing documents, the patent of 'a wind power magnetic suspension yaw motor control method based on model predictive control' (application number: 201810076334.5) provides a predictive control method based on the physical mechanism model design of a magnetic suspension system. The patent "a magnetic levitation ball position control method" (application number: 201510180614.7) proposes a predictive control method based on an autoregressive model with function weight coefficients. However, the two methods do not consider the influence of system modeling errors and uncertain interferences in the design process of the predictive controller, and the stability and robustness of the algorithm cannot be effectively guaranteed. Meanwhile, in the process of establishing a system state space model for subsequent predictive controller design, the patent "201510180614.7" directly uses the state quantity of the system at the current moment to approximate and replace the future state quantity of the system, and performs direct single-point linearization approximation processing on the future state space model of the system, and the method itself can greatly affect the accuracy of the model.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a robust prediction control method of a repulsive magnetic suspension device aiming at the defects of the prior art, consider the influence of system modeling errors and uncertain interference, and improve the robustness and applicability of the control method.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a robust prediction control method of a repulsive magnetic suspension device comprises the following steps:
1) acquiring historical data N groups of input voltage and output distance of the repulsion type magnetic suspension device, and establishing a nonlinear model as follows:
Figure BDA0002065404760000021
Figure BDA0002065404760000022
wherein y (t) is the distance between the bottom of a globe of the repulsion type magnetic suspension device and the infrared reflection position sensor at the time t, namely the output quantity of the repulsion type magnetic suspension device, u (t) is the voltage applied to a winding by a control board of the repulsion type magnetic suspension device at the time t, namely the input quantity of the repulsion type magnetic suspension device, ξ (t +1) is a term containing modeling error and uncertain disturbance, and | ξ (t +1) | is less than or equal to 1; { a%0,t,a1,t,b1,t,a2,t,b2,tIs an inverse quadratic time-varying coefficient with respect to y (t), and | L | · | | survival of the electrically non-woven hair2Representing a two-norm operation; relevant parameters of non-linear model
Figure BDA0002065404760000023
Are obtained by optimization calculation through an R-SNPOM optimization method;
2) establishing a convex polyhedron state space model of the repelling magnetic suspension device based on the nonlinear model;
3) and obtaining an optimized objective function for the robust control of the repelling magnetic suspension device based on the convex polyhedron state space model, and solving the objective function to obtain an input voltage value acting on a winding of the repelling magnetic suspension device at the moment t.
The specific implementation process of the step 2) comprises the following steps:
1) the input increment and the output increment of the repulsive magnetic levitation device are defined as follows:
Figure BDA0002065404760000031
wherein y (t + j) is the output of the repulsive magnetic suspension device at the moment t + j; y issetThe expected value of the repulsive magnetic suspension device at the time t is shown; u (t + j) is the input of the repulsion type magnetic suspension device at the moment t + j, and u (t + j-1) is the input of the repulsion type magnetic suspension device at the moment t + j-1; j is an integer less than or equal to zero;
2) one-step forward prediction polynomial model of repelling magnetic suspension device
Figure BDA0002065404760000032
The structure is as follows:
Figure BDA0002065404760000033
Figure BDA0002065404760000034
wherein θ (t) is derived
Figure BDA0002065404760000035
ξ (t +1| t) is the quantity containing system modeling error and uncertain disturbance, and | ξ (t +1| t) | is less than or equal to 1;
3) based on the one-step forward prediction polynomial model and the definition of the input increment and the output increment of the system, the state space model corresponding to the polynomial model of the repulsive magnetic suspension device is deduced as follows:
Figure BDA0002065404760000036
Figure BDA0002065404760000037
wherein, the coefficient matrix A of the one-step forward prediction state vector X (t +1| t) of the repulsion type magnetic suspension devicet，BtAnd X (t | t) are respectively a parameter and a state calculated by the nonlinear model at the time t;
Figure BDA0002065404760000038
is the input increment of the repulsion type magnetic suspension device at the time t; xi (t) in a vector
Figure BDA0002065404760000039
And
Figure BDA00020654047600000310
to (c) to (d); a. thet+g|t，Bt+g|tAnd predicting a coefficient matrix of a state vector X (t + g +1| t) for the repelling magnetic suspension device in the future g steps.
The coefficient matrix At+g|t，Bt+g|tThe variation range is within the following convex polyhedron range:
Figure BDA0002065404760000041
wherein, { lambda ]t+g|t,μ1,2,3,4 is the linear coefficient of the convex polyhedron; the 4 vertexes of the convex polyhedron are (A)1,B1)，(A2,B2)，(A3,B3) And (A)4,B4) And, and:
Figure BDA0002065404760000042
wherein the content of the first and second substances,
Figure BDA0002065404760000043
and
Figure BDA0002065404760000044
are functions relating to y (t), respectively
Figure BDA0002065404760000045
Maximum and minimum values of;
Figure BDA0002065404760000046
and
Figure BDA0002065404760000047
are functions relating to y (t), respectively
Figure BDA0002065404760000048
Maximum and minimum values of.
In step 3), the optimization objective function is designed as follows:
Figure BDA0002065404760000049
wherein the content of the first and second substances,
Figure BDA00020654047600000410
I2is a unit array; x (t + g | t) is the system state quantity of the step t + g predicted by the model at the moment t;
Figure BDA00020654047600000411
inputting a control increment for the t + g step repulsion type magnetic suspension device predicted at the t moment;
Figure BDA00020654047600000412
g≥1，Ftthe future feedback control rate of the repulsion type magnetic suspension device at the time t.
Solving the optimized objective function by the following set of inequalities:
Figure BDA0002065404760000051
wherein, the symbol represents the symmetric structure of the matrix; { Q μ1,2,3,4 is an intermediate matrix variable generated by solving the inequality set, namely the convex optimization problem; gamma ray0+ gamma is the optimized target value { (A) of the convex optimization problemμ,Bμ) 1,2,3,4 is the vertex of the convex polyhedron model; gamma, gamma0、{Y,G, Q μ1,2,3,4 |, and
Figure BDA0002065404760000052
are all the minimized variable gamma0+ gamma solving intermediate variables obtained in the process; in solving the minimization problem
Figure BDA0002065404760000053
Then, the optimization function automatically searches for the gamma satisfying the constraint conditions of the inequality set0+ gamma minimum intermediate variables gamma, gamma0、{Y,G, Q μ1,2,3,4 |, and
Figure BDA0002065404760000054
when the inequality group has feasible solution, the optimization process is ended, and the obtained result is
Figure BDA0002065404760000055
I.e. the value of the input voltage acting on the windings of the magnetic levitation system at time t.
Compared with the prior art, the invention has the beneficial effects that: the invention takes the influence of external interference which cannot be avoided by an actual magnetic suspension system into consideration, the invention utilizes a time-varying coefficient quasi-linear regression structure model based on data driving to model the magnetic suspension system, and the influence of modeling error and external uncertain interference of the system is taken into consideration in the modeling process. In order to overcome the defect that the stability and robustness of an algorithm are difficult to ensure by a common prediction control method, the invention provides a robust prediction control method which can be realized by solving a linear matrix inequality set based on an established time-varying coefficient regression model of a magnetic suspension system, and the influence of system modeling errors and uncertain interference is considered in the design of a controller, so that the method is a control method with stable robustness and strong applicability.
Drawings
Fig. 1 is a structural view of a repulsive magnetic levitation apparatus to which the present invention is directed.
Detailed Description
The structure of the repulsive magnetic suspension device to which the invention is directed is shown in fig. 1, wherein: the globe comprises a globe shell (the radius is 20 cm), a square cylindrical magnet 3, a support between the globe shell 1 and the square cylindrical magnet 3, an infrared reflection position sensor 4 (the model is ST178H), an iron core 5 (the section radius is 2.5 cm), a winding 6 (the number of turns is 3500), and a control circuit board 7 based on a single chip microcomputer. The system controls the distance (the control distance range is 5 cm-25 cm) between the bottom of the globe 2 and the infrared reflection position sensor 4 by adjusting the voltage applied to the winding 6 by the control board 7 (the output voltage range is 0V-20V). The specific embodiment of the robust control method of the repulsive magnetic suspension device comprises the following steps of:
step 1: for the repulsive magnetic levitation device shown in fig. 1, a historical data 2500 group of input voltage and output distance of the system is acquired, and the following nonlinear model of the system is established:
Figure BDA0002065404760000061
Figure BDA0002065404760000062
in the above formula, y (t) is the distance between the bottom of the globe 2 and the infrared reflection position sensor 4 at the time t, namely the output quantity of the system, u (t) is the voltage applied to the winding 6 by the control board 7 at the time t, namely the input quantity of the system, ξ (t +1) is a term containing modeling error and uncertain disturbance, and | ξ (t +1) | is less than or equal to 1, and { a +1 ≦ is0,t,a1,t,b1,t,a2,t,b2,tIs an inverse quadratic time-varying coefficient with respect to y (t), and | L | · | | survival of the electrically non-woven hair2Representing a two-norm operation; relevant parameters of the model
Figure BDA0002065404760000063
Are obtained by optimization calculation through an R-SNPOM optimization method (the R-SNPOM optimization method is detailed in the documents of Zeng X, Peng H, Zhou F, 2018, A customized SNPOM for standing parameter estimation of RBF-AR (X) model, IEEE Transactions on Neural networks and Learning Systems,29, No.4, 779-:
Figure BDA0002065404760000064
Figure BDA0002065404760000065
step 2: based on the magnetic suspension system inverse quadratic function type time-varying coefficient regression model (1) established in the step 1, a convex polyhedron state space model of the system is established, and the specific process is as follows:
the input increment and the output increment of the magnetic levitation system are defined as follows:
Figure BDA0002065404760000071
in the above formula, y (t + j) is the output of the system at the time t + j; y isset∈[5,25]The expected value of the system at the moment t; u (t + j) is the input of the system at the moment t + j, and u (t + j-1) is the input of the system at the moment t + j-1; j is 0, -1, -2. From the above definitions, one step forward prediction of the model can be derived
Figure BDA0002065404760000072
The structure is as follows:
Figure BDA0002065404760000073
Figure BDA0002065404760000074
in the above formula, θ (t) is derived
Figure BDA0002065404760000075
The intermediate quantities that are generated in the process,ξ (t +1| t) is the amount of uncertainty interference and system modeling error involved, and | ξ (t +1| t) | ≦ 1.
The state vector of the magnetic levitation system is defined as follows:
Figure BDA0002065404760000076
based on the above definition of the one-step forward prediction polynomial model and the input/output deviation amount of the system, the state space model corresponding to the polynomial model of the system can be derived as follows:
Figure BDA0002065404760000077
Figure BDA0002065404760000081
in the above equation, the coefficient matrix A of the one-step forward prediction state vector X (t +1| t) of the systemt，BtAnd X (t | t) are the parameters and states respectively calculated by the model identified in step S1 at time t;
Figure BDA0002065404760000082
the xi (t) cannot be accurately obtained at the moment t because the unknown interference term ξ (t +1| t) of the system is contained in the xi (t), but the change range of the xi (t) is less than or equal to 1 in the vector quantity because ξ (t +1| t) |
Figure BDA0002065404760000083
And
Figure BDA0002065404760000084
to (c) to (d); coefficient matrix A of forward predicted state vector X (t + g +1| t) for g steps in the future of the systemt+g|t，Bt+g|tThe variation range of the method cannot be directly calculated at the time t, but is within the following convex polyhedron range:
Figure BDA0002065404760000085
in the above formula, { λ t+g|t,μ1,2,3,4 is a linear coefficient of the polyhedron; the 4 vertexes of the polyhedron are (A)1,B1)，(A2,B2)，(A3,B3) And (A)4,B4) And is and
Figure BDA0002065404760000086
wherein the content of the first and second substances,
Figure BDA0002065404760000087
Figure BDA0002065404760000088
because y (t) e [5,25]Then, then
Figure BDA0002065404760000089
Figure BDA0002065404760000091
Thus, 4 vertices (A) of the convex polyhedron set (9) can be calculated1,B1)，(A2,B2)，(A3,B3) And (A)4,B4)。
And step 3: based on the system convex polyhedron state space model (7-8) established in the step 2, the optimized objective function design of the robust control method for the repulsive magnetic suspension device is as follows:
Figure BDA0002065404760000092
in the above formula, the first and second carbon atoms are,
Figure BDA0002065404760000093
i is a unit array; x (t + g | t) is the system state quantity of the step t + g predicted by the model at the moment t;
Figure BDA0002065404760000094
and inputting a control increment for the system at the step t + g predicted at the moment t. The future control rate structure design of the robust predictive controller is as follows:
Figure BDA0002065404760000095
g≥1，Ftthe future feedback control rate of the system at the time t.
Based on the designed controller optimization objective function, the optimal control rate of the robust control method for the repulsive magnetic levitation device is obtained by solving the following linear matrix inequality set:
Figure BDA0002065404760000096
in the above formula, the symbol represents a symmetric structure of the matrix; ft＝YG-1The future feedback control rate of the system at the moment t; { Q μ1,2,3,4 is an intermediate matrix variable generated by solving the convex optimization problem; gamma ray0+ gamma is the optimized target value of the convex optimization problem (12), and gamma are simultaneously0Also an intermediate quantity generated in the above optimization process; coefficient matrix At、Bt、
Figure BDA0002065404760000101
X (t | t) is a parameter matrix known at time t; { (A)μ,Bμ) And |. mu. ═ 1,2,3,4} is a vertex of the system polyhedron model (8) in the step 2. Gamma, gamma0、{Y,G, Q μ1,2,3,4 |, and
Figure BDA0002065404760000102
are all the minimized variable gamma0The intermediate variables obtained in the + gamma solution process. When solving the minimization problem (12), the optimization function automatically searches for gamma which meets the requirement according to the inequality constraint conditions (13-16)0+ gamma minimum intermediate variables gamma, gamma0、{Y,G, Q μ1,2,3,4 |, and
Figure BDA0002065404760000103
when the above is mentionedWhen the optimization problem (12-16) has a feasible solution, the optimization process is ended. At this time, obtained
Figure BDA0002065404760000104
I.e. the value of the input voltage acting on the windings of the magnetic levitation system at time t.

Claims (1)

1. A robust prediction control method of a repulsive magnetic suspension device is characterized by comprising the following steps:
1) acquiring historical data N groups of input voltage and output distance of the repulsion type magnetic suspension device, and establishing a nonlinear model as follows:
Figure FDA0002310325020000011
Figure FDA0002310325020000012
wherein y (t) is the distance between the bottom of a globe of the repulsion type magnetic suspension device and the infrared reflection position sensor at the time t, namely the output quantity of the repulsion type magnetic suspension device, u (t) is the voltage applied to a winding by a control board of the repulsion type magnetic suspension device at the time t, namely the input quantity of the repulsion type magnetic suspension device, ξ (t +1) is a term containing modeling error and uncertain disturbance, and | ξ (t +1) | is less than or equal to 1; { a%0,t,a1,t,b1,t,a2,t,b2,tIs an inverse quadratic time-varying coefficient with respect to y (t), and | L | · | | survival of the electrically non-woven hair2Representing a two-norm operation; relevant parameters of non-linear model
Figure FDA0002310325020000013
Are obtained by optimization calculation through an R-SNPOM optimization method;
2) establishing a convex polyhedron state space model of the repelling magnetic suspension device based on the nonlinear model;
3) based on the convex polyhedron state space model, obtaining an optimized objective function for robust control of the repelling magnetic suspension device, and solving the optimized objective function to obtain an input voltage value acting on a winding of the repelling magnetic suspension device at the moment t;
the specific implementation process of the step 2) comprises the following steps:
(1) the input increment and the output increment of the repulsive magnetic levitation device are defined as follows:
Figure FDA0002310325020000021
wherein y (t + j) is the output of the repulsive magnetic suspension device at the moment t + j; y issetThe expected value of the repulsive magnetic suspension device at the time t is shown; u (t + j) is the input of the repulsion type magnetic suspension device at the moment t + j, and u (t + j-1) is the input of the repulsion type magnetic suspension device at the moment t + j-1; j is an integer less than or equal to zero;
(2) one-step forward prediction polynomial model of repelling magnetic suspension device
Figure FDA00023103250200000213
The structure is as follows:
Figure FDA0002310325020000022
Figure FDA0002310325020000023
wherein the content of the first and second substances,
Figure FDA0002310325020000024
to derive
Figure FDA0002310325020000025
ξ (t +1| t) is the quantity containing system modeling error and uncertain disturbance, and | ξ (t +1| t) | is less than or equal to 1;
(3) based on the one-step forward prediction polynomial model and the definition of the input increment and the output increment of the system, the state space model corresponding to the polynomial model of the repulsive magnetic suspension device is deduced as follows:
Figure FDA0002310325020000026
Figure FDA0002310325020000027
Figure FDA0002310325020000028
Figure FDA0002310325020000029
wherein, the coefficient matrix A of the one-step forward prediction state vector X (t +1| t) of the repulsion type magnetic suspension devicet，BtAnd X (t | t) are respectively a parameter and a state calculated by the nonlinear model at the time t;
Figure FDA00023103250200000210
is the input increment of the repulsion type magnetic suspension device at the time t; xi (t) in a vector
Figure FDA00023103250200000211
And
Figure FDA00023103250200000212
to (c) to (d); a. thet+g|t，Bt+g|tPredicting a coefficient matrix of a state vector X (t + g +1| t) for the repelling magnetic suspension device in the future g steps;
the coefficient matrix At+g|t，Bt+g|tThe variation range is within the following convex polyhedron range:
Figure FDA0002310325020000031
wherein, { lambda ]t+g|t,μ1,2,3,4 is the linear coefficient of the convex polyhedron; the 4 vertexes of the convex polyhedron are (A)1,B1)，(A2,B2)，(A3,B3) And (A)4,B4) And, and:
Figure FDA0002310325020000032
wherein the content of the first and second substances,
Figure FDA0002310325020000033
and
Figure FDA0002310325020000034
are functions relating to y (t), respectively
Figure FDA0002310325020000035
Maximum and minimum values of;
Figure FDA0002310325020000036
and
Figure FDA0002310325020000037
are functions relating to y (t), respectively
Figure FDA0002310325020000038
Maximum and minimum values of;
in step 3), the optimization objective function is designed as follows:
Figure FDA0002310325020000039
wherein the content of the first and second substances,
Figure FDA00023103250200000310
I2is a unit array; x (t + g | t) is the system state quantity of the step t + g predicted by the model at the moment t;
Figure FDA0002310325020000041
t + g step rejection for prediction at time tInputting control increment by a magnetic suspension device;
Figure FDA0002310325020000042
Ftfor the future feedback control rate of the repulsion type magnetic suspension device at the time t,
solving the optimized objective function by the following set of inequalities:
Figure FDA0002310325020000043
Figure FDA0002310325020000044
Figure FDA0002310325020000045
Figure FDA0002310325020000046
Figure FDA0002310325020000047
wherein, the symbol represents the symmetric structure of the matrix; { Qμ1,2,3,4 is an intermediate matrix variable generated by solving the inequality set, namely the convex optimization problem; gamma ray0+ gamma is the optimized target value { (A) of the convex optimization problemμ,Bμ) 1,2,3,4 is the vertex of the convex polyhedron model; gamma, gamma0、{Y,G,Qμ1,2,3,4 |, and
Figure FDA00023103250200000411
are all the minimized variable gamma0+ gamma solving intermediate variables obtained in the process; in solving the minimization problem
Figure FDA0002310325020000048
The optimization function is based on the above inequalityFormula group constraint condition automatic search for gamma satisfying0+ gamma minimum intermediate variables gamma, gamma0、{Y,G,Qμ1,2,3,4 |, and
Figure FDA0002310325020000049
when the inequality group has feasible solution, the optimization process is ended, and the obtained result is
Figure FDA00023103250200000410
I.e. the value of the input voltage acting on the windings of the magnetic levitation system at time t.
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Citations (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000337434A (en) * 1999-05-25 2000-12-05 Delta Tooling Co Ltd Vibration mechanism
WO2007065608A1 (en) * 2005-12-08 2007-06-14 Eth Zurich Magnetic levitation system
CN102508433A (en) * 2011-11-06 2012-06-20 北京航空航天大学 Method for compensating digital control delay of magnetic bearing switch power amplifier
CN103940392A (en) * 2014-04-17 2014-07-23 江苏大学 Rotor position/displacement self-detection method of magnetic-levitation switched reluctance motor
CN104793645A (en) * 2015-04-16 2015-07-22 中南大学 Magnetic levitation ball position control method
CN105893654A (en) * 2016-03-11 2016-08-24 中南大学 Robust predictive control method for first-order continuous stirred tank reactor (CSTR)
CN106933107A (en) * 2017-05-15 2017-07-07 中南大学 A kind of output tracking Robust Predictive Control method based on the design of multifreedom controlling amount
CN107450352A (en) * 2017-09-18 2017-12-08 江苏海事职业技术学院 The simulation control method of non-linear Backstepping Controller based on Matlab
CN107589666A (en) * 2017-08-30 2018-01-16 湖北工业大学 A kind of maglev train system control method of the sliding formwork control based on power Reaching Law
CN107748543A (en) * 2017-09-21 2018-03-02 中南大学 A kind of nonlinear system modeling method based on DBN ARX models
CN108183650A (en) * 2018-01-26 2018-06-19 曲阜师范大学 A kind of wind-powered electricity generation magnetic suspension yaw motor control method based on Model Predictive Control
CN108681255A (en) * 2018-05-16 2018-10-19 江苏大学 A method of the weakening magnetically levitated flywheel based on Sliding mode variable structure control is buffeted
CN109062115A (en) * 2018-09-11 2018-12-21 长沙学院 A kind of spin control method based on double-closed-loop control
CN109491248A (en) * 2018-11-20 2019-03-19 中南大学 Magnetic levitation ball position prediction control method based on RBF-ARX model and laguerre function
CN109507882A (en) * 2018-11-20 2019-03-22 中南大学 A kind of fast robust forecast Control Algorithm based on RBF-ARX model

Family Cites Families (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2013188725A1 (en) * 2012-06-14 2013-12-19 President And Fellows Of Harvard College Levitation of materials in paramagnetic ionic liquids
FI126506B (en) * 2015-06-26 2017-01-13 Lappeenrannan Teknillinen Yliopisto Control device and method for controlling magnetic support and torque generation

Patent Citations (15)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2000337434A (en) * 1999-05-25 2000-12-05 Delta Tooling Co Ltd Vibration mechanism
WO2007065608A1 (en) * 2005-12-08 2007-06-14 Eth Zurich Magnetic levitation system
CN102508433A (en) * 2011-11-06 2012-06-20 北京航空航天大学 Method for compensating digital control delay of magnetic bearing switch power amplifier
CN103940392A (en) * 2014-04-17 2014-07-23 江苏大学 Rotor position/displacement self-detection method of magnetic-levitation switched reluctance motor
CN104793645A (en) * 2015-04-16 2015-07-22 中南大学 Magnetic levitation ball position control method
CN105893654A (en) * 2016-03-11 2016-08-24 中南大学 Robust predictive control method for first-order continuous stirred tank reactor (CSTR)
CN106933107A (en) * 2017-05-15 2017-07-07 中南大学 A kind of output tracking Robust Predictive Control method based on the design of multifreedom controlling amount
CN107589666A (en) * 2017-08-30 2018-01-16 湖北工业大学 A kind of maglev train system control method of the sliding formwork control based on power Reaching Law
CN107450352A (en) * 2017-09-18 2017-12-08 江苏海事职业技术学院 The simulation control method of non-linear Backstepping Controller based on Matlab
CN107748543A (en) * 2017-09-21 2018-03-02 中南大学 A kind of nonlinear system modeling method based on DBN ARX models
CN108183650A (en) * 2018-01-26 2018-06-19 曲阜师范大学 A kind of wind-powered electricity generation magnetic suspension yaw motor control method based on Model Predictive Control
CN108681255A (en) * 2018-05-16 2018-10-19 江苏大学 A method of the weakening magnetically levitated flywheel based on Sliding mode variable structure control is buffeted
CN109062115A (en) * 2018-09-11 2018-12-21 长沙学院 A kind of spin control method based on double-closed-loop control
CN109491248A (en) * 2018-11-20 2019-03-19 中南大学 Magnetic levitation ball position prediction control method based on RBF-ARX model and laguerre function
CN109507882A (en) * 2018-11-20 2019-03-22 中南大学 A kind of fast robust forecast Control Algorithm based on RBF-ARX model

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
.Nonlinear model predictive control of a magnetic levitation system.《Control Engineering Practice》.2013, *
RBF-ARX Model-based Robust MPC for Nonlinear Systems;彭辉等;《The 16th IFAC World Congress》;20051231;第1025-1030页 *
Thomas Bächle;Sebastian Hentzelt;Knut Graichen *
一种排斥式磁悬浮平台的磁场设计方法;余玲等;《科学技术与工程》;20101031;第7491-7493页 *
一种新的ARX 模型在磁悬浮系统建模中的应用;侯海良等;《计算机工程与应用》;20071231;第196-200、213页 *
基于线性函数型权重的RBF−ARX模型的磁悬浮球系统预测控制;覃业梅等;《中南大学学报（自然科学版）》;20160831;第2676-2684页 *

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