A method and system for controlling a magnetic levitation device based on fixed-time sliding mode control

Abstract

The present application belongs to the technical field of magnetic suspension control, and discloses a kind of control method and system of magnetic suspension device based on fixed time sliding mode control.The method of the present application aims at the deficiencies of traditional control methods in the face of system uncertainty, external disturbance and parameter variation, first presets the expected stable position or expected tracking trajectory of the levitation ball in the magnetic suspension device, then establishes the mechanism model of the magnetic suspension device, then constructs the nonsingular fixed time sliding mode surface containing subsection nonlinear term, and designs the fixed time sliding mode control law, finally constitutes the fixed time sliding mode controller to realize the trajectory tracking control of the levitation ball in the magnetic suspension device.The present application also combines Lyapunov method to analyze the stability of the magnetic suspension device controlled by the fixed time sliding mode controller, from the two links of approach stage and sliding stage, ensures that the system state converges to the equilibrium point within the fixed time independent of initial state, and then realizes the precise tracking control of the magnetic suspension device.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of magnetic suspension control, and particularly relates to a magnetic suspension device control method and system based on fixed-time sliding mode control. BACKGROUND

[0002] The existing magnetic suspension device control method mostly adopts PID control or traditional sliding mode control. However, such control methods usually have problems of insufficient response speed, poor robustness and stability when processing complex time-varying signals such as sinusoidal signals and performing position tracking control. Therefore, a magnetic suspension device control method capable of effectively improving the tracking accuracy, stability and robustness of the magnetic suspension device and ensuring that the system can stably converge to a preset position and signal within a fixed time is urgently needed.

[0003] As a kind of nonlinear control strategy, the sliding mode control is widely applied to various control systems due to its insensitivity to external disturbance and internal parameter perturbation, simple physical implementation, and excellent robustness and adaptability in the control system. However, the traditional sliding mode control method can only ensure that the system reaches the sliding mode surface within a limited time, but cannot guarantee that the controlled system reaches a stable state within a fixed time. This means that the convergence speed of the system may be affected by factors such as the initial state of the system and disturbance, resulting in a decrease in control accuracy and robustness.

[0004] As a new sliding mode control method, the fixed-time sliding mode control is further developed on the basis of the traditional sliding mode control. The main feature is that it can guarantee that the system reaches a stable state within a preset fixed time, and the fixed time is independent of the initial state of the system. The basic principle of the fixed-time sliding mode control is to introduce a fixed-time convergent sliding mode control law to ensure that the system converges to the sliding mode surface within a fixed time. At the same time, a fixed-time convergent sliding mode surface is introduced to ensure that any point on the sliding mode surface can converge to an equilibrium point within a fixed time. The two work together to achieve the convergence of the system to the equilibrium point within a fixed time, thereby realizing the control of the system. Compared with the traditional sliding mode control method, the fixed-time sliding mode control has faster convergence speed and higher control accuracy, and also has better dynamic performance and robustness. SUMMARY

[0005] The application aims to provide a magnetic suspension device control method based on fixed-time sliding mode control, which can enable the system to stably track a preset time-varying signal within a fixed time from any initial state and realize position tracking control of the magnetic suspension device.

[0006] In order to achieve the above-mentioned purpose, the application adopts the following technical solutions:

[0007] A kind of magnetic suspension device control method based on fixed time sliding mode control, comprising the following steps:

[0008] Step 1. The desired stable position or desired tracking trajectory of the suspended ball in the magnetic suspension device is preset.

[0009] Step 2. The electromagnetic force model equation of the magnetic suspension device is established, considering that the system electromagnetic force is balanced with the gravity of the suspended ball itself, the dynamic equilibrium equation of the magnetic suspension device is obtained, the linear differential equilibrium equation of the system at the equilibrium point is obtained by Taylor series expansion at the equilibrium point, and it is converted into a state space model.

[0010] Step 3. Based on the desired stable position or desired tracking trajectory of the suspended ball preset in step 1, the position tracking error is established based on the obtained actual position feedback information of the suspended ball, and a non-singular fixed time sliding mode surface is designed.

[0011] Step 4. Based on the state space model of step 1 and the non-singular fixed time sliding mode surface of step 3, a fixed time sliding mode control law is designed; a fixed time sliding mode controller is formed by the non-singular fixed time sliding mode surface and the fixed time sliding mode control law.

[0012] Step 5. The fixed time sliding mode controller of step 4 is used to realize the trajectory tracking control of the suspended ball in the magnetic suspension device.

[0013] In addition, based on the magnetic suspension device control method based on fixed time sliding mode control, the present application also proposes a magnetic suspension device control system based on fixed time sliding mode control, which is suitable for the technical scheme as follows:

[0014] A kind of magnetic suspension device control system based on fixed time sliding mode control, comprising:

[0015] Desired preset module, for presetting the desired stable position or desired tracking trajectory of the suspended ball in the magnetic suspension device.

[0016] Model establishment module, for establishing the electromagnetic force model equation of the magnetic suspension device, considering that the system electromagnetic force is balanced with the gravity of the suspended ball itself, the dynamic equilibrium equation of the magnetic suspension device is obtained, the linear differential equilibrium equation of the system at the equilibrium point is obtained by Taylor series expansion at the equilibrium point, and it is converted into a state space model.

[0017] Sliding mode surface design module, for establishing the position tracking error based on the desired stable position or desired tracking trajectory of the suspended ball, and designing a non-singular fixed time sliding mode surface based on the obtained actual position feedback information of the suspended ball.

[0018] A controller design module is configured to design a fixed-time sliding mode control law based on the state space model and the nonsingular fixed-time sliding surface, and to form a fixed-time sliding mode controller by the nonsingular fixed-time sliding surface and the fixed-time sliding mode control law.

[0019] A tracking control module is configured to realize trajectory tracking control of the levitation ball in the magnetic levitation device by using the fixed-time sliding mode controller.

[0020] In addition, based on the above-mentioned magnetic levitation device control method based on fixed-time sliding mode control, the present application further provides a computer device comprising a memory and one or more processors.

[0021] The memory stores executable code, and the processor executes the executable code to implement the steps of the above-mentioned magnetic levitation device control method based on fixed-time sliding mode control.

[0022] In addition, based on the above-mentioned magnetic levitation device control method based on fixed-time sliding mode control, the present application further provides a computer-readable storage medium having a program stored thereon; the program is executed by a processor to implement the steps of the above-mentioned magnetic levitation device control method based on fixed-time sliding mode control.

[0023] The present application has the following advantages:

[0024] 1. The magnetic levitation device control method proposed by the present application has fixed-time convergence.

[0025] The conventional sliding mode control method can only achieve finite-time convergence, and its convergence speed is seriously dependent on the initial state. The larger the initial deviation, the slower the convergence, and the quantitative controllability of the convergence time is lacking. In contrast, the present application constructs a nonsingular fixed-time sliding surface containing a segmented nonlinear term, designs a fixed-time sliding mode control law, forms a fixed-time sliding mode controller by the nonsingular fixed-time sliding surface and the fixed-time sliding mode control law, and conducts stability analysis by Lyapunov method, thereby ensuring that the system state converges to the equilibrium point within a fixed time independent of the initial state from the approaching stage and the sliding stage.

[0026] 2. The magnetic levitation device control method proposed by the present application can enhance robustness.

[0027] The traditional sliding mode control method adopts a fixed gain switching term, and has inherent contradiction between anti-interference and chattering, that is, when the gain is large, the anti-interference is strong, but the chattering is severe; when the gain is small, the chattering is weak, but the anti-interference is poor. The application introduces a disturbance compensation term to offset the influence of external disturbance and system parameter change, simultaneously divides the state region, adopts the differentiated control strategy of high gain anti-interference in large error region and low gain smooth convergence in small error region, avoids the inherent contradiction caused by fixed gain in the traditional sliding mode control method, and makes the tracking error of the magnetic suspension device still stable at 10 -4 mm level under 0.1 mm sinusoidal disturbance, and can effectively cope with external disturbance and system parameter change, and has strong robustness.

[0028] 3. The magnetic suspension device control method provided by the application has better time-varying signal tracking capability.

[0029] In the traditional sliding mode control method, the sliding mode surface is mostly linear or simple nonlinear structure, and the tracking of time-varying signal is prone to phase lag and amplitude deviation. The application tracks speed change, eliminates static error and accelerates dynamic convergence by designing a nonsingular fixed-time sliding mode surface, so as to realize accurate tracking of the preset time-varying signal, and the method of the application can also realize accurate tracking of the preset trajectory. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 The figure is a flow chart of the magnetic suspension device control method based on fixed-time sliding mode control in the embodiment of the application.

[0031] Figure 2 The figure is a schematic diagram of the composition and working principle of the magnetic suspension device in the embodiment of the application.

[0032] Figure 3 The figure is a schematic diagram of the magnetic suspension device controlled by the fixed-time sliding mode controller in the embodiment of the application.

[0033] Figure 4 The figure is a schematic diagram of state space region division in the specific example of the application.

[0034] Figure 5 The figure is a simulation structure diagram of the fixed-time sliding mode controller-fixed position tracking in the embodiment of the application.

[0035] Figure 6 The figure is an effect simulation diagram of the fixed-time sliding mode controller-fixed position tracking in the embodiment of the application.

[0036] Figure 6 (a) in the figure is a schematic diagram of the fixed position tracking effect of the fixed-time sliding mode controller, Figure 6 (b) in the figure is a schematic diagram of the fixed position tracking error of the fixed-time sliding mode controller.

[0037] Figure 7 The simulation structure diagram of the fixed time sliding mode controller-sine signal trajectory tracking in the embodiment of the application.

[0038] Figure 8 The effect simulation diagram of the fixed time sliding mode controller-sine signal trajectory tracking in the embodiment of the application.

[0039] Figure 8 (a) in the figure is a schematic diagram of the sine signal tracking effect of the fixed time sliding mode controller, Figure 8 (b) in the figure is a schematic diagram of the sine signal tracking error of the fixed time sliding mode controller.

[0040] Figure 9 The schematic diagram of the magnetic levitation device control system based on the fixed time sliding mode control of the magnetic levitation device. DETAILED DESCRIPTION

[0041] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0042] Embodiment 1

[0043] In the embodiment, a magnetic levitation device control method based on fixed time sliding mode control is proposed, which overcomes the shortcomings of traditional control methods in the face of system uncertainty, external disturbance and parameter variation by designing a fixed time sliding mode control strategy, so as to realize the stable convergence of the system state to the expected value within a fixed time.

[0044] The method of the application is aimed at the mechanism model of the magnetic levitation device including the electromagnetic force model equation and the dynamic equilibrium equation of the magnetic levitation device, and combines the fixed time control theory to construct a sliding mode controller with fixed convergence time, i.e., a fixed time sliding mode controller. In the control process, the adaptive sliding mode gain adjustment mechanism is introduced, and the adaptive sliding mode gain adjustment is realized through the state area differentiated gain distribution, which is specifically embodied in the cooperative process of the design and stability analysis of the fixed time sliding mode controller. The magnetic levitation device controlled by the fixed time sliding mode controller can adjust the control parameters according to the actual dynamic changes of the system, so as to further improve the control precision and robustness.

[0045] Meanwhile, the method adopts a new sliding mode surface design method, i.e., designing a nonsingular fixed-time sliding mode surface containing a segmented nonlinear term, combining a double-power reaching law control law, i.e., a fixed-time sliding mode control law, and Lyapunov stability analysis, to ensure that the system can converge in a fixed time from any initial state, and the convergence time is independent of the initial state. For example, for a GML-2001 device, the initial deviation is 0.3mm to 0.7mm, and the magnetic suspension device control method proposed in the application can converge in a fixed time of 1.7s. The method ensures that the convergence time of the control system is fixed and independent of the initial state, thereby avoiding the overshoot and oscillation phenomena that may occur in traditional sliding mode control.

[0046] In addition, the method not only has the characteristics of fast response, but also considers external disturbances such as air flow interference, system parameter perturbations such as coil resistance changes, and incorporates them into the disturbance term When designing the fixed-time sliding mode control law, the gain parameter related to disturbance suppression is introduced , and the robustness is enhanced by differentiating the gain distribution of the state region. Through stability analysis, it is verified that the system can still achieve fixed-time convergence under disturbance, thereby effectively suppressing the influence of external disturbance and system uncertainty on control performance, and being particularly suitable for precise positioning and high requirement signal tracking applications.

[0047] In addition, the experimental results in the embodiment show that the magnetic suspension device control method proposed in the application has significant advantages in stability, anti-interference and precision compared with traditional control methods.

[0048] The magnetic suspension device in the embodiment is introduced as follows.

[0049] In the embodiment, the working principle of the magnetic suspension device is to use MATLAB software and a 1711 data acquisition card in a PC to accurately control the current intensity in the electromagnet winding, thereby generating the required electromagnetic force, so that the electromagnetic force and the gravity of the suspended ball are balanced, thereby realizing stable suspension of the suspended ball.

[0050] The magnetic levitation device uses a laser displacement sensor to measure the changes in the levitation ball's suspended position. The laser displacement sensor can detect the distance changes between the levitation ball and the electromagnet in real time, and also detect the rate of distance change, i.e. the speed of the levitation ball. When an electric current passes through the electromagnet's winding, a magnetic field is generated. This magnetic field interacts with the magnet inside the levitation ball, generating an electromagnetic force. By precisely adjusting the current intensity in the electromagnet winding, the size and direction of the electromagnetic force can be controlled to balance the gravity of the levitation ball. When the electromagnetic force and the gravity of the levitation ball are balanced, the levitation ball will be in a stable suspended state, i.e. it will remain in a constant position. This stable state is achieved by continuously monitoring and adjusting the electromagnetic force. The MATLAB software reads the position information of the levitation ball in real time and adjusts the size of the electromagnetic force based on this information to ensure that the levitation ball always remains in a balanced state.

[0051] In this embodiment, the structure of the magnetic levitation device is shown in Figure 2 The laser sensor specifically refers to a laser displacement sensor. The laser displacement sensor is used to collect the actual displacement information of the levitation ball in real time and transmit the data to the A / D module through the displacement signal transmission. After the A / D module converts the displacement signal of the laser sensor into a digital signal, it is transmitted to the 1711 data acquisition card in the PC through data storage. The 1711 data acquisition card transmits the data to the MATLAB control platform through digital signal transmission. The control platform runs the magnetic levitation device control method based on fixed-time sliding mode control proposed by the present application according to the preset expected displacement and actual displacement information, and outputs a digital control signal. After the digital control signal is converted into an analog signal by the D / A module, it is transmitted to the driving circuit through the analog signal transmission. The driving circuit provides driving power to the electromagnet by providing current, and the control signal is derived from the instructions transmitted by the analog signal transmission. The electromagnet receives the current provided by the driving circuit and generates an electromagnetic force. The levitation ball is suspended under the action of the electromagnetic force and gravity, and finally forms a closed loop of "collection-computation-control-execution".

[0052] The magnetic levitation device control method based on fixed-time sliding mode control proposed by the present application will be described in detail below.

[0053] As shown in Figure 1 A magnetic levitation device control method based on fixed-time sliding mode control, specifically comprising the following steps:

[0054] Step 1. Preset the expected stable position or expected tracking trajectory of the levitation ball in the magnetic levitation device.

[0055] Wherein, the expected tracking trajectory is continuous and at least twice differentiable, which is a necessary condition for designing a fixed-time sliding mode controller.

[0056] Step 2. Establish the electromagnetic force model equations of the magnetic levitation device, considering the balance between the electromagnetic force of the system and the gravity of the levitated ball, to obtain the dynamic equilibrium equations of the magnetic levitation device; perform Taylor series expansion of the obtained dynamic equilibrium equations at the equilibrium point to obtain the linear differential equilibrium equations of the system at the equilibrium point, and transform them into a state-space model.

[0057] In step 2 of this embodiment, a mechanistic model of the magnetic levitation device is established, which includes the electromagnetic force model equation and the dynamic equilibrium equation of the magnetic levitation device. Step 2 first establishes the electromagnetic force model equation of the magnetic levitation device based on relevant physics knowledge. Based on this model, considering the balance between the system's electromagnetic force and the gravity of the levitated ball, the dynamic equilibrium equation of the magnetic levitation device is obtained. Further, a Taylor series expansion of the dynamic equilibrium equation at the equilibrium point is performed, and second-order and higher-order terms in the Taylor expansion are ignored, resulting in a linear differential equilibrium equation of the system near the equilibrium point. Then, a suitable state is selected to transform this differential equation model, i.e., the linear differential equilibrium equation, into a state-space model.

[0058] In this embodiment, step 2 specifically includes:

[0059] Based on Ohm's law for magnetic circuits and the energy method, the electromagnetic force exerted by the excitation coil on the suspended ball is derived. The electromagnetic force model equations for the magnetic levitation device are established as follows:

[0060] .

[0061] in, This represents the current in the excitation coil. This represents the air gap between the center of mass of the suspended sphere and the magnetic poles of the electromagnet. Indicates magnetic co-energy. Represents the permeability of free space. This refers to the area parameters related to electromagnets, namely the magnetic permeable area. This indicates the number of turns in the excitation coil. The coefficient representing the electromagnetic force is called the electromagnetic force coefficient.

[0062] From parameters A Overall decision:

[0063] .

[0064] Based on Newton's second law, the force balance of the suspended sphere is analyzed. Considering the balance between the electromagnetic force of the system and the gravity of the suspended sphere, the dynamic equilibrium equation of the magnetic levitation device is obtained as follows:

[0065] .

[0066] in, This indicates the mass of the suspended ball. express The air gap between the center of mass of the suspended sphere and the magnetic poles of the electromagnet is constantly suspended. It represents the acceleration due to gravity.

[0067] set up For the system to be in equilibrium, the following conditions must be met when the forces are balanced: ,in Indicates the balanced current. Indicate the equilibrium position; substituting it into the dynamic equilibrium equation of the magnetic levitation device yields... This aligns with the actual direction of force, meaning the electromagnetic force counteracts gravity upwards.

[0068] The obtained dynamic equilibrium equations of the magnetic levitation device are expanded using Taylor series at the equilibrium point to obtain the linear differential equilibrium equations of the system at the equilibrium point, which are then transformed into a state-space model:

[0069] .

[0070] in, The electromagnetic force model equations are shown in to The partial derivatives, The electromagnetic force model equations are shown in to The partial derivatives of .

[0071] Step 3. Based on the desired stable position or desired tracking trajectory of the suspended ball preset in Step 1, establish the position tracking error and design a non-singular fixed-time sliding surface after obtaining the actual position feedback information of the suspended ball.

[0072] In this embodiment, step 3 specifically includes:

[0073] Desired stable position based on the suspended sphere and expected speed Based on the feedback information of the actual position of the suspended ball, a tracking error is established:

[0074] , .

[0075] in, Indicates the actual position of the suspended ball. This indicates the position tracking error. This indicates the speed tracking error.

[0076] Let the position tracking error Error in rate of change of velocity .

[0077] Construct a nonsingular fixed-time sliding surface function containing nonlinear terms. for:

[0078] .

[0079] in, and It is a positive odd number.

[0080] coefficients related to disturbances Defined as:

[0081] .

[0082] in, Used to compensate for time-varying lumped disturbances in a system, which include model uncertainties and external disturbances; combined with fixed-time stability requirements. and Represents the gain coefficient, and , , and It is a positive odd number that satisfies , and To ensure It is positive and adapts to disturbance compensation.

[0083] Differentiating the nonsingular fixed-time sliding mode surface function, we obtain:

[0084] .

[0085] right Taking the derivative, we get:

[0086] .

[0087] Therefore, we get:

[0088] .

[0089] in, Indicates control input, Represents the parameters in the system model. This represents the disturbance experienced by the system. Among them... That is, gravitational acceleration, which corresponds to the dynamic equilibrium equation of the magnetic levitation device. of .

[0090] Step 4. Based on the state-space model from Step 1 and the non-singular fixed-time sliding surface from Step 3, design a fixed-time sliding mode control law. A fixed-time sliding mode controller is constructed using the non-singular fixed-time sliding surface and the fixed-time sliding mode control law.

[0091] In this embodiment, step 4 specifically includes:

[0092] Based on the non-singular fixed-time sliding surface designed in step 3, a fixed-time sliding mode control law needs to be designed. The function of the fixed-time sliding mode control law is to control the input... This allows each state of the system to reach a non-singular fixed-time sliding surface within a fixed time interval. Once the system state reaches the non-singular fixed-time sliding surface, its change is determined by the non-singular fixed-time sliding surface and is no longer subject to control input. Therefore, the design of a fixed-time sliding mode control law only needs to consider designing a control mechanism that ensures that each state of the system reaches the non-singular fixed-time sliding surface designed in step 3 within a fixed time.

[0093] Based on the state-space model obtained in step 1, the relationship between position tracking error and control quantity is derived to achieve accurate sliding surface and control law design. Based on the non-singular fixed-time sliding surface designed in step 3, the fixed-time sliding control law is designed as follows:

[0094] .

[0095] The fixed-time sliding mode control law is essentially a function of the non-singular fixed-time sliding surface.

[0096] in, This represents the gain parameter related to disturbance suppression. This represents a non-singular fixed-time sliding surface. and This represents a positive gain coefficient. , . , , , It is a positive odd number and satisfies , , , , .

[0097] Parameters related to control gain That is , Defined as:

[0098] .

[0099] in, Represents a constant.

[0100] A fixed-time sliding mode controller consists of a non-singular fixed-time sliding surface and a fixed-time sliding mode control law.

[0101] .

[0102] In step 4 of this embodiment, after completing the design of the fixed-time sliding mode controller, a stability analysis is performed on the magnetic levitation device controlled by the fixed-time sliding mode controller.

[0103] The process of stability analysis for a magnetic levitation device controlled by a fixed-time sliding mode controller is as follows:

[0104] Design Lyapunov functions for:

[0105] .

[0106] Among them, the function of the non-singular fixed-time sliding surface It is the core element of fractional sliding mode control, reflecting information such as the deviation between the system state and the desired state, and is used to guide the system state to converge toward the target trajectory.

[0107] For Lyapunov functions Taking the derivative, we get: .

[0108] Differentiating the nonsingular fixed-time sliding mode surface function, we obtain:

[0109] .

[0110] right Taking the derivative, we get:

[0111] .

[0112] The results were:

[0113] .

[0114] Substituting into the Lyapunov function, we get:

[0115] .

[0116] The results were:

[0117] .

[0118] in We obtain the inequality: Therefore, we get:

[0119] .

[0120] Pick Then we have:

[0121] .

[0122] From the above equation, we can deduce that the derivative of the selected Lyapunov function is similar to that of the defined function. related.

[0123] state space in accordance with The definition is divided into two different regions. and :

[0124] , .

[0125] Among them, the region The width is .

[0126] When the system state In the region hour, This holds true for all cases, and the derivative of the non-singular fixed-time sliding surface is:

[0127] .

[0128] For the derivative of the Lyapunov function, we have:

[0129] .

[0130] When the system state is not on a non-singular fixed-time sliding surface, i.e. hour, ,Pick ,have:

[0131] .

[0132] Therefore, we get:

[0133] .

[0134] System status At a fixed time It reaches a non-singular fixed-time sliding surface within a fixed time interval, i.e., it converges within a fixed time interval. Upper bound of convergence time for:

[0135] .

[0136] When the system state In the region At that time, if Then, without considering complex numbers, it satisfies ,have:

[0137] .

[0138] in, ,and . ,and .

[0139] System status At a fixed time It reaches a non-singular fixed-time sliding surface within a fixed time interval, i.e., it converges within a fixed time interval. Upper bound of convergence time for:

[0140] .

[0141] Because the fixed-time sliding mode control law contains Item, and Therefore, the system state The initial value cannot be 0; otherwise, the designed fixed-time sliding mode controller will not work. Therefore, this discussion focuses on... That is, system state The situation when it approaches 0. Moreover, in real-world systems, due to various disturbances, the system state... A strictly zero state is extremely rare, therefore we can discuss states here. In the case of the state At that time, Right now When the value approaches 1, the output of the fixed-time sliding mode controller is:

[0142] .

[0143] in, These are parameters in the system model, related to the inherent characteristics of the magnetic levitation device, such as electromagnetic and mechanical properties.

[0144] Substitute system status ,get:

[0145] .

[0146] because and Then when hour, .when hour, .

[0147] System status The area will be traversed monotonously within a limited time. Entering the area From the region Entering the area Time Depends on constant , The value is determined by the boundary width of the partitioned region. Decide.

[0148] This proves that the fixed-time sliding mode controller designed by the method of the present invention, such as Figure 4 As shown, this enables state variables to... It converges from any state in space to a non-singular fixed-time sliding surface within a fixed time interval.

[0149] Step 5. Using the fixed-time sliding mode controller from Step 4, track tracking control of the suspended ball in the magnetic levitation device is achieved.

[0150] In this embodiment, step 5 specifically includes:

[0151] like Figure 3 As shown, the entire process is based on a fixed-time sliding mode controller, which forms the core of a closed-loop control architecture.

[0152] The preset position of the suspended ball, i.e. the desired stable position or the desired tracking trajectory, is input to the fixed-time sliding mode controller. The first derivative of the tracking signal is the rate of change of the position of the tracking trajectory, and the second derivative of the tracking signal is the rate of change of the velocity of the tracking trajectory.

[0153] The fixed-time sliding mode controller outputs control commands to drive the magnetic levitation device based on the input information, thereby controlling the electronic devices to generate voltage and current to drive the magnetic levitation device to generate electromagnetic force.

[0154] After the system responds, it outputs the actual position of the suspended ball and the first derivative of the actual position, which is the actual velocity of the suspended ball.

[0155] The actual position of the suspended ball is processed by the first feedback coefficient to generate the first feedback signal, and the actual velocity of the suspended ball is processed by the second feedback coefficient to generate the second feedback signal. The first and second feedback signals are synchronously transmitted back to the fixed-time sliding mode controller to calculate the position tracking error and velocity tracking error of the suspended ball in real time. Under the action of the non-singular fixed-time sliding surface and the fixed-time sliding mode control law, the system state finally achieves the tracking of the preset trajectory within a fixed time.

[0156] Figure 3 The first derivative of the preset position is the first derivative of the tracking signal, and the second derivative of the preset position is the second derivative of the tracking signal. Feedback signal 1 is the first feedback signal, and feedback signal 2 is the second feedback signal. Feedback coefficient 1 is the first feedback coefficient, and feedback coefficient 2 is the second feedback coefficient. The magnetic levitation system is the magnetic levitation device.

[0157] The purpose of this invention is to provide a control method for a magnetic levitation device based on fixed-time sliding mode control to suppress errors. This method can effectively describe the desired behavior of the system, achieve state convergence within a fixed time, and enable the system to stably track a preset sinusoidal signal and a fixed position from any initial state within a fixed time.

[0158] In this embodiment, simulation experiments and physical verification were also conducted using the designed fixed-time sliding mode controller to demonstrate the effectiveness of the magnetic levitation device control method proposed in this invention and its fixed-time convergence characteristics.

[0159] Figure 5 The following is a simulation structure diagram of a fixed-time sliding mode controller-fixed-position tracking simulation in an embodiment of the present invention. The Simulink simulation structure of the magnetic levitation device under the control of the fixed-time sliding mode controller is established using the S-function module in the Simulink toolbox. Figure 5 In this diagram, out.t represents the time series output; ctr2 represents the fixed-time sliding mode controller designed in this invention; out.e1, out.e2, out.e3, and out.e4 represent the output error value sequences of the actual and preset positions of the suspended ball in the four experiments, respectively. The difference between these four experiments lies in the selection of the initial state, which is 0.3, 0.5, 0.7, and 0.4, respectively; out.x1, out.x2, out.x3, and out.x4 represent the actual position output sequence of the suspended ball; and plant, plant1, plant2, and plant3 represent the magnetic levitation system models obtained by selecting different states in the four experiments.

[0160] From simulation results Figure 6 As can be seen, the tracking stabilization time is approximately 1.7 seconds, the convergence process is relatively smooth, and the tracking stabilization error is on the order of 10. -4 Based on the sliding surface and sliding control parameters designed according to the present invention, the upper bound of the convergence time is estimated to be about 6.625s. Simulation verifies the effectiveness of the fixed-time sliding controller designed in this invention for tracking fixed positions, which can achieve tracking of fixed positions within a preset fixed time.

[0161] Figure 7 The diagram shows the simulation structure of a fixed-time sliding mode controller-sinusoidal signal tracking in a specific embodiment of the present invention. The Simulink simulation structure of the magnetic levitation device under the control of the fixed-time sliding mode controller is established using the S-function module of the Simulink toolbox. Figure 7In this diagram, out.xd represents the preset trajectory output sequence, out.t represents the output time sequence, and ctrl_1 represents the fixed-time sliding mode controller designed in this invention. out.e1, out.e2, out.e3, and out.e4 represent the output error value sequences of the actual motion trajectory of the suspended ball and the preset tracking trajectory in the four experiments, respectively, with 0.3, 0.5, 0.7, and 0.4 selected as the initial states for the four experiments. out.x1, out.x2, out.x3, and out.x4 represent the actual motion trajectory output sequence of the suspended ball. plant, plant1, plant2, and plant3 represent the magnetic levitation system models obtained by selecting different states in the four experiments.

[0162] from Figure 8 As can be seen, the fixed-time sliding mode controller designed in this invention achieves tracking of time-varying continuous signals, and simulations verify the effectiveness of the controller in tracking sinusoidal signals. Its tracking settling time is approximately 1.5 seconds, the convergence process is smooth, and the tracking stability error is on the order of 10. -4 The system achieves tracking of a preset trajectory sinusoidal signal within a preset fixed time period, and the upper bound of the convergence time does not depend on the initial state of the system. Simulations verify the fixed-time stability of the fixed-time sliding mode controller proposed in this invention, and also prove the rationality and effectiveness of the design of the fixed-time sliding mode controller.

[0163] Figure 9 This is a fixed-time sliding mode control module for loading a magnetic levitation device in a specific embodiment of the present invention. Figure 9 In the diagram, u1, u2, and u3 represent the parameters required for generating the tracking trajectory, and the trajectory format is as follows: ; t represents the time series; yd represents the generated trajectory dyd represents the first derivative of yd, ddyd represents the second derivative of yd; z represents the transformation factor of z-transformation; x1 and x2 represent the two states of the magnetic levitation device; fcn is short for function in the Simulink toolbox; u_new represents the controller output, Pos(mm) represents the actual position feedback, Vol(V) represents the actual limiting voltage feedback, Uin(V) represents the control input of the magnetic levitation system, Uout(V) represents the actual output voltage of the magnetic levitation device, and Usensor(V) represents the actual limiting output voltage of the magnetic levitation device.

[0164] Figure 9 In the diagram, the numbers "1" at position transition 1, position transition 2, and position transition 3 represent the base values ​​of u1, u2, and u3, respectively. "2", "2", and "40" refer to the multiple gains of u1, u2, and u3 on their respective base values, which facilitates the adjustment of tracking trajectory parameters.

[0165] Compared with traditional PID control or general sliding mode control methods, the control method of the present invention has the following advantages:

[0166] 1. Fixed-time convergence.

[0167] Traditional sliding mode control can only achieve finite-time convergence, and its convergence speed is heavily dependent on the initial state. The larger the initial deviation, the slower the convergence, and there is a lack of quantitative controllability of the convergence time. This invention designs a fixed-time sliding mode controller. During the sliding surface design, a non-singular fixed-time sliding surface with piecewise nonlinear terms is constructed, and a fixed-time sliding mode control law is introduced. Combined with the Lyapunov method for stability analysis, the system state is guaranteed to converge to the equilibrium point within a fixed time independent of the initial state, through both the approach phase and the sliding phase. Taking the magnetic levitation device in this embodiment as an example, regardless of whether the initial position deviation is 0.3mm or 0.7mm, the system state can be guaranteed to converge to the equilibrium point within approximately 1.7s within a fixed time, and the upper bound of the convergence time can be precisely controlled by parameters.

[0168] 2. Enhanced robustness.

[0169] Traditional sliding mode control uses a fixed gain switching term, which inherently presents a trade-off between disturbance rejection and chattering. High gain results in strong disturbance rejection but severe chattering, while low gain results in weak chattering but poor disturbance rejection. This invention addresses this by introducing a disturbance compensation term. This is used to counteract the effects of external disturbances and changes in system parameters. Simultaneously, in terms of state region division, a differentiated control strategy is adopted: high-gain disturbance rejection in the large error region and low-gain smooth convergence in the small error region. This avoids the contradiction of "weak disturbance rejection" or "large chattering" caused by the fixed gain in traditional sliding mode control, ensuring that the tracking error of the magnetic levitation device remains stable at 10 under a 0.1mm sinusoidal disturbance. -4 The system operates on the order of mm, which effectively addresses external disturbances and changes in system parameters, demonstrating the robustness of the proposed control method.

[0170] 3. Improved time-varying signal tracking capability.

[0171] Traditional sliding mode control often uses linear or simple nonlinear sliding surfaces, which are prone to phase lag and amplitude deviation when tracking time-varying signals. This invention, by designing a non-singular fixed-time sliding surface, can accurately track preset time-varying signals and also achieve precise tracking of fixed positions.

[0172] Example 2

[0173] This embodiment 2 describes a magnetic levitation device control system based on fixed-time sliding mode control. This system is based on the same inventive concept as the magnetic levitation device control method based on fixed-time sliding mode control in embodiment 1.

[0174] Specifically, the magnetic levitation device control system based on fixed-time sliding mode control includes the following modules:

[0175] The desired preset module is used to preset the desired stable position or desired tracking trajectory of the suspended ball in the magnetic levitation device.

[0176] The model building module is used to establish the electromagnetic force model equations of the magnetic levitation device. It considers the balance between the electromagnetic force of the system and the gravity of the levitated ball to obtain the dynamic equilibrium equations of the magnetic levitation device. The obtained dynamic equilibrium equations are expanded by Taylor series at the equilibrium point to obtain the linear differential equilibrium equations of the system at the equilibrium point, and then transformed into a state-space model.

[0177] The sliding surface design module is used to establish the position tracking error based on the desired stable position or desired tracking trajectory of the suspended ball, and to design a non-singular fixed-time sliding surface based on the feedback information of the actual position of the suspended ball.

[0178] The controller design module is used to design fixed-time sliding mode control laws based on state-space models and non-singular fixed-time sliding mode surfaces; a fixed-time sliding mode controller is constructed by combining non-singular fixed-time sliding mode surfaces and fixed-time sliding mode control laws.

[0179] And a tracking control module, which uses a fixed-time sliding mode controller to achieve trajectory tracking control of the suspended ball in the magnetic levitation device.

[0180] It should be noted that the implementation process of the functions and roles of each functional module in the magnetic levitation device control system based on fixed-time sliding mode control is detailed in the implementation process of the corresponding steps in the method of Example 1, and will not be repeated here.

[0181] Example 3

[0182] This embodiment 3 describes a computer device that includes a memory and one or more processors.

[0183] The memory stores executable code, which, when executed by the processor, is used to implement the steps of the magnetic levitation device control method based on fixed-time sliding mode control in Embodiment 1 above.

[0184] In this embodiment, the computer device can be any device or apparatus with data processing capabilities, and will not be described in detail here.

[0185] Example 4

[0186] This embodiment 4 describes a computer-readable storage medium storing a program that, when executed by a processor, implements the steps of a magnetic levitation device control method based on fixed-time sliding mode control.

[0187] The computer-readable storage medium can be an internal storage unit of any device or apparatus with data processing capabilities, such as a hard disk or memory, or an external storage device of any device with data processing capabilities, such as a plug-in hard disk, smart media card (SMC), SD card, flash card, etc.

[0188] Of course, the above description is only a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. It should be noted that any equivalent substitutions or obvious modifications made by those skilled in the art under the guidance of this specification fall within the scope of this specification and should be protected by the present invention.

Claims

1. A control method for a magnetic levitation device based on fixed-time sliding mode control, characterized in that, Includes the following steps: Step 1. Preset the desired stable position or desired tracking trajectory of the suspended ball in the magnetic levitation device; Step 2. Establish the electromagnetic force model equation of the magnetic levitation device, considering the balance between the electromagnetic force of the system and the gravity of the levitated ball, and obtain the dynamic equilibrium equation of the magnetic levitation device; perform Taylor series expansion of the obtained dynamic equilibrium equation at the equilibrium point to obtain the linear differential equilibrium equation of the system at the equilibrium point, and transform it into a state-space model. Step 3. Based on the desired stable position or desired tracking trajectory of the suspended ball preset in Step 1, establish the position tracking error and design a non-singular fixed-time sliding surface after obtaining the actual position feedback information of the suspended ball. Step 4. Based on the state-space model in Step 1 and the non-singular fixed-time sliding surface in Step 3, design a fixed-time sliding control law; construct a fixed-time sliding controller using the non-singular fixed-time sliding surface and the fixed-time sliding control law. Step 5. Using the fixed-time sliding mode controller from Step 4, track and control the trajectory of the suspended ball in the magnetic levitation device. Step 4 specifically involves: make , , Indicates position tracking error. Indicates speed tracking error; Based on the state-space model obtained in step 1 and the non-singular fixed-time sliding mode surface designed in step 3, the fixed-time sliding mode control law is designed as follows: ； in, Indicates control input, Represents the parameters in the system model. Indicates the gain parameter. This represents a non-singular fixed-time sliding surface. Represents gravitational acceleration; coefficient Defined as: ； in, Used to compensate for time-varying lumped disturbances in a system, which include model uncertainties and external disturbances; and Represents the gain coefficient, and , ; and It is a positive odd number; and It is a positive odd number; it satisfies , and ; and Represents the gain coefficient, and , ; , , , It is a positive odd number and satisfies , , , , ; parameter That is , Defined as: ； in, Represents a constant; A fixed-time sliding mode controller consists of a non-singular fixed-time sliding surface and a fixed-time sliding mode control law. ； in, It is a non-singular fixed-time sliding surface function.

2. The control method for a magnetic levitation device based on fixed-time sliding mode control according to claim 1, characterized in that, Step 2 specifically involves: The electromagnetic force model equations for the magnetic levitation device are established as follows: ； in, Represents electromagnetic force; This represents the current in the excitation coil; This represents the air gap between the center of mass of the suspended sphere and the magnetic poles of the electromagnet. Indicates magnetic co-energy. Represents the permeability of free space. For magnetically conductive area, Indicates the number of turns of the excitation coil. It is the electromagnetic force coefficient; Considering the balance between the electromagnetic force of the system and the gravity of the levitated ball, the dynamic equilibrium equation of the magnetic levitation device is obtained as follows: ； in, Indicates the mass of the suspended ball; express The air gap between the center of mass of the suspended sphere and the magnetic poles of the electromagnet is constantly suspended. set up For the system to be in equilibrium, the following conditions must be met when the forces are balanced: ,in Indicates the balanced current. Indicates the equilibrium position; The obtained dynamic equilibrium equations of the magnetic levitation device are expanded using Taylor series at the equilibrium point to obtain the linear differential equilibrium equations of the system at the equilibrium point, which are then transformed into a state-space model: ； in, The electromagnetic force model equations are shown in to The partial derivatives, The electromagnetic force model equations are shown in to The partial derivatives of .

3. The control method for a magnetic levitation device based on fixed-time sliding mode control according to claim 2, characterized in that, Step 3 specifically involves: Desired stable position based on the suspended sphere and expected speed Based on the feedback information of the actual position of the suspended ball, a tracking error is established: ， ； in, Indicates the actual position of the suspended ball; Design a nonsingular fixed-time sliding surface function. for: ； Differentiating the nonsingular fixed-time sliding mode surface function, we obtain: ； right Taking the derivative, we get: ； Therefore, we get: ； in, This indicates the disturbance experienced by the system.

4. The control method for a magnetic levitation device based on fixed-time sliding mode control according to claim 3, characterized in that, In step 4, after completing the design of the fixed-time sliding mode controller, a stability analysis is performed on the magnetic levitation device controlled by the fixed-time sliding mode controller.

5. The control method for a magnetic levitation device based on fixed-time sliding mode control according to claim 4, characterized in that, The process of stability analysis for a magnetic levitation device controlled by a fixed-time sliding mode controller is as follows: Design Lyapunov functions for: ； For Lyapunov functions Taking the derivative, we get: ; Differentiating the nonsingular fixed-time sliding mode surface function, we obtain: ； right Taking the derivative, we get: ； The results were: ； Substituting into the Lyapunov function, we get: ； The results were: ； in We obtain the inequality: Therefore, we get: ； Pick Then we have: ； state space in accordance with The definition is divided into two different regions. and : ， ； Among them, the region The width is ; When the system state In the region hour, For all conditions to hold true, the derivative of a non-singular fixed-time sliding surface is: ； For the derivative of the Lyapunov function, we have: ； When the system state is not on a non-singular fixed-time sliding surface, i.e. hour, ,Pick ,have: ； Therefore, we get: ； System status At a fixed time It reaches a non-singular fixed-time sliding surface within a fixed time interval, i.e., it converges within a fixed time interval. Upper bound of convergence time for: ； When the system state In the region At that time, if Then, without considering complex numbers, it satisfies ,have: ； in, ,and ; ,and ; System status At a fixed time It reaches a non-singular fixed-time sliding surface within a fixed time interval, i.e., it converges within a fixed time interval. Upper bound of convergence time for: ； When the system state When it approaches 0, then Approaching 1, the output of the fixed-time sliding mode controller is: ； Substitute system status ,get: ； because and Then when hour, ;when hour, ; System status The area will be traversed monotonously within a limited time. Entering the area From the region Entering the area time Depends on constant , The value is determined by the boundary width of the partitioned region. Decide; State variables in a magnetic levitation device controlled by a fixed-time sliding mode controller It can converge from any state in space to a non-singular fixed-time sliding surface within a fixed time.

6. The control method for a magnetic levitation device based on fixed-time sliding mode control according to claim 5, characterized in that, Step 5 specifically involves: The preset position of the suspended ball, i.e. the desired stable position or the desired tracking trajectory, is input to the fixed-time sliding mode controller. The first derivative of the tracking signal is the rate of change of the position of the tracking trajectory, and the second derivative of the tracking signal is the rate of change of the velocity of the tracking trajectory. The fixed-time sliding mode controller outputs control commands to drive the magnetic levitation device based on the input information, thereby controlling the electronic devices to generate voltage and current to drive the magnetic levitation device to generate electromagnetic force. After the system responds, it outputs the actual position of the suspended ball and the first derivative of the actual position, which is the actual velocity of the suspended ball. The actual position of the suspended ball is processed by the first feedback coefficient to generate the first feedback signal, and the actual velocity of the suspended ball is processed by the second feedback coefficient to generate the second feedback signal. The first and second feedback signals are synchronously transmitted back to the fixed-time sliding mode controller to calculate the position tracking error and velocity tracking error of the suspended ball in real time. Under the action of the non-singular fixed-time sliding surface and the fixed-time sliding mode control law, the system state finally achieves the tracking of the preset trajectory within a fixed time.

7. A magnetic levitation device control system based on fixed-time sliding mode control for implementing the control method of the magnetic levitation device based on fixed-time sliding mode control as described in claim 1, characterized in that, The magnetic levitation device control system based on fixed-time sliding mode control includes: The desired preset module is used to preset the desired stable position or desired tracking trajectory of the suspended ball in the magnetic levitation device; The model building module is used to establish the electromagnetic force model equations of the magnetic levitation device. It considers the balance between the electromagnetic force of the system and the gravity of the levitated ball to obtain the dynamic equilibrium equations of the magnetic levitation device. The obtained dynamic equilibrium equations are expanded by Taylor series at the equilibrium point to obtain the linear differential equilibrium equations of the system at the equilibrium point, and then transformed into a state-space model. The sliding surface design module is used to establish the position tracking error based on the desired stable position or desired tracking trajectory of the suspended ball, and to design a non-singular fixed-time sliding surface based on the actual position feedback information of the suspended ball. The controller design module is used to design fixed-time sliding mode control laws based on state-space models and non-singular fixed-time sliding mode surfaces; a fixed-time sliding mode controller is constructed by combining non-singular fixed-time sliding mode surfaces and fixed-time sliding mode control laws. And a tracking control module, which uses a fixed-time sliding mode controller to achieve trajectory tracking control of the suspended ball in the magnetic levitation device.

8. A computer device comprising a memory and one or more processors, wherein the memory stores executable code, characterized in that, When the processor executes the executable code, it implements the steps of the magnetic levitation device control method based on fixed-time sliding mode control as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the magnetic levitation device control method based on fixed-time sliding mode control as described in any one of claims 1 to 6.

Images