Linear Active Disturbance Rejection Control Method for Suppressing Coupling Disturbance of Macro-Micro Linear Motion Platform

Abstract

A linear anti-disturbance control method for suppressing coupling interference of macro-micro linear motion platforms belongs to the field of motor control. The present invention solves the problem that the control law design process of the existing coupling interference suppression method is cumbersome and the decoupling effect is poor. The main technical scheme adopted by the present invention is: step one, establish the mechanical equation of the macro-micro linear motion platform; step two, perform Laplace transform on the established mechanical equation to obtain the equivalent coupling model of the macro-micro linear motion platform; step three, establish the spatial equation of the linear motor and the voice coil motor, estimate the state variables and coupling errors of the macro-motion platform based on the spatial equation of the linear motor and the extended state observer, and estimate the state variables and coupling errors of the micro-motion platform based on the spatial equation of the voice coil motor and the extended state observer; and design a linear state error feedback control law based on the estimated state variables and coupling errors. The method of the present invention can be used to suppress the coupling interference of macro-micro linear motion platforms.

Description

Technical Field

[0001] The invention belongs to the field of motor control, and in particular relates to a linear anti-disturbance control method for suppressing coupling interference of a macro-micro linear motion platform. Background Art

[0002] With the development and progress of technologies such as motion control, optical measurement, piezoelectric ceramics and precision machining, high-precision motion platforms are widely used in various scientific fields. They are strategic, basic and leading industries for national economic and social development, the core and foundation for cultivating and developing strategic emerging industries and promoting the deep integration of informatization and industrialization, and are strategic industries for the country. As one of the key equipment in high-end precision manufacturing equipment, the macro-micro linear motion platform combines the motion characteristics of high-speed, large-stroke motion and high-precision positioning, and is an important motion method to achieve high-speed, large-stroke and precise positioning.

[0003] In the macro-micro linear motion platform, the macro stage completes the rapid motion under large stroke, and the micro stage performs nanometer-level high-precision high-frequency compensation, ultimately achieving high-precision positioning of the macro-micro linear motion platform. However, since the driver will generate reaction force when working, there will be force coupling between the macro and micro parts, especially when the driving force of the macro platform is much greater than the driving force of the micro platform, it will affect the precision control of the micro platform, and then affect the positioning accuracy and control performance of the macro-micro linear motion platform.

[0004] In order to improve the control performance of the macro-micro linear motion platform, it is necessary to suppress the coupling interference between the macro-motion stage and the micro-motion stage. The existing coupling interference suppression method is to decouple the coupling model by designing an appropriate control law, but there are problems such as poor decoupling effect and cumbersome control law design process. Summary of the invention

[0005] The purpose of the present invention is to solve the problems of complicated control law design process and poor decoupling effect of existing coupling interference suppression methods, and to propose a linear auto-disturbance rejection control method for suppressing coupling interference of macro-micro linear motion platforms.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] A linear auto-disturbance rejection control method for suppressing coupling interference of a macro-micro linear motion platform, the method specifically comprising the following steps:

[0008] Step 1: Establish the mechanical equation of the macro-micro linear motion platform according to the motion model of the macro-micro linear motion platform;

[0009] Step 2: Perform Laplace transform on the established mechanical equation to obtain an equivalent coupling model of the macro-micro linear motion platform;

[0010] Step 3: Establish the spatial equations of the linear motor and the voice coil motor respectively, and then estimate the state variables and coupling errors of the macro-motion stage based on the spatial equations of the linear motor and the extended state observer, and estimate the state variables and coupling errors of the micro-motion stage based on the spatial equations of the voice coil motor and the extended state observer;

[0011] A linear state error feedback control law is designed based on the estimated state variables and coupling errors, and the macro-micro linear motion platform is controlled based on the designed linear state error feedback control law and the equivalent coupling model.

[0012] The beneficial effects of the present invention are:

[0013] The present invention regards the error caused by coupling as disturbance, and uses an extended state observer to estimate the disturbance, and then designs a linear state error feedback control law to compensate for the disturbance error of the estimated disturbance in the input of the control system, thereby improving the decoupling effect, suppressing the coupling of the macro-micro linear motion platform, effectively improving the dynamic performance of the system, and improving the positioning accuracy of the system. Moreover, the extended state observer can estimate the state of the system without the need for an accurate model of the system, thus avoiding the cumbersome design process of the linear state error feedback control law. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is the motion model of the macro-micro linear motion platform;

[0015] Figure 2 It is a schematic diagram of the equivalent coupling structure between the macro-motion system and the micro-motion system;

[0016] In the figure, I ref,v (s) represents the input reference current of the voice coil motor, ACR represents the current loop controller, U v (s) represents the coil voltage of the voice coil motor, L v Represents the voice coil motor coil inductance, R v Represents the voice coil motor coil resistance, I v Represents the voice coil motor coil current, K e,v Represents the back EMF coefficient of the voice coil motor, K T,v Represents the thrust coefficient of the voice coil motor, M v Represents the voice coil motor rotor and load mass, M l Represents the linear motor rotor and load mass, K e,l Represents the linear motor back electromotive force coefficient, K T,l Represents the linear motor thrust coefficient, I l Represents the linear motor armature current, L l represents the linear motor armature inductance, Rl represents the linear motor armature resistance, U l (s) represents the armature voltage of the linear motor, I ref,l(s) represents the linear motor input reference current;

[0017] Figure 3 It is the structure diagram of the second-order linear active disturbance rejection control;

[0018] Figure 4 This is the structure diagram of the macro-micro linear motion platform's anti-disturbance control;

[0019] Figure 5 It is the tracking error curve of the macro-micro linear motion platform;

[0020] Figure 6 It is the tracking error curve of the macro-micro linear motion platform when LADRC is introduced. DETAILED DESCRIPTION

[0021] The present application is further described in detail below through specific implementations in combination with the accompanying drawings. Obviously, the described implementations are only part of the implementations of the present invention, not all of the implementations. Based on the implementations in the present invention, other implementations obtained by ordinary technicians in the field without making creative work are all within the scope of protection of the present invention.

[0022] Specific implementation method 1. Combination Figure 1 The present embodiment is described as follows. The present embodiment describes a linear auto-disturbance rejection control method for suppressing coupling interference of a macro-micro linear motion platform, and the method specifically comprises the following steps:

[0023] Step 1: Establish the mechanical equation of the macro-micro linear motion platform according to the motion model of the macro-micro linear motion platform;

[0024] Step 2: Perform Laplace transform on the established mechanical equation to obtain an equivalent coupling model of the macro-micro linear motion platform;

[0025] Step 3: The linear motor controlling the macro-motion stage and the voice coil motor controlling the micro-motion stage are typical second-order control systems. The tracking differentiator (TD) is used to establish the spatial equations of the linear motor and the voice coil motor respectively. Then, the state variables and coupling errors of the macro-motion stage are estimated based on the spatial equations of the linear motor and the extended state observer (ESO). The state variables and coupling errors of the micro-motion stage are estimated based on the spatial equations of the voice coil motor and the extended state observer.

[0026] According to the estimated state variables and coupling errors, a linear state error feedback control law (LESF) is designed, and then the macro-micro linear motion platform is controlled according to the designed linear state error feedback control law and the equivalent coupling model. That is, the coupling error is compensated in the motor input by designing a linear state error feedback control law, thereby achieving decoupling.

[0027] Step 3 in the present invention is implemented based on linear active disturbance rejection control: linear active disturbance rejection control can directly obtain the state variables and "total disturbance" of the controlled system from the input and output information of the controlled system in real time without relying on the precise model of the system, so as to eliminate the "total disturbance" from the controlled system using the control signal. In the macro-micro coupling problem, the coupling error is regarded as a disturbance, the coupling error is estimated using the extended state observer, and then the coupling error is compensated in the input to achieve decoupling.

[0028] The main components of the linear active disturbance rejection control (LADRC) control structure include: Tracking Differentiator (TD) is used to obtain the differential signal and configure the transition process; Extended State Observer (ESO) is used to observe the total disturbance of the control system; Linear State Error Feedback (LSEF) is used to generate the control quantity of the control system. The basic structural block diagram of the linear active disturbance rejection control (LADRC) control structure is shown in the figure below: Figure 3 shown.

[0029] In order to reduce the complexity of the algorithm and improve the response speed, the tracking differentiator (TD) is replaced by position / velocity curve planning. The macro- and micro-motor are typical second-order control systems, and the space equation can be established as:

[0030]

[0031] in is the sum of the internal and external disturbances of the system; w(t) is the external disturbance of the system; b is the compensation factor, and u is the control quantity.

[0032] The spatial equation of the linear extended state observer (LESO) can be obtained:

[0033]

[0034] Where z1, z2, z3 are the observer's estimated values ​​of the system variables; β1, β2, β3 are the control parameters of the extended state observer; b0 is the estimated value of b.

[0035] Subtract the given signal r1 and its differential value r2 from the state variables z1 and z2 obtained by the extended state observer, and the linear state error feedback control law (LESF) is obtained as follows:

[0036] u0=K p (r1-z1)-K d (r2-z2)

[0037]

[0038] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the viscous damping C of the air film is ignored. l , C v and elastic modulus k l , k v In the case of, the mechanical equation of the macro-micro linear motion platform is:

[0039]

[0040] Among them, m l is the mass of the macro-motion platform, m v is the mass of the micro-motion stage, F l is the linear motor driving force, F v is the driving force of the voice coil motor, Y l is the absolute position of the macro stage, Y v is the relative position between the macro-motion stage and the micro-motion stage, Y is the absolute position of the micro-motion stage, and t is the time.

[0041] The other steps and parameters are the same as those in the first embodiment.

[0042] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that both the macro-motion stage and the micro-motion stage are guided by air-floating guide rails.

[0043] The other steps and parameters are the same as those in the first or second embodiment.

[0044] The purpose of this embodiment is to achieve frictionless motion.

[0045] Specific implementation method 4: This implementation method is different from specific implementation methods 1 to 3 in that the specific process of step 2 is as follows:

[0046] Pick As input, take As the output, perform Laplace transform on equation (1) and obtain the equivalent coupling model of the macro-micro linear motion platform of equation (2):

[0047]

[0048] Here, s is a complex variable.

[0049] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0050] According to the equivalent coupling model of formula (2), we can get Figure 2 The equivalent coupling structure of the macro-micro system is shown.

[0051] Specific implementation method V. Combination Figure 4This embodiment is different from the first to fourth embodiments in that the specific process of step three is as follows:

[0052] Step 31. Establish the spatial equation of the linear motor:

[0053]

[0054] Where x1 is the position of the linear motor, is the first derivative of x1, x2 is the speed of the linear motor, is the first-order derivative of x2, x3 is the coupling error of the linear motor, is the first-order derivative of x3, b is the compensation factor corresponding to the linear motor, u is the linear state error feedback control law of the linear motor, f(x1,x2,w(t),t) is the sum of the internal disturbance and external disturbance of the linear motor, w(t) is the external disturbance of the linear motor, is the first-order derivative of f(x1,x2,w(t),t), y l is the absolute position of the macro stage;

[0055] Step 32: Estimate the state variables and coupling errors of the macro-motion stage based on the spatial equation of the linear motor and the extended state observer;

[0056]

[0057] Among them, z1 is the estimated value of x1, z2 is the estimated value of x2, z3 is the estimated value of x3, is the first derivative of z1, is the first derivative of z2, is the first-order derivative of z3, ε is an intermediate variable, β1, β2 and β3 are the control parameters of the extended state observer, and b0 is the estimated value of b;

[0058] Step 33, design the linear state error feedback control law u of the linear motor according to z1, z2 and z3;

[0059]

[0060] Among them, K p1 is the linear motor's proportionality factor, K d1 is the integral coefficient of the linear motor, r1 is the reference position of the linear motor, and r2 is the reference speed of the linear motor;

[0061] Step 34: Establish the spatial equation of the voice coil motor:

[0062]

[0063] Where x1′ is the position of the voice coil motor, is the first derivative of x1′, x2′ is the speed of the voice coil motor, is the first-order derivative of x′2, x3′ is the coupling error of the voice coil motor, is the first-order derivative of x3′, b′ is the compensation factor corresponding to the voice coil motor, u′ is the linear state error feedback control law of the voice coil motor, f(x1′,x′2,w′(t),t) is the sum of the internal disturbance and external disturbance of the voice coil motor, w′(t) is the external disturbance of the voice coil motor, is the first-order derivative of f(x1′,x′2,w′(t),t), y v is the absolute position of the micro-motion stage;

[0064] Step 35: Estimate the state variables and coupling errors of the micro-motion stage based on the spatial equation of the voice coil motor and the extended state observer;

[0065]

[0066] Among them, z1′ is the estimated value of x1′, z′2 is the estimated value of x′2, z3′ is the estimated value of x3′, is the first-order derivative of z1′, is the first-order derivative of z′2, is the first-order derivative of z3′, ε′ is an intermediate variable, and b1 is the estimated value of b′;

[0067] Step 36: Design the linear state error feedback control law u′ of the voice coil motor according to z1′, z′2 and z3′;

[0068]

[0069] Among them, K p is the proportionality factor of the voice coil motor, K d is the integral coefficient of the voice coil motor, r1′ is the reference position of the voice coil motor, and r2′ is the reference speed of the voice coil motor.

[0070] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0071] This implementation method selects state variables based on the micro-motion voice coil motor and the macro-motion linear motor. The z1 and z2 observed by the linear extended state observer are estimates of the position and velocity information, respectively, and z3 is an estimate of the system coupling error and disturbance. The designed linear extended state observer and linear state error feedback control law are applied to the macro-micro closed-loop control system. The control structure block diagram is shown in the figure. Figure 4 As shown in the figure: By introducing linear anti-disturbance control, the error caused by coupling is also treated as disturbance, the disturbance size is estimated using the extended state observer, and then the disturbance error is compensated in the input, thereby suppressing the coupling of macro-micro systems and improving the positioning accuracy of the system.

[0072] The extended state observer can estimate the state of the system without the need for an accurate model of the system. It is based on the state observer and defines the uncertainty within the system and the external disturbance as an expanded state. It only needs to know the order of the system state. It can not only track the states of each order of the system, but also observe the expanded state through feedback, thereby achieving the purpose of suppressing interference and compensating for the unknown quantities of the system.

[0073] Experimental Section

[0074] Observe the influence of the coupling part of the model on the macro-micro system. Without adding external interference force to the micro-motion system, input the third-order S curve trajectory and run the macro-micro control system without LADRC. Figure 5 In order to form a comparison, the coupling between the macro and micro models is removed and the running system is obtained. Figure 5 The solid curve in .

[0075] right Figure 5 Analysis shows that in the macro-motion following micro-motion control structure, the coupling effect between the macro-micro system mainly acts on the acceleration stage. When there is coupling, the maximum tracking error of the system is about 6.1μm, which is 1.2μm higher than the maximum tracking error without coupling. It can be concluded that the coupling part of the macro-micro system model will increase the acceleration tracking error, which will have a certain impact on the positioning accuracy and dynamic performance of the macro-micro system.

[0076] Verify the compensation effect of LESO on model coupling interference. Given a third-order S curve as the position command, run as follows Figure 4 The LADRC shown in the figure compensates the coupling interference of the macro-micro system and obtains Figure 6 In order to contrast with it, the simulation curve of the macro-micro system including the model coupling is drawn in a coordinate system, which is Figure 6 The solid curve in .

[0077] Depend on Figure 6 It can be seen that in the acceleration section of the S curve, the maximum tracking error is about 6.1μm without LADRC, and the maximum tracking error is about 3.7μm after LADRC is added. The maximum error in the acceleration section is significantly reduced. And the addition of LADRC plays a significant role in suppressing overshoot at the beginning of the uniform speed section. Therefore, it can be concluded that the linear active disturbance rejection control method has a significant effect on suppressing the response error caused by the coupling of macro-micro models.

[0078] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A linear auto-disturbance rejection control method for suppressing coupling interference between macro-micro linear motion platforms, characterized in that: The method specifically comprises the following steps: Step 1: Establish the mechanical equation of the macro-micro linear motion platform according to the motion model of the macro-micro linear motion platform; The mechanical equation of the macro-micro linear motion platform is: Among them, m l is the mass of the macro stage, m v is the mass of the micro-motion stage, F l is the linear motor driving force, F v is the driving force of the voice coil motor, Y l is the absolute position of the macro stage, Y v is the relative position between the macro-motion stage and the micro-motion stage, Y is the absolute position of the micro-motion stage, and t is the time; Step 2: Perform Laplace transform on the established mechanical equation to obtain an equivalent coupling model of the macro-micro linear motion platform; The specific process of step 2 is as follows: Pick As input, take As the output, perform Laplace transform on equation (1) and obtain the equivalent coupling model of the macro-micro linear motion platform of equation (2): Among them, s is a complex variable; Step 3: Establish the spatial equations of the linear motor and the voice coil motor respectively, and then estimate the state variables and coupling errors of the macro-motion stage based on the spatial equations of the linear motor and the extended state observer, and estimate the state variables and coupling errors of the micro-motion stage based on the spatial equations of the voice coil motor and the extended state observer; A linear state error feedback control law is designed based on the estimated state variables and coupling errors, and then the macro-micro linear motion platform is controlled based on the designed linear state error feedback control law and the equivalent coupling model; The specific process of step three is: Step 31. Establish the spatial equation of the linear motor: Where x1 is the position of the linear motor, is the first derivative of x1, x2 is the speed of the linear motor, is the first-order derivative of x2, x3 is the coupling error of the linear motor, is the first-order derivative of x3, b is the compensation factor corresponding to the linear motor, u is the linear state error feedback control law of the linear motor, f(x1,x2,w(t),t) is the sum of the internal disturbance and external disturbance of the linear motor, w(t) is the external disturbance of the linear motor, is the first-order derivative of f(x1,x2,w(t),t), y l is the absolute position of the macro stage; Step 32: Estimate the state variables and coupling errors of the macro-motion stage based on the spatial equation of the linear motor and the extended state observer; Among them, z1 is the estimated value of x1, z2 is the estimated value of x2, z3 is the estimated value of x3, is the first derivative of z1, is the first derivative of z2, is the first-order derivative of z3, ε is an intermediate variable, β1, β2 and β3 are the control parameters of the extended state observer, and b0 is the estimated value of b; Step 33, design the linear state error feedback control law u of the linear motor according to z1, z2 and z3; u0=K p1 (r1-z1)-K d1 (r2-z2) Among them, K p1 is the linear motor's proportionality factor, K d1 is the differential coefficient of the linear motor, r1 is the reference position of the linear motor, and r2 is the reference speed of the linear motor; Step 34: Establish the spatial equation of the voice coil motor: Where x1′ is the position of the voice coil motor, is the first derivative of x1′, x2′ is the speed of the voice coil motor, is the first-order derivative of x′2, x3′ is the coupling error of the voice coil motor, is the first-order derivative of x3′, b′ is the compensation factor corresponding to the voice coil motor, u′ is the linear state error feedback control law of the voice coil motor, f(x1′,x2′,w′(t),t) is the sum of the internal disturbance and external disturbance of the voice coil motor, w′(t) is the external disturbance of the voice coil motor, is the first-order derivative of f(x1′,x2′,w′(t),t), y v is the absolute position of the micro-motion stage; Step 35: Estimate the state variables and coupling errors of the micro-motion stage based on the spatial equation of the voice coil motor and the extended state observer; Among them, z1′ is the estimated value of x1′, z′2 is the estimated value of x′2, z3′ is the estimated value of x3′, is the first-order derivative of z1′, is the first-order derivative of z′2, is the first-order derivative of z3′, ε′ is an intermediate variable, and b1 is the estimated value of b′; Step 36: Design the linear state error feedback control law u′ of the voice coil motor according to z1′, z′2 and z3′; Among them, K p is the proportionality factor of the voice coil motor, K d is the differential coefficient of the voice coil motor, r1′ is the reference position of the voice coil motor, and r2′ is the reference speed of the voice coil motor.

2. A linear auto-disturbance rejection control method for suppressing coupling interference of macro-micro linear motion platforms according to claim 1, characterized in that: The macro-motion stage and the micro-motion stage are both guided by air-floating guide rails.

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