CN110007605A - A kind of Robust Predictive Control method of repulsion formula magnetic levitation system - Google Patents
A kind of Robust Predictive Control method of repulsion formula magnetic levitation system Download PDFInfo
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Abstract
The invention discloses a kind of Robust Predictive Control methods of repulsion formula magnetic levitation system, acquire the input voltage of repulsion formula magnetic levitation system, export the historical data N group of distance, establish nonlinear model；Based on nonlinear model, the convex polyhedron state-space model of repulsion formula magnetic levitation system is established；Based on the convex polyhedron state-space model, the optimization object function of repulsion formula magnetic levitation system robust control is obtained, the objective function is solved, obtains the input voltage value that t moment acts on repulsion formula magnetic levitation system winding.The present invention considers the influence of system modelling error and uncertain noises in controller design, is the control method of a kind of robust stability, strong applicability.
Description
Technical field
The present invention relates to automation fields, more particularly to a kind of for the Robust Prediction control for repelling formula magnetic levitation system
Method processed.
Background technique
Magnetic levitation technology is a kind of electromechanical integration technology, is vortexed by being formed using high frequency magnetic field in metal surface,
And then generate long-range navigation magnetic force and metal equipment is suspended, it effectively prevents the contact between equipment, reduce phase mutual friction,
It has broad application prospects.Magnetic suspension system is the complex nonlinear for integrating the controls such as electromagnetic force, air gap, electric current
System is difficult to obtain its accurate mathematical model in practical application.Identification modeling method based on data-driven is that one kind is disobeyed
Rely in the Mathematical Modeling Methods of system physical mechanism, is modeled, be widely used merely with the inputoutput data of object
In the modeling of Complex Nonlinear System.
PID controller is because its control algolithm structure is simple, and independent of the accurate mathematical model of controlled device, in magnetic
It suspends and has obtained wide application in controlling.But PID controller is poor for the global control characteristic of complex nonlinear object,
Especially for the high magnetic levitation ball control system of stability requirement, easily there is suspension ball in the larger range for closing on boundary
The case where falling out of control moment.Linearquadratic regulator is a kind of control algolithm based on controlled device state-space model,
Also in the wide control applied to complication system.But because its height relies on the accuracy of plant model, control
Robustness and stability or to be improved.Model Predictive Control is a kind of advanced meter generated in industrial stokehold practice
Calculation machine control algolithm, is widely used in the control of Complex Industrial Systems.Pass through the retrieval discovery to existing document, patent
" a kind of wind-powered electricity generation magnetic suspension yaw motor control method based on Model Predictive Control " (application number: 201810076334.5), mentions
A kind of forecast Control Algorithm based on magnetic suspension system Physical Mechanism modelling is gone out.A kind of patent " magnetic levitation ball position control
Method processed " (application number: 201510180614.7), proposes a kind of pre- observing and controlling based on tape function weight coefficient type autoregression model
Method processed.But above-mentioned two classes method does not consider system modelling error and uncertain noises during Design of Predictive
It influences, the stability and robustness of algorithm, which are unable to get, to be effectively ensured.Meanwhile patent " 201510180614.7 " is used in foundation
In the system state space model process of subsequent prediction controller design, directly replaced with the quantity of state at system current time come approximate
For the quantity of state in system future, direct single-point linearization approximate is carried out to the state-space model in system future and has been handled, the party
Method itself can affect greatly the precision of model.
Summary of the invention
The technical problem to be solved by the present invention is in view of the shortcomings of the prior art, provide a kind of repulsion formula magnetic levitation system
Robust Predictive Control method, consider system modelling error and uncertain noises influence, improve control method robustness and
Applicability.
In order to solve the above technical problems, the technical scheme adopted by the invention is that: a kind of Shandong of repulsion formula magnetic levitation system
Stick forecast Control Algorithm, comprising the following steps:
1) it acquires the input voltage of repulsion formula magnetic levitation system, export the historical data N group of distance, establish following non-linear
Model:
Wherein, y (t) is that t moment is repelled between formula magnetic levitation system tellurion bottom and infrared external reflection position sensor
Distance repels the output quantity of formula magnetic levitation system；U (t) is that t moment repulsion formula magnetic levitation system control panel is applied to winding
Voltage swing repels the input quantity of formula magnetic levitation system；ξ (t+1) is the item comprising modeling error and uncertain disturbance, and | ξ
(t+1)|≤1；{a0,t,a1,t,b1,t,a2,t,b2,tIt is inverse quadratic function type time-varying coefficient about y (t), and | | | |2It represents
Two norm operations；The relevant parameter of nonlinear modelIt is excellent by R-SNPOM
The optimization of change method is calculated；
2) it is based on above-mentioned nonlinear model, establishes the convex polyhedron state-space model of repulsion formula magnetic levitation system；
3) it is based on the convex polyhedron state-space model, obtains the optimization aim of repulsion formula magnetic levitation system robust control
Function solves the objective function, obtains the input voltage value that t moment acts on repulsion formula magnetic levitation system winding.
The specific implementation process of step 2) includes:
1) input increment and the output increment for defining repulsion formula magnetic levitation system are as follows:
Wherein, y (t+j) is the output for repelling formula magnetic levitation system at the t+j moment；ysetRepel formula magnetic levitation system for t moment
Desired value；U (t+j) is the input for repelling formula magnetic levitation system at the t+j moment, and u (t+j-1) is to repel formula magnetcisuspension at the t+j-1 moment
The input of floating device；J is the integer less than or equal to zero；
2) repel a step forward prediction multinomial model of formula magnetic levitation systemStructure is as follows:
Wherein, θ (t) is to deriveThe intermediate quantity generated in the process；ξ (t+1 | t) it is to include system modelling error
With the amount of uncertain noises, and | ξ (t+1 | t) |≤1；
3) definition of input increment, output increment based on above-mentioned step forward prediction multinomial model and system, derives
The corresponding state-space model of multinomial model for repelling formula magnetic levitation system out is as follows:
Wherein, repel the coefficient matrices A of a step forward prediction state vector X (t+1 | t) for formula magnetic levitation systemt, BtAnd X
(t | t) it is respectively the calculated parameter of t moment nonlinear model and state；Repel formula magnetic suspension dress for t moment
The input increment set；The variation range of Ξ (t) is in vectorWithBetween；At+g|t,
Bt+g|tTo repel the coefficient matrix that formula magnetic levitation system future g walks forward prediction state vector X (t+g+1 | t).
The coefficient matrices At+g|t, Bt+g|tVariation range is within the scope of following convex polyhedron:
Wherein, { λt+g|t,μ| μ=1,2,3,4 } be convex polyhedron linear coefficient；4 vertex of convex polyhedron are (A1,
B1), (A2,B2), (A3,B3) and (A4,B4), and:
Wherein,WithRespectively about
The function of y (t)Maximum value and minimum value；WithRespectively about the function of y (t)Maximum value and most
Small value.
In step 3), the optimization object function design is as follows:
Wherein,I2For unit battle array；X (t+g | t) is that the t+g of t moment model prediction walks system state amount；T+g for t moment prediction walks repulsion formula magnetic levitation system input control increment；
G >=1, FtRepel the feedback rate control in formula magnetic levitation system future for t moment.
The optimization object function is solved by following inequality group:
Wherein, symbol * represents the symmetrical structure of matrix；{Qμ| μ=1,2,3,4 } it is to solve above-mentioned inequality group, i.e., it is convex excellent
Change problem and the intermediary matrix variable generated；γ0+ γ is the optimization target values { (A of above-mentioned convex optimization problemμ,Bμ) | μ=1,2,
It 3,4 } is the vertex of convex polyhedron model；γ,γ0、{Y,G,Qμ| μ=1,2,3,4 } andIt is to minimize variable γ0+γ
Intermediate variable obtained in solution procedure；Solving minimization problemWhen, majorized function according to it is above-mentioned not
Equation set constraint condition Automatic-searching meets the γ made0+ γ the smallest intermediate variable γ, γ0、{Y,G,Qμ| μ=1,2,3,4 } andWhen above-mentioned inequality group has feasible solution, then optimization process terminates, and obtains at this timeAs t
Moment acts on the input voltage value of magnetic suspension system winding.
Compared with prior art, the advantageous effect of present invention is that: the present invention in view of practical magnetic suspension system without
What method avoided will receive the influence of external interference, and the present invention returns knot using a kind of time-varying coefficient almost linear based on data-driven
Structure model models magnetic suspension system, and the modeling error and extraneous uncertain noises of system are considered in modeling process
It influences.The shortcomings that in order to overcome general forecast control method to be difficult to ensure algorithm stability and robustness, the present invention is based on foundation
Magnetic suspension system time-varying coefficient regression model propose it is a kind of can be pre- by solving the robust that linear matrix inequality group is realized
Survey control method, the influence of system modelling error and uncertain noises considered in controller design, be a kind of robust stability,
The control method of strong applicability.
Detailed description of the invention
Fig. 1 is the targeted repulsion formula magnetic levitation system structure chart of the present invention.
Specific embodiment
The targeted repulsion formula magnetic levitation system structure of the present invention is as shown in Figure 1, in which: 1 is that (radius is globe shell
20 centimetres), 3 be square column type magnet, 2 for globe shell 1 and square column type magnet 3 between bracket, 4 be infrared external reflection position sensing
Device (model ST178H), 5 be iron core (section radius is 2.5 centimetres), and 6 be winding (the number of turns 3500), and 7 is based on single-chip microcontrollers
Control circuit board.The system by adjust control panel 7 be applied to winding 6 voltage swing (output voltage range be 0V~
20V), come control the distance between 2 bottom of tellurion and infrared external reflection position sensor 4 (command range range be 5cm~
25cm).A kind of specific embodiment of the robust control method of repulsion formula magnetic levitation system of the present invention comprises the steps of:
Step 1: being directed to repulsion formula magnetic levitation system shown in FIG. 1, the input voltage of acquisition system, the history for exporting distance
2500 groups of data, establish the following nonlinear model of system:
In above formula, y (t) is the distance between 2 bottom of t moment tellurion and infrared external reflection position sensor 4, i.e. system
Output quantity；U (t) is the voltage swing that t moment control panel 7 is applied to winding 6, the i.e. input quantity of system；ξ (t+1) is comprising building
The item of mould error and uncertain disturbance, and | ξ (t+1) |≤1；{a0,t,a1,t,b1,t,a2,t,b2,tIt is about the inverse secondary of y (t)
Function type time-varying coefficient, and | | | |2Represent two norm operations；The relevant parameter of model(R-SNPOM optimization is calculated by the optimization of R-SNPOM optimization method
Method is detailed in document: Zeng X., Peng H., Zhou F., 2018, A regularized SNPOM for stable
parameter estimation of RBF-AR(X)model,IEEE Transactions on Neural Networks
And Learning Systems, 29, No.4,779-791.), the design parameter value optimized are as follows:
Step 2: the magnetic suspension system based on step 1 foundation establishes system against quadratic function type time-varying coefficient regression model (1)
The convex polyhedron state-space model of system, detailed process is as follows:
Input increment and the output increment for defining magnetic suspension system are as follows:
In above formula, the output of etching system when y (t+j) is t+j；yset∈ [5,25] is the desired value of t moment system；u(t+
J) be t+j when etching system input, u (t+j-1) be t+j-1 when etching system input；J=0, -1, -2 ....By above-mentioned fixed
Justice can derive a step forward prediction of modelStructure is as follows:
In above formula, θ (t) is to deriveThe intermediate quantity generated in the process, can be by the output expectation of system and history
Data are calculated；ξ (t+1 | t) it is the amount comprising system modelling error and uncertain noises, and | ξ (t+1 | t) |≤1.
The state vector for defining magnetic suspension system is as follows:
The definition of input and output bias amount then based on above-mentioned step forward prediction multinomial model and system, can shift onto out
The corresponding state-space model of the multinomial model of system is as follows:
In above formula, the coefficient matrices A of a step forward prediction state vector X of system (t+1 | t)t, BtIt is respectively with X (t | t)
The calculated parameter of model and state that t moment can be recognized by step S1；For the defeated of t moment system
Enter increment, is algorithm amount to be optimized；Ξ (t) can not be obtained accurately in t moment, because in Ξ (t) including the unknown disturbances of system
ξ (t+1 | t), but because of ξ (t+1 | t) |≤1 it is found that the variation range of Ξ (t) in vectorWithBetween；System future g walks the coefficient matrices A of forward prediction state vector X (t+g+1 | t)t+g|t, Bt+g|t
It can not directly be calculated in t moment, but its variation range is within the scope of following convex polyhedron:
In above formula, { λt+g|t,μ| μ=1,2,3,4 } it is polyhedral linear coefficient；Polyhedral 4 vertex are (A1,B1),
(A2,B2), (A3,B3) and (A4,B4), and
Wherein, Because of y (t) ∈ [5,25], then Therefore it can count
Calculate 4 vertex (A of convex polyhedron collection (9)1,B1), (A2,B2), (A3,B3) and (A4,B4)。
Step 3: based on the system convex polyhedron state-space model (7-8) established in step 2, one kind of the present invention
Optimization object function design for the robust control method for repelling formula magnetic levitation system is as follows:
In above formula,I is unit battle array；X (t+g | t) is that the t+g of t moment model prediction walks system state amount；T+g for t moment prediction walks system input control increment.The following control rate knot of Robust Predictive Control device of the present invention
Structure design is as follows:G >=1, FtFor the feedback rate control in t moment system future.
Controller optimization objective function based on above-mentioned design, it is of the present invention a kind of for repulsion formula magnetic levitation system
The optimum control rate of robust control method obtained by solving following linear matrix inequality group:
In above formula, symbol * represents the symmetrical structure of matrix；Ft=YG-1For the feedback rate control in t moment system future；{Qμ
| μ=1,2,3,4 } it is the intermediary matrix variable for solving above-mentioned convex optimization problem and generating；γ0+ γ is above-mentioned convex optimization problem
(12) optimization target values, while γ and γ0And the intermediate quantity generated in above-mentioned optimization process；Coefficient matrices At、Bt、X (t | t) it is parameter matrix known to t moment；{(Aμ,Bμ) | μ=1,2,3,4 } be step 2 in system polyhedron
The vertex of model (8).γ,γ0、{Y,G,Qμ| μ=1,2,3,4 } andIt is to minimize variable γ0In+γ solution procedure
The intermediate variable arrived.When solving minimization problem (12), majorized function can be according to above-mentioned inequality constraints condition (13-16) certainly
It is dynamic to find the γ for meeting and making0+ γ the smallest intermediate variable γ, γ0、{Y,G,Qμ| μ=1,2,3,4 } andWhen above-mentioned optimization
When problem (12-16) has feasible solution, then optimization process terminates.At this point, obtainAs t moment acts on
In the input voltage value of magnetic suspension system winding.
Claims (5)
1. a kind of Robust Predictive Control method of repulsion formula magnetic levitation system, which comprises the following steps:
1) it acquires the input voltage of repulsion formula magnetic levitation system, export the historical data N group of distance, establish following nonlinear model
Type:
Wherein, y (t) is that t moment repels the distance between formula magnetic levitation system tellurion bottom and infrared external reflection position sensor,
Repel the output quantity of formula magnetic levitation system；U (t) is the voltage that t moment repels that formula magnetic levitation system control panel is applied to winding
Size repels the input quantity of formula magnetic levitation system；ξ (t+1) is the item comprising modeling error and uncertain disturbance, and | ξ (t+
1)|≤1；{a0,t,a1,t,b1,t,a2,t,b2,tIt is inverse quadratic function type time-varying coefficient about y (t), and | | | |2Represent two
Norm operation；The relevant parameter of nonlinear modelIt is excellent by R-SNPOM
The optimization of change method is calculated；
2) it is based on above-mentioned nonlinear model, establishes the convex polyhedron state-space model of repulsion formula magnetic levitation system；
3) it is based on the convex polyhedron state-space model, obtains the optimization aim letter of repulsion formula magnetic levitation system robust control
Number, solves the objective function, obtains the input voltage value that t moment acts on repulsion formula magnetic levitation system winding.
2. the Robust Predictive Control method of repulsion formula magnetic levitation system according to claim 1, which is characterized in that step 2)
Specific implementation process include:
1) input increment and the output increment for defining repulsion formula magnetic levitation system are as follows:
Wherein, y (t+j) is the output for repelling formula magnetic levitation system at the t+j moment；ysetRepel the phase of formula magnetic levitation system for t moment
Prestige value；U (t+j) is the input for repelling formula magnetic levitation system at the t+j moment, and u (t+j-1) is to repel formula magnetic suspension dress the t+j-1 moment
The input set；J is the integer less than or equal to zero；
2) repel a step forward prediction multinomial model of formula magnetic levitation systemStructure is as follows:
Wherein,To deriveThe intermediate quantity generated in the process；ξ (t+1 | t) it is comprising system modelling error and not true
Surely the amount interfered, and | ξ (t+1 | t) |≤1；
3) definition of input increment, output increment based on above-mentioned step forward prediction multinomial model and system, the row of deriving
The corresponding state-space model of multinomial model of reprimand formula magnetic levitation system is as follows:
Wherein, repel the coefficient matrices A of a step forward prediction state vector X (t+1 | t) for formula magnetic levitation systemt, BtWith X (t | t)
The respectively calculated parameter of t moment nonlinear model and state；Repel formula magnetic levitation system for t moment
Input increment；The variation range of Ξ (t) is in vectorWithBetween；At+g|t, Bt+g|tFor
Repulsion formula magnetic levitation system future g walks the coefficient matrix of forward prediction state vector X (t+g+1 | t).
3. the Robust Predictive Control method of repulsion formula magnetic levitation system according to claim 2, which is characterized in that the system
Matrix number At+g|t, Bt+g|tVariation range is within the scope of following convex polyhedron:
Wherein, { λt+g|t,μ| μ=1,2,3,4 } be convex polyhedron linear coefficient；4 vertex of convex polyhedron are (A1,B1),
(A2,B2), (A3,B3) and (A4,B4), and:
Wherein,WithRespectively about y (t)
FunctionMaximum value and minimum value；WithRespectively about the function of y (t)Maximum value and most
Small value.
4. the Robust Predictive Control method of repulsion formula magnetic levitation system according to claim 3, which is characterized in that step 3)
In, the optimization object function design is as follows:
Wherein,I2For unit battle array；X (t+g | t) is that the t+g of t moment model prediction walks system state amount；T+g for t moment prediction walks repulsion formula magnetic levitation system input control increment；G >=1, FtRepel the feedback rate control in formula magnetic levitation system future for t moment.
5. the Robust Predictive Control method of repulsion formula magnetic levitation system according to claim 4, which is characterized in that by with
Lower inequality group solves the optimization object function:
Wherein, symbol * represents the symmetrical structure of matrix；{Qμ| μ=1,2,3,4 } it is to solve above-mentioned inequality group, i.e., convex optimization is asked
The intermediary matrix variable inscribed and generated；γ0+ γ is the optimization target values { (A of above-mentioned convex optimization problemμ,Bμ) | μ=1,2,3,4 }
For the vertex of convex polyhedron model；γ,γ0、{Y,G,Qμ| μ=1,2,3,4 } andIt is to minimize variable γ0+ γ is solved
Intermediate variable obtained in process；Solving minimization problemWhen, majorized function is according to above-mentioned inequality
Group constraint condition Automatic-searching meets the γ made0+ γ the smallest intermediate variable γ, γ0、{Y,G,Qμ| μ=1,2,3,4 } andWhen above-mentioned inequality group has feasible solution, then optimization process terminates, and obtains at this timeAs t
Moment acts on the input voltage value of magnetic suspension system winding.
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| CN112286054A (en) * | 2020-10-20 | 2021-01-29 | 江苏科技大学 | Prediction control method based on magnetic suspension damping device |
| TWI724888B (en) * | 2020-05-05 | 2021-04-11 | 崑山科技大學 | Deep learning proportional derivative control method for magnetic levitation system |
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