CN110187723B - Vibration control method of rigid-flexible coupling electromechanical servo system - Google Patents
Vibration control method of rigid-flexible coupling electromechanical servo system Download PDFInfo
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Abstract
The invention discloses a vibration control method of a rigid-flexible coupling electromechanical servo system, which comprises the following steps: respectively acquiring encoder data on a driving motor and a load motor, acquiring torsion angles at two ends of a flexible shaft rod in real time, calculating to obtain a infinitesimal torsion angle at any position on the flexible shaft rod, and calculating to obtain a frequency domain characteristic equation according to the length, the polar inertia moment, the elastic modulus and the rotational inertia of the flexible shaft rod; calculating to obtain the coupling torque between the flexible shaft lever and the rigid driving flywheel by utilizing the frequency domain characteristic equation; establishing a balance equation of the rigid driving flywheel; substituting the coupling moment into the balance equation to obtain a fractional order transfer function model of the system; and establishing a fractional order controller according to the fractional order transfer function model, and performing vibration control on the system by using the controller. The method accurately describes the dynamic behavior of the viscoelastic material through the fractional order model, and effectively inhibits the residual vibration of the system.
Description
Technical Field
The invention relates to the technical field of power and transmission, in particular to a vibration control method of a rigid-flexible coupling electromechanical servo system.
Background
The rigid-flexible coupling electromechanical servo system is widely applied to the industrial fields of aerospace, mechanical manufacturing, robots and the like. The system is composed of a driving motor, an encoder, a conveyor belt, a rigid driving flywheel, a flexible shaft rod, a rigid load flywheel, a load motor, an encoder and the like. In order to improve the response speed of the system and reduce the power consumption, the flexible shaft is made of light and flexible viscoelastic materials, and then an electromechanical servo system in which a rigid flywheel and the flexible shaft are coupled with each other is formed. The existence of the flexible structure can lead the system to generate continuous residual vibration after the servo control is finished, thereby weakening the precision of the servo control and even endangering the production safety in severe cases. In order to suppress the residual vibration, it is necessary to first grasp the dynamic characteristics of the flexible structure and construct a dynamic model. However, the conventional integer-order Maxwell's model, the Voigt's model, the Kelvin model, the Zener model, and the polynomial combined mathematical model cannot accurately describe the dynamic behavior of the light flexible materials such as the viscoelastic material and the carbon nanocomposite material.
Disclosure of Invention
The invention aims to provide a vibration control method of a rigid-flexible coupling electromechanical servo system, which aims to solve the problem that the vibration control method in the prior art cannot accurately describe the dynamic behavior of light flexible materials such as viscoelastic materials and carbon nano composite materials and the continuous residual vibration generated after the servo control is finished. The vibration control method can accurately describe the dynamic behavior of the viscoelastic material, is simple in structure and can effectively inhibit the residual vibration of the system.
The invention provides a vibration control method of a rigid-flexible coupling electromechanical servo system, which comprises the following steps:
a vibration control method of a rigid-flexible coupled electromechanical servo system, comprising:
respectively collecting encoder data on a driving motor and a load motor to obtain the flexible shaft in real time
Calculating the torsion angles at the two ends of the rod to obtain the infinitesimal elements at any position on the flexible shaft lever
According to the length, polar moment of inertia, modulus of elasticity and
the rotational inertia is calculated to obtain a frequency domain characteristic equation;
calculating to obtain the flexible shaft lever and the rigid driving flywheel by using the frequency domain characteristic equation
A coupling moment therebetween;
establishing a balance equation of the rigid driving flywheel;
substituting the coupling moment into the balance equation to obtain a fractional order transfer function model of the system;
and establishing a fractional order controller according to the fractional order transfer function model, and performing vibration control on the system by using the controller.
The invention provides a vibration control method of a rigid-flexible coupling electromechanical servo system, and a device
Compared with the prior art, the fractional calculus has the advantages that on the premise of keeping the integral calculus characteristic,
also has history memory effect, and can accurately depict the light flexibility with viscoelastic property
Complex kinetic behavior of the material; fractional calculus can also provide additional consideration to the designer
The design freedom of the controller improves and improves the control performance of the prior controller to obtain better
And (5) vibration control effect. The present patent thus constitutes a device capable of describing a rigid-flexible coupling
Fractional order dynamic model of electromechanical servo system, and a set of dynamic models developed based on the fractional order dynamic model
A fractional order PD controller to suppress residual vibration of the system.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a schematic structural diagram of an electromechanical servo system according to an embodiment of the present invention;
FIG. 2 is a diagram of a single-unit negative feedback control system according to an embodiment of the present invention;
fig. 3 is a response curve provided by an embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
As shown in fig. 1, an embodiment of the present invention discloses a vibration control method for a rigid-flexible coupled electromechanical servo system shown in fig. 1, and the implementation steps thereof are specifically set forth as follows:
1. defining a system physical quantity symbol and an actual elastic modulus expression of the flexible shaft rod, and constructing a fractional order constitutive relation of the flexible shaft rod, which specifically comprises the following steps:
1.1 symbols of physical quantities defining a system
Respectively recording the moment of inertia and the rotation angle of a rigid driving flywheel as I1And theta1The moment of inertia, the length, the actual elastic modulus, the nominal elastic modulus and the section half of the flexible shaft rodThe diameter, shear stress, shear strain and torsion angle are respectively marked as I2L, E (t), E, R, τ (t), γ (t), and θ (t, x), respectively, the moment of inertia and the angle of rotation of the rigid load flywheel are denoted as I3And theta2The control torque output by the drive motor is denoted as T1And the coupling torque between the flexible shaft and the rigid driving flywheel is denoted as T2And the coupling torque between the flexible shaft and the rigid load flywheel is denoted as T3，θ1And theta2Which can be measured by encoders on the drive motor and the load motor, respectively.
1.2 actual elastic modulus expression for a defined flexible shaft
Characterizing the actual elastic modulus of a flexible shaft as
Where Γ is a Gamma function, t is time, and α is a constant between (0, 1).
1.3 constructing fractional order constitutive relations of Flexible shafts
Characterizing the shear stress of a flexible shaft as
Then, the actual elastic modulus E (t) obtained in the step 1.1 is substituted into tau (t), and the fractional order constitutive relation describing the flexible shaft rod can be obtained by combining the Caputo definition of fractional order calculus
Wherein
Indicates the alpha-th derivative of the element "·" in parentheses.
2. Obtaining the infinitesimal elements of the flexible shaft rod, analyzing and processing the infinitesimal elements, and calculating to obtain a frequency domain characteristic equation of the system, wherein the method specifically comprises the following steps:
2.1 obtaining the infinitesimal of the flexible shaft lever for analysis and solving the balance equation of the infinitesimal
Taking a infinitesimal element at any position of the flexible shaft lever for analysis, and using the rotation inertia of the infinitesimal elementThe quantity, length and torque are denoted i2Dx and dT, the distance from any point on the circular cross section of the infinitesimal to the center of the circle is recorded as r, and the relation is given
Where ρ represents density and J represents polar moment of inertia. On the basis, applying Newton's second law to the infinitesimal element to obtain an equilibrium equation
2.2 solving the expression of the torsional moment on the flexible shaft lever according to the geometric relationship on the infinitesimal
According to the geometric relationship on the section of the infinitesimal element, the strain of any point on the section can be characterized as
Substituting the formula into the fractional order constitutive relation obtained in step 1.3 to obtain a fractional order expression of the stress on the point on the infinitesimal section as
Further, the stress is integrated along the section radius on the infinitesimal section, and the fractional order expression of the total torsion moment is obtained as
2.3 substituting the expression of the torsion moment on the flexible shaft lever into the balance equation to obtain a fractional order characteristic equation
Substituting the torsion moment expression obtained in the step 2.2 into the balance equation obtained in the step 2.1 to obtain a fractional order characteristic equation of the rigid-flexible coupling electromechanical servo system:
2.4 carrying out Laplace transform on the fractional order characteristic equation to obtain a frequency domain expression
Laplace transform is carried out on the characteristic equation obtained in the step 2.3, and the characteristic equation on the frequency domain can be obtained
When θ (s, x) is simply denoted as θ (x), the formula can be further simplified to
3. Calculating to obtain the coupling torque between the flexible shaft rod and the rigid driving flywheel according to a frequency domain characteristic equation of the system, and specifically comprising the following steps:
3.1 defining the boundary conditions at both ends of the Flexible shaft
Defining the boundary condition of the flexible shaft at the end of the rigid driving flywheel as theta (x) & gtx＝0＝θ1The boundary condition of the flexible shaft at the flywheel end of the rigid load is defined as
3.2 solving the fractional order characteristic equation in the step 2.4 according to the boundary condition and obtaining the only solution, namely the torsion angle of the flexible shaft rod
The frequency domain characteristic equation in step 2.4 is solved according to the boundary conditions in step 3.1, and the solution can be obtained
Wherein
3.3 obtaining the rotation angle of the rigid load flywheel according to the solution obtained in the step 3.2
For the solution θ (x) obtained in step 3.2, let x be l, one can obtain
3.4 obtaining the coupling torque between the flexible shaft and the rigid driving flywheel according to the solution obtained in the step 3.2 and the rigid load flywheel rotation angle obtained in the step 3.3
The solution theta (x) obtained in step 3.2 is subjected to derivative on x, and theta in step 3.3 is subjected to derivative2In the result of the derivation, the coupling torque T can be obtained2Expression (2)
4. Applying Newton's second law to rigidly driven flywheel to obtain its equilibrium equation
Applying Newton's second law to rigidly driven flywheel to obtain equation T1+T2＝I1s2θ1And acquiring data of an encoder on the driving motor, calculating to obtain the angular acceleration of the rigid driving flywheel, and calculating to obtain the balance equation of the rigid driving flywheel according to the angular acceleration of the rigid driving flywheel and the rotational inertia of the driving flywheel.
5. Substituting the coupling torque obtained in the step 3.4 into the balance equation in the step 4, and obtaining a fractional order transfer function model of the system after arrangement
The T obtained in the step 3.4 is2The fractional order transfer function model of the rigid-flexible coupling electromechanical servo system can be obtained after being arranged in the equation in the step 4
Wherein,
6. establishing a fractional order controller according to the fractional order transfer function model, and performing vibration control on the system by using the controller
And designing a fractional order PD controller to inhibit the residual vibration of the system based on the control idea of unit negative feedback according to the fractional order transfer function model in the step 5. And establishing a fractional order controller according to the fractional order model, acquiring encoder data on the driving motor by the controller, subtracting the data from expected data to obtain error data, generating a control command by the controller according to the error data, applying the control command to the driving motor to enable the driving motor to generate a control torque, and finally realizing vibration control on the system through the conveyor belt.
After a fractional order model of the system is obtained, in order to suppress residual vibration of the system, a fractional order PD controller C(s) -K is designedp(1+Kdsβ) Wherein, K ispIndicating the proportionality coefficient of the controller, KdDenotes a differential coefficient of the controller, and β denotes an order of fractional order differentiation of the controller. Finally, a unit negative feedback control system shown in FIG. 2 is constructed, in which
Namely the fractional order kinetic model obtained in step 5.
The embodiment of the invention is as follows: taking fractional order model physical parameter I1＝1、I2＝0.1432、I3＝1、E＝7.484×106、J＝1.54×10-4、ρ＝9.3×1021 and 0.02, and simultaneously taking the controller parameter Kp＝0.1341、KdThe negative feedback vibration control system shown in fig. 2 is substituted with 1.1966 and β 0.7 to perform numerical simulation verification, so that the response curve shown in fig. 3 (the upper graph is an amplitude-frequency characteristic curve, and the lower graph is a phase-frequency characteristic curve) can be obtained, where a blue solid line represents the open-loop transfer function g(s), and a red dotted line represents the response curve of the closed-loop control system. Observing a blue solid line in the amplitude-frequency characteristic curve, finding that a fractional order dynamic model well describes a series of vibration modes of the rigid-flexible coupling structure; in addition, the red dotted line in the amplitude-frequency characteristic curve is observed, so that the fractional order PD controller effectively inhibits the vibration mode of the system, and the red dotted line is almost below a 0dB line, so that the residual vibration of the system is effectively inhibited.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. A vibration control method of a rigid-flexible coupled electromechanical servo system, comprising:
respectively acquiring encoder data on a driving motor and a load motor, acquiring torsion angles at two ends of a flexible shaft rod in real time, calculating to obtain a infinitesimal torsion angle at any position on the flexible shaft rod, and calculating to obtain a frequency domain characteristic equation according to the length, the polar inertia moment, the elastic modulus and the rotational inertia of the flexible shaft rod;
calculating to obtain the coupling torque between the flexible shaft lever and the rigid driving flywheel by using the frequency domain characteristic equation;
step (3) establishing a balance equation of the rigid driving flywheel;
step (4) bringing the coupling torque into the balance equation to obtain a fractional order transfer function model of the system;
step (5) establishing a fractional order controller according to the fractional order transfer function model, and performing vibration control on the system by using the controller;
the step (1) specifically comprises:
obtaining a infinitesimal of the flexible shaft lever for analysis and solving a balance equation of the infinitesimal;
solving an expression of the torsion moment on the flexible shaft lever according to the geometric relation on the micro element;
substituting an expression of the torsion moment on the flexible shaft lever into the balance equation to obtain a fractional order characteristic equation;
and carrying out Laplace transformation on the fractional order characteristic equation to obtain a frequency domain expression.
2. The method according to claim 1, wherein the step (2) specifically comprises:
acquiring boundary conditions at two ends of a flexible shaft lever;
calculating the frequency domain characteristic equation according to the boundary condition to obtain the torsion angle of the flexible shaft rod;
acquiring a rotation angle of the rigid load flywheel according to the torsion angle of the flexible shaft lever;
and calculating to obtain the coupling torque between the flexible shaft lever and the rigid driving flywheel according to the torsion angle of the flexible shaft lever and the rotation angle of the rigid load flywheel.
3. The method according to claim 2, wherein the step (3) comprises,
and acquiring data of an encoder on the driving motor, calculating to obtain the angular acceleration of the rigid driving flywheel, and calculating to obtain the balance equation of the rigid driving flywheel according to the angular acceleration of the rigid driving flywheel and the rotational inertia of the driving flywheel.
4. The method according to claim 3, wherein the step (5) comprises in particular:
the controller collects the encoder data of the driving motor, error data is obtained after the data is differed with expected data, the controller generates a control command according to the error data, the driving motor generates a control torque according to the control command, and the conveyor belt realizes vibration control of the system according to the control torque.
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| CN113415282B (en) * | 2021-07-27 | 2023-03-14 | 重庆长安汽车股份有限公司 | Active control system for torsional vibration of hybrid electric vehicle and design method |
| CN114035626B (en) * | 2021-11-12 | 2022-10-04 | 中国科学院长春光学精密机械与物理研究所 | Vibration control device and control method thereof |
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