CN113009830A - Nonlinear modeling and control method of piezoelectric actuator - Google Patents
Nonlinear modeling and control method of piezoelectric actuator Download PDFInfo
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Abstract
The invention discloses a nonlinear modeling and control method of a piezoelectric actuator, relating to the technical field of piezoelectric actuators; the method comprises the following steps: the method comprises the following steps: according to the basic principle of the piezoelectric ceramics, the influence of the temperature characteristic, the hysteresis characteristic, the creep characteristic and the vibration characteristic of the piezoelectric ceramics on the performance of the actuator is researched to provide a basis for the following nonlinear modeling and control; step two: respectively modeling the hysteresis characteristic and the creep characteristic of the piezoelectric ceramics; step three: according to the properties of the established nonlinear model; step four: after a relatively accurate model is obtained, designing an open-loop feedforward compensation controller according to the accurate model; step five: by adopting an improved sliding mode control method, the invention has the series characteristics of high response speed, higher power density, high displacement resolution, electromagnetic interference resistance and the like; the stability of the whole is improved, and the time is saved.
Description
Technical Field
The invention belongs to the technical field of piezoelectric actuators, and particularly relates to a nonlinear modeling and control method of a piezoelectric actuator.
Background
The piezoelectric actuator utilizes the inverse piezoelectric effect of the piezoelectric ceramic, so that the piezoelectric ceramic can generate corresponding deformation with different degrees under the action of an electric signal, and the generated mechanical deformation is converted into mechanical motion through friction force to be output. Piezoelectric actuators have found wide application in the fields of aerospace, optical instruments, biological devices, and microelectromechanical systems. Since the micro actuator can save much space, there is a strong demand in the fields of micro robots, fine positioning systems, and the like. The piezoelectric driver effectively supplements and improves the defects of the traditional electromagnetic motor, widens the application field of the motor, reduces the requirements on the application environment, and promotes the development of semiconductor processing technology, medical equipment, precision positioning technology and the like which have dependency on the driving technology.
However, the non-linear characteristics of the piezoelectric material, such as inherent hysteresis and creep, directly affect the positioning accuracy and the motion tracking accuracy. The creep characteristic is that when the voltage applied to the piezoelectric ceramic is stopped at a certain value, the response displacement thereof is not stopped but still changes with time, and reaches a stable value after a certain time.
When a step input voltage is applied to a piezoelectric actuator as shown in fig. 1, the displacement output exhibits a slow drift phenomenon. The hysteresis characteristic is a very complex nonlinear process and has nonlinear characteristics such as multivalue mapping and memory. For example, the response displacement may be different for the same input voltage; corresponding input voltages may be different for the same response displacement, which means that the voltage boosting response displacement curve and the voltage reducing response displacement curve of the piezoelectric ceramic do not coincide with each other, and a certain displacement difference is formed between the two curves, that is, a hysteresis loop is shown in fig. 2.
Disclosure of Invention
To solve the problems of the background art; the invention aims to provide a nonlinear modeling and control method of a piezoelectric actuator.
The invention discloses a nonlinear modeling and control method of a piezoelectric actuator, which comprises the following steps:
the method comprises the following steps: according to the basic principle of the piezoelectric ceramics, the influence of the temperature characteristic, the hysteresis characteristic, the creep characteristic and the vibration characteristic of the piezoelectric ceramics on the performance of the actuator is researched to provide a basis for the following nonlinear modeling and control;
step two: respectively modeling the hysteresis characteristic and the creep characteristic of the piezoelectric ceramic, researching a BW hysteresis model and improving the BW model, so that the improved model can accurately describe the hysteresis characteristic; selecting a proper description method by researching a creep modeling method; providing a coupling model according to the coupling relation between the hysteresis and the creep in the piezoelectric actuator, so that the established model can describe the creep characteristic brought by low frequency and simultaneously describe the hysteresis influence brought by high frequency;
step three: analyzing and concluding model parameters according to the properties of the established nonlinear model, carrying out online identification on the parameters by using a particle swarm algorithm, and testing the accuracy of the model under different driving voltage signals;
step four: after a relatively accurate model is obtained, designing an open-loop feedforward compensation controller according to the accurate model, and designing a feedback control system by combining a PID (proportion integration differentiation) controller on the basis of feedforward control compensation because the anti-interference capability of the feedforward model is poor;
step five: an improved sliding mode control method is adopted, the fractional calculus theory is the popularization from conventional integration and differentiation to non-integer order, a fractional order operator replaces an integer order calculus operator to enable the sliding mode surface to be added with one more variable parameter, and the optimal order is selected to enable the control system to obtain the best dynamic performance.
Compared with the prior art, the invention has the beneficial effects that:
the method has the characteristics of high response speed, high power density, high displacement resolution, electromagnetic interference resistance and the like;
and secondly, the overall stability is improved, and the time is saved.
Drawings
For ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.
FIG. 1 is a graphical representation of a creep characteristic curve in the prior art;
FIG. 2 is a diagram illustrating a hysteresis characteristic curve in the prior art;
FIG. 3 is a flowchart of the PSO parameter identification step of the present invention;
FIG. 4 is a schematic block diagram of a composite controller according to the present invention.
Detailed Description
In order that the objects, aspects and advantages of the invention will become more apparent, the invention will be described by way of example only, and in connection with the accompanying drawings. It is to be understood that such description is merely illustrative and not intended to limit the scope of the present invention. The structure, proportion, size and the like shown in the drawings are only used for matching with the content disclosed in the specification, so that the person skilled in the art can understand and read the description, and the description is not used for limiting the limit condition of the implementation of the invention, so the method has no technical essence, and any structural modification, proportion relation change or size adjustment still falls within the range covered by the technical content disclosed by the invention without affecting the effect and the achievable purpose of the invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and/or processing steps closely related to the scheme according to the present invention are shown in the drawings, and other details not so relevant to the present invention are omitted.
The specific implementation mode adopts the following technical scheme: the positioning and tracking control of the piezoelectric ceramic actuator are researched, and the influence of the nonlinear characteristics such as hysteresis, creep and the like of the piezoelectric ceramic material on the system performance is solved. And selecting a proper hysteresis model and selecting a corresponding control method according to the model to realize high-precision control on the output displacement of the piezoelectric ceramic actuator system.
(1) According to the basic principle of the piezoelectric ceramics, the influence of the temperature characteristic, the hysteresis characteristic, the creep characteristic, the vibration characteristic and the like of the piezoelectric ceramics on the performance of the actuator is researched to provide a basis for the following nonlinear modeling and control.
(2) Respectively modeling the hysteresis characteristic and the creep characteristic of the piezoelectric ceramic, researching a BW hysteresis model and improving the BW model, so that the improved model can accurately describe the hysteresis characteristic; selecting a proper description method by researching a creep modeling method; a coupling model is provided according to the coupling relation between the hysteresis and the creep in the piezoelectric actuator, so that the established model can describe the creep characteristic brought by low frequency and can describe the hysteresis influence brought by high frequency.
(3) According to the properties of the established nonlinear model, analyzing and concluding model parameters, carrying out online identification on the parameters by using a particle swarm algorithm, and testing the accuracy of the model under different driving voltage signals.
(4) After a relatively accurate model is obtained, an open-loop feedforward compensation controller is designed according to the accurate model, and a feedback control system is designed by combining a PID controller on the basis of feedforward control compensation because the feedforward model has poor anti-interference capability.
(5) An improved sliding mode control method is adopted, the fractional calculus theory is the popularization from conventional integration and differentiation to non-integer order, a fractional order operator replaces an integer order calculus operator to enable the sliding mode surface to be added with one more variable parameter, and the optimal order is selected to enable the control system to obtain the best dynamic performance.
The specific embodiment of the present embodiment is as follows:
firstly, establishing a hysteresis-creep model:
1.1, hysteresis is a nonlinear characteristic, which has global memory characteristics (the output of the current system is related to not only the current environmental factors but also the past environmental accumulation), so that the precision of the piezoelectric actuator is reduced, and the BW model is selected to model the nonlinear characteristic of the piezoelectric ceramic due to the simple form and few parameters of the BW model.
1.2, the time memory property of the fractional calculus can describe the physical phenomena with memory and heredity more accurately than the integral. In an attempt to introduce fractional calculus into the classical BW, BW is improved, and the effect needs further simulation verification.
1.3, creep is one of the main effects of piezoelectric actuators at low frequencies, and a slow drift phenomenon occurs when a step input is applied. Creep may lead to larger positioning errors as operating time increases. If the creep characteristics are modeled using a transfer function method, the creep characteristic dynamics can be modeled as a mass-spring-damper system, with the transfer function for the creep characteristics as follows:
secondly, identifying model parameters:
in order to describe the hysteresis characteristic of the piezoelectric actuator, a particle swarm optimization algorithm is used to obtain the BW hysteresis model parameter value by using a sine signal as an input signal.
Particles have only two properties: speed, which represents how fast the movement is, and position, which represents the direction of the movement. And (3) the optimal solution searched by each particle independently is called an individual extremum, the optimal individual extremum in the particle swarm is used as the current global optimal solution, iteration is continuously performed, the speed and the position are updated, and the optimal solution meeting the termination condition is finally obtained.
And 2.1, setting the maximum iteration times, the independent variable number of the objective function, the maximum speed of the particles and the position information as the whole search space, and randomly initializing the speed and the position in a speed interval and the search space.
And 2.2, defining a fitness function, finding an optimal solution for each particle by an individual extreme value, and finding a global value from the optimal solutions, wherein the global value is called the global optimal solution. And comparing with the historical global optimum, and updating.
2.3 formula for update speed and position
Wherein
Is an inertia factor (C ═ C)1+c2＞4)，c1＝c2∈[0,4]Referred to as the acceleration constant, r (0,1) is [0,1 ]]The random number of (2).
Is the ith iteration in the kth iterationThe current best fitness of the particle is,
representing the best fitness of the current population of particles. The flow chart for model identification in the time domain is shown in fig. 3.
Thirdly, designing a controller:
3.1, a composite controller:
solving the inverse model according to the above, when the expected track is yr(t) designing an inverse model-based compensator to determine the input voltage of the piezoelectric actuator as u (t). So that the expected displacement y of the piezoelectric micro positioning platformr(t) and the actual output displacement y (t) are linearized, thereby achieving cancellation of hysteresis nonlinearity. The open-loop control system cannot provide feedback quantity for correcting errors, so that the control effect depends on the accuracy of a mathematical model of the piezoelectric ceramic actuator to a great extent, and the controller is required to have high stable performance and poor anti-interference capability. Thus, PID feedback control is combined with the PID feedback control to design a composite closed-loop controller.
3.2, a sliding mode controller:
in order to design a sliding mode controller, a fractional order sliding mode surface and an appropriate control signal are designed so that the state trajectory reaches and remains on the sliding mode surface.
And 3.2.1, designing a sliding mode surface according to the determined piezoelectric actuator system model. (ensuring that a sliding mode exists and making the sliding mode surface s ═ 0, namely t → ∞ time s → 0 within a limited time)
3.2.2, sign functions sgn (x) are usually adopted for designing a sliding mode approach law, control input can oscillate due to discontinuity of the sign functions, and the oscillation can be eliminated by selecting a proper approach law.
And 3.2.3, solving the control input u (t), and carrying out stability analysis and verification on the solved controller.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (1)
1. A nonlinear modeling and control method of a piezoelectric actuator is characterized in that: the method comprises the following steps:
the method comprises the following steps: according to the basic principle of the piezoelectric ceramics, the influence of the temperature characteristic, the hysteresis characteristic, the creep characteristic and the vibration characteristic of the piezoelectric ceramics on the performance of the actuator is researched to provide a basis for the following nonlinear modeling and control;
step two: respectively modeling the hysteresis characteristic and the creep characteristic of the piezoelectric ceramic, researching a BW hysteresis model and improving the BW model, so that the improved model can accurately describe the hysteresis characteristic; selecting a proper description method by researching a creep modeling method; providing a coupling model according to the coupling relation between the hysteresis and the creep in the piezoelectric actuator, so that the established model can describe the creep characteristic brought by low frequency and simultaneously describe the hysteresis influence brought by high frequency;
step three: analyzing and concluding model parameters according to the properties of the established nonlinear model, carrying out online identification on the parameters by using a particle swarm algorithm, and testing the accuracy of the model under different driving voltage signals;
step four: after a relatively accurate model is obtained, designing an open-loop feedforward compensation controller according to the accurate model, and designing a feedback control system by combining a PID (proportion integration differentiation) controller on the basis of feedforward control compensation because the anti-interference capability of the feedforward model is poor;
step five: an improved sliding mode control method is adopted, the fractional calculus theory is the popularization from conventional integration and differentiation to non-integer order, a fractional order operator replaces an integer order calculus operator to enable the sliding mode surface to be added with one more variable parameter, and the optimal order is selected to enable the control system to obtain the best dynamic performance.
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| CN114460847A (en) * | 2022-01-28 | 2022-05-10 | 哈尔滨理工大学 | Piezoelectric ceramic driver driven by asymmetric voltage |
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| DE19825859A1 (en) * | 1998-06-10 | 1999-12-23 | Klaus Kuhnen | Compensation arrangement for creep and hysteresis effects in the transfer characteristics of control elements |
| 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 |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114460847A (en) * | 2022-01-28 | 2022-05-10 | 哈尔滨理工大学 | Piezoelectric ceramic driver driven by asymmetric voltage |
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