A linear motor tracking control method and system

Abstract

The application relates to the field of motor control, and particularly discloses a linear motor tracking control method and system, which comprises the following steps: constructing a linear motor dynamics model considering external disturbance factors; obtaining a first auxiliary variable, constructing an adaptive state observer based on the linear motor dynamics model and the first auxiliary variable; constructing an adaptive sliding mode disturbance observer according to the adaptive state observer; obtaining a second auxiliary variable, and constructing a tracking controller based on the linear motor dynamics model, the second auxiliary variable and an external disturbance estimation value of the linear motor. The method and system provided by the application can reduce the influence of external disturbance and chattering on the linear motor, obtain an external disturbance estimation value with high accuracy, and use the external disturbance estimation value for tracking control of the linear motor, so that the trajectory tracking error accurately converges to the system state within a limited time, and the precision and stability of linear motor trajectory tracking are improved.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and in particular to a linear motor tracking control method and system. Background Technology

[0002] Compared to traditional rotary motors, linear motors offer advantages such as simple structure and the ability to drive loads without a transmission device. This eliminates common problems in mechanical transmissions, such as backlash, dead zones, and inconsistencies, enabling high-speed, high-precision linear motion. Therefore, linear motors have been widely used in precision manufacturing and machining in recent years.

[0003] However, in practical industrial applications, unpredictable external disturbances may negatively affect the motion performance of linear motors, causing phenomena such as chattering.

[0004] Therefore, how to accurately predict external disturbances of linear motors and effectively suppress chattering in order to improve the accuracy of linear motor trajectory tracking has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a linear motor tracking control method and system, which solves the problems in related technologies such as difficulty in effectively estimating external disturbances of linear motors and suppressing chattering caused by external disturbances.

[0006] As a first aspect of the present invention, a linear motor tracking control method is provided, comprising:

[0007] Construct a dynamic model of the linear motor that considers external disturbance factors;

[0008] Obtain the first auxiliary variable, and construct an adaptive state observer based on the linear motor dynamics model and the first auxiliary variable. The adaptive state observer is used to obtain the unmeasurable state information of the linear motor in real time, and the first auxiliary variable is used to provide the first tracking error information of the linear motor.

[0009] An adaptive sliding mode disturbance observer is constructed based on the adaptive state observer. The adaptive sliding mode disturbance observer is used to obtain the estimated value of the external disturbance of the linear motor in real time.

[0010] A second auxiliary variable is obtained, and a tracking controller is constructed based on the linear motor dynamics model, the second auxiliary variable, and the estimated external disturbance of the linear motor. The tracking controller is used to track and control the running trajectory of the linear motor according to the estimated external disturbance of the linear motor. The second auxiliary variable is used to provide the second tracking error information of the linear motor.

[0011] Furthermore, the first tracking error information of the linear motor includes at least: the first tracking error, the first tracking error derivative, the first virtual control variable, and the first error variable;

[0012] An adaptive state observer is constructed based on the linear motor dynamics model and the first auxiliary variable, including:

[0013] Determine the initial state of the first tracking error, and based on the initial state of the first tracking error, obtain the initial state of the derivative of the first tracking error, the initial state of the first virtual control variable, and the initial state of the first error variable;

[0014] The actual running trajectory of the linear motor is obtained based on the linear motor dynamics model. An adaptive state observer is constructed based on the actual running trajectory of the linear motor, the initial state of the first tracking error, the initial state of the first virtual control variable, and the initial state of the first error variable. The adaptive state observer can adaptively update by following the actual running trajectory of the linear motor.

[0015] Furthermore, the expression for the first tracking error is:

[0016] σ1=z a1 -x,

[0017] The expression for the derivative of the first tracking error is:

[0018]

[0019] The expression for the first virtual control variable is:

[0020]

[0021] The expression for the first error variable is:

[0022] η1=σ2-α1,

[0023] Where x represents the displacement of the actual running trajectory of the linear motor. Let z be the derivative of σ1. a1 This represents the state tracking variable used to track the displacement of the actual running trajectory of the linear motor. a1 represents a constant, 0 < a1 < 1, and ε1 represents a diagonal positive definite matrix, ε1 = diag(ε 11 ...ε 1n ).

[0024] Furthermore, the expression for the adaptive state observer is:

[0025]

[0026] Where M represents the equivalent mass of the linear motor mover, τ represents the output of the tracking controller, and B represents parameters related to velocity and displacement. V represents the actual speed of the linear motor, and V represents the dynamic characteristics of the unmodeled part of the linear motor. Let ε1 represent the derivative of the first dummy control variable, and ε2 represent the diagonal positive definite matrix, ε2 = diag(ε1). 21 ...ε 2n ), This represents the adaptive law of the state observer. δ1 represents a constant, k d Let I denote a constant, sgn denote the identity matrix, and sgn denote the sign function.

[0027] Furthermore, an adaptive sliding mode perturbation observer is constructed based on the adaptive state observer, including:

[0028] Obtain the unmeasurable state information of the linear motor from the output of the adaptive state observer;

[0029] The actual running trajectory of the linear motor is obtained based on the linear motor dynamics model;

[0030] An adaptive sliding mode disturbance observer is constructed based on the actual running trajectory of the linear motor, the unmeasurable state information of the linear motor, and the derivative of the first tracking error in the first tracking error information. The adaptive sliding mode disturbance observer can adaptively update according to the actual running trajectory of the linear motor.

[0031] Furthermore, the expression for the adaptive sliding mode perturbation observer is:

[0032]

[0033] in, z represents the estimated external disturbance of the linear motor. a1 Let M represent the displacement of the linear motor's actual running trajectory, M represent the equivalent mass of the linear motor's mover, B represent parameters related to velocity and displacement, V represent the dynamic characteristics of the unmodeled part of the linear motor, and λ2 and k both represent the gains of the adaptive sliding mode disturbance observer and are constants. v = σ2 + λ1σ2, λ1 = ||M -1 B||, This represents the adaptive law of the perturbation observer. λ0 represents a real number, τ represents the output of the tracking controller, and sgn represents the sign function.

[0034] Furthermore, the second tracking error information of the linear motor includes at least: the second tracking error, the derivative of the second tracking error, the second virtual control variable, and the second error variable;

[0035] A tracking controller is constructed based on the linear motor dynamics model, the second auxiliary variable, and the external disturbance information of the linear motor, including:

[0036] Determine the initial state of the second tracking error, and based on the initial state of the second tracking error, obtain the initial state of the derivative of the second tracking error, the initial state of the second virtual control variable, and the initial state of the second error variable;

[0037] The actual running trajectory of the linear motor is obtained based on the linear motor dynamics model. A tracking controller is constructed based on the actual running trajectory of the linear motor, the initial state of the second tracking error, the initial state of the second virtual control variable, and the initial state of the second error variable. The tracking controller can adaptively update by following the actual running trajectory of the linear motor.

[0038] Furthermore, the expression for the second tracking error is:

[0039] e1 = xx d ,

[0040] The expression for the derivative of the second tracking error is:

[0041]

[0042] The expression for the second virtual control variable is:

[0043]

[0044] The expression for the second error variable is:

[0045] z = e² - γ,

[0046] Where x represents the displacement of the actual running trajectory of the linear motor, x d This indicates the preset reference trajectory for the linear motor. Let μ1 denote the derivative of e1, and let μ1 denote the diagonal positive definite matrix, μ1 = diag(μ 11 ...μ 1n b1 represents a constant, and 0 < b1 ≤ 1;

[0047] The expression for the tracking controller is:

[0048]

[0049] Where B represents a parameter related to velocity and displacement. V represents the actual speed of the linear motor, V represents the dynamic characteristics of the unmodeled part of the linear motor, and M represents the equivalent mass of the linear motor's mover. The second derivative represents the actual acceleration of the linear motor. Let μ2 be the derivative of the second virtual control variable, and μ2 be a diagonal positive definite matrix. μ2 = diag(μ 21 ...μ 2n K represents the adjustment parameters of the tracking controller, and K is a diagonal positive definite matrix, K = diag{K1...K} i}, sgn represents the sign function, This indicates the external disturbance information of the linear motor.

[0050] Furthermore, the expression for the linear motor dynamics model is as follows:

[0051]

[0052] Where M represents the equivalent mass of the linear motor's mover, and x represents the displacement of the actual running trajectory of the linear motor. This indicates the actual speed of the linear motor. Let τ represent the actual acceleration of the linear motor, τ represent the final control input, B represent parameters related to velocity and displacement, and V represent the unmodeled dynamic characteristics of the linear motor. d This indicates information about external disturbances.

[0053] As another aspect of the present invention, a linear motor tracking control system is provided, comprising:

[0054] The model building module is used to build a dynamic model of a linear motor that takes into account external disturbances.

[0055] An adaptive state observation module is used to acquire the first auxiliary variable. An adaptive state observer is constructed based on the linear motor dynamics model and the first auxiliary variable. The adaptive state observer is used to acquire the unmeasurable state information of the linear motor in real time. The first auxiliary variable is used to provide the first tracking error information of the linear motor.

[0056] The adaptive sliding mode disturbance observation module is used to construct an adaptive sliding mode disturbance observer based on the adaptive state observer. The adaptive sliding mode disturbance observer is used to obtain the estimated value of the external disturbance of the linear motor in real time.

[0057] The tracking control module is used to acquire the second auxiliary variable and construct a tracking controller based on the linear motor dynamics model, the second auxiliary variable and the estimated value of the external disturbance of the linear motor. The tracking controller is used to track and control the running trajectory of the linear motor according to the estimated value of the external disturbance of the linear motor. The second auxiliary variable is used to provide the second tracking error information of the linear motor.

[0058] The linear motor tracking control method and system provided by this invention constructs an adaptive sliding mode disturbance observer with exponential convergence and robustness by introducing a first auxiliary variable to obtain the external disturbance estimate of the linear motor to compensate for the disturbance and reduce the impact of disturbance and chattering. Furthermore, by introducing a second auxiliary variable to adjust the input amplitude of the tracking controller, a tracking controller based on the adaptive sliding mode disturbance observer is designed to perform trajectory tracking control of the linear motor, so as to achieve good tracking and anti-interference effects. Attached Figure Description

[0059] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the following detailed description to explain the invention, but do not constitute a limitation thereof.

[0060] Figure 1 A flowchart illustrating a linear motor tracking control method provided by the present invention;

[0061] Figure 2 A schematic diagram of the process for constructing an adaptive state observer provided by the present invention;

[0062] Figure 3 A schematic diagram of the process for constructing an adaptive sliding mode perturbation observer provided by the present invention;

[0063] Figure 4 A schematic diagram of the process for constructing a tracking controller provided by the present invention;

[0064] Figure 5 Structural block diagram of the adaptive state observer and adaptive sliding mode perturbation observer provided by the present invention;

[0065] Figure 6 The structural block diagram of the tracking controller provided by the present invention;

[0066] Figure 7 The present invention provides a structural block diagram of a linear motor tracking control system. Detailed Implementation

[0067] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0068] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0069] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of the invention described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0070] In practical applications of linear motors, the actuators that perform linear motor tracking control methods are usually subject to physical limitations, and the control input of the tracking control system is affected by external disturbances, which greatly reduces the performance of the tracking control system.

[0071] Based on this, a linear motor tracking control method is provided in this embodiment of the invention. Figure 1 This is a flowchart illustrating the linear motor tracking control method provided in an embodiment of the present invention, as shown below. Figure 1 As shown, it includes:

[0072] S1. Construct a dynamic model of the linear motor that considers external disturbance factors;

[0073] In this embodiment of the invention, external disturbance factors mainly include load resistance disturbance, static friction disturbance, sliding friction disturbance, and viscous friction disturbance.

[0074] S2. Obtain the first auxiliary variable. Based on the linear motor dynamics model and the first auxiliary variable, construct an adaptive state observer. The adaptive state observer is used to obtain the unmeasurable state information of the linear motor in real time. The first auxiliary variable is used to provide the first tracking error information of the linear motor.

[0075] By introducing a first auxiliary variable to provide the first tracking error information of the linear motor, a stable adaptive state observer and an adaptive sliding mode disturbance observer can be designed. Under the condition that the adaptive state observer and the adaptive sliding mode disturbance observer remain stable, by selecting an appropriate first auxiliary variable, the adaptive state observer and the adaptive sliding mode disturbance observer can achieve superior performance indicators such as faster convergence speed and smaller estimation error.

[0076] S3. Construct an adaptive sliding mode disturbance observer based on the adaptive state observer. The adaptive sliding mode disturbance observer is used to obtain the estimated value of the external disturbance of the linear motor in real time.

[0077] Based on the aforementioned external disturbance factors, the external disturbance estimates in the embodiments of the present invention may include load resistance disturbance estimates, static friction disturbance estimates, sliding friction disturbance estimates, and viscous friction disturbance estimates, etc.

[0078] S4. Obtain the second auxiliary variable. Based on the linear motor dynamics model, the second auxiliary variable, and the estimated external disturbance of the linear motor, construct a tracking controller. The tracking controller is used to track and control the running trajectory of the linear motor according to the estimated external disturbance of the linear motor. The second auxiliary variable is used to provide the second tracking error information of the linear motor.

[0079] As with the first auxiliary variable, by introducing the second auxiliary variable, the second tracking error information of the linear motor can be provided, which can design a stable tracking controller. When the tracking controller remains stable, by selecting an appropriate second auxiliary variable, the tracking controller can achieve superior performance indicators such as faster convergence speed and smaller control error.

[0080] The linear motor tracking control method provided by this invention introduces a first auxiliary variable to adjust the input amplitude of an adaptive sliding mode disturbance observer, thereby constructing an adaptive sliding mode disturbance observer with exponential convergence and robustness to obtain an estimate of the external disturbance of the linear motor to compensate for the disturbance and reduce the impact of disturbance and chattering. Furthermore, by introducing a second auxiliary variable to adjust the input amplitude of the tracking controller, a tracking controller is designed based on the adaptive sliding mode disturbance observer to perform trajectory tracking control of the linear motor, ultimately achieving semi-global stability of closed-loop control and achieving good tracking and anti-interference effects.

[0081] Specifically, the expression for the linear motor dynamics model provided in this embodiment of the invention is as follows:

[0082]

[0083] Where M represents the equivalent mass of the linear motor's mover, and x represents the displacement of the actual running trajectory of the linear motor. This indicates the actual speed of the linear motor. Let τ represent the actual acceleration of the linear motor, τ represent the final control input, B represent parameters related to velocity and displacement, and V represent the unmodeled dynamic characteristics of the linear motor. d This indicates information about external disturbances.

[0084] In this embodiment of the invention, the first tracking error information of the linear motor includes at least: a first tracking error, a first tracking error derivative, a first virtual control variable, and a first error variable;

[0085] like Figure 5 As shown, the expression for the first tracking error is:

[0086] σ1=z a1 -x,

[0087] The expression for the derivative of the first tracking error is:

[0088]

[0089] The expression for the first virtual control variable is:

[0090]

[0091] The expression for the first error variable is:

[0092] η1=σ2-α1,

[0093] Where x represents the displacement of the actual running trajectory of the linear motor. Let z be the derivative of σ1. a1 This represents the state tracking variable used to track the displacement of the actual running trajectory of the linear motor. a1 represents a constant, 0 < a1 < 1, and ε1 represents a diagonal positive definite matrix, ε1 = diag(ε 11 ...ε 1n ).

[0094] An adaptive state observer is constructed based on the linear motor dynamics model and the first auxiliary variable, such as... Figure 2 As shown, it specifically includes:

[0095] S21. Determine the initial state of the first tracking error, and obtain the initial state of the derivative of the first tracking error, the initial state of the first virtual control variable, and the initial state of the first error variable based on the initial state of the first tracking error.

[0096] S22. Obtain the actual running trajectory of the linear motor according to the linear motor dynamics model. Based on the actual running trajectory of the linear motor, the initial state of the first tracking error, the initial state of the first virtual control variable, and the initial state of the first error variable, construct an adaptive state observer. The adaptive state observer can adaptively update by following the actual running trajectory of the linear motor.

[0097] Specifically, the Lyapunov function is defined as follows:

[0098]

[0099] Differentiate the above V1:

[0100]

[0101] This means that when the convergence of η1 is properly verified, the finite convergence of σ1 can be guaranteed. Therefore, we further define the Lyapunov function:

[0102]

[0103] Differentiate the above V2:

[0104]

[0105] Based on this, the adaptive state observer provided in this embodiment of the invention is constructed, and its expression is:

[0106]

[0107] Where M represents the equivalent mass of the linear motor mover, τ represents the output of the tracking controller, and B represents parameters related to velocity and displacement. V represents the actual speed of the linear motor, and V represents the dynamic characteristics of the unmodeled part of the linear motor. Let ε1 represent the derivative of the first dummy control variable, and ε2 represent the diagonal positive definite matrix, ε2 = diag(ε1). 21 ...ε 2n ), This represents the adaptive law of the state observer. δ1 represents a constant, k d Let I denote a constant, sgn denote the identity matrix, and sgn denote the sign function.

[0108] The above Substitute In the middle, we get:

[0109]

[0110] when When the convergence is properly verified, the finite convergence of the first error variable η1 and the first tracking error σ1 can be guaranteed. Therefore, the Lyapunov function is further defined as follows:

[0111]

[0112] in δ1 is a positive constant.

[0113] Differentiate V3:

[0114]

[0115] Based on the above derivation, we get:

[0116]

[0117] According to the finite-time theorem, the first tracking error σ1 and the first error variable η1 will converge to zero in a finite time, and the state tracking variable z a1 It will also approach x in a finite amount of time, while introducing an adaptive law for the state observer. Construct an adaptive state observer. The displacement is adaptively updated following the actual running trajectory of the linear motor, due to z a1 It includes It is adaptively updated, which avoids large fluctuations caused by the parameters before sgn becoming too large, thus ensuring that the state tracking variable z... a1 This can offset the dependency on the upper bound.

[0118] Furthermore, since the performance of the adaptive sliding mode disturbance observer, i.e. the accuracy of the external disturbance estimate of the linear motor monitored by the adaptive sliding mode disturbance observer, depends on whether the state tracking variable in the adaptive state observer can accurately reflect the state value of the linear motor tracking control system, it is necessary to gradually eliminate the nonlinear terms in the dynamic equation of the linear motor tracking control system through the iterative process of the virtual control input of the state tracking variable, so that the closed-loop performance of the linear motor tracking control system meets the design requirements and achieves accurate control of the nonlinear system, the embodiments of the present invention select the displacement of the actual running trajectory of the linear motor for tracking.

[0119] like Figure 3 As shown, an adaptive sliding mode perturbation observer is constructed based on the adaptive state observer, specifically including:

[0120] S31. Obtain the unmeasurable state information of the linear motor output by the adaptive state observer;

[0121] S32. Obtain the actual running trajectory of the linear motor based on the linear motor dynamics model;

[0122] S33. An adaptive sliding mode disturbance observer is constructed based on the actual running trajectory of the linear motor, the unmeasurable state information of the linear motor, and the first tracking error derivative in the first tracking error information. The adaptive sliding mode disturbance observer can adaptively update following the actual running trajectory of the linear motor.

[0123] like Figure 5 As shown, the expression for the adaptive sliding mode perturbation observer provided in this embodiment of the invention is:

[0124]

[0125] in, z represents the estimated external disturbance of the linear motor. a1Let M represent the displacement of the linear motor's actual running trajectory, M represent the equivalent mass of the linear motor's mover, B represent parameters related to velocity and displacement, V represent the dynamic characteristics of the unmodeled part of the linear motor, and λ2 and k both represent the gains of the adaptive sliding mode disturbance observer and are constants. v = σ2 + λ1σ2, λ1 = ||M -1 B||, This represents the adaptive law of the perturbation observer. λ0 represents a real number, τ represents the output of the tracking controller, and sgn represents the sign function.

[0126] Based on the expression for the adaptive sliding mode perturbation observer above, we can obtain:

[0127]

[0128] The derivative of d and The derivative of the error between the derivatives, i.e. The Lyapunov function selected for this stage is as follows:

[0129]

[0130] Differentiate V4:

[0131]

[0132] in,

[0133]

[0134] At the same time:

[0135]

[0136] Because the adaptive state observer incorporates a state tracking variable z a1 To track the displacement of the actual running trajectory of a linear motor, which is relatively easy to measure, a corresponding first auxiliary variable is designed by flexibly using backstepping technology. Based on the first auxiliary variable, an adaptive sliding mode disturbance observer with exponential convergence and robustness is proposed.

[0137] According to the finite-time theorem, the error of the external disturbance estimate of the linear motor observed in real time by the adaptive sliding mode disturbance observer provided in this embodiment of the invention converges exponentially, and the invention further... Adaptive updates were implemented because excessive control gain could cause the linear motor tracking control system to oscillate continuously around the control point. The settings can prevent the linear motor tracking control system from becoming overly sensitive and generating severe oscillations when reaching the target state if the gain is set too high. Therefore, the adaptive sliding mode disturbance observer designed in this invention can be applied to linear motor tracking control systems with nonlinear, time-varying, coupled, uncertain, and complex disturbance characteristics, and has strong ability to suppress linear motor chattering and anti-interference capabilities.

[0138] Specifically, the second tracking error information of the linear motor includes at least: the second tracking error, the derivative of the second tracking error, the second virtual control variable, and the second error variable;

[0139] like Figure 6 As shown, the expression for the second tracking error provided in this embodiment of the invention is:

[0140] e1 = xx d ,

[0141] The expression for the derivative of the second tracking error is:

[0142]

[0143] The expression for the second virtual control variable is:

[0144]

[0145] The expression for the second error variable is:

[0146] z = e² - γ,

[0147] Where x represents the displacement of the actual running trajectory of the linear motor, x d This indicates the preset reference trajectory for the linear motor. Let μ1 denote the derivative of e1, and let μ1 denote the diagonal positive definite matrix, μ1 = diag(μ 11 ...μ 1n b1 represents a constant, and 0 < b1 ≤ 1;

[0148] By introducing a second tracking error, a second virtual control variable, and a second error variable to adjust the input amplitude of the tracking controller, a tracking controller based on an adaptive sliding mode disturbance observer is further designed to perform trajectory tracking control of the linear motor, so as to achieve good tracking and anti-interference effects.

[0149] Furthermore, such as Figure 4 As shown, a tracking controller is constructed based on the linear motor dynamics model, the second auxiliary variable, and the external disturbance information of the linear motor, specifically including:

[0150] S41 determines the initial state of the second tracking error, and obtains the initial state of the derivative of the second tracking error, the initial state of the second virtual control variable, and the initial state of the second error variable based on the initial state of the second tracking error.

[0151] S42 obtains the actual running trajectory of the linear motor based on the linear motor dynamics model, and constructs a tracking controller based on the actual running trajectory of the linear motor, the initial state of the second tracking error, the initial state of the second virtual control variable, and the initial state of the second error variable; the tracking controller can adaptively update following the actual running trajectory of the linear motor.

[0152] Specifically, the expression for the tracking controller is as follows: Figure 6 As shown, it is:

[0153]

[0154] Where B represents a parameter related to velocity and displacement. V represents the actual speed of the linear motor, V represents the dynamic characteristics of the unmodeled part of the linear motor, and M represents the equivalent mass of the linear motor's mover. The second derivative represents the actual acceleration of the linear motor. Let μ2 be the derivative of the second virtual control variable, and μ2 be a diagonal positive definite matrix. μ2 = diag(μ 21 ...μ 2n K represents the adjustment parameters of the tracking controller, and K is a diagonal positive definite matrix, K = diag{K1...K} i}, sgn represents the sign function, This indicates the external disturbance information of the linear motor.

[0155] Based on this, the Lyapunov function is constructed as follows:

[0156]

[0157] Substitute the designed controller into the above... have to

[0158]

[0159] Based on the above derivation, we obtain:

[0160]

[0161] Where, μ min =min{μ 1i ,μ 2i}

[0162] The above proof demonstrates that the tracking error of the linear motor tracking control system can converge to a very small range within a finite time. By selecting appropriate tracking controller parameters K, the tracking control error can be accurately converged to zero within a finite time, while ensuring the stability of the linear motor tracking control system and stable tracking.

[0163] Another embodiment of the present invention provides a linear motor tracking control system, such as... Figure 4 The system includes: a model building module 1, used to build a linear motor dynamics model considering external disturbances; an adaptive state observation module 2, used to acquire a first auxiliary variable and build an adaptive state observer based on the linear motor dynamics model and the first auxiliary variable. The adaptive state observer is used to acquire unmeasurable state information of the linear motor in real time, and the first auxiliary variable is used to provide the first tracking error information of the linear motor; an adaptive sliding mode disturbance observation module 3, used to build an adaptive sliding mode disturbance observer based on the adaptive state observer. The adaptive sliding mode disturbance observer is used to acquire the external disturbance estimate of the linear motor in real time; and a tracking control module 4, used to acquire a second auxiliary variable and build a tracking controller based on the linear motor dynamics model, the second auxiliary variable, and the external disturbance estimate of the linear motor. The tracking controller is used to track and control the running trajectory of the linear motor according to the external disturbance estimate of the linear motor, and the second auxiliary variable is used to provide the second tracking error information of the linear motor.

[0164] The linear motor tracking control system provided in this embodiment of the invention constructs a linear motor dynamic model considering external disturbance factors through a model building module 1. Then, through an adaptive state observation module 2 and an adaptive sliding mode disturbance observation module 3, an adaptive sliding mode disturbance observer with exponential convergence and robustness is constructed by introducing a first auxiliary variable to obtain the external disturbance estimate of the linear motor to compensate for the disturbance and reduce the impact of disturbance and chattering. The tracking control module 4 adjusts the input amplitude of the tracking controller by introducing a second auxiliary variable. Furthermore, a tracking controller based on the adaptive sliding mode disturbance observer is designed to perform trajectory tracking control of the linear motor to achieve good tracking and anti-interference effects.

[0165] The specific working principle of the linear motor tracking control system in this embodiment of the invention can be referred to the description of the linear motor tracking control method above, and will not be repeated here.

[0166] It is understood that the above embodiments are merely exemplary implementations used to illustrate the principles of the present invention, and the present invention is not limited thereto. For those skilled in the art, various modifications and improvements can be made without departing from the spirit and essence of the present invention, and these modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A linear motor tracking control method, characterized by, The method comprises the following steps: constructing a linear motor dynamics model considering external disturbance factors; obtaining a first auxiliary variable, constructing an adaptive state observer based on the linear motor dynamics model and the first auxiliary variable, the adaptive state observer being used to obtain real-time unobservable state information of the linear motor, and the first auxiliary variable being used to provide first tracking error information of the linear motor; constructing an adaptive sliding mode disturbance observer according to the adaptive state observer, the adaptive sliding mode disturbance observer being used to obtain real-time external disturbance estimation of the linear motor; obtaining a second auxiliary variable, constructing a tracking controller based on the linear motor dynamics model, the second auxiliary variable and the external disturbance estimation of the linear motor, the tracking controller being used to track control the operation trajectory of the linear motor according to the external disturbance estimation of the linear motor, and the second auxiliary variable being used to provide second tracking error information of the linear motor.

2. The method of claim 1, wherein, The first tracking error information of the linear motor at least comprises a first tracking error, a first tracking error derivative, a first virtual control variable and a first error variable; The step of constructing the adaptive state observer based on the linear motor dynamics model and the first auxiliary variable comprises the following steps: determining an initial state of the first tracking error, and obtaining an initial state of the first tracking error derivative, an initial state of the first virtual control variable and an initial state of the first error variable based on the initial state of the first tracking error; obtaining an actual operation trajectory of the linear motor according to the linear motor dynamics model, and constructing the adaptive state observer based on the actual operation trajectory of the linear motor, the initial state of the first tracking error, the initial state of the first virtual control variable and the initial state of the first error variable, the adaptive state observer being able to adaptively update following the actual operation trajectory of the linear motor.

3. The method of claim 2, wherein, The expression of the first tracking error is: ， The expression of the first tracking error derivative is: ， The expression of the first virtual control variable is: ， The expression of the first error variable is: ， wherein represents a displacement of an actual operating trajectory of the linear motor, represents derivative of represents a state tracking variable for tracking the displacement of the actual operating trajectory of the linear motor, represents a constant, , represents a positive definite matrix, .

4. The method of claim 3, wherein, The expression of the adaptive state observer is: ， wherein represents the equivalent mass of the moving part of the linear motor, represents the output of the tracking controller, represents parameters related to velocity and displacement, represents the actual velocity of the linear motor, represents the dynamics of the unmodeled part of the linear motor, represents the derivative of the first virtual control variable, represents a positive definite diagonal matrix, , represents the state observer adaptation law, , , represents a constant, represents a constant, represents the identity matrix, represents the sign function.

5. The method according to any one of claims 1 to 4, characterized in that, The step of constructing the adaptive sliding mode disturbance observer according to the adaptive state observer comprises the following steps: obtaining the unobservable state information of the linear motor output by the adaptive state observer; obtaining an actual operation trajectory of the linear motor according to the linear motor dynamics model; constructing the adaptive sliding mode disturbance observer based on the actual operation trajectory of the linear motor, the unobservable state information of the linear motor and the first tracking error derivative in the first tracking error information, the adaptive sliding mode disturbance observer being able to adaptively update following the actual operation trajectory of the linear motor.

6. The method of claim 5, wherein, The expression of the adaptive sliding mode disturbance observer is: ， wherein represents an external disturbance estimation of the linear motor, represents a state tracking variable for tracking the displacement of the actual operating trajectory of the linear motor, represents the equivalent mass of the moving part of the linear motor, represents parameters related to the speed and displacement, represents the dynamic characteristics of the unmodeled part of the linear motor, and both represent the gain of the adaptive sliding mode disturbance observer and are constants, , represents the disturbance observer adaptive law, , represents a real number, represents the output result of the tracking controller, represents a sign function.

7. The method according to any one of claims 1 to 4, characterized in that, The second tracking error information of the linear motor at least comprises a second tracking error, a second tracking error derivative, a second virtual control variable and a second error variable; The step of constructing the tracking controller based on the linear motor dynamics model, the second auxiliary variable and the external disturbance information of the linear motor comprises the following steps: determining an initial state of the second tracking error, obtaining an initial state of the derivative of the second tracking error, an initial state of the second virtual control variable and an initial state of the second error variable based on the initial state of the second tracking error; obtaining an actual operation trajectory of the linear motor according to the linear motor dynamics model, and constructing a tracking controller based on the actual operation trajectory of the linear motor, the initial state of the second tracking error, the initial state of the second virtual control variable and the initial state of the second error variable; the tracking controller can adaptively update following the actual operation trajectory of the linear motor.

8. The method of claim 7, wherein, an expression of the second tracking error is: ， an expression of the derivative of the second tracking error is: ， an expression of the second virtual control variable is: ， an expression of the second error variable is: ， wherein, denotes a displacement of an actual operating trajectory of the linear motor, denotes a preset linear motor operating reference trajectory, denotes a derivative of denotes a diagonal positive definite matrix, , denotes a constant, and ; an expression of the tracking controller is: ， wherein denotes a parameter related to velocity and displacement, denotes the actual velocity of the linear motor, denotes the dynamics of the unmodeled part of the linear motor, denotes the equivalent mass of the mover of the linear motor, denotes the second derivative of the actual acceleration of the linear motor, denotes the derivative of the second virtual control variable, is a diagonal positive definite matrix, , denotes a tuning parameter of the tracking controller, is a diagonal positive definite matrix, , denotes a sign function, denotes external disturbance information of the linear motor.

9. The method according to any one of claims 1 to 4, characterized in that, an expression of the linear motor dynamics model is: ； wherein, represents the equivalent mass of the linear motor mover, represents the displacement of the actual trajectory of the linear motor, represents the actual velocity of the linear motor, represents the actual acceleration of the linear motor, represents the final control input, represents parameters related to velocity and displacement, represents the dynamics of the linear motor unmodeled part, represents external disturbance information.

10. A linear motor tracking control system characterized by, comprising: a model construction module, configured to construct a linear motor dynamics model considering external disturbance factors; an adaptive state observation module, configured to obtain a first auxiliary variable, and construct an adaptive state observer based on the linear motor dynamics model and the first auxiliary variable; the adaptive state observer is used to obtain real-time unobservable state information of the linear motor, and the first auxiliary variable is used to provide first tracking error information of the linear motor; an adaptive sliding mode disturbance observation module, configured to construct an adaptive sliding mode disturbance observer according to the adaptive state observer; the adaptive sliding mode disturbance observer is used to obtain real-time external disturbance estimation value of the linear motor; a tracking control module, configured to obtain a second auxiliary variable, and construct a tracking controller based on the linear motor dynamics model, the second auxiliary variable and the external disturbance estimation value of the linear motor; the tracking controller is used to perform tracking control on the operation trajectory of the linear motor according to the external disturbance estimation value of the linear motor, and the second auxiliary variable is used to provide second tracking error information of the linear motor.

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