CN110007605B  Robust prediction control method of repelling magnetic suspension device  Google Patents
Robust prediction control method of repelling magnetic suspension device Download PDFInfo
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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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 239000000725 suspension Substances 0.000 title claims abstract description 62
 230000001846 repelling Effects 0.000 title claims abstract description 15
 238000004804 winding Methods 0.000 claims abstract description 8
 238000005094 computer simulation Methods 0.000 claims abstract description 7
 238000005457 optimization Methods 0.000 claims description 24
 239000011159 matrix material Substances 0.000 claims description 18
 238000000034 method Methods 0.000 claims description 14
 238000005339 levitation Methods 0.000 claims description 13
 239000000126 substance Substances 0.000 claims description 6
 238000004364 calculation method Methods 0.000 claims description 3
 230000000875 corresponding Effects 0.000 claims description 3
 230000004083 survival Effects 0.000 claims description 3
 238000004422 calculation algorithm Methods 0.000 description 5
 238000005516 engineering process Methods 0.000 description 2
 239000002184 metal Substances 0.000 description 2
 229910052751 metal Inorganic materials 0.000 description 2
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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

 H—ELECTRICITY
 H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
 H02N—ELECTRIC MACHINES NOT OTHERWISE PROVIDED FOR
 H02N15/00—Holding or levitation devices using magnetic attraction or repulsion, not otherwise provided for
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
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 highfrequency 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 singlepoint 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:
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},a_{1,t},b_{1,t},a_{2,t},b_{2,t}Is an inverse quadratic timevarying coefficient with respect to y (t), and  L  ·   survival of the electrically nonwoven hair_{2}Representing a twonorm operation; relevant parameters of nonlinear modelAre obtained by optimization calculation through an RSNPOM 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:
wherein y (t + j) is the output of the repulsive magnetic suspension device at the moment t + j; y is_{set}The 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 + j1) is the input of the repulsion type magnetic suspension device at the moment t + j1; j is an integer less than or equal to zero;
2) onestep forward prediction polynomial model of repelling magnetic suspension deviceThe structure is as follows:
wherein θ (t) is derivedξ (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 onestep 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:
wherein, the coefficient matrix A of the onestep forward prediction state vector X (t +1 t) of the repulsion type magnetic suspension device_{t}，B_{t}And X (t  t) are respectively a parameter and a state calculated by the nonlinear model at the time t;is the input increment of the repulsion type magnetic suspension device at the time t; xi (t) in a vectorAndto (c) to (d); a. the_{t+gt}，B_{t+gt}And 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 A_{t+gt}，B_{t+gt}The variation range is within the following convex polyhedron range:
wherein, { lambda ]_{t+gt,μ}1,2,3,4 is the linear coefficient of the convex polyhedron; the 4 vertexes of the convex polyhedron are (A)_{1},B_{1})，(A_{2},B_{2})，(A_{3},B_{3}) And (A)_{4},B_{4}) And, and:
wherein the content of the first and second substances,andare functions relating to y (t), respectivelyMaximum and minimum values of;andare functions relating to y (t), respectivelyMaximum and minimum values of.
In step 3), the optimization objective function is designed as follows:
wherein the content of the first and second substances,I_{2}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;inputting a control increment for the t + g step repulsion type magnetic suspension device predicted at the t moment;g≥1，F_{t}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:
wherein, the symbol represents the symmetric structure of the matrix; { Q_{μ}1,2,3,4 is an intermediate matrix variable generated by solving the inequality set, namely the convex optimization problem; gamma ray_{0}+ gamma is the optimized target value { (A) of the convex optimization problem_{μ},B_{μ}) 1,2,3,4 is the vertex of the convex polyhedron model; gamma, gamma_{0}、{Y,G,Q_{μ}1,2,3,4 , andare all the minimized variable gamma_{0}+ gamma solving intermediate variables obtained in the process; in solving the minimization problemThen, the optimization function automatically searches for the gamma satisfying the constraint conditions of the inequality set_{0}+ gamma minimum intermediate variables gamma, gamma_{0}、{Y,G,Q_{μ}1,2,3,4 , andwhen the inequality group has feasible solution, the optimization process is ended, and the obtained result isI.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 timevarying coefficient quasilinear 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 timevarying 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 cm25 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 0V20V). 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:
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 ≦ is_{0,t},a_{1,t},b_{1,t},a_{2,t},b_{2,t}Is an inverse quadratic timevarying coefficient with respect to y (t), and  L  ·   survival of the electrically nonwoven hair_{2}Representing a twonorm operation; relevant parameters of the modelAre obtained by optimization calculation through an RSNPOM optimization method (the RSNPOM optimization method is detailed in the documents of Zeng X, Peng H, Zhou F, 2018, A customized SNPOM for standing parameter estimation of RBFAR (X) model, IEEE Transactions on Neural networks and Learning Systems,29, No.4, 779:
step 2: based on the magnetic suspension system inverse quadratic function type timevarying 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:
in the above formula, y (t + j) is the output of the system at the time t + j; y is_{set}∈[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 + j1) is the input of the system at the moment t + j1; j is 0, 1, 2. From the above definitions, one step forward prediction of the model can be derivedThe structure is as follows:
in the above formula, θ (t) is derivedThe 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:
based on the above definition of the onestep 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:
in the above equation, the coefficient matrix A of the onestep forward prediction state vector X (t +1 t) of the system_{t}，B_{t}And X (t  t) are the parameters and states respectively calculated by the model identified in step S1 at time t;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) Andto (c) to (d); coefficient matrix A of forward predicted state vector X (t + g +1 t) for g steps in the future of the system_{t+gt}，B_{t+gt}The variation range of the method cannot be directly calculated at the time t, but is within the following convex polyhedron range:
in the above formula, { λ_{t+gt,μ}1,2,3,4 is a linear coefficient of the polyhedron; the 4 vertexes of the polyhedron are (A)_{1},B_{1})，(A_{2},B_{2})，(A_{3},B_{3}) And (A)_{4},B_{4}) And is and
wherein the content of the first and second substances, because y (t) e [5,25]Then, then Thus, 4 vertices (A) of the convex polyhedron set (9) can be calculated_{1},B_{1})，(A_{2},B_{2})，(A_{3},B_{3}) And (A)_{4},B_{4})。
And step 3: based on the system convex polyhedron state space model (78) established in the step 2, the optimized objective function design of the robust control method for the repulsive magnetic suspension device is as follows:
in the above formula, the first and second carbon atoms are,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;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:g≥1，F_{t}the 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:
in the above formula, the symbol represents a symmetric structure of the matrix; f_{t}＝YG^{1}The future feedback control rate of the system at the moment t; { Q_{μ}1,2,3,4 is an intermediate matrix variable generated by solving the convex optimization problem; gamma ray_{0}+ gamma is the optimized target value of the convex optimization problem (12), and gamma are simultaneously_{0}Also an intermediate quantity generated in the above optimization process; coefficient matrix A_{t}、B_{t}、X (t  t) is a parameter matrix known at time t; { (A)_{μ},B_{μ}) And . mu. ═ 1,2,3,4} is a vertex of the system polyhedron model (8) in the step 2. Gamma, gamma_{0}、{Y,G,Q_{μ}1,2,3,4 , andare all the minimized variable gamma_{0}The 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 (1316)_{0}+ gamma minimum intermediate variables gamma, gamma_{0}、{Y,G,Q_{μ}1,2,3,4 , andwhen the above is mentionedWhen the optimization problem (1216) has a feasible solution, the optimization process is ended. At this time, obtainedI.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:
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},a_{1,t},b_{1,t},a_{2,t},b_{2,t}Is an inverse quadratic timevarying coefficient with respect to y (t), and  L  ·   survival of the electrically nonwoven hair_{2}Representing a twonorm operation; relevant parameters of nonlinear modelAre obtained by optimization calculation through an RSNPOM 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:
wherein y (t + j) is the output of the repulsive magnetic suspension device at the moment t + j; y is_{set}The 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 + j1) is the input of the repulsion type magnetic suspension device at the moment t + j1; j is an integer less than or equal to zero;
(2) onestep forward prediction polynomial model of repelling magnetic suspension deviceThe structure is as follows:
wherein the content of the first and second substances,to deriveξ (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 onestep 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:
wherein, the coefficient matrix A of the onestep forward prediction state vector X (t +1 t) of the repulsion type magnetic suspension device_{t}，B_{t}And X (t  t) are respectively a parameter and a state calculated by the nonlinear model at the time t;is the input increment of the repulsion type magnetic suspension device at the time t; xi (t) in a vectorAndto (c) to (d); a. the_{t+gt}，B_{t+gt}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 A_{t+gt}，B_{t+gt}The variation range is within the following convex polyhedron range:
wherein, { lambda ]_{t+gt,μ}1,2,3,4 is the linear coefficient of the convex polyhedron; the 4 vertexes of the convex polyhedron are (A)_{1},B_{1})，(A_{2},B_{2})，(A_{3},B_{3}) And (A)_{4},B_{4}) And, and:
wherein the content of the first and second substances,andare functions relating to y (t), respectivelyMaximum and minimum values of;andare functions relating to y (t), respectivelyMaximum and minimum values of;
in step 3), the optimization objective function is designed as follows:
wherein the content of the first and second substances,I_{2}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;t + g step rejection for prediction at time tInputting control increment by a magnetic suspension device;F_{t}for 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:
wherein, the symbol represents the symmetric structure of the matrix; { Q_{μ}1,2,3,4 is an intermediate matrix variable generated by solving the inequality set, namely the convex optimization problem; gamma ray_{0}+ gamma is the optimized target value { (A) of the convex optimization problem_{μ},B_{μ}) 1,2,3,4 is the vertex of the convex polyhedron model; gamma, gamma_{0}、{Y,G,Q_{μ}1,2,3,4 , andare all the minimized variable gamma_{0}+ gamma solving intermediate variables obtained in the process; in solving the minimization problemThe optimization function is based on the above inequalityFormula group constraint condition automatic search for gamma satisfying_{0}+ gamma minimum intermediate variables gamma, gamma_{0}、{Y,G,Q_{μ}1,2,3,4 , andwhen the inequality group has feasible solution, the optimization process is ended, and the obtained result isI.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)
Publication number  Priority date  Publication date  Assignee  Title 

JP2000337434A (en) *  19990525  20001205  Delta Tooling Co Ltd  Vibration mechanism 
WO2007065608A1 (en) *  20051208  20070614  Eth Zurich  Magnetic levitation system 
CN102508433A (en) *  20111106  20120620  北京航空航天大学  Method for compensating digital control delay of magnetic bearing switch power amplifier 
CN103940392A (en) *  20140417  20140723  江苏大学  Rotor position/displacement selfdetection method of magneticlevitation switched reluctance motor 
CN104793645A (en) *  20150416  20150722  中南大学  Magnetic levitation ball position control method 
CN105893654A (en) *  20160311  20160824  中南大学  Robust predictive control method for firstorder continuous stirred tank reactor (CSTR) 
CN106933107A (en) *  20170515  20170707  中南大学  A kind of output tracking Robust Predictive Control method based on the design of multifreedom controlling amount 
CN107450352A (en) *  20170918  20171208  江苏海事职业技术学院  The simulation control method of nonlinear Backstepping Controller based on Matlab 
CN107589666A (en) *  20170830  20180116  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) *  20170921  20180302  中南大学  A kind of nonlinear system modeling method based on DBN ARX models 
CN108183650A (en) *  20180126  20180619  曲阜师范大学  A kind of windpowered electricity generation magnetic suspension yaw motor control method based on Model Predictive Control 
CN108681255A (en) *  20180516  20181019  江苏大学  A method of the weakening magnetically levitated flywheel based on Sliding mode variable structure control is buffeted 
CN109062115A (en) *  20180911  20181221  长沙学院  A kind of spin control method based on doubleclosedloop control 
CN109491248A (en) *  20181120  20190319  中南大学  Magnetic levitation ball position prediction control method based on RBFARX model and laguerre function 
CN109507882A (en) *  20181120  20190322  中南大学  A kind of fast robust forecast Control Algorithm based on RBFARX model 
Family Cites Families (2)
Publication number  Priority date  Publication date  Assignee  Title 

WO2013188725A1 (en) *  20120614  20131219  President And Fellows Of Harvard College  Levitation of materials in paramagnetic ionic liquids 
FI126506B (en) *  20150626  20170113  Lappeenrannan Teknillinen Yliopisto  Control device and method for controlling magnetic support and torque generation 

2019
 20190520 CN CN201910419115.7A patent/CN110007605B/en active Active
Patent Citations (15)
Publication number  Priority date  Publication date  Assignee  Title 

JP2000337434A (en) *  19990525  20001205  Delta Tooling Co Ltd  Vibration mechanism 
WO2007065608A1 (en) *  20051208  20070614  Eth Zurich  Magnetic levitation system 
CN102508433A (en) *  20111106  20120620  北京航空航天大学  Method for compensating digital control delay of magnetic bearing switch power amplifier 
CN103940392A (en) *  20140417  20140723  江苏大学  Rotor position/displacement selfdetection method of magneticlevitation switched reluctance motor 
CN104793645A (en) *  20150416  20150722  中南大学  Magnetic levitation ball position control method 
CN105893654A (en) *  20160311  20160824  中南大学  Robust predictive control method for firstorder continuous stirred tank reactor (CSTR) 
CN106933107A (en) *  20170515  20170707  中南大学  A kind of output tracking Robust Predictive Control method based on the design of multifreedom controlling amount 
CN107589666A (en) *  20170830  20180116  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) *  20170918  20171208  江苏海事职业技术学院  The simulation control method of nonlinear Backstepping Controller based on Matlab 
CN107748543A (en) *  20170921  20180302  中南大学  A kind of nonlinear system modeling method based on DBN ARX models 
CN108183650A (en) *  20180126  20180619  曲阜师范大学  A kind of windpowered electricity generation magnetic suspension yaw motor control method based on Model Predictive Control 
CN108681255A (en) *  20180516  20181019  江苏大学  A method of the weakening magnetically levitated flywheel based on Sliding mode variable structure control is buffeted 
CN109062115A (en) *  20180911  20181221  长沙学院  A kind of spin control method based on doubleclosedloop control 
CN109491248A (en) *  20181120  20190319  中南大学  Magnetic levitation ball position prediction control method based on RBFARX model and laguerre function 
CN109507882A (en) *  20181120  20190322  中南大学  A kind of fast robust forecast Control Algorithm based on RBFARX model 
NonPatent Citations (6)
Title 

.Nonlinear model predictive control of a magnetic levitation system.《Control Engineering Practice》.2013, * 
RBFARX Modelbased Robust MPC for Nonlinear Systems;彭辉等;《The 16th IFAC World Congress》;20051231;第10251030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74917493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196200、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26762684页 * 
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