CN112051738B - Casting crane control method and device, computer readable storage medium - Google Patents
Casting crane control method and device, computer readable storage medium Download PDFInfo
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Abstract
The invention discloses a casting crane control method, a casting crane control device and a computer readable storage medium, wherein the casting crane control method comprises the following steps: constructing a multi-mass-spring-damping model, designing a control method of the ladle crane based on the multi-mass-spring-damping model, fully considering the mass center offset of the shaking liquid and the damping applied to the liquid in the shaking process, and considering the mass part of the shaking liquid, the mass part of the static liquid and the mass of the container, so that the control is more accurate; the global sliding mode controller is constructed by adopting a high-order feedback global dynamic sliding mode surface, high-frequency signals are effectively eliminated according to the characteristic of low frequency passing of a low-pass filter, shaking is eliminated, and therefore all state quantities of the casting crane can be converged more smoothly.
Description
Technical Field
The invention relates to the technical field of automation control, in particular to a casting crane control method and device and a computer readable storage medium.
Background
In a common pendulum model of a casting crane, because the molten liquid and the ladle are regarded as a whole, the influence caused by the mass center offset of the molten liquid and the shaking damping of the molten liquid and the interior of the ladle is ignored; in some control models for ladle cranes, the influence of the damping of the molten metal sloshing is taken into account, but it is neglected that the center of mass of the molten metal shifts during sloshing.
The shaking phenomenon and the mass center offset of the load liquid of the casting crane are difficult to embody in the existing particle model, the liquid shaking is a complex fluid motion phenomenon with strong uncertainty, the liquid shaking phenomenon can be more obvious under the condition of external interference, the control difficulty of the system can be greatly improved, the needed mathematical model is more accurate, and the particle model with fixed mass is difficult to realize. In the existing casting crane model, most models adopt pendulum models with fixed mass, and mass center deviation and shaking damping of load liquid are not considered.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides a control method of the ladle crane, which can fully consider the shaking process of the liquid and the damping received in the shaking process, thereby improving the stability and the control performance of the ladle crane.
The invention also provides an operation control device with the casting crane control method.
The invention also provides a computer readable storage medium with the casting crane control method.
According to the control method of the ladle crane, a multi-mass-spring-damping model is constructed, wherein the multi-mass-spring-damping model comprises the ladle crane, the ladle crane comprises a crane and a container, the crane and the container are connected through a steel rod, the container is filled with liquid, and the liquid is divided into static liquid and a plurality of shaking liquids;
the casting crane control method comprises the following steps:
based on the multi-mass-spring-damping model, calculating to obtain the mass of static liquid, the height of the static liquid, a plurality of spring vibrators, the mass of a plurality of shaking liquid and the height of the plurality of shaking liquid according to the total mass of the liquid, the height of the liquid level of the liquid and the length of a container, wherein the mass of the spring vibrators, the mass of the shaking liquid and the height of the shaking liquid are in one-to-one correspondence;
acquiring system kinetic energy of the casting crane, wherein the system kinetic energy comprises static liquid kinetic energy, shaking liquid kinetic energy, container kinetic energy and crane kinetic energy;
acquiring system potential energy of the casting crane, wherein the system potential energy comprises static liquid potential energy, shaking elastic potential energy and crane potential energy, the static liquid potential energy is obtained according to the mass of the static liquid and the height of the static liquid, the shaking liquid potential energy is obtained according to the mass of the shaking liquid and the height of the shaking liquid, and the shaking elastic potential energy is obtained according to the displacement of the spring vibrator and the shaking liquid;
obtaining a Lagrange operator according to the system kinetic energy and the system potential energy;
obtaining a dissipation energy function according to the mass of the shaking liquid, the spring vibrator and the displacement of the shaking liquid, wherein the displacement of the shaking liquid corresponds to the mass of the shaking liquid;
according to the Lagrange operator and the dissipation energy function, respectively obtaining a first kinetic equation of the casting crane under a transverse generalized coordinate, a second kinetic equation under a steel rod included angle generalized coordinate, and a plurality of third kinetic equations under a plurality of shaking liquid displacement generalized coordinates;
obtaining a system dynamic equation of the casting crane according to the first dynamic equation, the second dynamic equation and a plurality of third dynamic equations;
constructing a global dynamic sliding mode surface;
constructing a low-pass filter, and obtaining a filtered combined external force system equation according to the system dynamics equation and the low-pass filter;
obtaining a global sliding mode control rate according to the combined external force system equation and the global dynamic sliding mode surface;
and controlling the casting crane by adjusting the global sliding mode control rate.
The control method of the casting crane according to the embodiment of the invention has at least the following beneficial effects: a multi-mass-spring-damping model is constructed, a control method of a casting crane is designed based on the multi-mass-spring-damping model, the liquid load is divided into countless mass-spring-damping structures by utilizing the idea of a infinitesimal method, namely, the liquid is divided into static liquid and a plurality of layers of shaking liquid, the mass center deviation of the shaking liquid and the damping applied in the liquid shaking process are fully considered, and the mass of the shaking liquid, the mass of the static liquid and the mass of a steel ladle are considered, so that the control is more accurate; the global sliding mode controller is constructed by adopting a high-order feedback global dynamic sliding mode surface, so that the control of the casting crane can realize the balance control of a second-order feedback system, the convergence rate is very high, and the robustness to external interference signals is very good. In addition, the high-frequency signals generated in the working process of the casting crane are effectively eliminated by means of the low-frequency passing characteristic of the low-pass filter, shaking is effectively eliminated, so that the convergence of each state quantity of the casting crane is smoother, the convergence of each state quantity of the casting crane is ensured to be quicker by the global sliding mode controller, the anti-interference capability of the system is enhanced, and the stability and the control performance of the casting crane are effectively improved.
According to some embodiments of the invention, in the multi-mass-spring-damping model, the total mass of liquid is equal to the sum of the mass of the stationary liquid and the mass of the number of shaking liquids.
According to some embodiments of the invention, the method for obtaining the system kinetic energy of the casting crane further comprises the following steps:
respectively constructing unit vectors along the transverse direction and the longitudinal direction of the multi-mass-spring-damping model;
presetting an origin of coordinates, and obtaining a plurality of vectors of the crane according to the origin of coordinates and the unit vector;
obtaining corresponding velocity vectors according to the vectors;
and acquiring the system kinetic energy of the casting crane according to the speed vector.
According to some embodiments of the invention, the system potential energy is calculated by the formula:
wherein m ispFor the container mass, l is the length of the steel rod, and theta is the length of the steel rod and the vertical directionThe included angle of the direction, b is the height of the centroid of the container relative to the bottom of the container, a is the overall height of the container, and M0For the mass of the stationary liquid, MiFor the shaking of the liquid mass, KiIs the spring vibrator, riDisplacing the sloshing liquid.
According to some embodiments of the invention, the first kinetic equation is:
the second kinetic equation is:
the third kinetic equation is:
wherein x is the lateral displacement length of the crane, M is the crane mass, and M is the crane masspFor container mass, MiFor the shaking liquid mass, MtFor the total mass of the liquid, l is the length of the steel rod, theta is the included angle between the steel rod and the vertical direction, and riFor the displacement of the sloshing liquid, u is the driving force to which the crane is subjected, f is the friction force of the ladle crane, KiIs the spring vibrator, CiIs the liquid viscosity coefficient.
According to some embodiments of the invention, the system dynamics equation is:
wherein the content of the first and second substances,
G(q)∈R5respectively expressed as inertia matrix, centripetal-Heshi moment matrix and gravity matrix, U is the driving force of crane, df∈R5For drag of ladle crane, q ∈ R5Is a state variable of the ladle crane;
the state variable q is:
q＝[x,θ,r1,r2,r3,....,rn]T
wherein x is the length of the transverse displacement of the crane, theta is the included angle between the steel rod and the vertical direction, and riFor the sloshing liquid displacement, i ═ 1,2, 3.
According to some embodiments of the invention, the calculation formula of the global dynamic sliding-mode surface is:
wherein e isεF (t) is a global sliding mode dynamic function, and alpha and beta are undetermined parameters;
the global sliding mode control rate is as follows:
mu and epsilon are control rate parameters, s is the global dynamic sliding mode surface, th(s) is a switching function, and rho is a stabilizing function which enables the global sliding mode control rate u to accord with the Lyapunov stability criterion.
By adopting a global dynamic sliding mode surface with high-order feedback, the global sliding mode controller can realize the balance control of a second-order feedback system and improve the anti-interference capability of the system.
According to some embodiments of the invention, the switching function is calculated by:
wherein s is the global dynamic sliding mode surface, and e is a natural logarithm.
A continuous switching function th(s) is designed to replace a traditional sign function sgn(s), an exponential approaching law is improved, shaking is effectively eliminated, convergence of each state quantity of the casting crane is smoother, the overall sliding mode controller can have a very high convergence speed, good robustness to external interference signals is achieved, and high-frequency shaking of the casting crane in the working process is avoided.
The operation control device according to the embodiment of the second aspect of the present invention comprises at least one control processor, and a memory communicatively connected with the at least one control processor;
wherein the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the ladle crane control method of the first aspect.
The operation control device of the embodiment of the invention at least has the following technical effects: all the advantageous effects of the first aspect of the invention are obtained in that the apparatus of the embodiment of the invention performs the casting crane control method as described in any one of the embodiments of the first aspect of the invention.
A computer-readable storage medium according to an embodiment of the third aspect of the present invention stores computer-executable instructions for causing a computer to perform the ladle crane control method of the first aspect described above.
The computer-readable storage medium according to the embodiment of the invention has at least the following technical effects: all the advantageous effects of the first aspect of the present invention are obtained because the computer-readable storage medium of the embodiment of the present invention executes the casting crane control method as set forth in any one of the embodiments of the first aspect of the present invention.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic flow diagram of a ladle crane control method according to one embodiment of the present invention;
FIG. 2 is a schematic flow diagram of a ladle crane control method of FIG. 1 illustrating the process of obtaining system kinetic energy of a ladle crane;
FIG. 3 is a schematic flow diagram of a foundry crane modeling and controller design in accordance with an embodiment of the present invention;
FIG. 4 is a schematic illustration of a control system for a casting crane according to an embodiment of the present invention;
FIG. 5 is a schematic representation of a multiple mass-spring-damped ladle crane model provided in accordance with an embodiment of the present invention;
fig. 6 is a schematic structural diagram of an operation control device according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, front, rear, left, right, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. If the first and second are described for the purpose of distinguishing technical features, they are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, unless otherwise explicitly limited, terms such as arrangement, installation, connection and the like should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.
A casting crane control method according to an embodiment of the present invention is described below with reference to the accompanying drawings.
As shown in fig. 1 and 5, according to the ladle crane control method of the embodiment of the invention, a multi-mass-spring-damping model is constructed, wherein the multi-mass-spring-damping model comprises a ladle crane, the ladle crane comprises a crane and a container, the crane and the container are connected through a steel rod, the container is filled with liquid, and the liquid is divided into static liquid and a plurality of shaking liquids;
as shown in fig. 1, a foundry crane control method includes:
step S100: based on a multi-mass-spring-damping model, calculating to obtain the mass of static liquid, the height of the static liquid, a plurality of spring vibrators, the mass of shaking liquid and the height of the shaking liquid according to the total mass of the liquid, the height of the liquid level of the liquid and the length of a container, wherein the spring vibrators, the mass of the shaking liquid and the height of the shaking liquid correspond to one another;
step S200: acquiring system kinetic energy of the ladle crane, acquiring system potential energy of the ladle crane, and acquiring Lagrangian operators according to the system kinetic energy and the system potential energy; the system kinetic energy comprises static liquid kinetic energy, shaking liquid kinetic energy, container kinetic energy and crane kinetic energy, the system potential energy comprises static liquid potential energy, shaking elastic potential energy and crane potential energy, the static liquid potential energy is obtained according to the static liquid mass and the static liquid height, the shaking liquid potential energy is obtained according to the shaking liquid mass and the shaking liquid height, and the shaking elastic potential energy is obtained according to the spring oscillator and the shaking liquid displacement;
step S300: obtaining a dissipation energy function according to the mass of the shaking liquid, the spring oscillator and the displacement of the shaking liquid, wherein the displacement of the shaking liquid corresponds to the mass of the shaking liquid;
step S400: according to the Lagrange operator and the dissipation energy function, respectively obtaining a first kinetic equation of the casting crane under a transverse generalized coordinate, a second kinetic equation under a steel rod included angle generalized coordinate and a plurality of third kinetic equations under a plurality of shaking liquid displacement generalized coordinates;
step S500: obtaining a system kinetic equation of the casting crane according to the first kinetic equation, the second kinetic equation and a plurality of third kinetic equations;
step S600: and constructing a global dynamic sliding mode surface, constructing a low-pass filter, obtaining a filtered combined external force system equation according to the system dynamic equation and the low-pass filter, obtaining a global sliding mode control rate according to the combined external force system equation and the global dynamic sliding mode surface, and controlling the casting crane by adjusting the global sliding mode control rate.
In the casting crane, the load is a rigid cuboid container filled with liquid, and deformation of the container caused by liquid impact is not considered when a multi-mass-spring-damping model is constructed. In the transportation process, in order to prevent the load (namely the container and the liquid contained in the container) from rotating, the crane is connected with the load by adopting two steel rods, the connection part is not fixed and can rotate, and the buffering effect of the liquid is facilitated, as shown in figure 5. For liquid shaking, the motion state of the liquid is complex, the liquid level of the liquid shaking and the pressure of the liquid everywhere are difficult to accurately describe, and the center of mass of the liquid is difficult to represent by an accurate mathematical model. To better approximate the true value, the present example uses a multi-mass-spring model to describe the fluidNamely, the liquid shaking system is equivalent to a static liquid mass M0And a series of shaking liquid masses MiAnd spring vibrator KiWherein, a shaking mode pair of liquid has a corresponding spring vibrator KiA shaking liquid mass MiAnd a shaking liquid level hiSpring vibrator KiIs equal to the sloshing modal frequency of the liquid. In the actual molten steel transportation process, the operation is finished indoors, the interference of strong wind is generally avoided, so that the air resistance of the casting crane is usually smaller, the influence of the air resistance can not be considered in modeling, but for the friction force of the casting crane, the mass of a crane and a load is usually larger, so that the friction force of the casting crane cannot be ignored, and the friction force is recorded as f.
The front view of the ladle crane during the movement is shown in fig. 5, the crane moves in the x direction and is driven by a driving force u in the x direction, the mass of the crane is M, the length of the steel rod is l, the included angle between the steel rod and the vertical direction is theta, and the mass of the container is MpThe length of the container is 2d, the overall height of the container is a, and the height of the centroid of the container relative to the bottom surface of the container is b; in the multiple-mass-spring-damping model, the total mass of the liquid is MtThe liquid level height of the liquid is H; the static liquid mass of the static part without shaking of the bottom of the liquid is M0Height of h0(ii) a The mass of the shaking liquid at the shaking part of the liquid is MiHeight of hiCorresponding spring oscillator is KiThe viscosity coefficient of the partial liquid is CiWherein i ═ 1,2,3, …, n;
in the embodiment of the present invention, i is 1,2,3, i is the number of layers of the sloshing liquid in the sloshing part, and it is conceivable that the sloshing liquid may be divided into two layers, four layers, or five layers, in addition to three layers, i is 1,2, 3.
According to the above-described multi-mass-spring-damping model, steps S100 to S600 are performed, as shown in fig. 3.
According to the control method of the ladle crane provided by the embodiment of the invention, a multi-mass-spring-damping model is constructed, the control method of the ladle crane is designed on the basis of the multi-mass-spring-damping model, the liquid load is divided into countless mass-spring-damping structures by utilizing the thought of a infinitesimal method, the mass center offset of the shaking liquid and the damping applied to the liquid in the shaking process are fully considered, and the mass of the shaking liquid mass part, the static liquid mass part and the mass of a container are considered, so that the control is more accurate, as shown in fig. 3; the global sliding mode controller is constructed by adopting a global dynamic sliding mode surface with high-order feedback, so that the global sliding mode controller can realize the balance control of a second-order feedback system and has good robustness on external interference signals. In addition, the high-frequency signals generated in the working process of the ladle crane are effectively eliminated by means of the low-frequency passing characteristic of the low-pass filter, shaking is effectively eliminated, so that the convergence of each state quantity of the ladle crane is smoother, the convergence of each state quantity of the ladle crane is ensured to be quicker by the global sliding mode controller, the anti-interference capability of a system is enhanced, and the stability and the control performance of the ladle crane are effectively improved.
In some embodiments of the invention, in the multiple mass-spring-damping model, the total mass of the liquid is equal to the sum of the mass of the stationary liquid and the mass of the number of sloshing liquids.
Dividing the liquid into a static liquid and a plurality of shaking liquids; the total mass of liquid is equal to the sum of the mass of stationary liquid and the mass of several shaking liquids, i.e.:
wherein, M0For stationary liquid masses, MiFor sloshing the mass of the liquid, i is (1, 2,3, …, n), MtIs the total mass of the liquid;
the centre of mass of the model must be at the same height as the centre of mass of the liquid, i.e. the centre of mass of the model must be at the same height as the centre of mass of the liquid
Wherein h is0At a static liquid level, hiIs the height of the shaking liquid level;
according to the fact that the counter force and the counter moment of the liquid to the container are equal, the following results are obtained:
wherein, KiIs a spring vibrator, the total mass of the liquid is Mt2 ρ dH, H being the liquid level height, the container length 2d,
is the first order rocking modal circular frequency of the liquid.
Based on the motion of the liquid is rocked in a small amplitude, because the container is a rectangular rigid container, under the action of horizontal acceleration, the liquid moves along with the container, and the liquid returns to a balance point again under the action of gravity, so that the liquid is rocked. In order to approach the actual situation as much as possible, it is often required that the equivalent system corresponds to the counter force and counter moment of its actual liquid against the containerWherein the equivalent system is the container and the liquid contained therein, thereby obtaining each parameter of the equivalent system, namely Ki、M0、h0、Mi、hi。
Through the design, the mass of the static liquid, the height of the static liquid, the spring vibrators, the mass of the shaking liquid and the heights of the shaking liquid can be calculated; the shaking liquid is divided into a plurality of layers, and data required by the static liquid part and a series of shaking liquid parts are obtained and applied to subsequent control, so that the control is more accurate.
In some embodiments of the present invention, as shown in fig. 2, the method for capturing the kinetic energy of the ladle crane system further comprises the following steps:
step S210: respectively constructing unit vectors along the transverse direction and the longitudinal direction of the multi-mass-spring-damping model;
step S220: presetting an origin of coordinates, and obtaining a plurality of vectors of the crane according to the origin of coordinates and the unit vector;
step S230: obtaining corresponding velocity vectors according to the plurality of vectors;
step S240: and acquiring the system kinetic energy of the casting crane according to the speed vector.
Constructed unit vectors of respectively
And
and taking the initial position of the crane as a coordinate origin to obtain vector representations of all parts of the crane in the casting crane:
wherein m ispFor the container mass, x is the transverse displacement length of the crane, l is the length of the steel rod, theta is the included angle between the steel rod and the vertical direction, and b is the mass center of the container relative to the bottom of the containerHeight of the section, a being the overall height of the container, M0For static liquid mass, MiTo shake the mass of the liquid, riTo shake the liquid displacement; the shaking liquid displacement is the displacement of the mass center of the shaking liquid relative to the mass center of the shaking liquid in a static state.
According to the vectors of all the parts, obtaining corresponding velocity vectors:
and acquiring the system kinetic energy of the casting crane according to the velocity vector:
wherein M is the crane mass, M1，M2，M3，MiTo shake the mass of the liquid.
Shifting the center of mass of the sloshing liquid, i.e. sloshing liquid displacement riIn consideration of the kinetic energy of the system, the consideration factor is more comprehensive, and the obtained kinetic energy of the system is more accurate. The control error of the casting crane is reduced, and the control stability and accuracy of the casting crane are improved.
In some embodiments of the present invention, the potential energy of the system is calculated by the following formula:
wherein m ispFor the container mass, l is the length of the steel rod, theta is the included angle between the steel rod and the vertical direction, b is the height of the container mass center relative to the container bottom, a is the overall height of the container, and M is the total height of the container0For static liquid mass, MiTo shake the mass of the liquid, KiIs a spring vibrator, riTo shake the liquid displacement.
In some embodiments of the invention, the first kinetic equation is:
the second kinetic equation is:
the third kinetic equation is:
wherein x is the lateral displacement length of the crane, M is the crane mass, and M is the crane masspFor container mass, MiTo shake the mass of the liquid, MtThe total mass of the liquid, l is the length of the steel rod, theta is the included angle between the steel rod and the vertical direction, and r isiFor shaking the liquid displacement, u is the driving force to which the crane is subjected, f is the friction force of the ladle crane, KiIs a spring vibrator, CiIs the liquid viscosity coefficient.
The first kinetic equation, the second kinetic equation and the third kinetic equation are derived from a Lagrange operator and a dissipated energy function.
For better description of the embodiments, i in the present embodiment is 1,2, and 3.
Lagrange operator is L, from system kinetic energy EkAnd system potential energy EpIs obtained by difference of (a), (b) is
Dissipation effect caused by liquid sloshing uses liquid viscosity coefficient CiTo describe, a portion of the kinetic energy of the oscillating liquid is dissipated during each cycle of the oscillation. The dissipation energy function in the liquid shaking process is obtained as follows:
wherein
Ci＝2Miwiζi
In the process of liquid shaking, the center of mass offset distance of the shaking liquid of each layer is riNamely, the liquid displacement is shaken,
a first order rocking modal circular frequency for the liquid; zetaiIs a liquid viscosity coefficient CiSince the Reynolds number of water at normal temperature is almost the same as that of molten iron or molten aluminum at high temperature, ζ is largeriAbout 0.01.
In the lateral generalized coordinates:
solving the L pair
First order partial derivation:
will be provided with
The first derivation of time:
obtaining a first-order partial derivative of L to x
Reusing dissipation function QcTo pair
Obtaining a first order partial derivative
Under the combined action of the driving force u and the friction force f under the transverse generalized coordinate, the motion of the trolley can be directly influenced, and the swinging of a load and the shaking of liquid are indirectly influenced;
is composed of
And formula
From the laplace equation:
i.e. the first kinetic equation.
The following can be obtained by the same method:
kinetic equation under steel rod included angle theta generalized coordinate
Namely a second kinetic equation;
in the shaking liquid displacement r1Kinetic equation in generalized coordinates
Namely a third kinetic equation;
in the shaking liquid displacement r2Kinetic equation in generalized coordinates
Namely a third kinetic equation;
in the shaking liquid displacement r3Kinetic equation in generalized coordinates
I.e. the third kinetic equation.
A dynamic equation of the casting machine system under different generalized coordinates is constructed by utilizing a Lagrange equation, and various factors of the casting crane during working are considered in the dynamic equation of the casting machine system, so that the problem of complex particle system motion is solved, and the control of the casting crane is more accurate and stable.
In some embodiments of the invention, the system dynamics equation is:
wherein the content of the first and second substances,
G(q)∈R5respectively expressed as inertia matrix, centripetal-Heshi moment matrix and gravity matrix, U is the driving force received by crane, df∈R5For drag of ladle crane, q ∈ R5Is a state variable of the ladle crane;
the state variable q is:
q＝[x,θ,r1,r2,r3,....,rn]T
wherein, x is the transverse displacement length of the crane, theta is the included angle between the steel rod and the vertical direction, and riTo shake the liquid displacement, i ═ 1,2, 3.
The above system dynamics equation is in the form of a matrix of the system dynamics equation of the ladle crane, and the derivation process of the system dynamics equation is described below by taking i as 1,2, and 3 as an example:
and integrating the first kinetic equation, the second kinetic equation and three third kinetic equations to obtain a system kinetic equation of the casting crane:
wherein, according to the property of the friction force, the system friction force model is established as follows:
in the formula, frx,εx,krx∈R+Corresponding to the friction factor.
The system dynamics equation is rewritten into a matrix form, so that the following conditions can be obtained:
from the system dynamics equation, we can get:
to M (q) and
after matrix operation, it can be known that:
properties 1: m (q) is a positive definite symmetric matrix;
properties 2:
is a skew symmetric matrix, i.e. satisfies
In some embodiments of the present invention, the calculation formula of the global dynamic sliding mode surface is:
wherein e isεF (t) is a global sliding mode dynamic function, and alpha and beta are undetermined parameters;
the global sliding mode control rate is as follows:
mu and epsilon are control rate parameters, s is a global dynamic sliding mode surface, th(s) is a switching function, and rho is a stabilizing function which enables the global sliding mode control rate u to accord with the Lyapunov stability criterion.
By adopting a global sliding mode surface with high-order feedback, the global sliding mode controller can realize the balance control of a second-order feedback system and improve the anti-interference capability of the system, as shown in fig. 4.
In this embodiment, the target state quantity is set to q ∈ R5×1To obtainTracking error eεIs composed of
eε＝q-qd
f (t) is a global sliding mode dynamic function, and f (t) meets the following three conditions in order to achieve the global sliding mode: (1) when s is 0, t is 0,
(2) when t → ∞ or eε→ 0, f (t) → 0; (3) f (t) has a first derivative. Thus, f (t) can be designed as:
f(t)＝f(0)e-kt
wherein f (0) ═ β eεAnd beta is a parameter to be determined.
For only one driving force (i.e., u), five dimensions (i.e., x, θ, r)1,r2,r3) The design of a controller for effectively realizing accurate positioning and inhibiting load swing and liquid shaking is particularly important for the under-actuated casting crane. As shown in fig. 4, based on property 1 and property 2, a LPF-GSMC (Low Pass Filter-Global Sliding Mode Controller) Controller is designed, so that the system is on the Sliding Mode surface from the beginning, the reaching motion stage of the Sliding Mode control can be eliminated, and the system has robustness in the whole response process. The LPF-GSMC controller is characterized in that a low-pass filter is connected to the output end of the global sliding mode controller, high-frequency signals can be filtered, the effect of effectively inhibiting oscillation is achieved, the crane can reach a required position, and the swing angles of a load and a hook completely disappear at a payload destination.
Similarly, taking i as 1,2, and 3 as an example, the derivation process of the global sliding mode control rate u is described:
the low-pass filter is designed as follows:
wherein s isiIs Laplace operator, gammai>0。
From P(s)i) Performing an inverse laplacian transform to obtain:
wherein the content of the first and second substances,
n is the number of control input signals.
Derived from the system dynamics equation
Wherein τ ∈ R5×1Is a resultant force matrix.
And obtaining a filtered combined external force system equation through the two formulas:
according to the Lyapunov stability criterion, defining a Lyapunov function as:
the first derivative is obtained for V:
according to property 1, m (q) is a positive definite symmetric matrix, and the following results are obtained:
as can be seen from the property 2, the,
is a skew symmetric matrix to obtain：
According to the three formulas, the following are obtained:
obtaining the following according to a resultant external force system equation:
will be provided with
Substitution into
Obtaining:
wherein the content of the first and second substances,
according to the Lyapunov stability criterion, when s is 0, V is 0; in order for the system to reach a stable arrangement, it must be satisfied
Therefore, the global sliding mode control rate is obtained as follows:
casting craneThe bridge crane system is used as a prototype, so the casting crane is a typical underactuated system, and the output parameter is only the crane driving force, therefore,
in some embodiments of the present invention, the switching function is calculated by the following formula:
wherein s is a global dynamic sliding mode surface, and e is a natural logarithm.
A continuous switching function th(s) is designed to replace a traditional sign function sgn(s), an exponential approaching law is improved, shaking is effectively eliminated, convergence of each state quantity of the casting crane is smoother, the overall sliding mode controller can have a very high convergence speed, good robustness to external interference signals is achieved, and high-frequency shaking of the casting crane in the working process is avoided.
In a second aspect of the embodiments of the present invention, an operation control device 6000 is provided, where the operation control device may be any type of intelligent terminal, such as a mobile phone, a tablet computer, a personal computer, and the like.
As shown in fig. 6, according to some embodiments of the present invention, the operation control device 6000 includes: one or more control processors 6001 and a memory 6002, for example control processor 6001 in fig. 6.
The control processor 6001 and memory 6002 might be connected by a bus or otherwise, as exemplified by the connection via a bus in fig. 6.
The memory 6002 serves as a non-transitory computer readable storage medium and can be used for storing non-transitory software programs, non-transitory computer executable programs, and units, such as program instructions/units corresponding to the operation control device 6000 in the embodiment of the present invention. The control processor 6001 executes non-transitory software programs, instructions and units stored in the memory 6002 to perform various functional applications and data processing, i.e., to implement the casting crane control method of the above-described method embodiment.
The memory 6002 may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application program required for at least one function; the storage data area may store data created according to program instructions/units, and the like. Further, the memory 6002 can include high-speed random access memory, and can also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, the memory 6002 may optionally include memory located remotely from the control processor 6001, which may be connected to the operational control apparatus 6000 via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
One or more units are stored in memory 6002 and when executed by one or more control processors 6001 perform a ladle crane control method as in any of the method embodiments described above. For example, the above-described method steps S100 to S600 in fig. 1 and method steps S210 to S240 in fig. 2 are performed.
In a third aspect of the embodiments of the present invention, there is also provided a computer-readable storage medium storing computer-executable instructions, which are executed by one or more control processors 6001, for example, by one control processor 6001 in fig. 6, and which can cause the one or more control processors 6001 to perform the casting crane control method in the above-described method embodiment, for example, the above-described method steps S100 to S600 in fig. 1 and the method steps S210 to S240 in fig. 2.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a general hardware platform, and certainly can also be implemented by hardware. It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware related to instructions of a computer program, and the program can be stored in a computer readable storage medium, and when executed, the program can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (10)
1. A control method of a casting crane is characterized in that a multi-mass-spring-damping model is constructed, wherein the multi-mass-spring-damping model comprises the casting crane, the casting crane comprises a crane and a container, the crane and the container are connected through a steel rod, liquid is filled in the container, and the liquid is divided into static liquid and a plurality of shaking liquids;
the casting crane control method comprises the following steps:
based on the multi-mass-spring-damping model, calculating to obtain the mass of static liquid, the height of the static liquid, a plurality of spring vibrators, the mass of shaking liquid and the height of the shaking liquid according to the total mass of the liquid, the height of the liquid level of the liquid and the length of a container, wherein the spring vibrators, the mass of the shaking liquid and the height of the shaking liquid correspond to one another;
acquiring system kinetic energy of the casting crane, wherein the system kinetic energy comprises static liquid kinetic energy, shaking liquid kinetic energy, container kinetic energy and crane kinetic energy;
acquiring system potential energy of the casting crane, wherein the system potential energy comprises static liquid potential energy, shaking elastic potential energy and crane potential energy, the static liquid potential energy is obtained according to the mass of static liquid and the height of static liquid, the shaking liquid potential energy is obtained according to the mass of shaking liquid and the height of shaking liquid, and the shaking elastic potential energy is obtained according to the displacement of the spring vibrator and the shaking liquid;
obtaining a Lagrange operator according to the system kinetic energy and the system potential energy;
obtaining a dissipation energy function according to the mass of the shaking liquid, the spring vibrator and the displacement of the shaking liquid, wherein the displacement of the shaking liquid corresponds to the mass of the shaking liquid;
according to the Lagrange operator and the dissipation energy function, respectively obtaining a first dynamic equation of the casting crane under a transverse generalized coordinate, a second dynamic equation under a steel rod included angle generalized coordinate and a plurality of third dynamic equations under a plurality of shaking liquid displacement generalized coordinates;
obtaining a system dynamic equation of the casting crane according to the first dynamic equation, the second dynamic equation and a plurality of third dynamic equations;
constructing a global dynamic sliding mode surface;
constructing a low-pass filter, and obtaining a filtered combined external force system equation according to the system dynamics equation and the low-pass filter;
obtaining a global sliding mode control rate according to the combined external force system equation and the global dynamic sliding mode surface;
and controlling the casting crane by adjusting the global sliding mode control rate.
2. Ladle crane control method according to claim 1, wherein in the multi-mass-spring-damping model the total liquid mass is equal to the sum of the static liquid mass and a number of sloshing liquid masses.
3. The ladle crane control method as recited in claim 1, wherein the capturing of the system kinetic energy of the ladle crane further comprises the steps of:
respectively constructing unit vectors along the transverse direction and the longitudinal direction of the multi-mass-spring-damping model;
presetting an origin of coordinates, and obtaining a plurality of vectors of the crane according to the origin of coordinates and the unit vector;
obtaining corresponding velocity vectors according to the vectors;
and acquiring the system kinetic energy of the casting crane according to the speed vector.
4. The ladle crane control method as recited in claim 1, wherein the system potential energy is calculated by the formula:
wherein m ispFor the mass of the container, l is the length of the steel rod, theta is an included angle between the steel rod and the vertical direction, b is the height of the mass center of the container relative to the bottom of the container, a is the integral height of the container, and M is the total height of the container0For the mass of the stationary liquid, MiFor the shaking of the liquid mass, KiIn order to provide the spring oscillator with a high frequency,rifor the displacement of the shaking liquid, h0Is the static liquid height, hiG is the gravity coefficient for the height of the shaking liquid.
5. The ladle crane control method as recited in claim 1, wherein the first kinetic equation is:
the second kinetic equation is:
wherein x is the lateral displacement length of the crane, M is the crane mass, and M is the crane masspIs the mass of the container, NiFor the shaking liquid mass, MtFor the total mass of the liquid, l is the length of the steel rod, theta is the included angle between the steel rod and the vertical direction, and riFor the displacement of the sloshing liquid, u is the driving force to which the crane is subjected, f is the friction force of the ladle crane, KiIs the spring vibrator, CiIs the liquid viscosity coefficient.
6. Method for controlling a ladle crane, according to claim 1 or 5, wherein the system dynamics equation is:
wherein the content of the first and second substances,
G(q)∈R5respectively expressed as inertia matrix, centripetal-Heshi moment matrix and gravity matrix, U is the driving force of crane, df∈R5For drag of ladle crane, q ∈ R5Is a state variable of the ladle crane;
the state variable q is:
q＝[x,θ,r1,r2,r3,....,rn]T
wherein, x is the transverse displacement length of the crane, theta is the included angle between the steel rod and the vertical direction, and riFor the sloshing fluid displacement, i ═ 1,2, 3.
7. Ladle crane control method according to claim 6, wherein the global dynamic sliding-mode surface is calculated by the formula:
wherein e isεF (t) is a global sliding mode dynamic function, and alpha and beta are undetermined parameters;
the global sliding mode control rate is as follows:
mu and epsilon are control rate parameters, s is the global dynamic sliding mode surface, th(s) is a switching function, and rho is a stabilizing function which enables the global sliding mode control rate u to accord with the Lyapunov stability criterion.
8. Ladle crane control method according to claim 7, wherein the switching function is calculated by the formula:
wherein s is the global dynamic sliding mode surface, and e is a natural logarithm.
9. An operation control device characterized by comprising:
at least one control processor, and a memory communicatively coupled to the at least one control processor;
wherein the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the ladle crane control method as claimed in any one of claims 1 to 8.
10. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the foundry crane control method of any one of claims 1 to 8.
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