Control method for direct-drive gantry motion platform

Abstract

The invention discloses a control method for a direct-drive gantry motion platform, and belongs to the field of precise motion platform trajectory tracking control. The problems that an existing control algorithm is poor in tracking performance, high in design complexity and large in calculation burden are solved. According to the method, the adjustment function is introduced when the unknown system state initial value problem is processed, it is guaranteed that the position tracking error is converged to the given performance boundary within the given time, and the tracking performance is improved; the method does not need to carry out derivation calculation on a virtual control signal and an expected tracking signal, and does not need to depend on a system state initial value, a model structure parameter, unknown disturbance and actuator fault information, so that the complexity of a controller structure is effectively reduced; and moreover, the information does not need to be identified by using any approaching or identification technology, so that the calculation complexity of a control algorithm is greatly reduced. The method can be applied to precise motion platform trajectory tracking control.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of trajectory tracking control of precision motion platforms, and particularly relates to a control method for a direct-drive gantry motion platform. BACKGROUND

[0002] The direct-drive gantry motion platform is a core component of a high-end manufacturing equipment motion system, and the trajectory tracking control effect thereof determines the product quality and efficiency of the manufacturing equipment. Therefore, the manufacturing equipment puts forward strict tracking convergence speed and tracking precision requirements for the trajectory tracking control performance of the direct-drive motion system. However, the control of the actual direct-drive gantry motion platform system is often affected by model uncertainties such as system inertia, friction, positioning force, environmental disturbance, coupling effect of X-Y axis three linear motors (i.e. unknown coupling of the X-axis load motion to the Y-axis motor), and the like, and the situation of physical parameter degradation failure of the actuator is inevitable, and the state initial value is unknown. These factors affect the improvement of tracking speed and tracking precision, and increase the difficulty and complexity of the control algorithm design. Moreover, the existing control algorithm needs to be realized based on a neural network and a fuzzy logic system. Therefore, the existing control algorithm has the problem of large calculation burden due to high calculation complexity.

[0003] In summary, in order to improve the trajectory tracking performance of the direct-drive gantry motion platform, it is urgent to propose a control method which meets the independent performance criterion of all errors under unknown nonlinear functions, actuator faults and arbitrary initial conditions, maintains arbitrary convergence time and precision range, and reduces the existing calculation complexity. SUMMARY

[0004] The purpose of the application is to solve the problems of poor tracking performance and high design complexity of the existing control algorithm due to model uncertainty, potential actuator failure and unknown initial state, and large calculation burden of the existing control algorithm, and a control method for a direct-drive gantry motion platform is proposed.

[0005] The technical solution adopted by the application to solve the above technical problems is: a control method for a direct-drive gantry motion platform, which specifically comprises the following steps:

[0006] Step 1, real-time acquisition of system state signals of the direct-drive gantry motion platform;

[0007] The system state signals include motion speed and actual position. The motion speed of the direct-drive gantry motion platform at time t is denoted as The actual position of the direct-drive gantry motion platform at time t is denoted as and and ;​​

[0008] wherein, represents the motion speed of the direct-drive gantry motion platform in the direction of the axis at the moment t;

[0009] represents the motion speed of the direct-drive gantry motion platform in the direction of the axis at the moment t;

[0010] represents the actual position of the direct-drive gantry motion platform in the direction of the axis at the moment t;

[0011] represents the actual position of the direct-drive gantry motion platform in the direction of the axis at the moment t; According to the desired trajectory input of the direct-drive gantry motion platform at the moment t

[0012] and the actual position of the direct-drive gantry motion platform at the moment t , the position error of the direct-drive gantry motion platform is obtained; Step two, the feedback controller of the direct-drive gantry motion platform is designed according to the position error and the motion speed of the direct-drive gantry motion platform;

[0013] Step three, the control signal output by the feedback controller is taken as the input of the actuator, and the output of the actuator is applied to the direct-drive gantry motion platform.

[0014] The beneficial effects of the present application are:

[0015] 1. The present application introduces a regulating function when dealing with unknown system state initial value problems, which ensures that the position tracking error converges to the given performance boundary within a given time , and then converges to the preset error set

[0016] at a speed not lower than the given , improving the tracking performance. 2. The controller design process of the present application does not require derivative calculation of the virtual control signal and the desired tracking signal, and does not depend on the initial value of the system state, the structure parameters of the system model, the unknown disturbance and the fault characteristics of the actuator, etc. related information, thereby effectively reducing the complexity of the controller structure. Moreover, any approximation or identification technology (neural network or fuzzy system, etc.) is not used to identify these information, so the calculation complexity of the control algorithm is greatly reduced.

[0017] 2. The controller design process of the present application does not require derivative calculation of the virtual control signal and the desired tracking signal, and does not depend on the initial value of the system state, the structure parameters of the system model, the unknown disturbance and the fault characteristics of the actuator, etc. related information, thereby effectively reducing the complexity of the controller structure. Moreover, any approximation or identification technology (neural network or fuzzy system, etc.) is not used to identify these information, so the calculation complexity of the control algorithm is greatly reduced. ​​​​​

[0018] 3. This invention proposes a control method for a direct-drive gantry motion platform with predetermined time tracking accuracy, which solves the problem of large-range trajectory tracking control of the direct-drive gantry motion platform under unknown model nonlinearity, actuator failure, external disturbance, and initial conditions, and eliminates the computational burden caused by using neural networks and fuzzy logic systems. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the position tracking control system for the direct-drive gantry motion platform of the present invention.

[0020] Figure 2 This is a physical image of a direct-drive gantry motion platform;

[0021] Figure 3 This is a trajectory tracking diagram of a direct-drive gantry motion platform on the X-axis and Y-axis two-dimensional planes.

[0022] Figure 4 Figure showing the position tracking error of the X-axis of the direct-drive gantry motion platform;

[0023] This indicates that the method of the present invention yields Axis position tracking error, Represents the traditional method obtained Axis position tracking error, This is the method of the present invention. Shaft preset performance functions, This is the method of the present invention. Shaft adjustment error variable;

[0024] Figure 5 The position tracking error diagram of the Y-axis of the direct-drive gantry motion platform;

[0025] This indicates that the method of the present invention yields Axis position tracking error, Represents the traditional method obtained Axis position tracking error, This is the method of the present invention. Shaft preset performance functions, This is the method of the present invention. Shaft adjustment error variable;

[0026] Figure 6 The output voltage diagram of the actuator on the X-axis of the direct-drive gantry motion platform under the PD controller;

[0027] Figure 7 The output voltage diagram of the actuator on the Y-axis of the direct-drive gantry motion platform under the PD controller;

[0028] Figure 8 Figure 1 shows the output voltage graph of the X-axis actuator of the direct-drive gantry motion platform under the control of the controller designed in the present application.

[0029] Figure 9 Figure 2 shows the output voltage graph of the Y-axis actuator of the direct-drive gantry motion platform under the control of the controller designed in the present application. DETAILED DESCRIPTION

[0030] Embodiment 1: Combination Figure 1 The present embodiment describes a control method for a direct-drive gantry motion platform, which specifically includes the following steps:

[0031] Step 1: Real-time acquisition of system state signals of the direct-drive gantry motion platform;

[0032] The system state signals include motion speed and actual position, and the motion speed of the direct-drive gantry motion platform at time t is denoted as and The actual position of the direct-drive gantry motion platform at time t is denoted as and ; wherein, denotes the motion speed of the direct-drive gantry motion platform in the X-axis direction at time t;

[0033] denotes the motion speed of the direct-drive gantry motion platform in the Y-axis direction at time t;

[0034] denotes the actual position of the direct-drive gantry motion platform in the X-axis direction at time t;

[0035] denotes the actual position of the direct-drive gantry motion platform in the Y-axis direction at time t;

[0036] denotes the actual position of the direct-drive gantry motion platform in the Y-axis direction at time t; According to the desired trajectory input of the direct-drive gantry motion platform at time t and the actual position of the direct-drive gantry motion platform at time t, the position error of the direct-drive gantry motion platform is obtained;

[0037] Step 2: Design of the feedback controller of the direct-drive gantry motion platform according to the position error and motion speed of the direct-drive gantry motion platform;

[0038] Step 2: Design of the feedback controller of the direct-drive gantry motion platform according to the position error and motion speed of the direct-drive gantry motion platform; ​​​​​​​​​​​

[0039] Step 3: Use the control signal output by the feedback controller as the input of the actuator, and apply the output of the actuator to the direct-drive gantry motion platform.

[0040] After the actuator output is applied to the direct-drive gantry motion platform, the actual system status signal of the direct-drive gantry motion platform is collected. Then, the control signal output by the feedback controller can be obtained again based on the collected actual system status signal. After the control signal is input to the actuator, the output of the actuator can continue to apply to the direct-drive gantry motion platform to realize the continuous control of the direct-drive gantry motion platform.

[0041] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One, wherein the direct-drive gantry motion platform is in Expected trajectory input at time and direct drive gantry motion platform The actual position at any given time yields the position error of the direct-drive gantry motion platform, specifically:

[0042]

[0043]

[0044] in, Indicates the desired trajectory input exist Components along the axial direction;

[0045] Indicates the desired trajectory input exist Components along the axial direction;

[0046] Indicates a direct-drive gantry motion platform Axial position error;

[0047] Indicates a direct-drive gantry motion platform Axial position error.

[0048] The other steps and parameters are the same as in Specific Implementation Method 1.

[0049] Specific Implementation Method Three: This implementation method is a further limitation of Specific Implementation Method Two. The specific process of step two is as follows:

[0050] Step 2.1: Design the adjustment function ,in, , ;

[0051] Step 22: Design the preset performance function ;

[0052] Step 2-3, design the adjusting error variable and the conversion error :

[0053]

[0054]

[0055] wherein, ;

[0056] Step 2-4, design the virtual control variable , the intermediate variable and the adaptive compensation variable :

[0057]

[0058] wherein, the intermediate variable , the intermediate variable ;

[0059] is a positive time-varying function, and and , is an integral variable, denotes the first order derivative of , denotes the absolute value of , and are both normal numbers;

[0060] the intermediate variable , ;

[0061] and are design parameters;

[0062] is a positive time-varying function, and , , denotes the first order derivative of , and are normal numbers;

[0063] is the first order derivative of the time-varying function , is the initial value of , ;

[0064] Step 2-5, design the virtual speed error variable and :

[0065]

[0066]

[0067] wherein, represents a virtual velocity error in the axis direction, represents a virtual velocity error in the axis direction;

[0068] Step two six, design a regulating error variable and a conversion error :

[0069]

[0070]

[0071] Step two seven, design an actual control variable , an intermediate variable and an adaptive compensation variable :

[0072]

[0073] wherein, the intermediate variable , , and ;

[0074] is a positive time-varying function, and , , represents a first derivative of , and are both normal numbers;

[0075] the intermediate variable , ;

[0076] is a positive time-varying function, and , , represents a first derivative of , and are both normal numbers;

[0077] is an initial value of the time-varying function , ;

[0078] and are design parameters, .

[0079] The other steps and parameters are the same as in embodiment two.

[0080] Embodiment four: This embodiment is a further limitation of embodiment three, wherein the adjustment function is:

[0081]

[0082] wherein, denotes a design parameter.

[0083] The other steps and parameters are the same as in embodiment three.

[0084] With the adjustment function designed in this embodiment, it can be guaranteed that, in the case that the initial value of the direct-drive motion platform is unknown, the tracking error enters into the given preset performance function envelope after a given adjustment time.

[0085] Embodiment five: This embodiment is a further limitation of embodiment four, wherein the preset performance function is:

[0086]

[0087] wherein, denotes the base number of natural logarithm;

[0088] , and all denote design parameters, , .

[0089] The other steps and parameters are the same as in embodiment four.

[0090] With the performance function designed in this embodiment, the direct-drive motion platform can be controlled by the controller to reduce the tracking error and converge at a given speed and accuracy.

[0091] Embodiment six: This embodiment is a further limitation of embodiment five, wherein the positive time-varying function .

[0092] The other steps and parameters are the same as in embodiment five.

[0093] With the positive time-varying function designed in this embodiment, it can be guaranteed that the closed-loop direct-drive motion platform control system is asymptotically stable tracking control.

[0094] Specific implementation seven: this implementation is a further limitation of the specific implementation six, the timing function .

[0095] Other steps and parameters are the same as specific implementation six.

[0096] The timing function designed by this implementation can ensure the asymptotic stable tracking control of the closed-loop direct drive motion platform control system.

[0097] Specific implementation eight: this implementation is a further limitation of the specific implementation seven, the output of the actuator is:

[0098]

[0099] Wherein, represents the output of the actuator, represents the multiplicative actuator fault, represents the additive actuator fault.

[0100] Other steps and parameters are the same as specific implementation seven.

[0101] Specific implementation nine: this implementation is a further limitation of the specific implementation eight, the multiplicative actuator fault is:

[0102]

[0103] Wherein, represents the time unit of second.

[0104] Other steps and parameters are the same as specific implementation eight.

[0105] Specific implementation ten: this implementation is a further limitation of the specific implementation eight, the additive actuator fault is:

[0106]

[0107] Other steps and parameters are the same as specific implementation eight.

[0108] Embodiment

[0109] As Figure 1 shown, the embodiment proposes a control method for direct drive gantry motion platform, which specifically includes the following steps:

[0110] Step one, real-time acquisition of system state signal of direct drive gantry motion platform;

[0111] The system state signal includes motion speed and actual position, and the direct drive gantry motion platform is controlled according to the system state signal The velocity at time t is denoted as and The direct-drive gantry platform will be in The actual position at that moment is denoted as and ;

[0112] in, express The instant-drive gantry sports platform is in Velocity of motion in the axial direction;

[0113] express The instant-drive gantry sports platform is in Velocity of motion in the axial direction;

[0114] express The instant-drive gantry sports platform is in The actual position in the axial direction;

[0115] express The instant-drive gantry sports platform is in The actual position in the axial direction;

[0116] According to the direct-drive gantry movement platform Expected trajectory input at time The desired predetermined trajectory can be obtained. , The control objective of the trajectory tracking control system for the direct-drive gantry motion platform is: system output Tracking the expected predetermined trajectory , The closed-loop system of the direct-drive gantry motion platform is based on the actual motion trajectory of the direct-drive gantry motion platform. Subtract the expected motion trajectory of the direct-drive gantry motion platform The position error of the direct-drive gantry motion platform is obtained. The closed-loop system of the direct-drive gantry motion platform is based on the actual motion trajectory of the direct-drive gantry motion platform. Subtract the expected motion trajectory of the direct-drive gantry motion platform The position error of the direct-drive gantry motion platform is obtained. ;

[0117] That is, the position error is described as:

[0118]

[0119]

[0120] in, representing the desired trajectory input in the axial direction, representing the desired trajectory input in the axial direction;

[0121] In the present embodiment:

[0122]

[0123] Step two, design a feedback controller for the direct-drive gantry motion platform according to the position error and the motion speed; the specific process of the step two is:

[0124] Step two one, design an adjustment function :

[0125]

[0126] wherein, representing the design parameter, , in the present embodiment ;

[0127] Step two two, design a preset performance function :

[0128]

[0129] wherein, representing the base number of the natural logarithm;

[0130] , and representing the design parameter, in the present embodiment, , , ;

[0131] Step two three, design an adjustment error variable and a conversion error :

[0132]

[0133]

[0134] wherein, ;

[0135] Step two four, design a virtual control variable , an intermediate variable and an adaptive compensation variable :

[0136]

[0137] where the intermediate variable , , ;

[0138] is a positive time-varying function, and satisfies , , is an integral variable, denotes the first derivative of , , are normal numbers;

[0139] the intermediate variable , ;

[0140] and are design parameters;

[0141] is a positive time-varying function, and satisfies , , denotes the first derivative of , , are normal numbers;

[0142] is the first derivative of , is the initial value of , and in the embodiment ;

[0143] It should be noted that in the embodiment, , , .

[0144] Step two five, design a virtual speed error variable and :

[0145]

[0146]

[0147] wherein denotes the virtual speed error in the axis direction, denotes the virtual speed error in the axis direction;

[0148] Step two six, design the adjusting error variable and conversion error :

[0149]

[0150]

[0151] Step two seven, design the actual control variable , intermediate variable and adaptive compensation variable :

[0152]

[0153] Wherein, the intermediate variable , , and satisfies ;

[0154] is a positive time-varying function, and satisfies , , denotes the first derivative of , and and are normal numbers;

[0155] The intermediate variable , ;

[0156] and are design parameters, in the embodiment, the design parameters are ;

[0157] is a positive time-varying function, and satisfies , , denotes the first derivative of , and and are normal numbers;

[0158] is the initial value of ;

[0159] In the embodiment , , , .

[0160] Step three, the control signal output by the feedback controller is taken as the input of the actuator, and the output of the actuator is applied to the direct-drive gantry motion platform;

[0161] When the fault form of the actuator is a multiplicative actuator fault and an additive actuator fault, the output of the actuator is:

[0162]

[0163] wherein, , represents a control signal of the feedback controller output;

[0164] and respectively represent a control signal in the axial direction and a control signal in the axial direction;

[0165] represents a multiplicative actuator fault, represents an additive actuator fault;

[0166] represents an output of the actuator;

[0167] In the present embodiment:

[0168]

[0169] Experimental part

[0170] The control method (PT) of the present application is applied to a direct-drive gantry motion platform system as shown in Figure 2 , and under the same experimental conditions, the control method of the present application is compared with the existing proportional-derivative controller (PD) based on preset performance, and the structure of the PD controller is , , and the control parameters .

[0171] As can be seen from Figure 3 , the controller designed in the present application and the existing proportional-derivative controller can both realize the response output trajectory tracking performance of the closed-loop system, but when the tracking trajectory speed changes greatly, the tracking performance of the PD controller significantly decreases.

[0172] As can be seen from Figure 4 and Figure 5 , the controller designed in the present application shows superior transient tracking behavior compared with the existing PD controller. Although the direct-drive gantry motion platform has model uncertainties such as unknown dynamics, actuator faults and environmental disturbances, the control method designed in the present application and the existing PD controller can both track the reference trajectory, meet the performance requirements of error convergence and steady-state error, but the robustness of the control method proposed in the present application is superior to that of the existing PD controller method. Figure 6 and Figure 7 ​X-axis and Y-axis input and output of the actuator of the existing PD controller are given respectively, Figure 8 and Figure 9 X-axis and Y-axis input and output of the actuator of the designed controller are given respectively.

[0173] The above calculation examples of the present application are only to illustrate the calculation model and calculation process of the present application, and are not limited to the embodiments of the present application. Other different forms of changes or variations can be made by those skilled in the art on the basis of the above description, and it is impossible to exhaust all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application still fall within the protection scope of the present application.

Claims

1. A control method for a direct drive gantry motion platform, characterized in that, The method specifically comprises the following steps: Step one, collecting system state signals of the direct-drive gantry motion platform in real time; The system state signals include motion speed and actual position, and the motion speed of the direct-drive gantry motion platform at time is recorded as and The actual position of the direct-drive gantry motion platform at time is recorded as and ; wherein, represents Direct drive gantry motion platform in axial direction of the motion speed; indicates Direct-drive gantry motion platform in axial direction of the motion speed; indicates The gantry motion platform directly drives at the moment actual position in the axial direction; indicates The direct-drive gantry motion platform at the moment actual position in the axis direction; According to the direct-drive gantry movement platform Expected trajectory input at time and direct drive gantry motion platform The actual position at any given moment is used to obtain the position error of the direct-drive gantry motion platform. Step two, designing a feedback controller of the direct-drive gantry motion platform according to position errors and motion speeds of the direct-drive gantry motion platform; Step three, taking the control signals output by the feedback controller as inputs of actuators, and taking the outputs of the actuators as actions on the direct-drive gantry motion platform.

2. The control method for a direct drive gantry motion platform according to claim 1, wherein, The expected trajectory input of the direct-drive gantry motion platform at the moment The actual position of the direct-drive gantry motion platform at the moment The actual position of the direct-drive gantry motion platform at the moment The position error of the direct-drive gantry motion platform is obtained, specifically: wherein, representing a desired trajectory input in component in the axial direction; representative of a desired trajectory input in component in the axial direction; representing a direct drive gantry motion platform axial direction position error; representing a direct drive gantry motion platform axial direction position error.

3. The control method for a direct drive gantry motion platform according to claim 2, wherein, The specific process of the step two is that: Step two one, design adjustment function wherein, , ; Step two, design a pre-set performance function ; Step two three, design the tuning error variable and conversion error : wherein ; Step two four, design virtual control variable , intermediate variable and adaptive compensation variable : wherein the intermediate variable , the intermediate variable ; is a positive time-varying function, and and , is an integral variable, denotes a first derivative, denotes an absolute value, and are both normal numbers; Intermediate variable , ; and are design parameters; is a positive time varying function, and , , denotes the first derivative of and is a positive constant; is a first derivative of a time-varying function is an initial value of ;​​ Step two five, design a virtual velocity error variable and : wherein represents a virtual velocity error in the axis direction, represents a virtual velocity error in the axis direction; Step two six, design the tuning error variable and conversion error : Step two seven, design actual control variable , intermediate variable and adaptive compensation variable : wherein the intermediate variable , , and ; is a positive time varying function, and , , denotes the first derivative of and are both positive constants; Intermediate variable , ; is a positive time-varying function, and , , denotes a first derivative of and are both normal numbers; is a time-varying function of the initial value, ; and are design parameters, .

4. The control method for a direct drive gantry motion platform according to claim 3, wherein, The adjustment function is: In the formulae, denote design parameters.

5. The control method for a direct drive gantry motion platform according to claim 4, wherein, The preset performance function : In the formula, denotes the base of the natural logarithm; , and each represent a design parameter, , .

6. The control method for a direct drive gantry motion platform according to claim 5, wherein, the timing function .

7. The control method for a direct drive gantry motion platform according to claim 6, wherein, the timing function .

8. The control method for a direct drive gantry motion platform according to claim 7, wherein, The output of the actuator is that wherein, represents the output of the actuator, represents a multiplicative actuator fault, represents an additive actuator fault.

9. The control method for a direct drive gantry motion platform according to claim 8, wherein, The multiplicative actuator fault Is: 。 10. The control method for a direct drive gantry motion platform according to claim 8, wherein, The additive actuator fault Is: 。

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