CN110597066B - Integral fuzzy sliding mode control method and equipment for thrust active magnetic suspension bearing - Google Patents
Integral fuzzy sliding mode control method and equipment for thrust active magnetic suspension bearing Download PDFInfo
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Abstract
The invention discloses an integral fuzzy sliding mode control method and equipment of a thrust active magnetic suspension bearing, wherein the method comprises the following steps: according to the displacement of the thrust active magnetic suspension bearing rotor in the X direction, obtaining a transfer function through Laplace transformation, converting the transfer function into a state equation, and calculating a first output of an integral fuzzy sliding mode controller; the method can ensure that the thrust active magnetic suspension bearing system can operate stably from start to run within a certain time without oscillation, improve the control precision of the magnetic suspension bearing, effectively reduce and eliminate sliding mode buffeting, and have strong robust anti-interference capability.
Description
Technical Field
The invention relates to the field of magnetic suspension bearing control, in particular to an integral fuzzy sliding mode control method and device for a thrust active magnetic suspension bearing.
Background
Active Magnetic Bearing (AMB) has a series of advantages such as no wear, long service life, no contamination of lubricant oil, etc., and has been used in hundreds of different rotating or reciprocating machines. The performance of the magnetic suspension bearing controller directly determines whether magnetic suspension can be realized, so the design of the high-performance controller becomes a hotspot of magnetic suspension bearing research.
At present, the proportional-integral-derivative PID controller is widely applied to the practical control of the magnetic suspension bearing, including the thrust active magnetic suspension bearing. However, since the thrust active magnetic suspension bearing is a typical strong nonlinear system, it is difficult to establish an accurate mathematical model thereof, so that the PID controller often has difficulty in obtaining good dynamic performance in engineering practice.
The sliding mode variable structure control has strong anti-interference capability, and is particularly suitable for state identification and control of a nonlinear system, so that the sliding mode variable structure control is widely researched. However, the sliding mode variable structure control has the inherent disadvantage of sliding mode buffeting, and the control performance of the controller is seriously affected along with the increase of the nonlinearity of the system, so that the sliding mode buffeting needs to be improved and eliminated.
Disclosure of Invention
The invention provides an integral fuzzy sliding mode control method and equipment of a thrust active magnetic suspension bearing, which aim to solve the problems.
According to one aspect of the invention, an integral fuzzy sliding mode control method of a thrust active magnetic suspension bearing is provided, which comprises the following steps:
step 3, calculating a first output of the integral fuzzy sliding mode controller according to a state equation;
and 4, adjusting equivalent control and switching control weight through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, calculating a second output of the integral fuzzy sliding mode controller, and controlling the position of the thrust active magnetic suspension bearing rotor by using the second output.
According to another aspect of the invention, an integral fuzzy sliding mode control device of a thrust active magnetic suspension bearing is provided, which comprises:
an integral fuzzy sliding mode control device of a thrust active magnetic suspension bearing is connected with the thrust active magnetic suspension bearing and comprises the following modules:
the mechanical conversion module of the magnetic suspension bearing rotor is used for calculating a mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation; converting the transfer function into a state equation;
the integral fuzzy sliding mode controller comprises an equivalent controller, a switching controller and a fuzzy controller and is used for calculating first output of the integral fuzzy sliding mode controller according to a state equation; obtaining the output of a fuzzy controller through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, adjusting the weights of the equivalent controller and the switching controller by using the output of the fuzzy controller, and calculating the second output of the integral fuzzy sliding mode controller; and controlling the position of the thrust active magnetic suspension bearing rotor by using the second output.
The integral fuzzy sliding mode control method and equipment for the thrust active magnetic suspension bearing, provided by the invention, can enable a system to stably run from starting within a certain time without oscillation, improve the control precision of the thrust active magnetic suspension bearing, effectively reduce and eliminate sliding mode buffeting and have stronger robust interference capability.
Drawings
Fig. 1 is a flowchart of an integral fuzzy sliding mode control method for a thrust active magnetic suspension bearing according to an embodiment of the present invention;
FIG. 2 is a diagram of membership functions of input variables of a fuzzy controller according to an embodiment of the present invention;
FIG. 3 is a diagram of membership function of output variables of a fuzzy controller according to an embodiment of the present invention;
fig. 4 is a structural diagram of an integral fuzzy sliding mode control device of a thrust active magnetic suspension bearing according to an embodiment of the present invention;
fig. 5 is an effect diagram after the control method provided by the embodiment of the invention is applied to a control object;
fig. 6 is a comparison graph of the control method provided by the embodiment of the invention and the control effect of the existing traditional equivalent sliding mode.
Detailed Description
The following description of specific embodiments of the present invention is provided to further illustrate the starting points and corresponding technical solutions of the present invention.
Fig. 1 is a flowchart of an integral fuzzy sliding mode control method of a thrust active magnetic suspension bearing according to an embodiment of the present invention, where the method includes:
step 101, calculating a mechanical equation of the rotor in the X direction according to the displacement of the rotor of the thrust active magnetic suspension bearing in the X direction, and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation.
And when other forces acting on the rotor are not considered, obtaining a mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction according to a Newton mechanical equation, and obtaining a transfer function of the thrust active magnetic suspension bearing rotor through Laplace transformation.
The thrust active magnetic suspension bearing system generally comprises an electromagnet, a rotor, a displacement sensor, a controller, a power amplifier and the like. The sensor detects the deviation of the rotor relative to the reference position, the sensor is used as a controller microprocessor to give a control signal, the control signal is converted into control current after passing through a power amplifier, the control current forms a corresponding electromagnetic field in the electromagnet actuator, and finally the formed magnetic field force always keeps the rotor suspended at the set position. The sensor detects the deviation of the rotor relative to the reference position, the deviation of the rotor is caused by the force, the mechanical equation of the magnetic suspension bearing rotor is obtained according to the Newton's mechanical equation, and the transfer function of the magnetic suspension bearing rotor is obtained through the Laplace transform.
Step 101, calculating a mechanical equation of the rotor in the X direction according to the displacement of the rotor of the thrust active magnetic suspension bearing in the X direction, and obtaining a transfer function of the thrust active magnetic suspension bearing through the raynaud transformation, which specifically comprises the following steps:
according to the displacement X of the thrust active magnetic suspension bearing rotor in the X direction, calculating a mechanical equation of the rotor in the X direction:
obtaining a Laplace transformation formula through Laplace transformation:
ms 2 X(s)＝K x X(s)+K i I(s)；
further obtaining a transfer function G(s) of the thrust active magnetic suspension bearing:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
for the second derivative of rotor displacement, i is the control current in the X direction, K x Is a force displacement stiffness coefficient, K i For force current stiffness coefficient, s is a variable of a transfer function of the thrust active magnetic suspension bearing rotor, X(s) represents an output quantity of the transfer function, and I(s) represents an input quantity of the transfer function. For the thrust active magnetic suspension bearing, current is input, and displacement is output, wherein the displacement is used for stabilizing the rotor at a reference position.
Step 102, converting a transfer function of the thrust active magnetic suspension bearing into a state equation, wherein the expression of the state equation is as follows:
wherein the matrix of rotor displacements x
Is the first derivative, matrix, of the rotor displacement x
Being the first derivative of the matrix X, the matrix
Matrix of
The matrix U 'is the matrix of the second output U' of the integral fuzzy sliding mode controller, m is the rotor mass, K x Is a force displacement stiffness coefficient, K i Is the force current stiffness coefficient.
And 103, calculating a first output of the integral fuzzy sliding mode controller according to the state equation. The method specifically comprises the following steps:
step 103-1, calculating a reference position command according to the state equation
And position error
Wherein X r As a reference position instruction x r In the form of a matrix of (a),
as a reference position instruction x r X is the matrix form of the rotor displacement X, E is the matrix form of the position error E,
is the first derivative of the position error e;
step 103-2, defining an integral sliding mode surface as
Wherein the parameter k of the sliding mode surface is integrated 1 And k 2 Is a non-zero positive constant, t represents the time of rotor operation, 0 represents the start of rotor operation,
as a reference position instruction x r The second derivative of (a);
calculating the first derivative of integral sliding-mode surface w:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
as the first derivative of rotor displacement, K x Is a force displacement stiffness coefficient, K i Is a force current stiffness coefficient, and u is a first output of the integral fuzzy sliding mode controller;
preferably, k is determined 1 And k 2 Wherein k is 1 ＝150，k 2 ＝200，k 1 And k 2 The gain constant of integral control has great help to overcome disturbance, and can effectively improve the system performance.
Integral first derivative of sliding mode surface w
Calculating the output of the equivalent controller as:
step 103-3, calculating the output of the switching controller:
u s ＝mηsgn(w)/(K i k 2 )，
wherein m is the rotor mass, η is a constant greater than zero, sgn (·) is a sign function;
step 103-4, calculating a first output u of the integral fuzzy sliding mode controller as follows:
u＝u eq +u s ，
wherein u is eq Is an output of the equivalent controller, u s Is the output of the switching controller; the condition existing due to the sliding mode is
Thus ensuring the systemStability, so the stability determination formula for the first output u is:
compared with the traditional two-input fuzzy controller, the method can adopt the integral sliding mode surface w as the input of the fuzzy controller, control the input u as the output of the fuzzy system to form a single-input/single-output fuzzy system, and construct a fuzzy rule base according to experience, thereby greatly reducing the number of fuzzy rules.
And 104, adjusting equivalent control and switching control weight through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, calculating a second output of the integral fuzzy sliding mode controller, and controlling the position of the thrust active magnetic suspension bearing rotor by using the second output. The method specifically comprises the following steps:
step 104-1, according to the parameter k of the integral sliding mode surface w 1 And k 2 And a first output u of the integral fuzzy sliding mode controller, determining a fuzzy Rule n of the fuzzy controller as
Wherein,
and alpha n Fuzzy sets which are input and output respectively, wherein N represents the nth fuzzy rule in the N fuzzy rules;
the preferred fuzzy Rule n includes the following 5 fuzzy rules:
(1)If(w is NB)then(u is PB)
(2)If(w is NS)then(u is PS)
(3)If(w is Z)then(u is Z)
(4)If(w is PS)then(u is NS)
(5)If(w is PB)then(u is NB)
membership functions of the integral sliding mode surface w and the first output u of the integral fuzzy sliding mode controller adopt negative large (NB), "negative small" (NS), "zero" (Z), "positive small" (PS) and "positive large" (PB) and are used for performing defuzzification in the next step by adopting a gravity center method.
Step 104-2, performing defuzzification by adopting a gravity center method to obtain the output of a fuzzy controller:
wherein, ω is n And alpha n Respectively are the membership degrees of the antecedent and the conclusion in the nth rule;
if any element delta in the range omega of the domain of discourse research has a number H (delta) epsilon [0, 1] corresponding to the element delta, H is called as a fuzzy set on omega, and H (delta) is called as the membership degree of delta to H, and represents the degree of association between a certain element and the domain of discourse.
And (3) establishing a fuzzy system by adopting an S function program of a matrix laboratory MATLAB, and keeping the rule base in the running process all the time through a command persistence. When the flag is 1, a membership function graph can be given.
Referring to fig. 2 and 3, fig. 2 is a graph of membership function of input variables of the fuzzy controller, the abscissa of fig. 2 represents a domain value, the ordinate represents the input value of the fuzzy controller, and "large negative NB," small negative NS, "zero" Z, "small positive PS, and large positive PB" in fig. 2 are linguistic variable values, and different domain values correspond to different linguistic variable values; fig. 3 is a diagram of membership function of output variable of the fuzzy controller, the abscissa of fig. 3 represents a theory domain value, the ordinate represents the output value of the fuzzy controller, NB, NS, Z, PS and PB in fig. 3 are linguistic variable values, and different theory domain values correspond to different linguistic variable values. FIGS. 2 and 3 show the derivation of a fuzzy output variable u from a fuzzy input variable w fz Fuzzy output u fz Coefficient, u, corresponding to the switching controller fz Multiplication by switching controller, since u fz The product of the variable quantity and the variable quantity is changed along with the variable quantity, so that the method can adapt to the change of a system more and achieve the aim of improving the control precision.
Step 104-3, calculating a second output of the integral fuzzy sliding mode controller:
u′＝u eq +u fz u s ，
wherein u is eq Is an output of the equivalent controller, u s For switching the output of the controller, u fz Is the output of the fuzzy controller; the second output u' of the integrating fuzzy sliding mode controller is the output in the form of the control current.
And step 104-4, taking the second output u' of the integral fuzzy sliding mode controller as a control signal, and applying the control signal to the thrust active magnetic suspension bearing system to change the position of the rotor.
Fig. 4 is a structural diagram of an integral fuzzy sliding mode control device of a thrust active magnetic suspension bearing according to an embodiment of the present invention. The equipment is connected with a thrust active magnetic suspension bearing and comprises the following modules:
the mechanical conversion module 410 of the magnetic suspension bearing rotor is used for calculating a mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation; converting the transfer function into a state equation;
the integral fuzzy sliding mode controller 420 comprises an equivalent controller 421, a switching controller 422 and a fuzzy controller 423, and is used for calculating a first output of the integral fuzzy sliding mode controller 420 according to a state equation; obtaining the output of the fuzzy controller 423 through a fuzzy rule according to the parameter of the integral sliding mode surface and the first output, adjusting the weights of the equivalent controller 421 and the switching controller 422 by using the output of the fuzzy controller 423, and calculating a second output of the integral fuzzy sliding mode controller 420; and controlling the position of the thrust active magnetic suspension bearing rotor by using the second output.
Preferably, the mechanical conversion module 410 of the magnetic suspension bearing rotor is specifically configured to:
according to the displacement X of the thrust active magnetic suspension bearing rotor in the X direction, calculating a mechanical equation of the rotor in the X direction:
obtaining a Laplace transformation formula through Laplace transformation:
ms 2 X(s)＝K x X(s)+K i I(s)；
further obtaining a transfer function G(s) of the thrust active magnetic suspension bearing:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
for the second derivative of the rotor displacement, i is the control current in the X direction, K x Is a force displacement stiffness coefficient, K i For a force current stiffness coefficient, s is a variable of a transfer function of a thrust active magnetic suspension bearing rotor, X(s) represents an output quantity of the transfer function, and I(s) represents an input quantity of the transfer function;
converting the transfer function to a state equation as:
wherein the matrix of rotor displacements x
Is the first derivative, matrix, of the rotor displacement x
Being the first derivative of the matrix X, the matrix
Matrix array
The matrix U 'is the matrix of the second output U' of the integral fuzzy sliding mode controller, m is the rotor mass, K x Is a force displacement stiffness coefficient, K i Is the force current stiffness coefficient.
Preferably, the calculating the first output of the integral fuzzy sliding mode controller 420 according to the state equation by the integral fuzzy sliding mode controller 420 comprises:
calculating a reference position command from a state equation
And position error
Wherein X r As a reference position instruction x r In the form of a matrix of (a),
as a reference position instruction x r X is the matrix form of the rotor displacement X, E is the matrix form of the position error E,
is the first derivative of the position error e;
defining an integral sliding mode surface as
Wherein k is 1 And k 2 Is a non-zero positive constant, t represents the time of rotor operation, 0 represents the start of rotor operation,
as a reference position instruction x r The second derivative of (a);
calculating the first derivative of integral sliding-mode surface w:
whereinX denotes the displacement of the rotor in the X direction, m is the rotor mass,
as the first derivative of rotor displacement, K x Is a force displacement stiffness coefficient, K i Is a force current stiffness coefficient, and u is a first output of the integral fuzzy sliding mode controller;
integral first derivative of sliding mode surface w
The output of the equivalent controller 421 is calculated as:
compute output of switching controller 422:
u s ＝mηsgn(w)/(K i k 2 )，
wherein m is the rotor mass, η is a constant greater than zero, sgn (·) is a sign function;
the first output u of the compute integral fuzzy sliding mode controller 420 is:
u＝u eq +u s ，
wherein u is eq Is an output of the equivalent controller, u s Is the output of the switching controller; the stability determination formula of the first output u is:
preferably, the calculating the second output of the integrating fuzzy sliding mode controller 420 by the integrating fuzzy sliding mode controller 420 comprises:
coefficient k according to integral sliding mode surface w 1 And k 2 And a first output u of the integral fuzzy sliding mode controller 420, determining a fuzzy Rule n of the fuzzy controller 423 as
Wherein,
and alpha n Fuzzy sets which are input and output respectively, wherein N represents the nth fuzzy rule in the N fuzzy rules;
defuzzification is performed by a gravity method to obtain the output of the fuzzy controller 423:
wherein, ω is n And alpha n Respectively is the membership of the precondition and the conclusion in the nth rule;
compute a second output of the integral fuzzy sliding mode controller 420:
u′＝u eq +u fz u s ，
wherein u is eq Is an output of the equivalent controller 421, u s For switching the output of the controller 422, u fz Is the output of the fuzzy controller 423.
According to the fuzzy sliding mode control method and the fuzzy sliding mode control equipment with the integral sliding mode surface, when a thrust active magnetic suspension bearing system is disturbed, the thrust active magnetic suspension bearing can still work normally, the control precision of the thrust active magnetic suspension bearing is improved, sliding mode buffeting is effectively reduced and eliminated, and the robust interference capability is strong.
According to specific parameters of an actual thrust active magnetic suspension bearing system, the effectiveness of the fuzzy sliding mode control method with the integral sliding mode surface is verified by comparing a position tracking result obtained by a traditional equivalent sliding mode control method and the fuzzy sliding mode control method with the integral sliding mode surface under the same simulation condition through simulation.
Fig. 5 is an effect diagram after the control method provided by the present invention is applied to a controlled object, when the system is running from start to steady, the system can be rapidly stabilized at 0.15s (second) under the control of integral fuzzy sliding mode, there is no oscillation phenomenon and the deviation value after stabilization is less than ± 0.001mm (millimeter) to meet the requirement of the system steady deviation value.
Fig. 6 is a comparison graph of the control effect of the present invention and the conventional equivalent sliding mode, and it can be seen from fig. 6 that the effect graph of the conventional equivalent sliding mode control method applied to the system appears, when the system runs from start to steady, the system generates oscillation phenomenon under the control effect of the conventional equivalent sliding mode and is stabilized at 0.21s, the deviation value after stabilization is between +0.001mm to +0.002mm, and the requirement for the system steady deviation value is partially satisfied. By contrast, the following conclusions can be drawn: compared with the conventional equivalent sliding mode control method, the fuzzy sliding mode control method with the integral sliding mode surface in the system has the advantages that the time required for achieving stable operation is shorter, the deviation value relative to a displacement reference instruction is smaller, the oscillation phenomenon does not exist, and the robust interference capability is stronger.
While the invention has been described in connection with specific embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. An integral fuzzy sliding mode control method of a thrust active magnetic suspension bearing is characterized by comprising the following steps:
step 1, calculating a mechanical equation of a rotor in the X direction according to the displacement of the rotor of the thrust active magnetic suspension bearing in the X direction, and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation;
step 2, converting a transfer function of the thrust active magnetic suspension bearing into a state equation;
step 3, calculating a first output of the integral fuzzy sliding mode controller according to a state equation;
step 4, adjusting equivalent control and switching control weight through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, calculating a second output of the integral fuzzy sliding mode controller, and controlling the position of the thrust active magnetic suspension bearing rotor by using the second output;
wherein, in the step 3, calculating the first output of the integral fuzzy sliding mode controller according to the state equation comprises:
step 301, calculating a reference position command according to a state equation
And position error
Wherein X r As a reference position instruction x r In the form of a matrix of (a),
as a reference position instruction x r X is the matrix form of the rotor displacement X, E is the matrix form of the position error E,
is the first derivative of the position error e;
step 302, defining the formula of the integral sliding mode surface w as
Wherein, the integral sliding mode surface parameter k 1 And k 2 Is a non-zero positive constant, t represents the time of rotor operation, 0 represents the start of rotor operation,
as a reference position instruction x r The second derivative of (a);
calculating the first derivative of integral sliding-mode surface w:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
as the first derivative of rotor displacement, K x Is a force displacement stiffness coefficient, K i The force current stiffness coefficient is, and u is a first output of the integral fuzzy sliding mode controller;
integral first derivative of sliding mode surface w
The output of the equivalent controller is calculated as:
step 303, calculate the output of the switching controller:
u s ＝mηsgn(w)/(K i k 2 )，
wherein m is the rotor mass, η is a constant greater than zero, sgn (·) is a sign function;
step 304, calculating a first output u of the integral fuzzy sliding mode controller as:
u＝u eq +u s ，
wherein u is eq Is an output of the equivalent controller, u s Is the output of the switching controller; the stability determination formula of the first output u is:
2. the method of claim 1, wherein step 1 comprises:
according to the displacement X of the thrust active magnetic suspension bearing rotor in the X direction, calculating a mechanical equation of the rotor in the X direction:
obtaining a Laplace transformation formula through Laplace transformation:
ms 2 X(s)＝K x X(s)+K i I(s)；
further obtaining a transfer function G(s) of the thrust active magnetic suspension bearing:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
for the second derivative of rotor displacement, i is the control current in the X direction, K x Is a force displacement stiffness coefficient, K i For force current stiffness coefficient, s is a variable of a transfer function of the thrust active magnetic suspension bearing rotor, X(s) represents an output quantity of the transfer function, and I(s) represents an input quantity of the transfer function.
3. The method of claim 1, wherein the expression of the state equation of step 2 is:
wherein the matrix of rotor displacements x
Is the first derivative, matrix, of the rotor displacement x
Being the first derivative of the matrix X, the matrix
Matrix array
The matrix U 'is the matrix of the second output U' of the integral fuzzy sliding mode controller, m is the rotor mass, K x Is a force displacement stiffness coefficient, K i Is the force current stiffness coefficient.
4. The method of claim 1, wherein step 4 comprises:
step 401, according to the parameter k of the integral sliding mode surface w 1 And k 2 And a first output u of the integral fuzzy sliding mode controller, determining a fuzzy Rule n of the fuzzy controller as
Wherein,
and alpha n Fuzzy sets which are input and output respectively, wherein N represents the nth fuzzy rule in the N fuzzy rules;
step 402, performing defuzzification by using a gravity center method to obtain the output of a fuzzy controller:
wherein, ω is n And alpha n Membership degrees of the antecedents and the conclusions in the nth rule respectively;
step 403, calculating a second output of the integral fuzzy sliding mode controller:
u'＝u eq +u fz u s ，
wherein u is eq Is an output of the equivalent controller, u s For switching the controllerOutput of u fz Is the output of the fuzzy controller;
and step 404, taking the second output u' of the integral fuzzy sliding mode controller as a control signal, and applying the control signal to the thrust active magnetic suspension bearing system to change the position of the rotor.
5. The utility model provides an integral fuzzy sliding mode controlgear of thrust initiative magnetic suspension bearing, is connected with thrust initiative magnetic suspension bearing which characterized in that includes:
the mechanical conversion module of the magnetic suspension bearing rotor is used for calculating a mechanical equation of the thrust active magnetic suspension bearing rotor in the X direction and obtaining a transfer function of the thrust active magnetic suspension bearing through Laplace transformation; converting the transfer function into a state equation;
the integral fuzzy sliding mode controller comprises an equivalent controller, a switching controller and a fuzzy controller and is used for calculating first output of the integral fuzzy sliding mode controller according to a state equation; obtaining the output of a fuzzy controller through a fuzzy rule according to the parameters of the integral sliding mode surface and the first output, adjusting the weights of the equivalent controller and the switching controller by using the output of the fuzzy controller, and calculating the second output of the integral fuzzy sliding mode controller; controlling a position of a thrust active magnetic bearing rotor using the second output;
the integral fuzzy sliding mode controller is used for calculating the first output of the integral fuzzy sliding mode controller according to a state equation, and comprises the following steps:
calculating a reference position command from a state equation
And position error
Wherein X r As a reference position instruction x r In the form of a matrix of (a),
as a reference position instruction x r First order ofNumber, X is the matrix form of the rotor displacement X, E is the matrix form of the position error E,
is the first derivative of the position error e;
defining an integral sliding mode surface as
Wherein k is 1 And k 2 Is a non-zero positive constant, t represents the time of rotor operation, 0 represents the start of rotor operation,
as a reference position instruction x r The second derivative of (a);
calculating the first derivative of integral sliding-mode surface w:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
as the first derivative of rotor displacement, K x Is a force displacement stiffness coefficient, K i Is a force current stiffness coefficient, and u is a first output of the integral fuzzy sliding mode controller;
integral first derivative of sliding mode surface w
The output of the equivalent controller is calculated as:
compute the output of the switching controller:
u s ＝mηsgn(w)/(K i k 2 )，
wherein m is the rotor mass, η is a constant greater than zero, sgn (·) is a sign function;
calculating a first output u of the integral fuzzy sliding mode controller as:
u＝u eq +u s ，
wherein u is eq Is an output of the equivalent controller, u s Is the output of the switching controller; the stability determination formula of the first output u is:
6. the apparatus according to claim 5, characterized in that the mechanical transformation module of the magnetic bearing rotor is specifically configured to:
according to the displacement X of the thrust active magnetic suspension bearing rotor in the X direction, calculating a mechanical equation of the rotor in the X direction:
obtaining a Laplace transformation formula through Laplace transformation:
ms 2 X(s)＝K x X(s)+K i I(s)；
further obtaining a transfer function G(s) of the thrust active magnetic suspension bearing:
where X denotes the displacement of the rotor in the X direction, m is the rotor mass,
for the second derivative of rotor displacement, i is the control current in the X direction, K x Is a force displacement steelCoefficient of degree, K i For a force current stiffness coefficient, s is a variable of a transfer function of a thrust active magnetic suspension bearing rotor, X(s) represents an output quantity of the transfer function, and I(s) represents an input quantity of the transfer function;
converting the transfer function to a state equation as:
wherein the matrix of rotor displacements x
Is the first derivative, matrix, of the rotor displacement x
Being the first derivative of the matrix X, the matrix
Matrix array
The matrix U 'is the matrix of the second output U' of the integral fuzzy sliding mode controller, m is the rotor mass, K x Is a force displacement stiffness coefficient, K i Is the force current stiffness coefficient.
7. The apparatus of claim 5, wherein the integral fuzzy sliding mode controller calculating the second output of the integral fuzzy sliding mode controller comprises:
parameter k from integral sliding mode surface w 1 And k 2 And a first output u of the integral fuzzy sliding mode controller, determining a fuzzy Rule n of the fuzzy controller as
Wherein,
and alpha n Fuzzy sets which are input and output respectively, wherein N represents the nth fuzzy rule in the N fuzzy rules;
performing defuzzification by adopting a gravity center method to obtain the output of a fuzzy controller:
wherein, ω is n And alpha n Membership degrees of the antecedents and the conclusions in the nth rule respectively;
calculating a second output of the integrating fuzzy sliding mode controller:
u'＝u eq +u fz u s ，
wherein u is eq Is an output of the equivalent controller, u s For switching the output of the controller, u fz Is the output of the fuzzy controller.
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| CN110138297A (en) * | 2019-05-31 | 2019-08-16 | 东南大学 | A kind of permanent magnetic linear synchronous motor speed and current double closed-loop control system and control method |
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| US6074180A (en) * | 1996-05-03 | 2000-06-13 | Medquest Products, Inc. | Hybrid magnetically suspended and rotated centrifugal pumping apparatus and method |
| CN110138297A (en) * | 2019-05-31 | 2019-08-16 | 东南大学 | A kind of permanent magnetic linear synchronous motor speed and current double closed-loop control system and control method |
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