CN-120742666-B - Finite time position tracking control method of magnetic suspension system with output constraint

CN120742666BCN 120742666 BCN120742666 BCN 120742666BCN-120742666-B

Abstract

The invention provides a finite time position tracking control method of a magnetic suspension system with output constraint, which comprises the steps of establishing a mathematical model of the magnetic suspension system, determining an error system to obtain upper and lower bounds of the suspension air gap constraint and system state information, designing a fractional obstacle Lyapunov function in consideration of the upper and lower bounds of the suspension air gap constraint, solving a bias guide to obtain a constraint processing mechanism function, designing a continuous finite time state feedback constraint controller by utilizing system state information based on the constraint processing mechanism function by applying a finite time control technology and a homogeneous system theory, designing a non-smooth filter when the system speed state information is not measurable based on the constraint processing mechanism function, and designing a finite time output feedback controller by utilizing filter output information and system output information. The invention realizes the uniform and limited time control of the magnetic suspension system under the constraint of the symmetrical/asymmetrical suspension gaps, and has high tracking precision, strong disturbance rejection robustness and engineering practicability.

Inventors

LAN QIXUN
WANG JIA
ZHAO PENGFEI
YUE PENGWEI
LIU NA
SUN JUNWEI
ZHANG XUNCAI
WANG YINGCONG
NIU JINGWEI
LIU SHENG
LIANG QINGQING

Assignees

郑州轻工业大学

Dates

Publication Date: 20260508
Application Date: 20250612

Claims (8)

1. A finite time position tracking control method of a magnetic suspension system with output constraint is characterized by comprising the following steps: Firstly, establishing a mathematical model of a magnetic suspension system, and determining an error system to obtain upper and lower bounds of suspension air gap constraint and system state information; step two, considering the upper and lower bounds of the magnetic suspension air gap constraint, designing a fractional obstacle Lyapunov function, and solving the partial derivative of the fractional obstacle Lyapunov function to obtain a constraint processing mechanism function; Step three, a finite time control technology and a homogeneous system theory are applied, and a continuous finite time state feedback constraint controller is designed by utilizing system state information based on constraint processing mechanism functions; Step four, based on constraint processing mechanism function, when the system speed state information is not measurable, designing a non-smooth filter, and designing a finite time output feedback controller by utilizing the output information of the non-smooth filter and the output information of the system; the mathematical model of the magnetic suspension system is as follows: ; Wherein, the The quality of the steel ball is represented, The acceleration of the gravity is that, The position of the steel ball at the moment t is shown, For the electromagnetic force generated by the electromagnet, The current flowing through the electromagnet at time t is indicated, Is the magnetic permeability of the vacuum and is equal to the magnetic permeability of the vacuum, Indicating the number of turns of the coil of the electromagnet, Indicating the interaction area between the steel ball and the magnetic pole, And The balance current and the balance position of the steel ball in a stable suspension state are respectively; the score type obstacle Lyapunov function is as follows: ; Wherein x 1 = Representing the output state of the error system, For the parameters of the lyapunov function, 、 Representing the upper and lower bounds, respectively, of the system levitation air gap constraint.
2. The method for finite time position tracking control of a magnetic levitation system with output constraint according to claim 1, wherein electromagnetic force is applied By Taylor expansion and ignoring higher order terms at the equilibrium point, we get: ; defining system control inputs And output of The mathematical model of the error system is obtained as follows: ; Wherein, the 、 =U (t) sum Y (t) respectively belong to the state of the error system, the control input and the output, And Respectively representing system nominal parameters; The error system meets the output safety constraint condition 。
3. A method for finite time position tracking control of a magnetic levitation system with output constraint according to claim 2, wherein the fractional obstacle lyapunov function Is positive and definite for output state Obtaining the deviation guide ; Wherein the constraint processing mechanism function , 。
4. A method of finite time position tracking control of a magnetic levitation system with output constraint according to claim 3, wherein the finite time state feedback constraint controller is: ; Wherein, the And Is a positive constant; A fractional power term representing the error system speed state.
5. The method for finite time position tracking control of a magnetic levitation system with output constraint of claim 4, wherein the finite time state feedback controller Substituting the error system to obtain a closed loop system: ; For the initial output state Error system meeting output safety constraint condition and having normal number And So that the closed loop system as above is stable for a limited time and does not violate safety constraints.
6. A method of finite time position tracking control of a magnetic levitation system with output constraint according to any of claims 3-5, wherein the non-smooth filter is: ; Wherein, the Representing state information of a filter, a filter gain parameter Is the normal number of the two groups of the, Representing the filter output information.
7. The method for finite time position tracking control of a magnetic levitation system with output constraint according to claim 6, wherein the finite time output feedback constraint controller is: ; Wherein the control parameter And Are normal numbers.
8. The method for finite time position tracking control of a magnetic levitation system with output constraint of claim 7, wherein the finite time output feedback constraint controller Substituting the error system to obtain a closed loop system: ; For the initial output state Error system meeting output safety constraint condition and having normal number , , And The closed loop system formed by the limited time output feedback constraint controller and the error system is stable in limited time and does not violate safety constraint conditions.

Description

Finite time position tracking control method of magnetic suspension system with output constraint Technical Field The invention relates to the technical field of magnetic suspension systems, in particular to a position tracking control method of a magnetic suspension system. Background The magnetic suspension system is widely applied to the fields of transportation, medical equipment, industrial equipment and the like by virtue of low noise, non-contact, low friction and the like, particularly in the aspect of control engineering application, but the control system is an open-loop unstable system and has high nonlinear characteristics, so that the position tracking control design of the system is very challenging. In recent years, many advanced control methods have been proposed for position tracking control of a magnetic levitation system, such as adaptive control, model predictive control, proportional-integral-derivative control, sliding mode control, and the like. These various and efficient control techniques significantly improve the position tracking control performance of the magnetic levitation system from different angles. Although the research results of the magnetic suspension system position tracking control method are rich, the methods are limited to the field of asymptotically stable control schemes to a great extent, which is obviously unfavorable for the deep exploration of the magnetic suspension system position tracking control research. The finite time control technology is used as a practical alternative, and has been widely used in engineering control systems in recent years due to the advantages of high convergence speed, high control accuracy, high robustness and the like. Meanwhile, researchers have conducted extensive researches on a magnetic levitation system using a limited time control technique. For example, to increase the convergence speed and obtain better stability and anti-interference capability, a super-local model-free adaptive super-torsion nonsingular terminal sliding mode control strategy, an integral terminal sliding mode controller control scheme, a limited time control method based on fractional power integral of a series of exponential functions and nested sign functions, an event triggering strategy consisting of sharp triggering rules and time-varying thresholds, and the like are applied to a magnetic suspension system so as to ensure the limited time convergence of the state of the magnetic suspension system. In actual engineering control systems, the output of the system is often constrained due to system safety considerations or inherent physical structure limitations. For example, a robot requires that the joints of the robot arm operate within a specific range to ensure safety due to the limitations of its mechanical structure. In order to maintain good performance and system stability of the electrical circuitry, it is necessary to limit the current to a certain range. Any behavior that violates the output constraint requirements can cause varying degrees of damage to the controlled system. Also, the levitation blocks of the magnetic levitation system must remain confined within a defined air gap to ensure stable levitation. It should be noted, however, that the aforementioned control strategy does not take into account the levitation air gap constraints of the magnetic levitation system. At present, for the control problem of the output limited system, it is common practice to incorporate constraint conditions into the controller design process in advance, and by designing a suitable controller, it is strictly ensured that the system output meets the preset constraint conditions from the theoretical point of view, for example, limited time control based on the barrier lyapunov function, event-triggered adaptive limited time control with preset performance, preset performance control assisted by the control barrier function, and the like are widely applied to the constraint system. In order to solve the challenges of position tracking control of a magnetic levitation system with levitation air gap constraint, researchers have designed a continuous finite-time state feedback controller based on tan-type obstacle lyapunov function, and successfully achieve convergence of the system state to zero in a finite time. Unfortunately, this approach is no longer applicable when only the output of the system is available for feedback design. Disclosure of Invention Aiming at the technical problems that the existing control strategy does not consider the suspension air gap constraint of the magnetic suspension system and the tracking precision is low, the invention provides the limited time position tracking control method of the magnetic suspension system with the output constraint, and the limited time stability control theory, the homogeneous system theory and the Lyapunov function stability analysis are comprehensively utilized, so that the position track trackin