CN104793645B - Magnetic Levitation ball position control method - Google Patents

Abstract

The present invention discloses a method for controlling the position of the magnetic levitation suspension, it is difficult to establish a precise physical model disadvantage for magnetic levitation suspension system, the system identification method for establishing a non-function weighting coefficients belt between the input voltage and the electromagnetic winding position of the ball will be described autoregressive model linear dynamic characteristics. The model with a linear function of the position of the ball as a Gaussian RBF network weights, and by the RBF network as a nonlinear function of the type coefficients from the regression model, so the model can characterize the dynamic properties of Magnetic Levitation System. This model is the regression coefficient at a time constant, similar to a linear ARX model. Based on this, the present invention is the design of a time-varying, local linear predictive controller, each time by solving the quadratic programming line to quickly achieve the optimum position of the ball control, to meet the magnetic levitation suspension system stable, fast requirements.

Description

_ The ball levitation position control method Species

FIELD

[0001] The present invention relates to technical field of automatic control, in particular a magnetic levitation position control method ball.

Background technique

[0002] is a set of electromagnetic levitation technology, electronic technology, control engineering, signal processing, mechanics, one of the kinetics, the typical mechatronics. Maglev technology because of its non-contact, no friction, low noise characteristics have been widely used in maglev trains, magnetic bearings, magnetic levitation motors and other projects. Magnetic Levitation System mainly through an electromagnetic force generated at a constant current through the electromagnetic coil, so that the ball equilibrium with gravity, steel balls suspended in the air is in a state of equilibrium, the purpose of stable operation of the system. Magnetic Levitation System has a single direction with a non-linear nature of open-loop unstable, the characteristics of fast response, vulnerability to power supply and the external environment, some parameters have strong uncertainty can not be accurately measured. And an electromagnetic field so that magnetic saturation field is not proportional to input current and flux linkage between the magnetic flux density, the relationship between an electromagnetic coil, and increases the nonlinear system model of the system results in an electromagnetic force can not be expressed in simple mathematical equations; the same time, electromagnetic field is generated in a steel ball eddy current, in turn, will affect the inductance of the electromagnetic coil, the electromagnetic coil such that the inductance is not constant but a function of the surface of the ball to the electromagnet pole gap g, and nonlinearity therewith relationship. Therefore, accurate physics model Magnetic Levitation System is very difficult, this is a difficult system to achieve stable levitation ball control lies.

[0003] PID control structure is simple and can adjust the input current / voltage causes ball suspension, without having to create a physical model of the suspension system, the control parameter requires manual tuning, poor adaptability, effective control of the nonlinear magnetic levitation system small, especially when the ball changes position quickly when the overshoot is large, larger jitter ball. Automatically adjusting the control parameters of PID fuzzy reasoning, one can improve the ability parameter electromagnet with an air gap between the ball and variations varies. However, the method relies on fuzzy rule base, which is subject to the establishment of the designer's experience. On the other hand, by analyzing the principle of magnetic suspension system, based on some assumptions on the physical model, and adaptive control may be implemented, synovial control, predictive control of the ball. These methods are the most difficult to achieve is that the more difficult to obtain accurate physical models that accurately describe the dynamic characteristics of the suspension system, since it is difficult to certain assumptions are met in engineering applications. Further, with the technique of linear physical model linear processing, a linear control strategy and then design, optimized speed control to speed up the line, but the loss characteristics of the nonlinear system, weakening the ability of the model description of the magnetic levitation system, thereby reducing control effect .

SUMMARY

[0004] The present invention solves the technical problem, for the deficiencies of the prior art, there is provided a magnetic levitation position control method ball.

[0005] To solve the above technical problem, the technical solution employed in the present invention is: A method of controlling the position of the magnetic levitation suspension, the degree of freedom for a single magnetic levitation suspension system moves up and down, the magnetic levitation suspension system comprises a single degree of freedom of generating an electromagnetic field and a detection coil winding photosensor ball position; said electromagnetic winding input voltage is given by a controller controls the driving circuit; a signal to the control computer the position of the photosensor balls collected by the data acquisition card transfer. Since the establishment of regression model Magnetic Levitation System:

[0007] wherein, g (t) is the position of the magnetic levitation suspension; u (t) is the input voltage of the electromagnetic coil; ξ (t) is white noise;

And Vju as the RBF network weights, is a linear function of the position of the ball type

Is a constant coefficient, by identifying methods to optimize SNPOM, obtained by calculation based on the least squares method to obtain the nonlinear parameters.

[0008] Then, based on the autoregressive model predictive controller design, the following quadratic programming optimization function J to obtain optimal control, controlling the position of the ball maglev g (t):

[0010] in which

Time t 1 is the position predictors paces ball, according to the time t obtained from the regression model prediction expression step 1, i.e.

^ Prediction coefficient matrix for the system, the time t and the multi-step autoregressive model independent predictors eligible

T is the time given a step forward reference position

3 is a time t to be optimized electromagnetic winding input voltage, taking only the first term u (t) acting on the charged magnetic levitation suspension;

Input voltage increment;

^ Towel and / autoregressive model regression function coefficients, φ '= 0; 1 is the identity matrix.

[0011] Compared with the prior art, the present invention has beneficial effects: the present invention uses thought identification modeling system using the actual operating system information input / output data including dynamic characteristics of the system to establish Magnetic Levitation System dynamic models can describe the maximum possible dynamic characteristics of the system, without regard to the effect of magnetic saturation and eddy current effect of the model (these effects have been included in the identification data). The method is applicable to such strongly nonlinear and uncertain complex system, may be extended to other similar systems; on RBF network RBF-ARX model coefficients with weight function of the present invention depends on establishing the position of the ball in the electromagnetic field, improve the RBF network function approximation capabilities, so that a set of pseudo-linear ARX model obtained better describe the dynamic behavior of nonlinear Magnetic levitation system. Step predictive model error within ± 0.4%; weight function with RBF-ARX model based design variant of the present invention, the local linear predictive controller calculates the optimal control can quickly optimize the amount of time to reduce the online optimization, facilitate optimization is done in the magnetic levitation suspension system sampling period (5 ms) is calculated, fast, stable position control of the ball.

BRIEF DESCRIPTION

[0012] FIG configuration diagram of a magnetic levitation suspension system of the present invention.

Detailed ways

[0013] Magnetic Levitation System architecture of the present invention as shown, is only a single degree of freedom system to control vertical movement of the ball 1. PC, the output voltage controlled by the controller 9, the D / A converter 8 is transmitted to the electromagnetic coil driving circuit 6, an electromagnetic coil 2 through electromagnetic induction in a corresponding current flow, an electromagnetic field is formed below the winding, in the field of the ball 1 is applied a magnetic force F, so that the ball moves up / down, adjusting the air gap G (i.e., the position of the ball) between the electromagnet and the ball, and the ball until the electromagnetic force F G balance gravity; Meanwhile, LED the light source 3 and the plate 4 photovoltaic photosensor for detecting the position of the balls, a corresponding voltage signal processing circuit 5 and a / D converter 7 outputs the PC returned. The system shown in Figure 1, ball 1 radius of 12.5 mm, mass of 22 g, the number of turns of the electromagnetic coil 2 of 2450, an equivalent resistance of 13.8 ohms.

[0014] The magnetic levitation suspension system of the present invention and the influence of the magnetic saturation by the eddy current effect is also influenced by the power supply and external disturbances. For this reason, the method using the RBF-ARX model modeling with weight function based on the dynamic model constructing an electromagnetic winding voltage input positional relationship between the ball and the electromagnetic field. In the present invention, the use of data identification techniques using linear weight coefficients as a function of the position of the ball, Gaussian RBF kernel nonlinear coefficient as a function of network ARX model. The model is a nonlinear model with varying linearly the ARX model structure, its argument is an input voltage of the electromagnetic coil, the amount of the return ball position, ball position signal indicative of an amount of the system state, and the ball position using Related constant linear function approximation RBF neural network weights, and then the structure parameters of the model RBF real time adjustments. With weight function RBF-ARX model in the linear interval local linear ARX model is very similar, additional parameters that can be automatically updated with the state of nonlinear systems, automatic adjustment, having a better global adaptability.

[0015] Construction of the ball between the position of the electromagnetic coil type weight coefficient function of input voltage RBF-ARX model of the dynamic characteristic model, using the method of Stewart 列维布格马奎 (Levenberg-Marquardt Method, LMM), and a linear least squares ( Least Square method, LSM) SNPOM combined optimization method (see:? Peng H, 0zaki T, Haggan-Ozaki VjToyoda Y.2003 a parameter optimization method for the radial basis function type models) identifying the model parameters, the following structure is obtained :

Regression function coefficients Φο, φ, and Cf are autoregressive model; [0019] g (t) is the position of the ball, the ball is an air gap between the electromagnet; u (t) is the input voltage of the electromagnetic coil ; W (t-ι) operating point for the system state, the position of the ball with g (ti) to characterize the status of the operating point of the system; ν'if a linear function of the position of the ball and G, as a function of the RBF neural network weights ; II · II for the 2-norm; ξ (t) is white noise;

Linear constant coefficient, by optimizing SNPOM identification method, to obtain LSM used calculated on the basis of the obtained nonlinear parameters. make

Θ # = {0.03,1.33,11,74, -3.82}, the formula is rewritten as ⑴

4000 observations were used [0021] wherein, 5V) is observed ball position data, SNPOM for model identification.

[0022] Magnetic Levitation System using local linear time-varying characteristics of the design, the linear predictive controller. The formula ⑴ rewritten as a polynomial

[0025] The definition of the system state variables:

[0027] ⑴ state space model is the formula:

[0031] [Phi] billion above formula, Φ f and Φ / 1 is not constant, but the position of the ball with g (t) is changed. Define the relevant predictor variables:

[0033] wherein, thiophene) is a multi-step ahead predicted state vector, numerous) position of the ball is a multi-step ahead prediction vector, ύ (square input voltage winding is a multi-step ahead prediction vector. Suppose u (t + j) = U (t + 3) (j San 4), from (5) to (7) can be obtained:

[0035] here:

Spoon prediction coefficient matrix system, ~⑶ obtained by equation (5), dependent on the position of the ball in the field at time t, both the position of the ball with the change in the value of g (t).

[0038] and therefore may be directed Magnetic Levitation System Design of Linear Predictive Controller t varies with local linear characteristic with RBF-ARX model function of time t weight.

[0039] defined incremental control MU) and the desired output variable i. (I)

[0041] There is a Local Linear Predictive Control quadratic programming optimization function

[0044] The magnetic levitation ball system, formula (13) is a quadratic programming optimization problem, you can obtain optimal control through online optimization. Thereby simplifying nonlinear predictive control for Magnetic Suspension System with a change in position of the ball, the linear predictive control, optimal control can greatly reduce the amount of time online optimization, allow the balls to quickly reach a steady state.

Claims (2)

1. A magnetic levitation ball position control method, characterized by comprising the following steps: 1) Magnetic Levitation System established autoregressive model:

   

   Wherein, g⑴ is a magnetic levitation position of the ball at time t; U⑴ input voltage to the electromagnetic coil; ξ⑴ white noise;

   

   ;

   

   Weights for the RBF network, is a linear function of the position of the ball;

   

   Is a constant coefficient, identification by SNPOM optimization; g (t-Ι) of t-Ι time levitation position of the ball; 2) based on the autoregressive model predictive controller design, the following quadratic programming optimization function J to obtain optimal control amount, controlling the position of the ball maglev g (t):

   

   among them:

   

   , Gi · (t + i) is given at time t 1 the reference step forward position, 1 = 1,2, ..., 12;

   

   , .U (t + p) is the time t to optimize electromagnetic winding input voltage, taking only the first term u (t) acting on the charged magnetic levitation suspension, p = 0,1,2,3;

   

   , Au (t) = u (t) -u (tl) is the input voltage increment;

   

   System prediction coefficient matrix;

   

   State vector;

   

   

   Autoregressive coefficients of the model regression function, a unit matrix; 112 is a unit matrix of order 12; I4 fourth-order matrix.

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