CN115047765B - Piezoelectric transducer sliding mode control method, device, computer and storage medium based on hysteresis inverse model - Google Patents
Piezoelectric transducer sliding mode control method, device, computer and storage medium based on hysteresis inverse model Download PDFInfo
- Publication number
- CN115047765B CN115047765B CN202210661061.7A CN202210661061A CN115047765B CN 115047765 B CN115047765 B CN 115047765B CN 202210661061 A CN202210661061 A CN 202210661061A CN 115047765 B CN115047765 B CN 115047765B
- Authority
- CN
- China
- Prior art keywords
- sliding mode
- hysteresis
- piezoelectric transducer
- control voltage
- linearization
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Landscapes
- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
A piezoelectric transducer sliding mode control method, a device, a computer and a storage medium based on a hysteresis inverse model relate to the technical field of piezoelectric hysteresis compensation control. The control method solves the problems that the traditional hysteresis inverse model is limited by an operation operator and threshold number, and a dynamic threshold function and a density function are required to be selected manually, so that the compensation effect and the tracking precision are affected. The method comprises the following steps: constructing a depth linearization hysteresis model and model identification according to the piezoelectric sensor; constructing a depth linearization hysteresis compensation inverse model according to the depth linearization hysteresis model, and acquiring a reference track; calculating a compensation control voltage sequence according to the reference track; constructing a sliding mode controller according to the compensation control voltage sequence; establishing a control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller; and controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer, and completing feedback of the sliding mode controller. Is suitable for the field of piezoelectric driving.
Description
Technical Field
The invention relates to the technical field of piezoelectric hysteresis compensation control, in particular to a sliding mode control method based on deep linearization hysteresis inverse model compensation.
Background
The piezoelectric transducer has the advantages of quick response, high motion resolution and the like, and is widely applied to ultra-precise positioning occasions, aerospace and biomedical industries. However, the piezoelectric transducer has hysteresis nonlinearity, which can lead to large output displacement error, low positioning accuracy and even unstable system. A large number of control methods have been presented for the hysteresis characteristics of piezoelectric transducers, such as the control method of PI hysteresis inverse model, but the hysteresis compensation accuracy is severely restricted due to the uncertain factors that are unavoidable in the actual system. The traditional hysteresis inverse model control method is limited by an operation operator and threshold number, dynamic threshold functions and density functions are required to be selected manually, the compensation effect and tracking precision can be directly affected, and uncertain factors existing in an actual system cannot be avoided.
Disclosure of Invention
The invention solves the problems that the traditional hysteresis inverse model control method is limited by an operation operator and threshold number, a dynamic threshold function and a density function are required to be selected manually, and the compensation effect and tracking precision are affected.
The invention provides a piezoelectric transducer sliding mode control method based on a hysteresis inverse model, which comprises the following steps:
constructing a depth linearization Koopman hysteresis model and model identification of the depth linearization Koopman model according to the piezoelectric sensor;
constructing a depth linearization Koopman hysteresis compensation inverse model according to the depth linearization Koopman hysteresis model, acquiring a reference track, and calculating a compensation control voltage sequence according to the reference track;
constructing a sliding mode controller according to the compensation control voltage sequence;
establishing a control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller;
and controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer, and completing feedback of the sliding mode controller, wherein the output displacement is a feedback value of the sliding mode controller.
Further, a preferred embodiment is provided, wherein the depth-linearized Koopman hysteresis model is constructed according to the input control voltage and the output displacement of the piezoelectric sensor, and the model identification of the depth-linearized Koopman model is specifically as follows:
displacement x of input piezoelectric sensor k To an encoder neural network which outputs a state variable z k ：
z k ＝Ψ(x k )，
Wherein ψ (·) is the encoder neural network to be identified;
input control voltage u k And state variable z k To a Koopman linearization neural network that outputs a predicted state variable z k+1 ：
z k+1 ＝Az k +Bu k ，
Wherein, A and B are both Koopman linearization neural networks;
the predicted state variable z k+1 Output of predictive displacements via decoder neural networks
Wherein ψ is -1 (-) is a decoder neural network.
Further, there is provided a preferred embodiment, wherein the calculating the compensation control voltage sequence according to the reference trajectory specifically includes:
constructing a depth linearization Koopman hysteresis compensation inverse model:
given a length of N, a reference trace of x ref The control voltage at each instant is:
wherein x is 0 For initial displacement value, obtaining control voltage sequence U of hysteresis compensation inverse model K ＝[u 0 ,…u N-1 ] T ,k＝0,...N-1。
Further, there is provided a preferred embodiment, wherein the sliding mode controller is constructed according to the compensation control voltage sequence, specifically:
analyzing and dynamically modeling the piezoelectric transducer, and obtaining a transfer function as follows:
wherein alpha is a first-order time constant, alpha is more than 0, x is the output displacement of the piezoelectric transducer, and u is the input voltage of the piezoelectric transducer;
the sliding mode surface function is:
s＝h 1 e
wherein h is 1 Is a sliding mode coefficient;
error of sliding mode controller and derivative thereof
Wherein x is ref Is a reference track;
derivative of sliding mode function s
The sliding approach law adopts an exponential approach law, and the control output of the sliding mode controller is that
Wherein k is s ＞0，ε＞0。
Further, there is provided a preferred embodiment, wherein the obtaining the control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller specifically includes:
control voltage sequence U according to obtained hysteresis compensation inverse model k In real-time voltage and obtained slip-mode controller output value u s Adding to obtain the overall control input of the piezoelectric transducer:
u＝U k +u s ,k＝0,...N-1。
the invention also provides a piezoelectric transducer sliding mode control device based on a hysteresis inverse model, which comprises:
the depth linearization Koopman hysteresis model acquisition unit is used for constructing a depth linearization Koopman hysteresis model and model identification of the depth linearization Koopman model according to the piezoelectric sensor;
the depth linearization Koopman hysteresis compensation inverse model acquisition unit is used for constructing a depth linearization Koopman hysteresis compensation inverse model according to the depth linearization Koopman hysteresis model, acquiring a reference track, and calculating a compensation control voltage sequence according to the reference track;
the sliding mode controller acquisition unit is used for constructing a sliding mode controller according to the compensation control voltage sequence;
the control law acquisition unit of the piezoelectric transducer is used for establishing the control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller;
and the feedback unit of the sliding mode controller is used for controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer so as to complete feedback of the sliding mode controller, wherein the output displacement is a feedback value of the sliding mode controller.
Further, there is provided a preferred embodiment, the depth linearization Koopman hysteresis model acquisition unit specifically including:
a state variable acquisition unit for inputting the displacement x of the piezoelectric sensor k To an encoder neural network which outputs a state variable z k ：
z k ＝Ψ(x k )，
Wherein ψ (·) is the encoder neural network to be identified;
a predicted state variable acquisition unit for inputting the control voltage u k And state variable z k To a Koopman linearization neural network that outputs a predicted state variable z k+1 ：
z k+1 ＝Az k +Bu k ，
Wherein, A and B are both Koopman linearization neural networks;
a predicted displacement acquisition unit for predicting the state variable z k+1 Output of predictive displacements via decoder neural networks
Wherein ψ is -1 (-) is a decoder neural network.
Further, there is provided a preferred embodiment, the reference trajectory calculation compensation control voltage sequence acquisition unit specifically including:
the depth linearization Koopman hysteresis compensation inverse model acquisition unit is used for constructing a depth linearization Koopman hysteresis compensation inverse model:
a control unit acquisition unit for obtaining a reference track x according to a given length N ref The control voltage obtained at each moment is:
wherein x is 0 Is the initial displacement value;
obtaining a control voltage sequence of a hysteresis compensation inverse model:
U K ＝[u 0 ,…u N-1 ] T ,k＝0,...N-1。
the invention also provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a piezoelectric transducer sliding mode control method based on a hysteresis inverse model.
The invention also provides a computer readable storage medium for storing a computer program for executing a piezoelectric transducer sliding mode control method based on the hysteresis inverse model.
The invention has the advantages that:
the piezoelectric transducer sliding mode control method based on the hysteresis inverse model solves the problems that the traditional hysteresis inverse model control method is limited by an operation operator and threshold number, dynamic threshold functions and density functions are required to be selected manually, the compensation effect and tracking precision can be directly affected, and uncertain factors existing in an actual system cannot be avoided. The model structure identification of the neural network is carried out by utilizing deep learning through establishing a deep linearization Koopman hysteresis model; constructing a depth linearization Koopman hysteresis compensation inverse model, and calculating a compensation control voltage sequence under a given reference track; analyzing and dynamically modeling the piezoelectric transducer, establishing a sliding mode controller of the system and finishing stability demonstration; the integral control law of the piezoelectric transducer is designed by comprehensively considering the inverse model hysteresis compensation control voltage and the sliding mode control voltage, the obtained control voltage is input into the piezoelectric transducer, the piezoelectric transducer is driven to generate output displacement, and the output displacement is collected to serve as a feedback value of the sliding mode controller. According to the invention, by utilizing the sliding mode control method based on the depth linearization Koopman hysteresis inverse model compensation, the hysteresis compensation precision of the piezoelectric transducer is effectively improved, the robustness and reliability of the system are increased, and the advantages of high bandwidth, high positioning precision and high response speed of the piezoelectric transducer are ensured.
The sliding mode control device of the piezoelectric transducer based on the hysteresis inverse model is not limited by an operation operator and threshold quantity, comprehensively considers hysteresis compensation control voltage and sliding mode control voltage of the inverse model, designs the overall control law of the piezoelectric transducer, inputs the obtained control voltage into the piezoelectric transducer, drives the piezoelectric transducer to generate output displacement, and collects the output displacement as a feedback value of a sliding mode controller. The hysteresis compensation precision of the piezoelectric transducer is effectively improved, the robustness and the reliability of the system are increased, and the advantages of high bandwidth, high positioning precision and high response speed of the piezoelectric transducer are ensured.
The invention is suitable for the field of piezoelectric driving.
Drawings
Fig. 1 is a schematic flow chart of a sliding mode control method based on depth linearization Koopman hysteresis inverse model compensation according to an embodiment of the invention.
Fig. 2 is a schematic diagram of a neural network structure of a deep linearization Koopman hysteresis model according to the second embodiment of the invention.
FIG. 3 is a schematic diagram of a depth linearization Koopman hysteresis compensation inverse model according to a third embodiment of the invention.
Fig. 4 is a schematic structural diagram of a sliding mode control method based on depth linearization Koopman hysteresis inverse model compensation according to a fourth embodiment of the invention.
Detailed Description
In order to make the technical solution and advantages of the present invention more apparent, several embodiments of the present invention will be described in further detail with reference to the accompanying drawings, but the following embodiments are only preferred embodiments of the present invention and are not intended to limit the invention.
Embodiment one, this embodiment will be described with reference to fig. 1. The sliding mode control method for the piezoelectric transducer based on the hysteresis inverse model according to the embodiment comprises the following steps:
constructing a depth linearization Koopman hysteresis model and model identification of the depth linearization Koopman model according to the piezoelectric sensor;
constructing a depth linearization Koopman hysteresis compensation inverse model according to the depth linearization Koopman hysteresis model, acquiring a reference track, and calculating a compensation control voltage sequence according to the reference track;
constructing a sliding mode controller according to the compensation control voltage sequence;
establishing a control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller;
and controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer, and completing feedback of the sliding mode controller, wherein the output displacement is a feedback value of the sliding mode controller.
According to the implementation mode, the sliding mode controller is built by building the depth linearization Koopman hysteresis compensation inverse model, so that the hysteresis compensation precision of the piezoelectric transducer is preferably improved, the robustness and the reliability of the system are improved, and the advantages of high bandwidth, high positioning precision and high response speed of the piezoelectric transducer are ensured.
Embodiment two, this embodiment will be described with reference to fig. 2. The present embodiment is further defined by the method for controlling a sliding mode of a piezoelectric transducer based on a hysteresis inverse model according to the first embodiment, wherein the model identification of the depth linearization Koopman hysteresis model and the depth linearization Koopman model is constructed according to an input control voltage and an output displacement of the piezoelectric transducer, and specifically includes:
displacement x of input piezoelectric sensor k To an encoder neural network which outputs a state variable z k ：
z k ＝Ψ(x k )，
Wherein ψ (·) is the encoder neural network to be identified;
input control voltage u k And state variable z k To a Koopman linearization neural network that outputs a predicted state variable z k+1 ：
z k+1 ＝Az k +Bu k ，
Wherein, A and B are both Koopman linearization neural networks;
the predicted state variable z k+1 Output of predictive displacements via decoder neural networks
Wherein ψ is -1 (-) is a decoder neural network.
Specifically, input control voltage and output displacement of the piezoelectric sensor are collected as a training set of the neural network structure shown in fig. 1, and the encoder neural network ψ (·) to be identified is finally identified through unfolding training of a machine learning working box, and KoopmanLinearization neural networks A and B and decoder neural network ψ -1 (. Cndot.) the Koopman hysteresis neural network model can be built by the above calculation of the formula, and the output displacement is predicted.
Embodiment three, this embodiment will be described with reference to fig. 3. The present embodiment is further defined by the method for controlling a sliding mode of a piezoelectric transducer according to the first embodiment, wherein the calculating the compensation control voltage sequence according to the reference track specifically includes:
constructing a depth linearization Koopman hysteresis compensation inverse model:
given a length of N, a reference trace of x ref The control voltage at each instant is:
wherein x is 0 For initial displacement value, obtaining control voltage sequence U of hysteresis compensation inverse model K ＝[u 0 ,…u N-1 ] T ,k＝0,...N-1。
The embodiment provides a specific calculation method of the compensation control voltage sequence, and realizes accurate compensation of the piezoelectric transducer.
Embodiment four, this embodiment will be described with reference to fig. 4. The present embodiment is further defined on the method for controlling a sliding mode of a piezoelectric transducer based on a hysteresis inverse model according to the first embodiment, wherein the sliding mode controller is constructed according to a compensation control voltage sequence, specifically:
analyzing and dynamically modeling the piezoelectric transducer, and obtaining a transfer function as follows:
wherein alpha is a first-order time constant, alpha is more than 0, x is the output displacement of the piezoelectric transducer, and u is the input voltage of the piezoelectric transducer;
the sliding mode surface function is:
s＝h 1 e
wherein h is 1 Is a sliding mode coefficient;
error of sliding mode controller and derivative thereof
Wherein x is ref Is a reference track;
derivative of sliding mode function s
The sliding approach law adopts an exponential approach law, and the control output of the sliding mode controller is that
Wherein k is s ＞0，ε＞0。
Specifically, the present embodiment further includes a stability demonstration for the sliding mode controller: to demonstrate global asymptotically consistent stability under bounded perturbations and parameter bias, the Lyapunov function is selected as
Then
The Lyapunov function is proved to be converged, and the design of the controller is effective.
To reduce the effects of buffeting, a sat function is used instead of the sign function sgn in the control output of the sliding mode controller,
wherein h is the boundary layer; at this time, the value of epsilon is enough to satisfy
To be negative, the control law is designed to stabilize the global.
In a fifth embodiment, the present embodiment is further defined by the method for controlling a sliding mode of a piezoelectric transducer based on a hysteresis inverse model according to the first embodiment, wherein the method includes the steps of:
control voltage sequence U according to obtained hysteresis compensation inverse model k In real-time voltage and obtained slip-mode controller output value u s Adding to obtain the overall control input of the piezoelectric transducer:
u＝U k +u s ,k＝0,...N-1。
in the present embodiment, according to the obtained overall control input u for controlling the piezoelectric transducer, the overall control input u is input into the piezoelectric transducer, the piezoelectric transducer is driven to generate output displacement, the output displacement is collected as a feedback value of the sliding mode controller, and calculation of the next moment is performed. The hysteresis compensation precision of the piezoelectric transducer is finished by the circulation, and the robustness and the reliability of the system are improved.
In a sixth embodiment, the piezoelectric transducer sliding mode control device based on a hysteresis inverse model according to the present embodiment includes:
the depth linearization Koopman hysteresis model acquisition unit is used for constructing a depth linearization Koopman hysteresis model and model identification of the depth linearization Koopman model according to the piezoelectric sensor;
the depth linearization Koopman hysteresis compensation inverse model acquisition unit is used for constructing a depth linearization Koopman hysteresis compensation inverse model according to the depth linearization Koopman hysteresis model, acquiring a reference track, and calculating a compensation control voltage sequence according to the reference track;
the sliding mode controller acquisition unit is used for constructing a sliding mode controller according to the compensation control voltage sequence;
the control law acquisition unit of the piezoelectric transducer is used for establishing the control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller;
and the feedback unit of the sliding mode controller is used for controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer so as to complete feedback of the sliding mode controller, wherein the output displacement is a feedback value of the sliding mode controller.
Compared with the traditional control method of the hysteresis inverse model, the device of the embodiment can effectively improve the hysteresis compensation precision, increase the robustness and reliability of the system, and ensure the advantages of high bandwidth, high positioning precision and high response speed of the piezoelectric transducer.
An seventh embodiment is further defined by the piezoelectric transducer sliding mode control device based on a hysteresis inverse model according to the sixth embodiment, wherein the depth linearization Koopman hysteresis model obtaining unit specifically includes:
a state variable acquisition unit for inputting the displacement x of the piezoelectric sensor k To an encoder neural network which outputs a state variable z k ：
z k ＝Ψ(x k )，
Wherein ψ (·) is the encoder neural network to be identified;
a predicted state variable acquisition unit for inputting the control voltage u k And state variable z k To a Koopman linearization neural network that outputs a predicted state variable z k+1 ：
z k+1 ＝Az k +Bu k ，
Wherein, A and B are both Koopman linearization neural networks;
a predicted displacement acquisition unit for predicting the state variable z k+1 Output of predictive displacements via decoder neural networks
Wherein ψ is -1 (-) is a decoder neural network.
The embodiment introduces the composition of the deep linearization Koopman hysteresis model acquisition unit in detail, and realizes the improvement of the hysteresis model.
An eighth embodiment is further defined by the piezoelectric transducer sliding mode control device based on a hysteresis inverse model according to the sixth embodiment, wherein the reference trajectory calculation compensation control voltage sequence obtaining unit specifically includes:
the depth linearization Koopman hysteresis compensation inverse model acquisition unit is used for constructing a depth linearization Koopman hysteresis compensation inverse model:
a control unit acquisition unit for obtaining a reference track x according to a given length N ref The control voltage obtained at each moment is:
wherein x is 0 Is the initial displacement value;
obtaining a control voltage sequence of a hysteresis compensation inverse model:
U K ＝[u 0 ,…u N-1 ] T ,k＝0,...N-1。
the embodiment provides a specific calculation method of the compensation control voltage sequence, and realizes accurate compensation of the piezoelectric transducer.
A computer device according to a ninth embodiment includes a memory and a processor, in which a computer program is stored, and when the processor runs the computer program stored in the memory, the processor executes a piezoelectric transducer sliding mode control method based on a hysteresis inverse model as described in any one of the first to fifth embodiments.
The tenth embodiment is a computer readable storage medium according to the fifth embodiment, wherein the computer readable storage medium is configured to store a computer program, and the computer program executes the method for controlling a sliding mode of a piezoelectric transducer based on a hysteresis inverse model according to any one of the first to fifth embodiments.
While the present application has been described in detail in connection with the specific embodiments, the foregoing description is a preferred embodiment of the present application and is not intended to limit the invention to the particular form set forth herein, but is intended to cover any adaptations, combinations of embodiments, equivalent alternatives, modifications, and variations of the present application without departing from the spirit and scope of the principles of the present application.
Claims (9)
1. The piezoelectric transducer sliding mode control method based on the hysteresis inverse model is characterized by comprising the following steps of:
constructing a depth linearization Koopman hysteresis model and model identification of the depth linearization Koopman model according to the piezoelectric sensor;
constructing a depth linearization Koopman hysteresis compensation inverse model according to the depth linearization Koopman hysteresis model, acquiring a reference track, and calculating a compensation control voltage sequence according to the reference track;
constructing a sliding mode controller according to the compensation control voltage sequence;
establishing a control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller;
controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer, and completing feedback of the sliding mode controller, wherein the output displacement is a feedback value of the sliding mode controller;
the sliding mode controller is constructed according to the compensation control voltage sequence, and specifically comprises the following steps:
analyzing and dynamically modeling the piezoelectric transducer, and obtaining a transfer function as follows:
wherein alpha is a first-order time constant and alpha is more than 0, x is the output displacement of the piezoelectric transducer, and u is the input voltage of the piezoelectric transducer;
the sliding mode surface function is:
s＝h 1 e
wherein h is 1 Is a sliding mode coefficient;
error of sliding mode controller and derivative thereof
Wherein x is ref Is a reference track;
derivative of sliding mode function s
The sliding approach law adopts an exponential approach law, and the control output of the sliding mode controller is that
Wherein k is s >0，ε>0。
2. The method for controlling the sliding mode of the piezoelectric transducer based on the inverse hysteresis model according to claim 1, wherein the construction of the depth linearization Koopman hysteresis model and the model identification of the depth linearization Koopman model according to the input control voltage and the output displacement of the piezoelectric transducer is specifically as follows:
displacement x of input piezoelectric sensor k To an encoder neural network which outputs a state variable z k ：
z k ＝Ψ(x k )，
Wherein ψ (·) is the encoder neural network to be identified;
input control voltage u k And state variable z k To a Koopman linearization neural network that outputs a predicted state variable z k+1 ：
z k+1 ＝Az k +Bu k ，
Wherein, A and B are both Koopman linearization neural networks;
the predicted state variable z k+1 Output of predictive displacements via decoder neural networks
Wherein ψ is -1 (-) is a decoder neural network.
3. The method for sliding mode control of a piezoelectric transducer based on a hysteresis inverse model according to claim 1, wherein the calculating the compensation control voltage sequence according to the reference trajectory is specifically as follows:
constructing a depth linearization Koopman hysteresis compensation inverse model:
given a length of N, a reference trace of x ref The control voltage at each instant is:
wherein x is 0 For initial displacement value, obtaining control voltage sequence U of hysteresis compensation inverse model K ＝[u 0 ，…u N-1 ] T ，k＝0，...N-1。
4. The sliding mode control method of the piezoelectric transducer based on the hysteresis inverse model according to claim 1, wherein the method is characterized in that the control law of the piezoelectric transducer is established according to the compensation control voltage sequence and the control voltage of the sliding mode controller, and specifically comprises the following steps:
control voltage sequence U according to obtained hysteresis compensation inverse model k In real-time voltage and obtained slip-mode controller output value u s Adding to obtain the overall control input of the piezoelectric transducer:
u＝U k +u s ,k＝0,...N-1。
5. a piezoelectric transducer slip-form control device based on a hysteresis inverse model, the control device comprising:
the depth linearization Koopman hysteresis model acquisition unit is used for constructing a depth linearization Koopman hysteresis model and model identification of the depth linearization Koopman model according to the piezoelectric sensor;
the reference track calculation compensation control voltage sequence acquisition unit is used for constructing a depth linearization Koopman hysteresis compensation inverse model according to the depth linearization Koopman hysteresis model, acquiring a reference track and calculating a compensation control voltage sequence according to the reference track;
the sliding mode controller acquisition unit is used for constructing a sliding mode controller according to the compensation control voltage sequence;
the control law building unit of the piezoelectric transducer is used for building the control law of the piezoelectric transducer according to the compensation control voltage sequence and the control voltage of the sliding mode controller;
the feedback unit of the sliding mode controller is used for controlling the piezoelectric transducer to acquire output displacement according to the control law and the input control voltage of the piezoelectric transducer so as to complete feedback of the sliding mode controller, wherein the output displacement is a feedback value of the sliding mode controller;
the sliding mode controller is constructed according to the compensation control voltage sequence, and specifically comprises the following steps:
analyzing and dynamically modeling the piezoelectric transducer, and obtaining a transfer function as follows:
wherein alpha is a first-order time constant and alpha is more than 0, x is the output displacement of the piezoelectric transducer, and u is the input voltage of the piezoelectric transducer;
the sliding mode surface function is:
s＝h 1 e
wherein h is 1 Is a sliding mode coefficient;
error of sliding mode controller and derivative thereof
e＝x-x ref ，
Wherein x is ref Is a reference track;
derivative of sliding mode function s
The sliding approach law adopts an exponential approach law, and the control output of the sliding mode controller is that
Wherein k is s >0，ε>0。
6. The piezoelectric transducer sliding mode control device based on the inverse hysteresis model according to claim 5, wherein the depth linearization Koopman hysteresis model obtaining unit specifically comprises:
a state variable acquisition unit for inputting the displacement x of the piezoelectric sensor k To an encoder neural network which outputs a state variable z k ：
z k ＝Ψ(x k )，
Wherein ψ (·) is the encoder neural network to be identified;
a predicted state variable acquisition unit for inputting the control voltage u k And state variable z k To a Koopman linearization neural network that outputs a predicted state variable z k+1 ：
z k+1 ＝Az k +Bu k ，
Wherein, A and B are both Koopman linearization neural networks;
a predicted displacement acquisition unit for predicting the state variable z k+1 Output of predictive displacements via decoder neural networks
Wherein ψ is -1 (. Cndot.) is the decoder nerveA network.
7. The piezoelectric transducer sliding mode control device based on the inverse hysteresis model according to claim 5, wherein the reference trajectory calculation compensation control voltage sequence obtaining unit specifically comprises:
the depth linearization Koopman hysteresis compensation inverse model acquisition unit is used for constructing a depth linearization Koopman hysteresis compensation inverse model:
a control unit acquisition unit for obtaining a reference track x according to a given length N ref The control voltage obtained at each moment is:
wherein x is 0 Is the initial displacement value;
obtaining a control voltage sequence of a hysteresis compensation inverse model:
U K ＝[u 0 ，…u N-1 ] T ，k＝0，...N-1。
8. a computer device comprising a memory and a processor, the memory having a computer program stored therein, the processor performing a hysteresis inverse model-based piezoelectric transducer sliding mode control method as claimed in any one of claims 1-4 when the processor runs the computer program stored in the memory.
9. A computer readable storage medium for storing a computer program for executing a method of controlling a sliding mode of a piezoelectric transducer based on a hysteresis inverse model according to any one of claims 1 to 4.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210661061.7A CN115047765B (en) | 2022-06-13 | 2022-06-13 | Piezoelectric transducer sliding mode control method, device, computer and storage medium based on hysteresis inverse model |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210661061.7A CN115047765B (en) | 2022-06-13 | 2022-06-13 | Piezoelectric transducer sliding mode control method, device, computer and storage medium based on hysteresis inverse model |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115047765A CN115047765A (en) | 2022-09-13 |
| CN115047765B true CN115047765B (en) | 2023-06-23 |
Family
ID=83160690
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210661061.7A Active CN115047765B (en) | 2022-06-13 | 2022-06-13 | Piezoelectric transducer sliding mode control method, device, computer and storage medium based on hysteresis inverse model |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115047765B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109557816A (en) * | 2018-12-28 | 2019-04-02 | 武汉工程大学 | A kind of suppressing method, system and the medium of piezoelectric ceramic actuator lagging characteristics |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111523236A (en) * | 2020-04-24 | 2020-08-11 | 哈尔滨工业大学 | Piezoelectric ceramic hysteresis model linearization identification method based on Koopman operator |
| CN113110064A (en) * | 2021-05-12 | 2021-07-13 | 中国科学院上海技术物理研究所 | Piezoelectric dynamic hysteresis feedforward compensation method based on Duhem inverse model |
| CN113916411B (en) * | 2021-09-18 | 2022-05-27 | 哈尔滨工业大学 | Pre-tightening force measurement method based on global linearization Koopman state observer |
| CN113885321B (en) * | 2021-09-28 | 2022-06-14 | 哈尔滨工业大学 | Memory-related Koopman-based dual-mode ultrasonic motor dead zone fuzzy compensation and linear prediction control method and system |
| CN114123853B (en) * | 2021-11-19 | 2024-03-19 | 华中科技大学 | Multi-axis coupling hysteresis prediction method for atomic force microscope piezoelectric driver |
-
2022
- 2022-06-13 CN CN202210661061.7A patent/CN115047765B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109557816A (en) * | 2018-12-28 | 2019-04-02 | 武汉工程大学 | A kind of suppressing method, system and the medium of piezoelectric ceramic actuator lagging characteristics |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115047765A (en) | 2022-09-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108731700B (en) | Weighted Euler pre-integration method in visual inertial odometer | |
| CN115509135B (en) | Laser scanning galvanometer model prediction control method and system | |
| CN110068326B (en) | Attitude calculation method and apparatus, electronic device, and storage medium | |
| CN108469269A (en) | A kind of resonance point test system of wideband inertial reference stabilized platform | |
| CN115280322A (en) | Hidden state planning actor control using learning | |
| CN111238535A (en) | IMU error online calibration method based on factor graph | |
| Chen et al. | Dynamic hysteresis model and control methodology for force output using piezoelectric actuator driving | |
| Burkhardt et al. | Experimental studies of control concepts for a parallel manipulator with flexible links | |
| CN113847915A (en) | Navigation method of strapdown inertial navigation/Doppler integrated navigation system | |
| Li et al. | Adaptive robust control of servo mechanisms with compensation for nonlinearly parameterized dynamic friction | |
| Lin et al. | Master general parking skill via deep learning | |
| CN108959787B (en) | Thermal deformation prediction method and system of macro-macro dual-drive system considering actual working conditions | |
| CN110189362A (en) | The efficient method for tracking target of network is fought from coding based on multiple-limb | |
| CN111168682A (en) | Limited time convergence sliding mode control method of parallel robot combined with robust precise differentiator for conveying | |
| CN112077839A (en) | Motion control method and device for mechanical arm | |
| CN110039537B (en) | Online self-learning multi-joint motion planning method based on neural network | |
| CN115047765B (en) | Piezoelectric transducer sliding mode control method, device, computer and storage medium based on hysteresis inverse model | |
| CN109902418B (en) | Simulation method for calculating dynamic response of EACLD center rigid body-cantilever beam model | |
| CN107340714B (en) | Self-adaptive inverse control method of nano servo system | |
| CN113885321A (en) | Memory-related Koopman-based dual-mode ultrasonic motor dead zone fuzzy compensation and linear prediction control method and system | |
| CN115179290B (en) | Mechanical arm and track control method and device thereof | |
| CN110605715A (en) | Robot dynamics parameter identification method independent of joint angular acceleration | |
| CN116338655A (en) | DVL speed error calibration method based on DMD-LSTM model | |
| CN112659125B (en) | Flexible mechanical arm self-adaptive boundary vibration control method based on input quantization mechanism | |
| CN115755603A (en) | Intelligent ash box identification method for ship motion model parameters and ship motion control method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |