CN113353799A - Swing suppression control method for double-pendulum tower crane with distributed mass loads - Google Patents
Swing suppression control method for double-pendulum tower crane with distributed mass loads Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/04—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack
- B66C13/06—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads
- B66C13/063—Auxiliary devices for controlling movements of suspended loads, or preventing cable slack for minimising or preventing longitudinal or transverse swinging of loads electrical
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/18—Control systems or devices
- B66C13/46—Position indicators for suspended loads or for crane elements
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B66—HOISTING; LIFTING; HAULING
- B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
- B66C13/00—Other constructional features or details
- B66C13/18—Control systems or devices
- B66C13/48—Automatic control of crane drives for producing a single or repeated working cycle; Programme control
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Abstract
The invention discloses a swing suppression control method of a double-pendulum tower crane with distributed mass loads, which comprises the steps of establishing a mathematical model of the double-pendulum tower crane with the distributed mass loads based on a Lagrange kinetic equation and analyzing characteristics; establishing an energy function of a mathematical model of the double-pendulum tower crane according to the characteristics, and establishing an adaptive controller based on the energy function of the mathematical model of the double-pendulum tower crane to inhibit external interference; establishing a fuzzy controller based on a fuzzy control rule, adding the fuzzy controller into an adaptive controller, and performing real-time regulation and control on the swing inhibition of the double-pendulum tower crane through the fuzzy controller; the invention can partially enhance the coupling between the driving mechanism and the non-driving mechanism of the double-pendulum tower crane, provides the fuzzy controller module to improve the real-time operation capability, effectively inhibits external disturbance by designing the self-adaptive controller, and realizes efficient track tracking and swing inhibition by combining the two mechanisms so as to achieve the control effect.
Description
Technical Field
The invention relates to the technical field of motion control of an under-actuated crane system, in particular to a swing suppression control method of a double-pendulum tower crane with distributed mass loads.
Background
Under-actuated systems, i.e. systems where the system inputs fewer degrees of freedom than the system. Among them, the crane system is a typical underactuated system, i.e. the cantilever turning force and the trolley running force are its inputs, and the angles of the load and the hook are its indirectly controllable forces. And the device has the advantages of simple structure, low power consumption, few actuating mechanisms, wide application occasions and the like. The tower crane is a crane for transporting goods in space, the transportation process of the tower crane is usually accompanied by the simultaneous movement of the translation of a trolley and the rotation of a cantilever, and the two movements with different properties are highly coupled, so that the difficulty in designing a dynamic model and a controller is increased. Meanwhile, when the mass of the lifting hook is similar to that of the load or the length of the lifting rope is similar to that of the suspension rope, the double-pendulum characteristic of the tower crane can obviously appear. Compared with a simple mass point double-pendulum system, the distributed mass load has a rotation condition in the swinging process due to the load, so that a system dynamic model is more complex, and the swinging of a lifting hook and the load is quickly restrained while the accurate positioning of the cantilever and the trolley is realized, which is a very challenging problem.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned conventional problems.
Therefore, the invention provides a swing suppression control method of a double-pendulum tower crane with distributed mass loads, which can solve the technical problems that: when the mass of the load is similar to that of the lifting hook or the length of the lifting rope is similar to that of the suspension rope, the double-pendulum characteristic of the tower crane can occur, and the load volume is different, the distributed mass load rotates and translates in the swinging process, so that a system dynamic model is more complex, and the swinging of the lifting hook and the load cannot be quickly inhibited while the accurate positioning of the cantilever and the trolley is realized.
In order to solve the technical problems, the invention provides the following technical scheme: establishing a mathematical model of a double-pendulum tower crane with distributed mass load based on a Lagrange kinetic equation and analyzing characteristics; establishing an energy function of a mathematical model of the double-pendulum tower crane according to the characteristics, and establishing an adaptive controller based on the energy function of the mathematical model of the double-pendulum tower crane to inhibit external interference; and establishing a fuzzy controller based on a fuzzy control rule, adding the fuzzy controller into the self-adaptive controller, and regulating and controlling the swing inhibition of the double-pendulum tower crane in real time through the fuzzy controller.
As a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the mathematical model of the double-pendulum tower crane comprises an order
The expression of the mathematical model of the double-pendulum tower crane is as follows:
G(q)＝[0 0 (m1+m2)gl1C2S1(m1+m2)gl1C1S2m2gl2C4S3m2gl2C3S4]T
wherein: m (q) is an inertia matrix of the double-pendulum tower crane system,
is a centripetal-Coriolis matrix, G (q) is a gravity vector, U is a control input vector, FsD is the mechanical friction and the wind resistance of the double-pendulum tower crane system respectively, q is the state variable of the double-pendulum tower crane system,
in the form of the first derivative of the signal,
is its second derivative; m is1And m2Mass of hook and load, respectively, /)1And l2The lengths from the suspension rope and the lifting hook to the center of mass of the load are respectively shown, g is the gravity acceleration, for describing the generalized state quantity of the double-pendulum tower crane system,
is the cantilever rotation angle, x is the trolley translation distance, thetaiI 1., 4 is the swing angle of the hook and the load, and for the driving force/torque,
for cantilever drive torque, FxIs the driving force of the trolley,
respectively the mechanical friction of the cantilever and the trolley,
is an air friction parameter.
As a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the method further comprises the step of establishing a friction feedforward compensation model to eliminate the friction generated by a driving mechanism of the double-pendulum tower crane, wherein the friction feedforward compensation model is expressed as follows:
wherein the content of the first and second substances,
Fx1、fx2、ε1and ε2For the parameters of the friction feed-forward compensation model,
and fx1The value of (b) corresponds to the maximum static friction force,
and
is the coefficient of viscous friction, ε1And ε2Is the static coefficient of friction.
As a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the energy function of the mathematical model of the double-pendulum tower crane comprises,
wherein:
respectively representing the cantilever, trolley, swing angle thetaiA speed signal of 1, 4,
is the kinetic energy part of a double-pendulum tower crane system, m2gl2(1-C3C4) Loading it with a potential energy portion.
As a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the self-adaptive controller comprises the following Lyapunov equation which is designed according to the dynamics rule of a tower crane model and based on the energy function of the mathematical model of the double-pendulum tower crane:
wherein:
ex＝x-xr,
in order to be an error in the rotational position of the cantilever,
error in the rotational speed of the cantilever, exIs the error of the translation distance of the trolley,
in order to determine the error in the speed of the trolley,
a cantilever rotation angle target value following the s-shaped track;
for the Lyapunov equation VEThe derivation is carried out to obtain:
wherein:
and
for the purpose of the parameters of the separation,
and
no parameters are determined for the purpose of the evaluation,
is an angle-related term;
designing the adaptive controller on the basis that:
wherein the content of the first and second substances,
kxpand kxdFor adaptive controller gain, TαForce in the direction of rotation of the cantilever, FxIs the force in the direction of the trolley.
As a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the fuzzy controller comprises a cantilever rotating angle
Error of trolley translation distance x and error thereofThe error derivative is used as the input of the fuzzy controller and is distributed in the membership degree interval of [ -33 ] by different quantization factors]To (c) to (d); according to expert experience, a membership table and the fuzzy control rule, the area center algorithm is used for defuzzification to obtain a setting parameter
ΔkxpAnd
as a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the adaptive controller gain comprises a gain of the adaptive controller,
wherein the content of the first and second substances,
and
is a controller base parameter.
As a preferable scheme of the swing suppression control method of the double-pendulum tower crane with distributed mass loads, the method comprises the following steps: the method further comprises the following step of performing tracking control on the double-pendulum tower crane system by using reference tracks of the cantilever and the trolley, wherein the reference tracks are S-shaped tracks:
wherein X represents the cantilever rotation angle
Or the trolley is translated by a distance x; q (X)d，q(χ)0And tq(χ)dTarget angle/position, initial angle/position and arrival time of the cantilever and the trolley respectively; chi shaperIndicating the angle of rotation of the cantilever
Or the target position where the trolley is translated a distance x.
The invention has the beneficial effects that: the invention can partially enhance the coupling between the driving mechanism and the non-driving mechanism of the double-pendulum tower crane, provides the fuzzy controller part to improve the real-time operation capability of the double-pendulum tower crane, provides the adaptive control to effectively inhibit external disturbance, and finally can realize efficient track tracking and swing inhibition by combining the fuzzy controller part and the fuzzy controller part so as to achieve the control effect.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
fig. 1 is a schematic diagram of an online adjustment flow of a fuzzy controller of a method for controlling swing suppression of a double-pendulum tower crane with distributed mass loads according to a first embodiment of the present invention;
fig. 2 is a schematic diagram of output slalom functions of a double-pendulum tower crane swing suppression control method for distributing mass loads according to a first embodiment of the present invention;
fig. 3 is a schematic diagram of input slalom functions of a double-pendulum tower crane swing suppression control method for distributing mass loads according to a first embodiment of the present invention;
fig. 4 is a schematic structural principle diagram of a mathematical model of a double-pendulum tower crane according to a method for controlling the swing suppression of the double-pendulum tower crane with distributed mass loads according to a first embodiment of the present invention;
fig. 5 is a schematic diagram of an experimental result of a fuzzy controller of a method for controlling the swing suppression of a double-pendulum tower crane according to a second embodiment of the present invention;
fig. 6 is a schematic diagram of an experimental result of a controller LQR (linear-orthogonal-regulator) of a swing suppression control method for a double-pendulum tower crane with distributed mass loads according to a second embodiment of the present invention;
fig. 7 is a schematic diagram of an experimental platform of a swing suppression control method for a double-pendulum tower crane with distributed mass loads according to a second embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Meanwhile, in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation and operate, and thus, cannot be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or 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.
Example 1
The conventional under-actuated crane positioning and anti-swing control is mainly aimed at a bridge crane system, even if a multi-degree-of-freedom bridge crane moving in a three-dimensional space is adopted, the dynamic property of a driving mechanism still belongs to linear force, the dynamic characteristic is still simple, and the control is convenient, but when driving force with different properties occurs in a crane conveying task, for example, the control is aimed at a tower crane, one direction of the control is the translation force of a trolley, and the other direction of the control is the rotating force of a cantilever; at the moment, the dynamic characteristics of the system become very complex due to the participation of centrifugal motion, meanwhile, when the mass of the load and the mass of the lifting hook are similar, or the lengths of the suspension rope and the lifting rope are similar, the double-pendulum characteristic of the crane system is more obvious, and in addition, the inevitable rotation in the transportation process of the distributed mass load inevitably causes the failure of the controller designed for the mass distributed load of single pendulum or double pendulum in the prior art; for conventional controllers, on the one hand, they have poor coupling between the drivable and the non-drivable mechanisms, resulting in that usually only positioning can be achieved, but the wobble suppression effect is poor; on the other hand, most controllers use an adjustment control mode aiming at a target position due to a complex design process, but the adjustment control can generate a very large initial output value of the controller in practical application, so that inevitable initial fluctuation is caused, the service life of a driver is damaged, and the anti-swing effect is influenced; specifically, the self-adaptive controller is designed by studying the energy of the under-actuated distributed mass load double-pendulum tower crane system, so that the external disturbance can be effectively inhibited, meanwhile, the fuzzy controller is provided to partially improve the real-time operation capability of the double-pendulum tower crane system, and the track tracking and the swing inhibition can be effectively realized by combining the fuzzy controller and the fuzzy controller.
Referring to fig. 1 to 4, a first embodiment of the present invention provides a swing suppression control method for a double-pendulum tower crane with distributed mass loads, including:
s1: and establishing a mathematical model of the double-pendulum tower crane with distributed mass load based on a Lagrange kinetic equation and analyzing the characteristics.
Order to
Establishing a mathematical model of the double-pendulum tower crane with distributed mass load:
G(q)＝[0 0 (m1+m2)gl1C2S1(m1+m2)gl1C1S2m2gl2C4S3m2gl2C3S4]T
wherein: m (q) is an inertia matrix of the double-pendulum tower crane system,
is a centripetal-Coriolis matrix, G (q) is a gravity vector, U is a control input vector, FSD is the mechanical friction and the wind resistance of the double-pendulum tower crane system respectively, q is the state variable of the double-pendulum tower crane system,
in the form of the first derivative of the signal,
is its second derivative; m is1And m2Mass of hook and load, respectively, /)1And l2The lengths from the suspension rope and the lifting hook to the center of mass of the load are respectively shown, g is the gravity acceleration, for describing the generalized state quantity of the double-pendulum tower crane system,
is the cantilever rotation angle, x is the trolley translation distance, thetaiI 1., 4 is the swing angle of the hook and the load, and for the driving force/torque,
for cantilever drive torque, FxIs the driving force of the trolley,
respectively the mechanical friction of the cantilever and the trolley,
is an air friction parameter.
Further, a friction force feedforward compensation model is established to eliminate friction force (mechanical friction force of a cantilever and a trolley) generated by a driving mechanism of the double-pendulum tower crane, and the friction force feedforward compensation model is expressed as follows:
wherein the content of the first and second substances,
fx1、fx2、ε1and ε2For the parameters of the friction feed-forward compensation model,
and fx1The value of (b) corresponds to the maximum static friction force,
and
is the coefficient of viscous friction, ε1And ε2Is the static coefficient of friction.
It should be noted that the inertia matrix of the double-pendulum tower crane system is as follows:
m11＝J+m1x2+m2x2+mtx2+l1 2m1+l1 2m2+l2 2m2-l1 2m1C1 2C2 2-l1 2m2C1 2C2 2-l2 2m2C3 2C4 2+2l1m1xC2S1+2l1m2xC2S1+2l2m2xC4S3+2l1l2m2S2S4+2l1l2m2C2C4S1S3
m12＝l1m1S2+l1m2S2+l2m2S4
m13＝l1 2m1C1C2S2+l1 2m2C1C2S2+l1l2m2C1C2S4
m14＝-l1 2m1S1-l1 2m2S1-l1m1xC2-l1m2xC2-l1l2m2C2C4S3-l1l2m2S1S2S4
m15＝l2 2m2C3C4S4+l1l2m2C3C4S2
m16＝-l2 2m2S3-l2m2xC4-l1l2m2S2S3S4-l1l2m2C2C4S1
m21＝l1m1S2+l1m2S2+l2m2S4
m22＝m1+m2+mt
m23＝l1m1C1C2+l1m2C1C2
m24＝-l1m1S1S2-l1m2S1S2
m25＝l2m2C3C4
m26＝-l2m2S3S4
m31＝l1 2m1C1C2S2+l1 2m2C1C2S2+l1l2m2C1C2S4
m32＝l1m1C1C2+l1m2C1C2
m33＝l1 2m1C2 2+l1 2m2C2 2
m34＝0
m35＝l1l2m2C2C4S1S3+l1l2m2C1C2C3C4
m36＝-l1l2m2C1C2S3S4+l1l2m2C2C3S1S4
m41＝-l1 2m1S1-l1 2m2S1-l1m1xC2-l1m2xC2-l1l2m2C2C4S3-l1l2m2S1S2S4
m42＝-l1m1S1S2-l1m2S1S2
m43＝0
m44＝l1 2m1+l1 2m2
m45＝l1l2m2C1C4S2S3-l1l2m2C3C4S1S2
m46＝l1l2m2C2C4+l1l2m2C1C3S2S4+l1l2m2S1S2S3S4
m51＝l2 2m2C3C4S4+l1l2m2C3C4S2
m52＝l2m2C3C4
m53＝l1l2m2C1C2C3C4+l1l2m2C2C4S1S3
m54＝l1l2m2C1C4S2S3-l1l2m2C3C4S1S2
m55＝lp 2m2/12+l2 2m2C4 2
m56＝0
m61＝-l2m2xC4-l2 2m2S3-l1l2m2C2C4S1-l1l2m2S2S3S4
m62＝-l2m2S3S4
m63＝-l1l2m2C1C2S3S4+l1l2m2C2C3S1S4
m64＝l1l2m2C2C4+l1l2m2C1C3S2S4+l1l2m2S1S2S3S4
m65＝0
m66＝m2l2 2
wherein m isijIndicating matrix coordinates, i 1, 2 … 6, j 1, 2 … 6.
Centripetal coriolis matrix
The following were used:
c22＝0
c32＝0
c44＝0
c52＝0
c66＝0
wherein c isijThe matrix coordinates are represented, i is 1, 2 … 6, and j is 1, 2 … 6.
Furthermore, characteristics are analyzed according to a mathematical model of the double-pendulum tower crane, and the characteristics specifically comprise swinging characteristics (a double-pendulum system), load (rod translation characteristics) and the like of the double-pendulum tower crane.
S2: and establishing an energy function of the mathematical model of the double-pendulum tower crane according to the characteristics, and establishing an adaptive controller based on the energy function of the mathematical model of the double-pendulum tower crane so as to inhibit external interference.
The energy function of the mathematical model of the double-pendulum tower crane is as follows:
wherein:
respectively representing the cantilever, trolley, swing angle thetaiA speed signal of 1, 4,
is the kinetic energy part of a double-pendulum tower crane system, m2gl2(1-C3C4) Loading it with a potential energy portion.
The following simplified expression can be obtained by derivation of an energy function in the mathematical model of the double-pendulum tower crane:
wherein the content of the first and second substances,
in order to be the cantilever rotation speed,
as the speed of the trolley,
is the angular velocity of its hook and load.
Further, the following Lyapunov equation is designed based on the energy function of the mathematical model of the double-pendulum tower crane and following the dynamics rule of the tower crane model:
wherein:
ex＝x-xr,
in order to be an error in the rotational position of the cantilever,
error in the rotational speed of the cantilever, exIs the error of the translation distance of the trolley,
in order to determine the error in the speed of the trolley,
a cantilever rotation angle target value following the s-shaped track;
P-Lyapunov equation VEThe derivation is carried out to obtain:
wherein:
and
for the purpose of the parameters of the separation,
and
no parameters are determined for the purpose of the evaluation,
is an angle-related term;
an adaptive controller is designed on the basis that:
wherein the content of the first and second substances,
kxpand kxdFor adaptive controller gain, TαForce in the direction of rotation of the cantilever, FxIs the force in the direction of the trolley.
S3: and establishing a fuzzy controller based on a fuzzy control rule, adding the fuzzy controller into the self-adaptive controller, and performing real-time regulation and control on the swing inhibition of the double-pendulum tower crane through the fuzzy controller.
Referring to FIGS. 1 to 3, the cantilever is rotated
The error of the translation distance x of the trolley and its error derivative are used as the input of the fuzzy controller, and are distributed in the membership degree range [ -33 ] by different quantization factors]To (c) to (d); NB (negative big), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium) and PB (positive big) are respectively used for representing the corresponding-3, -2, -1, 0,1, 2 and 3.
Obtaining a membership table (namely figures 2 and 3) and a fuzzy control rule according to expert experience and multiple experiments, and performing defuzzification by using an area center algorithm to obtain a setting parameter
ΔkxpAnd
to build a fuzzy controller.
Finally, the adaptive controller gain actually applied in the adaptive controller
kxpAnd kxdComprises the following steps:
wherein the content of the first and second substances,
and
is a controller base parameter.
Specifically, the fuzzy control rule is as follows:
preferably, for:
in adaptive controllers
ΔkxpAnd kxdUnder the condition of giving an initial value, a fuzzy controller is used for real-time regulation and control, so that better control performance (accurate positioning and quick and effective oscillation elimination) can be obtained in the whole motion process.
In particular, the gain of the PD-like part (b
kxpAnd kxd) The gains are positive gains, and the gains can be selected by self and also adjusted on line by using a fuzzy controller;
kxpand kxdAre respectively set as20. 5, 10 and 5, wherein the initial value and the fuzzy controller proportion can be adjusted according to actual conditions; it is noted that the adjustment
And kxpThe positioning speed can be improved, but the phenomenon of overshoot and oscillation can be generated when the adjustment is too large;
and kxpWill be too big
And kxpThe generated poor output response plays a certain role in damping; secondly, selecting 0.02 for the direction of the cantilever of the self-adaptive item, and selecting 10 for the direction of the trolley; finally, the parameters associated with the friction model are fed forward
fx1And fx2After offline recognition, without changing the value of the selection, ε1And ε2Is the static coefficient of friction, which is selected to be 0.01.
Further, the reference track of the cantilever and the trolley is utilized to carry out tracking control on the double-pendulum tower crane system so as to verify the positioning and pendulum eliminating functions, wherein the reference track is an S-shaped track:
wherein χ represents a cantilever rotation angle
Or the trolley is translated by a distance x; q (X)d，q(χ)0And tq(χ)dTarget angles/positions of the boom and the trolley, respectivelyPosition, initial angle/position and time of arrival; chi shaperIndicating the angle of rotation of the cantilever
Or the target position of the trolley translation distance x; for the reference track middle q (x)d，q(χ)0And tq(χ)dThe selection of (2) is to be freely selected according to the target position in actual operation, considering safety and according with actual conditions.
In practical application occasions, the double-pendulum characteristic of the tower crane is more obvious, so that the realization of a safe positioning task while inhibiting the pendulum angle has more challenging and practical engineering significance; therefore, the method mainly aims at the problems of track tracking and swing suppression of the double-pendulum tower crane, firstly establishes a mathematical model of the double-pendulum tower crane with distributed mass load based on a Lagrange kinetic equation and analyzes the characteristics. So as to facilitate the energy analysis of the whole system, wherein an adaptive controller is designed according to the energy of the system, and the controller can effectively restrain external disturbance (wind resistance, mechanical friction and the like); the requirement of crane operation (quick positioning and effective swing elimination) is met to a certain extent; then, considering the real-time performance of the crane in the actual operation process, a fuzzy controller is selectively added to effectively deal with the emergency situation, and the positioning and swing eliminating functions are further improved. The self-adaptive controller takes a friction feedforward compensation model as a feedforward compensation mode, and finally tracks the S-shaped track meeting the conditions through setting to verify the advantages of the self-adaptive controller; the method is mainly characterized in that the track tracking and the swing suppression of the double-swing distributed mass load tower crane can be quickly and effectively realized.
On the other hand, in the aspect of parameter selection, as the platform adopts fuzzy control to be combined with self-adaptive control, only the given value of the basic parameter and the proportional gain value of the parameter need to be adjusted; the method has simple process, the number of gains and parameters is small, the gain and the parameters are not limited by models and physical conditions too much, and the response effect corresponding to each gain is clear, so the parameter adjusting process in practical application is not complicated, and the gain with better response is easy to determine; the friction force feedforward compensation model is used for simply eliminating the influence of the friction force, so that the adverse influence of the friction generated by the motion of the driving mechanism on the control effect is effectively avoided, for example, the swinging caused by the positioning lag/lead is increased severely to eliminate the swinging control difficulty.
Example 2
Referring to fig. 5 to 7, a second embodiment of the present invention is different from the first embodiment in that, in order to better verify and explain the technical effects adopted in the method of the present invention, in the present embodiment, a conventional controller LQR is selected for testing, and the test results are compared by a scientific demonstration method to verify the real effects of the method.
Referring to fig. 7, in order to perform an experiment, an experiment platform is built in this embodiment, and the experiment platform is composed of a PC, a control board card, a servo motor driver, a trolley, a cantilever, a swing angle measuring mechanism and the like, on the aspect of an upper computer, codes are generated by MATLAB/Simulink compiling, then, the experiment data on the control board is monitored and recorded in real time through a control board (DSP) in a sampling period of 0.005s and serial port communication, and partial position signals can be driven to come from the counting of an encoder; the load/hook swing angle information comes from the contact type potentiometer sensor mechanism, the voltage signal of the contact type potentiometer sensor mechanism is transmitted to the control panel through the A/D converter, and for the output of the controller, the control panel generates a designed voltage signal to the motor driver through the D/A converter to drive the servo motor to operate.
The controller LQR and the controller using the control method are used for carrying out experiments, and the control formula of the controller LQR is as follows:
for LQR controllers, the state vector
And Q matrix and R matrix are set to Q ═ diag {200,100,20,20,20,20,5,5,5,5, 5}, and R ═ 1,1]TFinally, the gain of the controller is k11＝56.6，k12＝14.5，k13＝8.9，k14＝3.4，k15＝-2.5，k16＝-1.1，k21＝40.0，k22＝9.2，k23＝-19.1，k24＝-0.9，k25＝13.3，k26Using the experimental platform constructed above, the amplitude using the method and the method used by the LQR controller was calculated as 0.80, and the results are shown in table 1 below:
table 1: maximum amplitude experiments compare the results.
Referring to fig. 5 and 6, it can be seen that, under the condition that the positioning time is basically the same, the proposed controller can completely track the target track and realize the positioning function, and the LQR controller is in
The direction can not realize the positioning, the tracking and positioning process of the method is smooth, the positioning task can be completed within 3 seconds, and the amplitude of a lifting hook and a load caused by a controller of the method is not large and can not exceed 1.15[ deg ] in the aspect of swing inhibition]And the amplitude of the hook and the load caused by the traditional LQR method controller is too large, and is not lower than 1[ deg ]]And up to approximately 1.7[ deg. ]]And the swing of the method can be completely eliminated within 2-4 seconds after the positioning of the driving mechanism is finished, but the traditional method has a poor suppression effect, and the swing still remains after the driving mechanism is subjected to repeated violent oscillation until 20 seconds, so that the swing suppression efficiency of the method is extremely high, the positioning is accurate, and no overshoot and no steady-state error exist.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (8)
1. A swing suppression control method of a double-pendulum tower crane with distributed mass loads is characterized by comprising the following steps: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
establishing a mathematical model of the double-pendulum tower crane with distributed mass load based on a Lagrange kinetic equation and analyzing the characteristics;
establishing an energy function of a mathematical model of the double-pendulum tower crane according to the characteristics, and establishing an adaptive controller based on the energy function of the mathematical model of the double-pendulum tower crane to inhibit external interference;
and establishing a fuzzy controller based on a fuzzy control rule, adding the fuzzy controller into the self-adaptive controller, and regulating and controlling the swing inhibition of the double-pendulum tower crane in real time through the fuzzy controller.
2. The swing suppression control method of a double-pendulum tower crane with distributed mass load according to claim 1, characterized in that: the mathematical model of the double-pendulum tower crane comprises,
order to
The expression of the mathematical model of the double-pendulum tower crane is as follows:
G(q)＝[0 0(m1+m2)gl1C2S1 (m1+m2)gl1C1S2 m2gl2C4S3 m2gl2C3S4]T
wherein: m (q) is an inertia matrix of the double-pendulum tower crane system,
is a centripetal-Coriolis matrix, G (q) is a gravity vector, U is a control input vector, FSD is the mechanical friction and the wind resistance of the double-pendulum tower crane system respectively, q is the state variable of the double-pendulum tower crane system,
in the form of the first derivative of the signal,
is its second derivative; m is1And m2Mass of hook and load, respectively, /)1And l2The lengths from the suspension rope and the lifting hook to the center of mass of the load are respectively shown, g is the gravity acceleration, for describing the generalized state quantity of the double-pendulum tower crane system,
is the cantilever rotation angle, x is the trolley translation distance, thetaiI 1., 4 is the swing angle of the hook and the load, and for the driving force/torque,
for cantilever drive torque, FxIs the driving force of the trolley,
respectively the mechanical friction of the cantilever and the trolley,
is an air friction parameter.
3. The swing suppression control method of a double-pendulum tower crane with distributed mass loads according to claim 2, characterized in that: also comprises the following steps of (1) preparing,
establishing a friction feedforward compensation model to eliminate friction generated by a driving mechanism of the double-pendulum tower crane, wherein the friction feedforward compensation model is expressed as follows:
wherein the content of the first and second substances,
fx1、fx2、ε1and ε2For the parameters of the friction feed-forward compensation model,
and fx1The value of (b) corresponds to the maximum static friction force,
and
is the coefficient of viscous friction, ε1And ε2Is the static coefficient of friction.
4. The swing suppression control method of a double-pendulum tower crane with distributed mass load according to claim 1 or 2, characterized in that: the energy function of the mathematical model of the double-pendulum tower crane comprises,
wherein:
respectively representing the cantilever, trolley, swing angle thetaiA speed signal of 1, 4,
is the kinetic energy part of a double-pendulum tower crane system, m2gl2(1-C3C4) Loading it with a potential energy portion.
5. The swing suppression control method of a double-pendulum tower crane with distributed mass load according to claim 4, characterized in that: the adaptive controller comprises a first adaptive controller and a second adaptive controller,
following the dynamics rule of a tower crane model, and designing the following Lyapunov equation based on the energy function of the mathematical model of the double-pendulum tower crane:
wherein:
in order to be an error in the rotational position of the cantilever,
error in the rotational speed of the cantilever, exIs the error of the translation distance of the trolley,
in order to determine the error in the speed of the trolley,
a cantilever rotation angle target value following the s-shaped track;
for the Lyapunov equation VEThe derivation is carried out to obtain:
wherein:
seed of a plant
For the purpose of the parameters of the separation,
and
no parameters are determined for the purpose of the evaluation,
is an angle-related term;
designing the adaptive controller on the basis that:
wherein the content of the first and second substances,
kxpand kxdFor adaptive controller gain, TαForce in the direction of rotation of the cantilever, FxIs the force in the direction of the trolley.
6. The swing suppression control method of a double-pendulum tower crane with distributed mass load according to claim 5, characterized in that: the fuzzy controller comprises a fuzzy controller which is used for controlling the fuzzy logic unit,
rotating the cantilever by an angle
The error of the translation distance x of the trolley and its error derivative are used as the input of the fuzzy controller, and are distributed in the membership degree range [ -33 ] by different quantization factors]To (c) to (d);
according to expert experience, a membership table and the fuzzy control rule, the area center algorithm is used for defuzzification to obtain a setting parameter
ΔkxpAnd
7. the swing suppression control method of a double-pendulum tower crane with distributed mass load according to claim 6, characterized in that: the adaptive controller gain comprises a gain of the adaptive controller,
wherein the content of the first and second substances,
and
is a controller base parameter.
8. The swing suppression control method of a double-pendulum tower crane with distributed mass load according to claim 7, characterized in that: also comprises the following steps of (1) preparing,
the method comprises the following steps of performing tracking control on a double-pendulum tower crane system by using reference tracks of a cantilever and a trolley, wherein the reference tracks are S-shaped tracks:
wherein χ represents a cantilever rotation angle
Or the trolley is translated by a distance x; q (X)d，q(χ)0And tq(χ)dTarget angle/position, initial angle/position and arrival time of the cantilever and the trolley respectively; chi shaperIndicating the angle of rotation of the cantilever
Or the target position where the trolley is translated a distance x.
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