CN112859618B - Self-adaptive learning sliding mode control method for multi-degree-of-freedom magnetic suspension planar motor - Google Patents
Self-adaptive learning sliding mode control method for multi-degree-of-freedom magnetic suspension planar motor Download PDFInfo
- Publication number
- CN112859618B CN112859618B CN202110180359.1A CN202110180359A CN112859618B CN 112859618 B CN112859618 B CN 112859618B CN 202110180359 A CN202110180359 A CN 202110180359A CN 112859618 B CN112859618 B CN 112859618B
- Authority
- CN
- China
- Prior art keywords
- adaptive
- sliding mode
- freedom
- model
- iterative learning
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 55
- 239000000725 suspension Substances 0.000 title claims abstract description 39
- 230000003044 adaptive effect Effects 0.000 claims abstract description 30
- 230000006870 function Effects 0.000 claims description 20
- 230000008569 process Effects 0.000 claims description 14
- 238000005339 levitation Methods 0.000 claims description 13
- 230000003247 decreasing effect Effects 0.000 claims description 6
- 230000003252 repetitive effect Effects 0.000 claims description 6
- 230000001133 acceleration Effects 0.000 claims description 4
- 230000008859 change Effects 0.000 claims description 4
- 238000006073 displacement reaction Methods 0.000 claims description 3
- 230000005484 gravity Effects 0.000 claims description 3
- 230000002401 inhibitory effect Effects 0.000 claims description 3
- 239000011159 matrix material Substances 0.000 claims description 3
- 230000007423 decrease Effects 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 239000000126 substance Substances 0.000 description 3
- 238000006467 substitution reaction Methods 0.000 description 2
- 241000135164 Timea Species 0.000 description 1
- 238000007792 addition Methods 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
- 238000005859 coupling reaction Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000012938 design process Methods 0.000 description 1
- 238000007667 floating Methods 0.000 description 1
- 238000001459 lithography Methods 0.000 description 1
- 238000013507 mapping Methods 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention provides a self-adaptive learning sliding mode control method of a multi-degree-of-freedom magnetic suspension planar motor. The invention utilizes a dynamic decoupling method to convert a multi-freedom control model into mutually independent single-freedom-degree models, and establishes a general system parameter model containing uncertainty items and external interference aiming at the single-freedom-degree models; according to the model, an adaptive sliding mode controller model is constructed to inhibit external interference, and an iterative learning compensation item is designed according to an uncertain item. Combining the iterative learning compensation item and the sliding mode control item in a parallel mode to obtain a self-adaptive iterative learning sliding mode controller; performing stability analysis and error convergence analysis on the control algorithm through a Lyapunov theory; and applying the control algorithm to an actual magnetic suspension planar motor system, and verifying the effectiveness of the control algorithm. The control method solves the problems of external interference and tracking control under an uncertain item in a magnetic suspension plane motor system, and has the advantages of strong robustness of an algorithm, good self-adaptive capacity and high tracking precision.
Description
Technical Field
The invention belongs to the field of magnetic levitation planar motor control, and particularly relates to a self-adaptive learning sliding mode control method for a multi-degree-of-freedom magnetic levitation planar motor.
Technical Field
Magnetic levitation planar motors have been extensively studied and developed over the last decades as a new type of drive element. The magnetic suspension planar motor does not need a mechanical guide rail for supporting, can directly realize two-dimensional planar driving with large stroke, greatly simplifies a mechanical motion structure, has small volume and light weight, and can realize high-speed motion. In addition, because no mechanical or air-floating support is needed, precise movement can be realized under the vacuum condition. These advantages make it have wide application prospect in semiconductor lithography system and other high precision industrial fields.
The adaptive sliding mode control has good robustness and adaptive capacity to system parameters, but uncertain items related to states in the system are only suppressed through a simple robust item, so that the tracking effect is over conservative, and the steady-state error is larger.
The iterative learning algorithm belongs to a data driving technology, does not depend on an accurate system model, and can optimize control input in current iteration according to tracking error information in a previous iteration period so as to improve the control precision of the system.
Disclosure of Invention
In order to overcome the limitation of the existing control method of the multi-degree-of-freedom magnetic suspension motor, and improve the robustness and the parameter self-adaptive capacity of the controller while considering the tracking precision, the control method of the multi-degree-of-freedom magnetic suspension planar motor self-adaptive iterative learning sliding mode is provided, the control method ensures the stability and the parameter self-adaptive capacity of the system through the self-adaptive sliding mode control item, and meanwhile, the iterative learning control item is introduced to further eliminate the repetitive interference of the system, so that the tracking precision of the magnetic suspension system is improved. The adaptive sliding mode control term is combined with the iterative learning control term in a parallel manner.
The technical scheme for solving the technical problem is a self-adaptive learning sliding mode control method of a multi-degree-of-freedom magnetic levitation planar motor, which comprises the following steps:
step 1: converting the multi-freedom control model into mutually independent single-freedom-degree models by utilizing a dynamic decoupling model of the magnetic suspension planar motor, and establishing a general system parameter model containing uncertain items and external interference aiming at the single-freedom-degree models;
step 2: according to a general system parameter model, a self-adaptive sliding mode controller model is constructed by combining an expected motion track, and a robust item in a sliding mode controller can be used for inhibiting influence caused by external interference. And designing an iterative learning compensation item of the uncertain item aiming at the uncertain item in the system parameter model, and combining the iterative learning compensation item and the sliding mode control item in a parallel mode to obtain the self-adaptive iterative learning sliding mode controller model.
And step 3: and respectively carrying out stability analysis and error convergence analysis on the self-adaptive iterative learning sliding-mode controller model by a Lyapunov direct method.
And 4, step 4: the control algorithm is applied to an actual magnetic suspension planar motor system, track tracking is carried out under the condition that external interference exists, and the effectiveness of the control algorithm is verified.
Preferably, the dynamic decoupling model of the magnetic levitation planar motor in step 1 is specifically defined as:
wherein each item is defined as
M＝diag[Mm，Mm，Mm，Ixx，Iyy，Izz]
X＝[sx，sy，sz，α，β，γ]T
G＝[0，0，Mmg，0，0，0]T
U＝[sFx，sFy，sFz，sTx，sTy，sTz]T，
Wherein M ismIs the mover mass, Ixx、Iyy、IzzIn order to be the moment of inertia,sx、sy、sz is displacement in each direction, alpha, beta and gamma are rotation around each axis, g is gravity acceleration,sFx、sFy、sFzandsTx、sTy、sTzrespectively forces and moments in each direction.
Step 1, converting the multi-degree-of-freedom control model into mutually independent single-degree-of-freedom models, specifically comprising the following processes: according to a decoupling matrix gamma between current and magnetic force, using gamma-1The current distribution of each coil can be completed, and therefore mutual independence of control among all degrees of freedom is achieved.
Step 1, establishing an independent single degree of freedom model containing an uncertain item and external interference, which is specifically defined as:
where θ is a system parameter, x is a system state quantity, f (x, t) is a system unmodeled uncertainty term, and ΔdIs a non-repetitive external disturbance.
Preferably, the adaptive sliding mode controller model in step 2:
wherein
For the kth adaptive sliding mode controller output, skIs a slip form surface and is provided with a plurality of slip forms,
in order to obtain the estimation result of the system parameters,
as a model compensation term, ωkFor the robust term, gsIs a linear feedback coefficient.
Step 2, the iterative learning compensation item of the uncertainty item is specifically defined as:
wherein q is an iterative learning rate,
as a result of the (k-1) th iterative learning,
is the result of this iterative learning.
Step 2, the adaptive iterative learning sliding-mode controller model is specifically defined as:
wherein u iskAnd outputting the k-th time self-adaptive iterative learning sliding mode controller.
Preferably, the specific process of performing the stability analysis in step 3 is as follows: establishing a Lyapunov energy function EkFinally, Δ E can be verifiedk＝Ek-Ek-1≦ 0, therefore the energy function EkMonotonically decreasing due to the energy function EkAre positive numbers, so the control signal is bounded and the system asymptotically stabilizes.
The specific process for analyzing the error convergence in the step 3 is as follows: due to the energy function EkMonotonously decreases, and correspondingly, the error is also monotonously decreased, so that the tracking error of the system keeps convergence,
preferably, the step 4 is applied to an actual magnetic suspension planar motor system, and specifically includes:
and converting a control algorithm into a code form through labview software, and realizing the control of the magnetic suspension planar motor system through an NI real-time controller.
Step 4, performing trajectory tracking under the condition of external interference, specifically:
firstly, a reference tracking track is determined, the reference tracking track is converted into a function form taking time as a variable, a first derivative and a second derivative of the track relative to the time are obtained, an adaptive sliding mode controller is designed through the tracking track, iterative learning does not depend on the track and a model, therefore, the change is not needed, the adaptive sliding mode controller is combined with an iterative learning item to form an adaptive iterative learning sliding mode controller, the tracking track function can generate corresponding track values at different time points, the track values are compared with the actual position of the magnetic suspension planar motor, and the position of the magnetic suspension planar motor is adjusted by the adaptive iterative learning sliding mode controller according to the difference between the actual position and the reference track value, so that track tracking is realized.
Compared with the prior art, the invention has the advantages that: the tracking precision and robustness of the magnetic suspension system are further improved by combining self-adaptive sliding mode control and iterative learning control on the premise of not depending on an accurate system model. The control parameter self-adaptive method can estimate the system parameters on line, and meanwhile, the control method introduces a control parameter self-adaptive technology to update the control parameters on line under the condition of no accurate error boundary information so as to ensure the robustness of the system. In addition, in order to further improve the tracking accuracy, an iterative learning control item is added for compensating the influence caused by the coupling between the repetitive interference and the degree of freedom in the system, and the error can be converged to be near zero after a limited number of iterations. The control method solves the tracking control problems of the multi-degree-of-freedom magnetic suspension planar motor under the condition that the interference boundary is unknown and an uncertain item exists, and has strong robustness, good self-adaptive capacity and high tracking precision.
Drawings
FIG. 1: is a schematic diagram of a multi-degree-of-freedom magnetic suspension planar motor.
FIG. 2: the invention relates to a structure diagram of a sliding mode control algorithm of self-adaptive iterative learning of a multi-degree-of-freedom magnetic levitation planar motor.
FIG. 3: is a flow chart of the steps of one embodiment of the control method of the present invention.
FIG. 4: the method is a position tracking error convergence process diagram in the process of iterating 15 times by a control method actually applied to a magnetic suspension system.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to fig. 1 to 4 in the embodiments of the present invention.
The first embodiment of the invention is a sliding mode control method for self-adaptive iterative learning of a multi-degree-of-freedom magnetic levitation planar motor, which is characterized by comprising the following operation steps
Step 1: converting the multi-freedom control model into mutually independent single-freedom-degree models by utilizing a dynamic decoupling model of the magnetic suspension planar motor, and establishing a general system parameter model containing uncertain items and external interference aiming at the single-freedom-degree models;
step 1, the dynamic decoupling model of the magnetic suspension planar motor is specifically defined as follows:
wherein each item is defined as
Wherein M ismIs the mover mass, Ixx、Iyy、IzzIn order to be the moment of inertia,sx、sy、sz is displacement in each direction, alpha, beta and gamma are rotation around each axis, g is gravity acceleration,sFx、sFy、sFzandsTx、sTy、sTzrespectively forces and moments in each direction.
Step 1, converting the multi-degree-of-freedom control model into mutually independent single-degree-of-freedom models, specifically comprising the following processes: according to a decoupling matrix gamma between current and magnetic force, using gamma-1The current distribution of each coil can be completed, and therefore mutual independence of control among all degrees of freedom is achieved.
Step 1, establishing an independent single degree of freedom model containing an uncertain item and external interference, which is specifically defined as:
where θ is a system parameter, x is a system state quantity, f (x, t) is a system unmodeled uncertainty term, and ΔdIs a non-repetitive external disturbance.
Step 2: according to a general system parameter model, a self-adaptive sliding mode controller model is constructed by combining an expected motion track, and a robust item in a sliding mode controller can be used for inhibiting influence caused by external interference. And designing an iterative learning compensation item of the uncertain item aiming at the uncertain item in the system parameter model, and combining the iterative learning compensation item and the sliding mode control item in a parallel mode to obtain the self-adaptive iterative learning sliding mode controller model.
Step 2, the self-adaptive sliding mode controller model:
wherein
For the kth adaptive sliding mode controller output, skIs a slip form surface and is provided with a plurality of slip forms,
in order to obtain the estimation result of the system parameters,
as a model compensation term, wkFor the robust term, gsIs a linear feedback coefficient.
Step 2, the iterative learning compensation item of the uncertainty item is specifically defined as:
wherein q is an iterative learning rate,
is the k-1 th timeAs a result of the iterative learning,
is the result of this iterative learning.
Step 2, the adaptive iterative learning sliding-mode controller model is specifically defined as:
wherein u iskAnd outputting the k-th time self-adaptive iterative learning sliding mode controller.
And step 3: and respectively carrying out stability analysis and error convergence analysis on the self-adaptive iterative learning sliding-mode controller model by a Lyapunov direct method.
The specific process of stability analysis in step 3 is as follows: establishing a Lyapunov energy function EkFinally, Δ E can be verifiedk＝Ek-Ek-1≦ 0, therefore the energy function EkMonotonically decreasing due to the energy function EkAre positive numbers, so the control signal is bounded and the system asymptotically stabilizes.
The specific process for analyzing the error convergence in the step 3 is as follows: due to the energy function EkMonotonously decreases, and correspondingly, the error is also monotonously decreased, so that the tracking error of the system keeps convergence,
and 4, step 4: the control algorithm is applied to an actual magnetic suspension planar motor system, track tracking is carried out under the condition that external interference exists, and the effectiveness of the control algorithm is verified.
The step 4 of applying the method to an actual magnetic suspension planar motor system specifically comprises the following steps:
and converting a control algorithm into a code form through labview software, and realizing the control of the magnetic suspension planar motor system through an NI real-time controller.
The second embodiment of the invention provides a sliding mode control method for self-adaptive iterative learning of a multi-degree-of-freedom magnetic levitation planar motor, which is characterized by comprising the following operation steps of:
the invention provides a self-adaptive iterative learning sliding-mode control method (control method for short) of a multi-degree-of-freedom magnetic levitation planar motor, which is characterized by comprising the following operation steps of:
step 1: the dynamic decoupling of the magnetic suspension planar motor is utilized to convert multi-freedom control into independent single-freedom degrees for design, and a general system parameter model containing uncertain items and external interference is established for the single-freedom degrees.
Step 2: and (2) designing an adaptive sliding mode controller according to the system parameter model established in the step (1) and in combination with an expected motion track, designing a corresponding iterative learning compensation item aiming at an uncertain item in the system model, and combining the iterative learning item and the sliding mode control item in a parallel mode to obtain the adaptive iterative learning sliding mode controller.
And step 3: and (3) analyzing the stability and error convergence of the adaptive iterative learning sliding-mode controller obtained in the step (2) by utilizing a Lyapunov direct method.
And 4, step 4: the control algorithm is applied to an actual magnetic suspension planar motor system, track tracking is carried out under the conditions of external interference and load, and the effectiveness of the control algorithm is verified. The flow of the operation is shown in FIG. 3.
The nominal kinetic equation of the multi-degree-of-freedom magnetic suspension system is described as the following model:
wherein x and
position and acceleration of the system, theta a system parameter, f (x, t) an uncertainty of the system related to the system state, deltadIs a non-repetitive disturbance of the system.
The specific design method of the self-adaptive iterative learning sliding mode control comprises the following steps: taking the tracking error of the system as input, constructing a sliding mode surface, taking the sliding mode surface as input by an iterative learning control item, and combining a low-pass filter to carry out iterative learning; the uncertainty parameter of the system is estimated online by using parameter estimation in the adaptive sliding mode control, and meanwhile, the coefficient of a robust item in the adaptive sliding mode control is updated online to ensure the stability of the system; and finally combining the self-adaptive sliding mode control item and the iterative learning item in a parallel mode to form the self-adaptive iterative learning sliding mode control method.
In the control method, besides the sliding mode surface, the iterative learning item also adds the switching value of the sliding mode surface to improve the convergence rate.
The control parameter self-adaptive technology is introduced into the self-adaptive sliding mode control item of the control method, so that the robustness of the system can be ensured under the condition of no accurate system interference boundary information
The design process of the self-adaptive iterative learning sliding mode control controller is as follows:
firstly, a sliding mode surface is constructed according to the position error and the speed error of the system:
wherein xdFor the reference trajectory, x is the system position,
and
respectively, a reference trajectory speed and a system actual speed. The derivation can be obtained by the sliding mode surface
The derivative of the sliding mode surface is obtained by substituting the parameter model (1) of the system into the sliding mode surface:
where θ is a system parameter, u is a controller input, f (x, t) is an overall system uncertainty term, ΔdIs the non-repeatability error of the system. Designing an adaptive iteration according to equation (3)The learning-assistant sliding mode control is
Wherein the content of the first and second substances,
for the control output of the adaptive sliding mode control item at the kth iteration,
and outputting the control of the iterative learning item at the k iteration.
The design is as follows:
wherein, gsAs a linear feedback coefficient, sgn(s)k) For the switch robust term, vkFor the compensation of the system model for the k-th iteration,
the estimated value of the system parameter of the k iteration is obtained by the following updating law:
wherein the content of the first and second substances,
for discontinuous mapping functions, ζ is the adaptive gain, ξ1And xi2Is a fixed weight factor. In order to deal with the situation that the system disturbance boundary is not accurately known, the adaptive coefficient of the switch robust term is introduced
And design itThe rate of change was:
control input for kth iteration of de-generational learning term
The learning rule is as follows:
wherein q is the iterative learning rate. In the iterative learning process, except the sliding mode surface skAnd also introduces a sliding mode surface switching value sgn(s)k) To increase the convergence rate.
The specific expression of the saturation function is as follows:
wherein the content of the first and second substances,
the upper boundary value of the system uncertainty term. The adaptive iterative learning sliding mode control algorithm is shown in fig. 2.
Analyzing the stability and the error convergence of the obtained adaptive iterative learning sliding-mode controller by using a Lyapunov direct method, wherein the analysis process is as follows:
firstly, an energy function of the kth iteration is constructed by utilizing a Lyapunov direct method
Wherein
Therefore, E between k and (k-1) iterations of two adjacent iterationskDifference value Δ E ofkCan be expressed as:
first step to solve for Δ EkIn the pair, wherein Δ VkCan be expressed as a number of times as,
the integral representation and the control laws (4), (7), (8) and (11) can be rewritten as follows:
wherein
In combination with the iterative learning, the method can be used,
satisfies the following formula
Due to | skThe derivative of l with respect to time t is
Thus, it is possible to provide
Can be expressed as
According to the update law (6) of the system parameters,
can be expressed as:
according to the update law (6) of the system parameters,
can be rewritten as:
therefore, by combining the above results, the following equation (11) can be obtained
Thus, it can be seen that the kyapunov function E of two adjacent iterationskIs negative, by iteration EkWill decrease continuously due to EkThe error is more than or equal to 0, so the error is converged to 0 finally, and simultaneously, signals in the system are bounded, thereby ensuring the stability of the system.
The proposed control method is applied to the specific process of the magnetic suspension system: first, a reference trajectory needs to be determined, which must be continuously derivable. Further, it is necessary to recognize the boundary where the uncertainty term and the interference term are obtained in advance by the system, the control gain c in equation (6) is 0, and the linear feedback coefficient g issWhen 80, ζ is 0.1. The initial value of iterative learning is zero, and it is necessary to ensure that the error at the start position of each iteration is 0, and the iterative learning rate q is 0.1. To verify the effectiveness of the control method, external disturbances are presentIn the case of (2), the magnetic levitation system is made to track a sinusoidal track xd＝0.5sin(πt)(mm)。
The actual control effect of the control method is shown in fig. 4. According to the change of the tracking error, in the initial iteration, because the initial output of the iterative learning is 0, the initial control effect depends on the self-adaptive sliding mode control item, and the tracking error of the actual position and the expected motion track of the magnetic suspension rotor is obvious. With the increase of the iteration times, the tracking error of the magnetic suspension system is continuously reduced, after 15 iterations, the actual motion track of the magnetic suspension system is very close to the reference track, and the tracking root mean square error is less than 0.0031 mm.
Under the condition that external interference exists in the system, after a limited number of iterations, the position tracking error is obviously reduced, and the effectiveness of the control method is proved.
Nothing in this specification is said to apply to the prior art.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.
Claims (4)
1. A self-adaptive learning sliding mode control method of a multi-freedom-degree magnetic suspension planar motor is characterized by comprising the following steps:
step 1: converting the multi-freedom control model into mutually independent single-freedom-degree models by utilizing a dynamic decoupling model of the magnetic suspension planar motor, and establishing a general system parameter model containing uncertain items and external interference aiming at the single-freedom-degree models;
step 2: according to a general system parameter model, a self-adaptive sliding mode controller model is constructed by combining an expected motion track, and a robust item in a sliding mode controller can be used for inhibiting influence caused by external interference; designing an iterative learning compensation item of the uncertain item aiming at the uncertain item in the system parameter model, and combining the iterative learning compensation item and the sliding mode control item in a parallel mode to obtain a self-adaptive iterative learning sliding mode controller model;
step 2, the self-adaptive sliding mode controller model:
wherein
For the kth adaptive sliding mode controller output, skIs a slip form surface and is provided with a plurality of slip forms,
in order to obtain the estimation result of the system parameters,
as a model compensation term, wkFor the robust term, gsIs a linear feedback coefficient;
step 2, the iterative learning compensation item of the uncertainty item is specifically defined as:
wherein q is an iterative learning rate,
as a result of the (k-1) th iterative learning,
for the k-th iterationThe result of the learning;
step 2, the adaptive iterative learning sliding-mode controller model is specifically defined as:
wherein u iskOutputting for the kth self-adaptive iterative learning sliding mode controller;
and step 3: respectively carrying out stability analysis and error convergence analysis on the self-adaptive iterative learning sliding mode controller model by a Lyapunov direct method;
and 4, step 4: the control algorithm is applied to an actual magnetic suspension planar motor system, track tracking is carried out under the condition that external interference exists, and the effectiveness of the control algorithm is verified.
2. The self-adaptive learning sliding-mode control method of the multi-degree-of-freedom magnetic levitation planar motor according to claim 1, characterized in that: step 1, the dynamic decoupling model of the magnetic suspension planar motor is specifically defined as follows:
wherein each term is defined as M ═ diag [ M ═ Mm，Mm，Mm，Ixx，Iyy，Izz]
X＝[sx，sy，sz，α，β，γ]T
G＝[0，0，Mmg，0，0，0]T
U＝[sFx，sFy，sFz，sTx，sTy，sTz]T，
Wherein M ismIs the mover mass, Ixx、Iyy、IzzIn order to be the moment of inertia,sx、sy、sz is displacement in each direction, alpha, beta and gamma are rotation around each axis, g is gravity acceleration,sFx、sFy、sFzandsTx、sTy、sTzforces and moments in all directions respectively;
step 1, converting the multi-degree-of-freedom control model into mutually independent single-degree-of-freedom models, specifically comprising the following processes: according to a decoupling matrix gamma between current and magnetic force, using gamma-1The current of each coil can be distributed, so that the mutual independence of the control among all degrees of freedom is realized;
step 1, establishing an independent single degree of freedom model containing an uncertain item and external interference, which is specifically defined as:
where θ is a system parameter, x is a system state quantity, f (x, t) is a system unmodeled uncertainty term, and ΔdIs a non-repetitive external disturbance.
3. The self-adaptive learning sliding-mode control method of the multi-degree-of-freedom magnetic levitation planar motor according to claim 1, characterized in that: the specific process of stability analysis in step 3 is as follows: establishing a Lyapunov energy function EkFinally, Δ E can be verifiedk＝Ek-Ek-1≦ 0, therefore the energy function EkMonotonically decreasing due to the energy function EkAll the signals are positive numbers, so that the control signals are bounded, and the system is asymptotically stable;
the specific process for analyzing the error convergence in the step 3 is as follows: due to the energy function EkThe error is monotonically decreased, and the system tracking error is kept converged.
4. The self-adaptive learning sliding-mode control method of the multi-degree-of-freedom magnetic levitation planar motor according to claim 1, characterized in that: the step 4 of applying the method to an actual magnetic suspension planar motor system specifically comprises the following steps:
converting a control algorithm into a code form through labview software, and realizing the control of a magnetic suspension planar motor system through an NI real-time controller;
step 4, performing trajectory tracking under the condition of external interference, specifically:
firstly, a reference tracking track is determined, the reference tracking track is converted into a function form taking time as a variable, a first derivative and a second derivative of the track relative to the time are obtained, an adaptive sliding mode controller is designed through the tracking track, iterative learning does not depend on the track and a model, therefore, the change is not needed, the adaptive sliding mode controller is combined with an iterative learning item to form an adaptive iterative learning sliding mode controller, the tracking track function can generate corresponding track values at different time points, the track values are compared with the actual position of the magnetic suspension planar motor, and the position of the magnetic suspension planar motor is adjusted by the adaptive iterative learning sliding mode controller according to the difference between the actual position and the reference track value, so that track tracking is realized.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110180359.1A CN112859618B (en) | 2021-02-09 | 2021-02-09 | Self-adaptive learning sliding mode control method for multi-degree-of-freedom magnetic suspension planar motor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110180359.1A CN112859618B (en) | 2021-02-09 | 2021-02-09 | Self-adaptive learning sliding mode control method for multi-degree-of-freedom magnetic suspension planar motor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112859618A CN112859618A (en) | 2021-05-28 |
| CN112859618B true CN112859618B (en) | 2022-03-04 |
Family
ID=75989622
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110180359.1A Expired - Fee Related CN112859618B (en) | 2021-02-09 | 2021-02-09 | Self-adaptive learning sliding mode control method for multi-degree-of-freedom magnetic suspension planar motor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112859618B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113759721B (en) * | 2021-09-02 | 2023-07-14 | 大连交通大学 | Permanent magnet synchronous motor L1 self-adaptive iterative learning control method |
| CN114859715B (en) * | 2022-04-21 | 2024-04-26 | 武汉大学 | Fractional order sliding mode motion control method of magnetic suspension turntable motion control system |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101510745A (en) * | 2009-03-30 | 2009-08-19 | 东南大学 | Gas magnetic mixing suspension type plane motor with six freedom degrees |
| CN106907393A (en) * | 2017-03-02 | 2017-06-30 | 常州市翰琪电机有限公司 | The control method and its device of a kind of intelligent motorized spindle supported with AMB |
| CN111474855A (en) * | 2020-05-08 | 2020-07-31 | 哈尔滨工业大学 | Uncertain distribution parameter system control method and device |
| CN111522243A (en) * | 2020-05-20 | 2020-08-11 | 河北工业大学 | Robust iterative learning control strategy for five-degree-of-freedom upper limb exoskeleton system |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100222898A1 (en) * | 2009-01-27 | 2010-09-02 | Nikon Corporation | Stage-control systems and methods including inverse closed loop with adaptive controller |
| CN103163823B (en) * | 2011-12-08 | 2015-06-03 | 沈阳工业大学 | Control method of synchronous stable suspension of a plurality of maglev systems for numerically-controlled machine tools |
-
2021
- 2021-02-09 CN CN202110180359.1A patent/CN112859618B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101510745A (en) * | 2009-03-30 | 2009-08-19 | 东南大学 | Gas magnetic mixing suspension type plane motor with six freedom degrees |
| CN106907393A (en) * | 2017-03-02 | 2017-06-30 | 常州市翰琪电机有限公司 | The control method and its device of a kind of intelligent motorized spindle supported with AMB |
| CN111474855A (en) * | 2020-05-08 | 2020-07-31 | 哈尔滨工业大学 | Uncertain distribution parameter system control method and device |
| CN111522243A (en) * | 2020-05-20 | 2020-08-11 | 河北工业大学 | Robust iterative learning control strategy for five-degree-of-freedom upper limb exoskeleton system |
Non-Patent Citations (2)
| Title |
|---|
| Precision LARC motion controller design for a magnetically levitated planar motor;Ze Wang等;《2015 IEEE International Conference on Information and Automation》;20150810;第1359-1364页 * |
| 同心式绕组磁悬浮永磁同步平面电机建模及控制技术研究;邢丰;《中国优秀博硕士学位论文全文数据库（博士） 工程科技Ⅱ辑》;20210115(第01期);第Ⅱ、13-19、91、86页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112859618A (en) | 2021-05-28 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Wang et al. | Parameter estimation and adaptive control for servo mechanisms with friction compensation | |
| CN112904728B (en) | Mechanical arm sliding mode control track tracking method based on improved approach law | |
| CN112859618B (en) | Self-adaptive learning sliding mode control method for multi-degree-of-freedom magnetic suspension planar motor | |
| CN103780188B (en) | Based on the permanent magnetism spherical rotor adaptive control system of dynamic frictional compensation | |
| CN110552961A (en) | Active magnetic bearing control method based on fractional order model | |
| CN110131312B (en) | Five-degree-of-freedom alternating current active magnetic bearing active disturbance rejection decoupling controller and construction method | |
| CN108909524A (en) | Magnetic suspending flying wheel battery zero-power decoupling controller for electric vehicle based on dynamic model | |
| CN115890668A (en) | Distributed optimization learning control method and system for robot joint module | |
| Meng et al. | An EPCH control strategy for complex nonlinear systems with actuator saturation and disturbances | |
| CN112947083B (en) | Nonlinear model predictive control optimization method based on magnetic suspension control system | |
| CN117193001B (en) | Hyperbolic approach law sliding mode control method based on integral reinforcement learning | |
| CN116500908B (en) | Mechanical arm anti-interference constraint control method of double-disturbance observer | |
| CN116455278A (en) | Self-tuning method for pid parameters of permanent magnet synchronous motor control system based on neural network self-adaptive control | |
| CN113110069B (en) | Iterative neural network robust control method based on magnetic suspension planar motor | |
| CN116560375A (en) | Wheel type mobile robot track tracking control method based on neural network observer | |
| CN116638544A (en) | Joint module cooperative control method based on super local model | |
| CN116088299A (en) | Neural network backstepping control method for satellite antenna series-parallel motor mechanism | |
| CN114237045A (en) | Sensorless piezoelectric drive closed-loop control method | |
| Zheng et al. | Disturbance rejection in MEMS gyroscope: Problems and solutions | |
| Zhao et al. | Design of MRAC and Modified MRAC for the Turntable | |
| Khan et al. | Nonlinear reduced order observer design for elastic drive systems using invariant manifolds | |
| CN114454161B (en) | Manipulator rigid-flexible coupling system based on spherical motor drive | |
| CN114415517B (en) | Multi-agent consistency control method based on time synchronization stability | |
| CN114488818B (en) | Set point iterative learning optimization method of PID control system | |
| CN113659894B (en) | Asynchronous motor random limited time fuzzy self-adaptive control method based on instruction filtering |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20220304 |