CN104793645A - Magnetic levitation ball position control method - Google Patents

Abstract

The invention discloses a magnetic levitation ball position control method. The functional weight coefficient type autoregressive model is established to describe nonlinear dynamic characteristics between electromagnetic winding input voltage and the steel ball position by adopting a system identification method. The primary linear function of the steel ball position is taken as the weight coefficient of a gauss RBF (radial basis function) network, the gauss RBF network is taken as the functional coefficient of the nonlinear autoregressive model, and the model can better describe dynamic characteristics of a magnetic levitation ball system. The regressive coefficient of the model is a constant at a given time, and the model is similar to a linear ARX model. Based on this, a time-varying and partially linear predict controller is designed, optimal position control over the steel ball is rapidly realized by online solving quadratic programming all the time, and requirements of the magnetic levitation ball system on stability and rapidness are met.

Description

A kind of magnetic levitation ball position control method

Technical field

The present invention relates to automatic control technology field, particularly a kind of magnetic levitation ball position control method.

Background technology

Magnetic levitation technology is current collection magnetics, electronic technology, control engineering, signal transacting, mechanics, dynamics are integrated, typical electromechanical integration technology.Magnetic levitation technology is because it is contactless, be widely used in the engineering fields such as magnetic suspension train, magnetic suspension bearing, magnetic suspension motor without features such as friction, low noises.Maglev ball system mainly produces electromagnetic force by passing to certain electric current to electromagnetism winding, itself and steel ball gravity is balanced each other, makes steel ball hang be in equilibrium state aloft, reach the object of system stable operation.The maglev ball system with single direction has non-linear, open-loop unstable, the quick feature responded of essence, and be subject to the impact of power supply and external environment, some parameter has stronger uncertainty, cannot accurately measure.And electromagnetic field magnetic saturation phenomenon makes between the magnetic flux of elect magnetic field input current and magnetic induction density, electromagnetism winding not proportional, increases the non-linear of system and causes the electromagnetic force model of system cannot express with simple math equation; Meanwhile, the steel ball being in elect magnetic field produces current vortex, will affect the inductance of electromagnetism winding conversely, and the inductance making electromagnetism winding is not constant, but about the function of steel ball to the air gap g on electromagnet pole surface, and become nonlinear relationship with it.Therefore, the precise physical model setting up maglev ball system is very difficult, and this is the difficult point place that maglev ball system realizes stability contorting.

PID control structure is simple, current/voltage can be regulated to make steel ball hang, do not need the physical model setting up magnetic suspension system, but controling parameters needs manually to adjust, adaptivity is poor, less to effective range of control of Nonlinear Magnetic Suspension System, especially when steel ball change in location is quick, overshoot is comparatively large, and steel ball shake is larger.Automatically regulate the controling parameters of PID with fuzzy reasoning, the ability that parameter changes with air gap change between steel ball and electromagnet can be improved.But the method depends on fuzzy rule base, its foundation is limited by the experience of deviser.On the other hand, by analysis of magnetic suspension system principle of work, on the basis of some assumed conditions, set up physical model, then can implement adaptive control, synovial membrane control, PREDICTIVE CONTROL etc. to steel ball.The maximum difficult point that these methods realize is the precise physical model of more difficult acquisition energy accurate description magnetic suspension system dynamic perfromance, because some assumed condition is difficult to be met in engineer applied.In addition, utilize linearization technique to carry out linearization process to physical model, then design linear control strategies, On-line Control optimal speed can be accelerated, but have lost mission nonlinear characteristic, weaken the descriptive power of model to magnetic suspension system, thus reduce control effects.

Summary of the invention

Technical matters to be solved by this invention is, not enough for prior art, provides a kind of magnetic levitation ball position control method.

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of magnetic levitation ball position control method, be applicable to the single-degree-of-freedom magnetic levitation ball system moved up and down, described single-degree-of-freedom magnetic levitation ball system comprises the coil winding generated an electromagnetic field and the photoelectric sensor detecting steel ball position; Described electromagnetism winding input voltage controls driving circuit by controller and provides; The steel ball position signalling of described photoelectric sensor collection sends computer for controlling to by data collecting card.Autoregressive model is set up to maglev ball system:

$g\left(t\right)={\mathrm{\φ}}_0+\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\φ}}_i^{g}g(t-i)+\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\φ}}_i^{u}u(t-i)+\mathrm{\ξ}\left(t\right)$

Wherein, g (t) position that is magnetic levitation ball; U (t) is electromagnetism winding input voltage; ξ (t) is white noise; $\left\{\begin{array}{c}{\mathrm{\φ}}_0=c_0^0+{V_1}^0\exp (-0.03{\left|\right|W(t-1)-11.74\left|\right|}^2)\\ {\mathrm{\φ}}_i^g=c_{i,0}^g+V_{i,1}^g\exp (-0.03{\left|\right|W(t-1)-11.74\left|\right|}^2)\\ {\mathrm{\φ}}_j^u=c_{j,0}^u+V_{j.1}^u\exp (-1.33{\left|\right|W(t-1)+3.82\left|\right|}^2)\\ W(t-1)=g(t-1)\\ V^0=v_0^0+v_1^{0}g(t-1)\\ {V_i}^g=v_{i,0}^g+v_{i,1}^{g}g(t-1)\\ V_j^u=v_{j,0}^u+v_{j,1}^{u}g(t-1)\\ i=\mathrm{1,2},...,7;j=\mathrm{1,2},...,6\end{array}\right.;$ V ⁰, V _i ^gand V _j ^ufor the weight coefficient of RBF network, it is the once linear function of steel ball position; for constant coefficient, by the identification of SNPOM optimization method, the basis obtaining nonlinear parameter calculates by least square method and obtains.

Then based on described autoregressive model design predictive controller, optimize following quadratic programming function J and obtain optimum control amount, control position g (t) of magnetic levitation ball:

$\begin{array}{c}\underset{\hat{u}\left(t\right)}{\min }J={\left|\right|\hat{g}\left(t\right)-{\hat{g}}_r\left(t\right)\left|\right|}_{{1.8I}_{12}}^2+{\left|\right|\hat{u}\left(t\right)\left|\right|}_{{0.0002I}_4}^2+{\left|\right|\mathrm{\Δ}\hat{u}\left(t\right)\left|\right|}_{{0.16I}_4}^2\\ \begin{array}{cc}s.t.& -22\≤\hat{g}\left(t\right)\≤0\end{array}\\ \begin{array}{cc}& 0\≤\hat{u}\left(t\right)\≤10\end{array}\\ \begin{array}{cc}& -3\≤\mathrm{\Δ}\hat{u}\left(t\right)\≤3\end{array}\end{array}$

Wherein, $\hat{g}\left(t\right)={\left[\begin{array}{cccc}\hat{g}(t+1|t)& \hat{g}(t+2|t)& ...& \hat{g}(t+12|t)\end{array}\right]}^T,\hat{g}(t+l|t),l=1,...,12$ For t l walks steel ball position prediction variable forward, according to t, autoregressive model obtains the expression formula of l step prediction, namely $\hat{g}\left(t\right)=\stackrel{\‾}{C}{\stackrel{\‾}{A}}_{t}x\left(t\right)+\stackrel{\‾}{C}{\stackrel{\‾}{B}}_t\hat{u}\left(t\right)+\stackrel{\‾}{C}{\stackrel{\‾}{\mathrm{\Γ}}}_t{\stackrel{\‾}{\mathrm{\Φ}}}_t,{\stackrel{\‾}{A}}_t,{\stackrel{\‾}{B}}_t,\stackrel{\‾}{C}$ With for system prediction matrix of coefficients, obtained by autoregressive model described in t and multi-step prediction variable; ${\hat{g}}_r\left(t\right)={\left[\begin{array}{cccc}{g}_r(t+1)& g_r(t+2)& ...& g_r(t+12)\end{array}\right]}^T,$ G _r(t+l) for the l that t is given walks forward reference position; $\hat{u}\left(t\right)={\left[\begin{array}{cccc}u\left(t\right)& u(t+1)& u(t+2)& u(t+3)\end{array}\right]}^T,$ U (t+p), p=0,1,2, the 3 electromagnetism winding input voltages will optimized for t, only get Section 1 u (t) and act on controlled magnetic levitation ball; $\mathrm{\Δ}\hat{u}\left(t\right)={\left[\begin{array}{cccc}\mathrm{\Δu}\left(t\right)& \mathrm{\Δu}(t+1)& \mathrm{\Δu}(t+2)& \mathrm{\Δu}(t+3)\end{array}\right]}^T,$ △ u (t)=u (t)-u (t-1) is input voltage increment; $\left\{\begin{array}{c}x\left(t\right)={\left[\begin{array}{cccc}{x}_{1,t}& x_{2,t}& ...& x_{7,t}\end{array}\right]}^T\\ x_{1,t}=g\left(t\right)\\ x_{k,t}=\underset{i=1}{\overset{7-k+1}{\mathrm{\Σ}}}{\mathrm{\φ}}_{i+k-1}^{g}g(t-i)+\underset{i=1}{\overset{7-k+1}{\mathrm{\Σ}}}{\mathrm{\φ}}_{i+k-1}^{u}u(t-i)\\ k=\mathrm{2,3},...,7\end{array}\right.$ For state vector; ${\stackrel{\‾}{\mathrm{\Φ}}}_t={\left[\begin{array}{cccc}{\mathrm{\Φ}}_t^T& {\mathrm{\Φ}}_{t+1}^T& ...& {\mathrm{\Φ}}_{t+11}^T\end{array}\right]}^T,$ ${\mathrm{\Φ}}_t=\left[\begin{array}{c}{\mathrm{\φ}}_0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right];$ φ ₀, φ _i ^gand φ _j ^ufor the regression function coefficient of autoregressive model, φ ₇ ^u=0; I is unit matrix.

Compared with prior art, the beneficial effect that the present invention has is: the present invention adopts the thought of System Discrimination modeling, the relevant information utilizing the input/output data of running to comprise system dynamic characteristic sets up the dynamic model of maglev ball system, the dynamic perfromance of system can be described out most possibly, and need not consider that magnetic saturation phenomenon and eddy effect are on the impact (these impacts have been included in Identification Data all) of model.The method is applicable to this kind of strong nonlinearity, strong probabilistic complication system, may extend to other similar systems; The RBF net coefficients of the tape function power RBF-ARX model that the present invention sets up depends on the position of steel ball at elect magnetic field, improve the Function approximation capabilities of RBF network, make one of acquisition group of pseudo-linear ARX model can describe the dynamic perfromance of non-linear maglev ball system better.The one-step prediction of system exports modeling error within ± 0.4%; Predictive controller that become when the present invention is based on the RBF-ARX modelling of tape function power, local linear, rapid Optimum can calculate optimum control amount, reduce the on-line optimization time, be conducive to completing within the maglev ball system sampling period (5 milliseconds) optimizing and calculate, realize quick, the stability contorting to steel ball position.

Accompanying drawing explanation

Fig. 1 is maglev ball system structural drawing of the present invention.

Embodiment

The system architecture of maglev ball system of the present invention as shown in Figure 1, is a single-mode system that only can control the movement of steel ball above-below direction.PC 9 exports control voltage by controller, electromagnetism winding drive circuit 6 is transferred to through D/A converter 8, electromagnetism winding 2 produces electromagnetic induction when passing to phase induced current, electromagnetic field is formed below winding, electromagnetic induction power F is applied to the steel ball 1 be in field, steel ball up/down is moved, and the air gap g (i.e. steel ball position) between adjustment electromagnet and steel ball, until electromagnetic force F and steel ball gravity G balances; Meanwhile, the photoelectric sensor that LED light source 3 and electro-optical package 4 are formed is used for detecting steel ball position, and the treated circuit 5 of corresponding voltage signal and A/D converter 7 are passed PC back and exported.In system shown in Figure 1, the radius of steel ball 1 is 12.5 millimeters, quality is 22 grams, and the number of turn of electromagnetism winding 2 is 2450, equivalent resistance is 13.8 ohm.

Maglev ball system of the present invention is subject to magnetic saturation and eddy effect impact, is also subject to the impact of power supply and external interference.For this reason, adopt the modeling method based on tape function power RBF-ARX model, build the dynamic model of relation between electromagnetism winding input voltage and elect magnetic field steel ball position.In the present invention, utilize data identification technology, adopt the linear function of steel ball position do weight coefficient, the RBF network of gaussian kernel is as the function coefficients in Nonlinear A RX model.This model is a kind of nonlinear time-varying model with linear ARX model structure, its independent variable is the regressor of electromagnetism winding input voltage, steel ball position, steel ball position is the semaphore of characterization system state, adopt the constant of the approximation of function RBF neural relevant to steel ball position linearity to weigh, then by this RBF structure, real-time online adjustment is carried out to model parameter.Tape function power RBF-ARX model is very approximate with linear ARX model in the linear zone of local, and its parameter automatically can upgrade along with mission nonlinear state, automatically adjust in addition, has good overall adaptive character.

Build the function weight coefficient type RBF-ARX model of dynamic performance model between steel ball position and electromagnetism winding input voltage, adopt row dimension Bouguer Ma Kuier special formula method (Levenberg-Marquardt Method, and linear least square (LeastSquare Method LMM), LSM) the SNPOM optimization method combined (refers to: Peng H, Ozaki T, Haggan-Ozaki V, Toyoda Y.2003, A parameter optimization method for the radial basis function type models) this model parameter of identification, obtain following structure:

$g\left(t\right)={\mathrm{\φ}}_0+{\mathrm{\φ}}_1^{g}g(t-1)+{\mathrm{\φ}}_2^{g}g(t-2)+...+{\mathrm{\φ}}_7^{g}g(t-7)+{\mathrm{\φ}}_1^{u}u(t-1)+{\mathrm{\φ}}_2^{u}u(t-2)+...+{\mathrm{\φ}}_6^{u}u(t-6)+\mathrm{\ξ}\left(t\right)---\left(1\right)$

Wherein,

$\left\{\begin{array}{c}{\mathrm{\φ}}_0=c_0^0+{V_1}^0\exp (-0.03{\left|\right|W(t-1)-11.74\left|\right|}^2)\\ {\mathrm{\φ}}_i^g=c_{i,0}^g+V_{i,1}^g\exp (-0.03{\left|\right|W(t-1)-11.74\left|\right|}^2)\\ {\mathrm{\φ}}_j^u=c_{j,0}^u+V_{j.1}^u\exp (-1.33{\left|\right|W(t-1)+3.82\left|\right|}^2)\\ W(t-1)=g(t-1)\\ V^0=v_0^0+v_1^{0}g(t-1)\\ {V_i}^g=v_{i,0}^g+v_{i,1}^{g}g(t-1)\\ V_j^u=v_{j,0}^u+v_{j,1}^{u}g(t-1)\\ i=\mathrm{1,2},...,7;j=\mathrm{1,2},...,6\end{array}\right.---\left(2\right)$

The position that g (t) is steel ball is also the air gap between steel ball and electromagnet; U (t) is the input voltage of electromagnetism winding; φ ₀, φ _i ^gand φ _j ^ube respectively the regression function coefficient of autoregressive model; W (t-1) is system works dotted state, carrys out characterization system working point state with steel ball position g (t-1); V ⁰, with for the once linear function of steel ball position, as the function weight coefficient of RBF neural; || || be 2 norms; ξ (t) is white noise; for linear constant coefficient, by the identification of SNPOM optimization method, the basis obtaining nonlinear parameter calculates with LSM and obtains.Order ${\mathrm{\θ}}_L=\{c_0^0,c_{i,0}^g,c_{j,0}^u,v_0^0,v_{i,0}^g,v_{j,o}^u{v}_1^0,v_{i,1}^g,v_{j,1}^u|i=1,...,7,j=1,...,6\},$ ${\mathrm{\θ}}_N=\{\mathrm{0.03,1.33,11.74},-3.82\},$ Formula (1) is rewritten as then

Wherein, for the observation data of steel ball position, when SNPOM carries out Model Distinguish, use 4000 observation datas altogether.

Become when utilizing the characteristics design of maglev ball system local linear, linear predictive controller.Formula (1) is rewritten as polynomial expression

$g\left(t\right)=\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\φ}}_i^{g}g(t-i)+\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\φ}}_i^{u}u(t-i)+{\mathrm{\φ}}_0+\mathrm{\ξ}\left(t\right)---\left(4\right)$

Wherein, ${\mathrm{\φ}}_7^u=0.$

The state variable of define system:

$\left\{\begin{array}{c}x\left(t\right)={\left[\begin{array}{cccc}{x}_{1,t}& x_{2,t}& ...& x_{7,t}\end{array}\right]}^T\\ x_{1,t}=g\left(t\right)\\ x_{k,t}=\underset{i=1}{\overset{7-k+1}{\mathrm{\Σ}}}{\mathrm{\φ}}_{i+k-1}^{g}g(t-i)+\underset{i=1}{\overset{7-k+1}{\mathrm{\Σ}}}{\mathrm{\φ}}_{i+k-1}^{u}u(t-i)\\ k=\mathrm{2,3},...,7\end{array}\right.---\left(5\right)$

Then the state-space model of formula (1) is:

$\left\{\begin{array}{c}x(t+1)=A_{t}x\left(t\right)+B_{t}u\left(t\right)+{\mathrm{\Φ}}_t+\mathrm{\Ξ}(t+1)\\ g\left(t\right)=\mathrm{Cx}\left(t\right)\end{array}\right.---\left(6\right)$

Here

$\left\{\begin{array}{c}{A}_t=\left[\begin{array}{ccccc}{\mathrm{\φ}}_1^g& 1& 0& 0& 0\\ {\mathrm{\φ}}_2^g& 0& 1& 0& 0\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ {\mathrm{\φ}}_6^g& 0& 0& 0& 1\\ {\mathrm{\φ}}_7^g& 0& 0& 0& 0\end{array}\right],B_t=\left[\begin{array}{c}{\mathrm{\φ}}_1^u\\ {\mathrm{\φ}}_2^u\\ .\\ .\\ .\\ {\mathrm{\φ}}_6^u\\ 0\end{array}\right]\\ {\mathrm{\Φ}}_t=\left[\begin{array}{c}{\mathrm{\φ}}_0\\ 0\\ .\\ .\\ .\\ 0\end{array}\right],\mathrm{\Ξ}(t+1)=\left[\begin{array}{c}\mathrm{\ξ}(t+1)\\ 0\\ .\\ .\\ .\\ 0\end{array}\right],C={\left[\begin{array}{c}1\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]}^T\end{array}\right.---\left(7\right)$

φ in above formula ₀, φ _i ^gand φ _j ^unot constant, but change along with steel ball position g (t).The predictive variable that definition is relevant:

$\left\{\begin{array}{c}\hat{x}\left(t\right)={\left[\begin{array}{cccc}\hat{x}{(t+1|t)}^T& \hat{x}{(t+2|t)}^T& ...& \hat{x}{(t+12|t)}^T\end{array}\right]}^T\\ \hat{g}\left(t\right)={\left[\begin{array}{cccc}\hat{g}(t+1|t)& \hat{g}(t+2|t)& ...& \hat{g}(t+12|t)\end{array}\right]}^T\\ \hat{u}\left(t\right)={\left[\begin{array}{cccc}u\left(t\right)& t(t+1)& t(t+2)& t(t+3)\end{array}\right]}^T\\ {\stackrel{\‾}{\mathrm{\Φ}}}_t={\left[\begin{array}{cccc}{\mathrm{\Φ}}_t^T& {\mathrm{\Φ}}_{t+1}^T& ...& {\mathrm{\Φ}}_{t+11}^T\end{array}\right]}^T\end{array}\right.---\left(8\right)$

Wherein, multistep forward prediction state vector, steel ball position multistep forward prediction vector, it is winding input voltage multistep forward prediction vector.Suppose u (t+j)=u (t+3) (j >=4), from (5) ~ (7), can obtain:

$\left\{\begin{array}{c}\hat{x}\left(t\right)={\stackrel{\‾}{A}}_{t}x\left(t\right)+{\stackrel{\‾}{B}}_t\hat{u}\left(t\right)+{\stackrel{\‾}{\mathrm{\Γ}}}_t{\stackrel{\‾}{\mathrm{\Φ}}}_t\\ \hat{g}\left(t\right)=\stackrel{\‾}{C}\hat{x}\left(t\right)=\stackrel{\‾}{C}{\stackrel{\‾}{A}}_{t}x\left(t\right)+\stackrel{\‾}{C}{\stackrel{\‾}{B}}_t\hat{u}\left(t\right)+\stackrel{\‾}{C}{\stackrel{\‾}{\mathrm{\Γ}}}_t{\stackrel{\‾}{\mathrm{\Φ}}}_t\end{array}\right.---\left(9\right)$

Here, with for system prediction matrix of coefficients, can be obtained by formula (5) ~ (8), depend on the position of t elect magnetic field steel ball, be the value changed with steel ball position g (t).

${\stackrel{\‾}{A}}_t=\left[\begin{array}{c}{A}_t\\ {\left(A_t\right)}^2\\ .\\ .\\ .\\ {\left(A_t\right)}^{12}\end{array}\right],$

${\stackrel{\‾}{B}}_t=\left[\begin{array}{cccc}{B}_t& 0& 0& 0\\ A_t{B}_t& B_t& 0& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\left(A_t\right)}^3{B}_t& {\left(A_t\right)}^2{B}_t& A_t{B}_t& B_t\\ {\left(A_t\right)}^4{B}_t& {\left(A_t\right)}^3{B}_t& {\left(A_t\right)}^2{B}_t& \underset{i=3}{\overset{4}{\mathrm{\Σ}}}{\left(A_t\right)}^{4-i}{B}_t\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\left(A_t\right)}^{11}{B}_t& {\left(A_t\right)}^{10}{B}_t& {\left(A_t\right)}^9{B}_t& \underset{i=3}{\overset{11}{\mathrm{\Σ}}}{\left(A_t\right)}^{11-i}{B}_t\end{array}\right]---\left(11\right)$

So the linear predictive controller that can change with t in the local linear characteristics design of the tape function power RBF-ARX model of t for maglev ball system.

Definition controlling increment and desired output variable

$\left\{\begin{array}{c}\mathrm{\Δ}\hat{u}\left(t\right)={\left[\mathrm{\Δu}\left(t\right)\mathrm{\Δu}(t+1)\mathrm{\Δu}(t+2)\mathrm{\Δu}(t+3)\right]}^T\\ {\hat{g}}_r\left(t\right)={[g_r(t+1)g_r(t+2)...g_r(r+12)]}^T\\ \mathrm{\Δu}\left(t\right)=u\left(t\right)-u(t-1)\end{array}\right.---\left(12\right)$

Then there is the quadratic programming majorized function that Local-region Linear Prediction controls

$\begin{array}{c}\underset{\hat{u}\left(t\right)}{\min }J={\left|\right|\hat{g}\left(t\right)-{\hat{g}}_r\left(t\right)\left|\right|}_{{1.8I}_{12}}^2+{\left|\right|\hat{u}\left(t\right)\left|\right|}_{{0.0002I}_4}^2+{\left|\right|\mathrm{\Δ}\hat{u}\left(t\right)\left|\right|}_{{0.16I}_4}^2\\ \begin{array}{cc}s.t.& -22\≤\hat{g}\left(t\right)\≤0\end{array}\\ \begin{array}{cc}& 0\≤\hat{u}\left(t\right)\≤10\end{array}\\ \begin{array}{cc}& -3\≤\mathrm{\Δ}\hat{u}\left(t\right)\≤3\end{array}\end{array}---\left(13\right)$

Wherein, i is unit matrix.

To maglev ball system, formula (13) is the optimization problem of a quadratic programming, can obtain optimum control amount by on-line optimization.Thus the PREDICTIVE CONTROL of non-linear maglev ball system is reduced to the change of steel ball location status, linear PREDICTIVE CONTROL, greatly can save the on-line optimization time of optimum control amount, make steel ball reach steady state (SS) rapidly.

Claims (2)

1. a magnetic levitation ball position control method, is characterized in that, comprises the following steps:

1) autoregressive model is set up to maglev ball system:

$g\left(t\right)={\mathrm{\φ}}_0+\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\φ}}_i^{g}g(t-i)+\underset{i=1}{\overset{7}{\mathrm{\Σ}}}{\mathrm{\φ}}_i^{u}u(t-i)+\mathrm{\ξ}\left(t\right)$

Wherein, g (t) is the position of t magnetic levitation ball; U (t) is electromagnetism winding input voltage; ξ (t) is white noise; $\left\{\begin{array}{c}{\mathrm{\φ}}_0=c_0^0+V_1^0\exp (-0.03{\left|\right|W(t-1)-11.74\left|\right|}^2)\\ {\mathrm{\φ}}_i^g=c_{i,0}^g+V_{i,l}^g\exp (-0.03||W(t-1)-11.74{\left|\right|}^2)\\ {\mathrm{\φ}}_j^u=c_{j,0}^u+V_{j,1}^u\exp (-1.33|\left|{W(t-1)+3.82\left|\right|}^2\right)\\ W(t-1)=g(t-1)\\ V^0=v_0^0+v_1^{0}g(t-1)\\ V_i^g=v_{i,0}^g+v_{i,1}^{g}g(t-1)\\ V_j^u=v_{j,0}^g+v_{j,1}^{u}g(t-1)\\ i=\mathrm{1,2},...,7;j=\mathrm{1,2},...,6\end{array}\right.;$ V ⁰, with for the weight coefficient of RBF network, it is the once linear function of steel ball position; for constant coefficient, by the identification of SNPOM optimization method; The position that g (t-1) is t-1 moment magnetic levitation ball;

2) based on described autoregressive model design predictive controller, optimize following quadratic programming function J and obtain optimum control amount, control position g (t) of magnetic levitation ball:

$\left\{\begin{array}{cc}\underset{\hat{u}\left(t\right)}{\min }& J={\left|\right|\hat{g}\left(t\right)-{\hat{g}}_r\left(t\right)\left|\right|}_{{1.8I}_{12}}^2+{\left|\right|\hat{u}\left(t\right)\left|\right|}_{0.0002I_4}^2+{\left|\right|\mathrm{\Δ}\hat{u}\left(t\right)\left|\right|}_{{0.16I}_4}^2\\ s.t.& -22\≤\hat{g}\left(t\right)\≤0\\ & 0\≤\hat{u}\left(t\right)\≤10\\ & -3\≤\mathrm{\Δ}\hat{u}\left(t\right)\≤3\end{array}\right.$

Wherein, ${\hat{g}}_r\left(t\right)={\left[\begin{array}{cccc}{g}_r(t+1)& g_r(t+2)& \·\·\·& g_r(t+12)\end{array}\right]}^T,$ G _r(t+l) for the l that t is given walks forward reference position, l=1,2 ..., 12; $\hat{u}\left(t\right)={\left[\begin{array}{cccc}u\left(t\right)& u(t+1)& u(t+2)& u(t+3)\end{array}\right]}^T,$ The electromagnetism winding input voltage that u (t+p) will optimize for t, only gets Section 1 u (t) and acts on controlled magnetic levitation ball, p=0,1,2,3; $\mathrm{\Δ}u\left(t\right)={\left[\begin{array}{cccc}\mathrm{\Δu}\left(t\right)& \mathrm{\Δu}(t+1)& \mathrm{\Δu}(t+2)& \mathrm{\Δu}(t+3\end{array}\right]}^T,$ Δ u (t)=u (t)-u (t-1) is input voltage increment; $\hat{g}\left(t\right)=\stackrel{\‾}{C}{\stackrel{\‾}{A}}_{t}x\left(t\right)+\stackrel{\‾}{C}{\stackrel{\‾}{B}}_t\hat{u}\left(t\right)+\stackrel{\‾}{C}{\stackrel{\‾}{\mathrm{\Γ}}}_t{\stackrel{\‾}{\mathrm{\Φ}}}_t,$ with for system prediction matrix of coefficients; $\left\{\begin{array}{c}x\left(t\right){=}^{{\left[\begin{array}{cccc}{x}_{1,t}& x_{2,t}& \·\·\·& x_{7,t}\end{array}\right]}^T}\\ x_{1,t}=g\left(t\right)\\ x_{k,t}=\underset{i=1}{\overset{7-k+1}{\mathrm{\Σ}}}{\mathrm{\φ}}_{i+k-1}^{g}g(t-i)+\underset{i=1}{\overset{7-k+1}{\mathrm{\Σ}}}{\mathrm{\φ}}_{i+k-1}^{u}u(t-i)\\ k=\mathrm{2,3},...,7\end{array}\right.$ For state vector; ${\stackrel{\‾}{\mathrm{\Φ}}}_t={\left[\begin{array}{cccc}{\mathrm{\Φ}}_t^T& {\mathrm{\Φ}}_{t+1}^T& \·\·\·& {\mathrm{\Φ}}_{t+11}^T\end{array}\right]}^T,$ ${\mathrm{\Φ}}_t=\left[\begin{array}{c}{\mathrm{\φ}}_0\\ 0\\ \·\\ \·\\ \·\\ 0\end{array}\right];$ φ ₀, with for the regression function coefficient of autoregressive model, ${\mathrm{\φ}}_7^u=0;$ I is unit matrix.

2. magnetic levitation ball position control method according to claim 1, is characterized in that,

${\stackrel{\‾}{A}}_t=\left[\begin{array}{c}{A}_t\\ {\left(A_t\right)}^2\\ .\\ .\\ .\\ {\left(A_t\right)}^{12}\end{array}\right],$

${\stackrel{\‾}{B}}_t=\left[\begin{array}{cccc}{B}_t& 0& 0& 0\\ A_t{B}_t& B_t& 0& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\left(A_t\right)}^3{B}_t& {\left(A_t\right)}^2{B}_t& A_t{B}_t& B_t\\ {\left(A_t\right)}^4{B}_t& {\left(A_t\right)}^3{B}_t& {\left(A_t\right)}^2{B}_t& \underset{i=3}{\overset{4}{\mathrm{\Σ}}}{\left(A_t\right)}^{4-i}{B}_t\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ {\left(A_t\right)}^{11}{B}_t& {\left(A_t\right)}^{10}{B}_t& {\left(A_t\right)}^9{B}_t& \underset{i=3}{\overset{11}{\mathrm{\Σ}}}{\left(A_t\right)}^{11-i}{B}_t\end{array}\right];$

Wherein:

$\left\{\begin{array}{c}{A}_t=\left[\begin{array}{ccccc}{\mathrm{\φ}}_1^g& 1& 0& 0& 0\\ {\mathrm{\φ}}_2^g& 0& 1& 0& 0\\ .& .& .& .& .\\ .& .& .& .& .\\ .& .& .& .& .\\ {\mathrm{\φ}}_6^g& 0& 0& 0& 1\\ {\mathrm{\φ}}_7^g& 0& 0& 0& 0\end{array}\right],B_t\left[\begin{array}{c}{\mathrm{\φ}}_1^u\\ {\mathrm{\φ}}_2^u\\ .\\ .\\ .\\ {\mathrm{\φ}}_6^u\\ 0\end{array}\right]\\ {\left[\begin{array}{c}1\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]}^T\end{array}\right..$