CN112068428B - Design method and system of double-pendulum PI type Terminal sliding mode controller of bridge crane - Google Patents

Design method and system of double-pendulum PI type Terminal sliding mode controller of bridge crane Download PDF

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CN112068428B
CN112068428B CN202010896056.5A CN202010896056A CN112068428B CN 112068428 B CN112068428 B CN 112068428B CN 202010896056 A CN202010896056 A CN 202010896056A CN 112068428 B CN112068428 B CN 112068428B
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sliding mode
terminal sliding
double
pendulum
bridge crane
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CN112068428A (en
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王天雷
邱炯智
徐进钊
张京玲
张昕
李秀平
黄锦涛
赖远钦
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Wuyi University
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Abstract

The invention discloses a design method and a system for a double-pendulum PI type Terminal sliding mode controller of a bridge crane, wherein the design method comprises the following steps: defining a double-pendulum model of a bridge crane system; introducing a composite signal; defining a PI type deviation signal as a difference value between an expected track of the trolley and a composite signal; defining a Terminal sliding mode surface according to the PI type deviation signal; defining a nominal model according to a double-pendulum model of a bridge crane system; and obtaining the PI type Terminal sliding mode controller according to the Terminal sliding mode surface and the nominal model. By adopting a double-pendulum model, the sliding mode surface is converged in limited time, and the convergence time can be predicted; by introducing the composite signal, the coupling relation between trolley displacement and a swing angle of a lifting hook and a swing angle of a load is enhanced, the steady-state performance of a control system is ensured, the strong coupling of an underactuated nonlinear system is fully considered, and a better control effect is easily obtained in engineering application; by adopting a design method of a nominal model, the method has stronger robustness to external interference, parameter perturbation and unmodeled states.

Description

Design method and system of double-pendulum PI type Terminal sliding mode controller of bridge crane
Technical Field
The invention relates to the field of bridge cranes, in particular to a design method and a system of a double-pendulum PI type Terminal sliding mode controller of a bridge crane.
Background
The bridge crane system is a typical under-actuated system, wherein the under-actuated system is a nonlinear system with the number of control inputs less than the number of degrees of freedom, namely the control input dimension of the system is less than the dimension of a system configuration space, and the system has the advantages of compact structure, flexibility in movement, low cost, low energy consumption, light weight and the like. The control problem of the under-actuated bridge crane is concerned by numerous scholars at home and abroad, and a plurality of important research results are obtained. However, so far, some difficulties still remain to be solved.
At present, parameters of a bridge crane system have certain coupling, but a bridge crane sliding mode controller does not effectively utilize the coupling relation of state quantity, so that the adjustment process of the parameters is complex and tedious, the control effect is poor, the steady state performance of the control system cannot be ensured, the robustness to external interference, parameter perturbation and an un-built mode is poor, a sliding mode surface cannot be converged in limited time, and the convergence time cannot be predicted.
Disclosure of Invention
The invention aims to at least solve one of the technical problems in the prior art, and provides a design method and a system for a double-pendulum PI type Terminal sliding mode controller of a bridge crane, which can predict convergence time, ensure the steady-state performance of a control system and have stronger robustness.
The solution of the invention for solving the technical problem is as follows:
in a first aspect, the invention provides a design method of a double-pendulum PI type Terminal sliding mode controller of a bridge crane, which comprises the following steps:
defining a double-pendulum model of a bridge crane system;
introducing a composite signal;
defining a PI type deviation signal as a difference value between the expected track of the trolley and the composite signal;
defining a Terminal sliding mode surface according to the PI type deviation signal;
defining a nominal model according to the double-pendulum model of the bridge crane system;
and obtaining the PI type Terminal sliding mode controller according to the Terminal sliding mode surface and the nominal model.
Further, the composite signal is specifically:
Figure BDA0002658490910000021
wherein, delta (t) is a composite signal, alpha and beta are positive controller gains, x is trolley displacement, theta is a swing angle of a lifting hook,
Figure BDA0002658490910000022
is the load swing angle.
Further, the Terminal sliding mode surface is specifically as follows:
Figure BDA0002658490910000023
wherein s (t) is a Terminal sliding mode surface, ζ is a PI type deviation signal,
Figure BDA0002658490910000024
is the first derivative of ζ, γ1And gamma2Is a positive constant, q and p are odd numbers, and 0<p<2q。
Further, the nominal model specifically includes:
Figure BDA0002658490910000025
wherein q is a state vector
Figure BDA0002658490910000026
Is the first derivative of q and is,
Figure BDA0002658490910000027
is the second derivative of q, M0(q) is an approximation of the positive constant mass inertia matrix M (q),
Figure BDA0002658490910000028
is a centrifugal force matrix
Figure BDA0002658490910000029
Of the approximation matrix, G0(q) is an approximation matrix of the gravity vector G (q), Δ M is the modeling error of M (q), Δ C is
Figure BDA00026584909100000210
Δ G is the modeling error of G (q).
Further, the PI type Terminal sliding mode controller is specifically:
Figure BDA00026584909100000211
wherein M is0Being a positive constant mass inertia matrix M (q)Approximation matrix, C0Is a centrifugal force matrix
Figure BDA00026584909100000212
Of the approximation matrix, G0Is an approximate matrix of gravity vector g (q),
Figure BDA00026584909100000213
is the sliding mode surface vector χ and the first derivative of the state vector
Figure BDA00026584909100000214
The sum of (a) and (b),
Figure BDA00026584909100000215
as the first derivative of the sliding-mode surface vector
Figure BDA00026584909100000216
Second derivative of sum state vector
Figure BDA00026584909100000217
Of sliding mode surface vector χ is [ s 00 ]]TS is a Terminal slip form surface, KpEta is positive control gain, KiFor the controller gain, Λ is [ 100 ]]T。
Further, obtaining a PI type Terminal sliding mode controller according to the Terminal sliding mode surface and the nominal model, and the PI type Terminal sliding mode controller comprises the following steps:
obtaining an initialization controller according to the Terminal sliding mode surface and the nominal model;
and using a tanh function in the initialization controller to obtain the PI type Terminal sliding mode controller.
In a second aspect, the invention provides a double-pendulum PI type Terminal sliding mode controller for a bridge crane, which specifically comprises:
Figure BDA0002658490910000031
wherein M is0Is an approximation matrix of the positive constant mass inertia matrix M (q), C0As a centrifugal forceMatrix array
Figure BDA0002658490910000032
Of the approximation matrix, G0Is an approximate matrix of gravity vector g (q),
Figure BDA0002658490910000033
is the sliding mode surface vector χ and the first derivative of the state vector
Figure BDA0002658490910000034
The sum of (a) and (b),
Figure BDA0002658490910000035
as the first derivative of the sliding-mode surface vector
Figure BDA0002658490910000036
Second derivative of sum state vector
Figure BDA0002658490910000037
Of sliding mode surface vector χ is [ s 00 ]]TS is a Terminal slip form surface, KpEta is positive control gain, KiFor the controller gain, Λ is [ 100 ]]T。
Further, the Terminal sliding mode surface is specifically as follows:
Figure BDA0002658490910000038
wherein s (t) is a Terminal sliding mode surface, ζ is a PI type deviation signal,
Figure BDA0002658490910000039
is the first derivative of ζ, γ1And gamma2Is a positive constant, q and p are odd numbers, and 0<p<2q；
The PI type deviation signal is specifically:
Figure BDA00026584909100000310
where ζ (t) is a PI type deviation signal, pd(t) is the expected track of the trolley, and delta (t) is a composite signal;
the composite signal is specifically:
Figure BDA00026584909100000311
wherein, delta (t) is a composite signal, alpha and beta are positive controller gains, x is trolley displacement, theta is a swing angle of a lifting hook,
Figure BDA00026584909100000312
is the load swing angle.
In a third aspect, the invention provides a bridge crane double-pendulum PI type Terminal sliding mode controller design system, which comprises at least one control processor and a memory, wherein the memory is used for being in communication connection with the at least one control processor; the memory stores instructions executable by the at least one control processor to enable the at least one control processor to perform the bridge crane double pendulum PI Terminal sliding mode controller design method as described above.
In a fourth aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions for causing a computer to execute the method for designing a double-pendulum PI type Terminal sliding mode controller for a bridge crane as described above.
In a fifth aspect, the present invention also provides a computer program product comprising a computer program stored on a computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, cause the computer to perform the bridge crane double pendulum PI type Terminal sliding mode controller design method as described above.
One or more technical schemes provided in the embodiment of the invention have at least the following beneficial effects: the invention provides a design method and a system for a bridge crane double-pendulum PI type Terminal sliding mode controller, wherein a double-pendulum model is adopted, so that the time for a system state to reach a sliding mode surface can be calculated, the sliding mode surface is converged in limited time, and the convergence time can be predicted; by introducing the composite signal, the coupling relation between trolley displacement and a swing angle of a lifting hook and a swing angle of a load is enhanced, the steady-state performance of a control system is ensured, the strong coupling of an underactuated nonlinear system is fully considered, and a better control effect is easily obtained in engineering application; by adopting a design method of a nominal model, the method has stronger robustness to external interference, parameter perturbation and unmodeled states.
Drawings
The invention is further described with reference to the accompanying drawings and examples;
FIG. 1 is a schematic diagram of a bridge crane according to a first embodiment of the present invention, wherein the bridge crane is a double-pendulum PI type Terminal sliding mode controller design method;
FIG. 2 is a flow chart of a design method of a double-pendulum PI type Terminal sliding mode controller of a bridge crane according to a first embodiment of the invention;
FIG. 3 is a system block diagram of a design method of a double-pendulum PI type Terminal sliding-mode controller of a bridge crane according to a first embodiment of the invention;
FIG. 4 is a flowchart illustrating a specific method of step S600 in a method for designing a double-pendulum PI type Terminal sliding mode controller for a bridge crane according to a first embodiment of the present invention;
FIG. 5 is a schematic structural diagram of a design system of a double-pendulum PI type Terminal sliding-mode controller of a bridge crane according to a third embodiment of the invention;
reference numbers in the figures:
the system comprises a 100-bridge crane double-pendulum PI type Terminal sliding mode controller design system, a 110-control processor and a 120-memory.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
It should be noted that, if not conflicted, the various features of the embodiments of the invention may be combined with each other within the scope of protection of the invention. Additionally, while functional block divisions are performed in apparatus schematics, with logical sequences shown in flowcharts, in some cases, steps shown or described may be performed in sequences other than block divisions in apparatus or flowcharts.
In a first embodiment of the present invention, as shown in fig. 1 to 3, a flow chart of a method for designing a double-pendulum PI-type Terminal sliding mode controller of a bridge crane, which may also be executed by a system for designing a double-pendulum PI-type Terminal sliding mode controller of a bridge crane, specifically includes:
s100, defining a double-pendulum model of the bridge crane system;
s200, introducing a composite signal;
s300, defining a PI type deviation signal as a difference value between the expected track of the trolley and the composite signal;
s400, defining a Terminal sliding mode surface according to the PI type deviation signal;
s500, defining a nominal model according to a double-pendulum model of the bridge crane system;
s600, obtaining the PI type Terminal sliding mode controller according to the Terminal sliding mode surface and the nominal model.
The composite signal is specifically:
Figure BDA0002658490910000061
wherein, delta (t) is a composite signal, alpha and beta are positive controller gains, x is trolley displacement, theta is a swing angle of a lifting hook,
Figure BDA0002658490910000062
is the load swing angle.
The Terminal sliding mode surface specifically comprises the following steps:
Figure BDA0002658490910000063
wherein s (t) is a Terminal sliding formAnd ζ is a PI type deviation signal,
Figure BDA0002658490910000064
is the first derivative of ζ, γ1And gamma2Is a positive constant, q and p are odd numbers, and 0<p<2q。
The nominal model is specifically as follows:
Figure BDA0002658490910000065
wherein q is a state vector
Figure BDA0002658490910000066
Is the first derivative of q and is,
Figure BDA0002658490910000067
is the second derivative of q, M0(q) is an approximation of the positive constant mass inertia matrix M (q),
Figure BDA0002658490910000068
is a centrifugal force matrix
Figure BDA0002658490910000069
Of the approximation matrix, G0(q) is an approximation matrix of the gravity vector G (q), Δ M is the modeling error of M (q), and Δ G is
Figure BDA00026584909100000610
Δ G is the modeling error of G (q).
The PI type Terminal sliding mode controller comprises the following specific steps:
Figure BDA00026584909100000611
wherein M is0An approximation matrix, C, for the positive constant mass inertia matrix M (q)0Is a centrifugal force matrix
Figure BDA00026584909100000612
Of the approximation matrix, G0Is an approximate matrix of gravity vector g (q),
Figure BDA00026584909100000613
is the sliding mode surface vector χ and the first derivative of the state vector
Figure BDA00026584909100000614
The sum of (a) and (b),
Figure BDA00026584909100000615
as the first derivative of the sliding-mode surface vector
Figure BDA00026584909100000616
Second derivative of sum state vector
Figure BDA00026584909100000617
Of sliding mode surface vector χ is [ s 00 ]]TS is a Terminal slip form surface, KpEta is positive control gain, KiFor the controller gain, Λ is [ 100 ]]T。
In specific practice, the dynamic equation of the double-pendulum model of the bridge crane system is specifically as follows:
Figure BDA00026584909100000618
Figure BDA00026584909100000619
Figure BDA00026584909100000620
Figure BDA0002658490910000071
wherein m istIs the mass of the trolley, mhIs the mass of the hook, mpFor loading mass,/1Is the length of the lifting rope，l2The distance between the hook and the center of gravity of the load,
Figure BDA0002658490910000072
is the swing angle of the hook with respect to the vertical direction (i.e. the hook swing angle),
Figure BDA0002658490910000073
is the swing angle of the load about the vertical direction (i.e., the load swing angle), u is the driving force of the trolley in the horizontal direction, f is the friction force between the trolley and the track, ωtIs the air resistance, omega, to the trolleyhThe air resistance, omega, to the hookpIs the air resistance borne by the load, and g is the gravity acceleration;
from equations (1) to (3), the kinetic equations in matrix form are obtained as follows:
Figure BDA0002658490910000074
wherein M (q) ═ MT(q)∈R3x3Is a positive fixed mass inertia matrix;
Figure BDA0002658490910000075
representing a matrix of coriolis forces, centrifugal forces; g (q) ε R3Denotes the gravity vector, U ∈ R3Which represents the vector of the control force,
Figure BDA0002658490910000076
for the state vector, the specific definition is as follows:
Figure BDA0002658490910000077
Figure BDA0002658490910000078
Figure BDA0002658490910000079
Figure BDA00026584909100000710
the following properties are obtained by the double-pendulum dynamic system of the bridge crane to be underactuated: property 1, m (q) is a symmetric positive definite matrix; the properties of the glass are 2,
Figure BDA00026584909100000711
is an antisymmetric matrix;
introducing a composite signal, specifically:
Figure BDA00026584909100000712
the control method is used for improving the control performance of the double-pendulum system of the bridge crane, and is particularly used for enhancing the coupling relation between trolley displacement and a swing angle of a lifting hook and a swing angle of a load;
thus, a PI type deviation signal is constructed, specifically:
Figure BDA00026584909100000713
thereby obtaining the first derivative of the PI type deviation signal
Figure BDA0002658490910000081
Second derivative of sum PI type deviation signal
Figure BDA0002658490910000082
Thereby defining a Terminal sliding mode surface, specifically:
Figure BDA0002658490910000083
the matrix of the nominal model includes:
M(q)＝M0(q)+ΔM (13)，
Figure BDA0002658490910000084
G(q)＝G0(q)+ΔG (15)，
the equations (13) to (15) are equivalent to the equations (5) to (7), and the accurate values cannot be obtained due to the influence of parameter perturbation, non-constructed mode and external interference, and the approximate value M is used0(q)、
Figure BDA0002658490910000085
G0(q) and modeling errors Δ M, Δ C, Δ G, establishing a model as accurate as possible, which is obtained by equation (4):
Figure BDA0002658490910000086
wherein the content of the first and second substances,
Figure BDA0002658490910000087
Figure BDA0002658490910000088
Figure BDA0002658490910000089
the design steps of the PI type Terminal sliding mode controller are as follows:
defining the Lyapunov energy function V (t) as follows:
Figure BDA00026584909100000810
wherein, Ki∈R+For controller gain, χ is the sliding mode surface vector;
a slip form surface vector χ, specifically:
Figure BDA00026584909100000811
the first derivative of the Lyapunov energy function v (t) with respect to time is:
Figure BDA0002658490910000091
from property 2 it can be deduced:
Figure BDA0002658490910000092
by substituting formula (23) into formula (22), the following can be obtained:
Figure BDA0002658490910000093
defining an auxiliary state vector:
Figure BDA0002658490910000094
Figure BDA0002658490910000095
equation (4) can be expressed as:
Figure BDA0002658490910000096
after finishing, the following equation is obtained:
Figure BDA0002658490910000097
this formula (28) is substituted into formula (24) to obtain:
Figure BDA0002658490910000098
after expansion based on the nominal model by equations (29) and (16), we obtain:
Figure BDA0002658490910000099
in order to ensure the asymptotic stability of the control system in accordance with Lyapunov, the PI type Terminal sliding mode controller is designed as follows:
Figure BDA00026584909100000910
it can be understood that a control system is designed by using a bridge crane double-pendulum PI type Terminal sliding mode controller;
the control system conforms to asymptotic stability in the Lyapunov sense, and the controller is as follows:
Figure BDA0002658490910000101
wherein, Kp,η∈R+Control gain, which is both positive, and Λ is defined as:
Figure BDA0002658490910000102
the controller (31) is replaced in an equation (29), and after simplification:
Figure BDA0002658490910000103
if the positive control gain eta is larger than the modeling error influence
Figure BDA0002658490910000104
Then the
Figure BDA0002658490910000105
Is semi-negative, i.e., v (t) decreases monotonically, so the closed-loop control system is stable in the Lyapunov sense;
the slip-form surfaces converge in a limited time, which proves to be as follows:
from equation (12) for the Terminal sliding mode surface, it can be seen that when the system is in the sliding mode dynamic state, i.e., s (t) is 0, there are:
Figure BDA0002658490910000106
the following auxiliary signal y (t) ═ ζ (t) is defined1-q/pI.e. by
Figure BDA0002658490910000107
Then the following results are obtained:
Figure BDA0002658490910000108
the general solution of the first order linear differential equation is:
Figure BDA0002658490910000109
when t is 0, C is y (0) ζ (0)1-q/pObtaining:
Figure BDA00026584909100001010
when ζ is equal to 0, y is equal to 0, and T is equal to T, the control target indicated by the composite signal is achieved, and the simplified formula is obtained:
Figure BDA00026584909100001011
namely:
Figure BDA0002658490910000111
time for the system to converge from an arbitrary initial state s (0) ≠ 0 to an equilibrium state s ═ 0 on the sliding mode:
Figure BDA0002658490910000112
thus, the initial state is
Figure BDA0002658490910000113
When the time reaches the sliding mode surface s (t) is 0, namely the control system converges in a limited time, and the convergence time can be predicted;
by adopting a double-pendulum model, the time for the system state to reach the sliding mode surface can be calculated, and the coupling relation among trolley displacement, a lifting hook pendulum angle and a load pendulum angle is enhanced by introducing a composite signal, so that the steady-state performance of a control system is ensured, the strong coupling of an underactuated nonlinear system is fully considered, and a better control effect is easily obtained in engineering application; by adopting a design method of a nominal model, the method has stronger robustness to external interference, parameter perturbation and unmodeled states.
As shown in fig. 4, step S600 includes:
s610, obtaining an initialization controller according to the Terminal sliding mode surface and the nominal model;
and S620, using a tanh function in the initialization controller to obtain the PI type Terminal sliding mode controller.
It can be understood that equation (31) is an initialization controller, and in the initialization controller, a tanh function is used to obtain the PI type Terminal sliding mode controller, where the tanh function is a hyperbolic tangent function, and has the characteristic of continuous smoothness, and can weaken the shake phenomenon existing in the sliding mode control process, and the PI type Terminal sliding mode controller is specifically shown as follows:
Figure BDA0002658490910000114
in a second embodiment of the present invention, a double-pendulum PI type Terminal sliding mode controller for a bridge crane specifically includes:
Figure BDA0002658490910000115
wherein M is0Is an approximation matrix of the positive constant mass inertia matrix M (q), C0Is a centrifugal force matrix
Figure BDA0002658490910000116
Of the approximation matrix, G0Is an approximate matrix of gravity vector g (q),
Figure BDA0002658490910000117
is the sliding mode surface vector x and the first derivative of the state vector
Figure BDA0002658490910000118
The sum of (a) and (b),
Figure BDA0002658490910000119
as the first derivative of the sliding-mode surface vector
Figure BDA00026584909100001110
Second derivative of sum state vector
Figure BDA00026584909100001111
Of sliding mode surface vector χ is [ s 00 ]]TS is Terminal slip form surface, KpEta is positive control gain, KiFor the controller gain, Λ is [ 100 ]]T。
The Terminal slip form surface specifically comprises:
Figure BDA0002658490910000121
wherein s (t) is a Terminal sliding mode surface, ζ is a PI type deviation signal,
Figure BDA0002658490910000125
is the first derivative of ζ, γ1And gamma2Is a positive constant, q and p are odd numbers, and 0<p<2q；
The PI type deviation signal is specifically:
Figure BDA0002658490910000122
where ζ (t) is a PI type deviation signal, pd(t) is the expected track of the trolley, and delta (t) is a composite signal;
the composite signal is specifically:
Figure BDA0002658490910000123
wherein, delta (t) is a composite signal, alpha and beta are positive controller gains, x is trolley displacement, theta is a swing angle of a lifting hook,
Figure BDA0002658490910000124
is the load swing angle.
It can be understood that, since the design method of the double-pendulum PI-type Terminal sliding mode controller for the bridge crane in the present embodiment is based on the same inventive concept as the design method of the double-pendulum PI-type Terminal sliding mode controller for the bridge crane, the corresponding contents in the method embodiment are also applicable to the present embodiment, and are not described in detail herein.
In the third embodiment of the present invention, as shown in fig. 5, the bridge crane double-pendulum PI-type Terminal sliding mode controller design system 100 may be any type of intelligent Terminal, such as a mobile phone, a tablet computer, a personal computer, and the like.
Specifically, the bridge crane double-pendulum PI type Terminal sliding mode controller design system 100 includes: one or more control processors 110 and memory 120, one control processor 110 being exemplified in fig. 5.
The control processor 110 and the memory 120 may be connected by a bus or other means, and fig. 5 illustrates the connection by a bus as an example.
The memory 120 is a non-transitory computer readable storage medium, and can be used to store non-transitory software programs, non-transitory computer executable programs, and modules, such as program instructions/modules corresponding to the design method of the double-pendulum PI type Terminal sliding mode controller of the bridge crane in the embodiment of the present invention, for example, the receiving module 110 and the processing module 120 shown in fig. 5. The control processor 110 implements the bridge crane double pendulum PI type Terminal sliding mode controller design method of the above-described method embodiments by running non-transitory software programs, instructions, and modules stored in the memory 120.
The memory 120 may include a storage program area and a storage data area, wherein the storage program area may store an operation method, an application program required for at least one function; the storage data area may store data created using the same, and the like. Further, the memory 120 may include high speed random access memory, and may 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 120 optionally includes memory remotely located from the control processor 110, and these remote memories may be connected to the overhead crane double-swing PI type Terminal sliding mode controller design system 100 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 modules are stored in the memory 120, and when executed by the one or more control processors 110, perform the bridge crane double pendulum PI type Terminal sliding mode controller design method in the above-described method embodiment, for example, perform the above-described method steps S100 to S600 in fig. 2, and the method steps S610 to S620 in fig. 4.
Embodiments of the present invention further provide a computer-readable storage medium, which stores computer-executable instructions, which are executed by one or more control processors 110, for example, by one control processor 110 in fig. 5, and can cause the one or more control processors 110 to execute the method for designing a bridge crane double pendulum PI type Terminal sliding mode controller in the above method embodiment, for example, execute the above-described method steps S100 to S600 in fig. 2, and the method steps S610 to S620 in fig. 4.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, may be located in one place, or may be distributed over a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment.
Through the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be implemented by software plus a general hardware platform. Those skilled in the art will appreciate that all or part of the processes of the methods of the above embodiments may be implemented by hardware related to instructions of a computer program, which may be stored in a computer readable storage medium, and when executed, may 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.
While the preferred embodiments of the present invention have been described in detail, it will be understood by those skilled in the art that the foregoing and various other changes, omissions and deviations in the form and detail thereof may be made without departing from the scope of this invention.

Claims (9)

1. A design method of a double-pendulum PI type Terminal sliding mode controller of a bridge crane is characterized by comprising the following steps:
defining a double-pendulum model of a bridge crane system;
introducing a composite signal;
defining a PI type deviation signal as a difference value between the expected track of the trolley and the composite signal;
defining a Terminal sliding mode surface according to the PI type deviation signal;
defining a nominal model according to the double-pendulum model of the bridge crane system;
obtaining a PI type Terminal sliding mode controller according to the Terminal sliding mode surface and the nominal model;
the PI type Terminal sliding mode controller specifically comprises the following components:
Figure FDA0003520425630000011
wherein M is0Is an approximation matrix of the positive constant mass inertia matrix M (q), C0Is a centrifugal force matrix
Figure FDA0003520425630000012
Of the approximation matrix, G0Is an approximate matrix of gravity vector g (q),
Figure FDA0003520425630000013
is the sliding mode surface vector χ and the first derivative of the state vector
Figure FDA0003520425630000014
The sum of (a) and (b),
Figure FDA0003520425630000015
as the first derivative of the sliding-mode surface vector
Figure FDA0003520425630000016
Second derivative of sum state vector
Figure FDA0003520425630000017
Of sliding mode surface vector χ is [ s 00 ]]TS is a Terminal slip form surface, KpEta is positive control gain, KiFor the controller gain, Λ is [ 100 ]]T。
2. The design method of the double-pendulum PI type Terminal sliding-mode controller of the bridge crane according to claim 1, wherein the composite signal is specifically:
Figure FDA0003520425630000018
wherein, delta (t) is a composite signal, alpha and beta are positive controller gains, x is trolley displacement, theta is a swing angle of a lifting hook,
Figure FDA0003520425630000019
is the load swing angle.
3. The design method of the double-pendulum PI type Terminal sliding mode controller of the bridge crane according to claim 1, wherein the Terminal sliding mode surface is specifically as follows:
Figure FDA00035204256300000110
wherein s (t) is a Terminal sliding mode surface, ζ is a PI type deviation signal,
Figure FDA00035204256300000111
is the first derivative of ζ, γ1And gamma2Is a positive constant, q and p are odd numbers, and 0<p<2q。
4. The design method of the double-pendulum PI type Terminal sliding-mode controller of the bridge crane according to claim 1, wherein the nominal model is specifically as follows:
Figure FDA0003520425630000021
wherein q is a state vector [ x, θ, φ [ ]]T，
Figure FDA0003520425630000022
Is the first derivative of q and is,
Figure FDA0003520425630000023
is the second derivative of q, M0(q) is an approximation of the positive constant mass inertia matrix M (q),
Figure FDA0003520425630000024
is a centrifugal force matrix
Figure FDA0003520425630000025
Of the approximation matrix, G0(q) is an approximation matrix of the gravity vector G (q), Δ M is the modeling error of M (q), and Δ C is
Figure FDA0003520425630000026
Δ G is the modeling error of G (q).
5. The design method of the double-pendulum PI type Terminal sliding mode controller of the overhead traveling crane as claimed in claim 1, wherein the PI type Terminal sliding mode controller is obtained according to the Terminal sliding mode surface and the nominal model, and comprises the following steps:
obtaining an initialization controller according to the Terminal sliding mode surface and the nominal model;
and in the initialization controller, using a tanh function to obtain a PI type Terminal sliding mode controller.
6. The utility model provides a bridge crane double pendulum PI type Terminal sliding mode controller which characterized in that specifically is:
Figure FDA0003520425630000027
wherein M is0Is an approximation matrix of the positive constant mass inertia matrix M (q), C0Is a centrifugal force matrix
Figure FDA0003520425630000028
Approximate matrix of G0Is an approximate matrix of gravity vector g (q),
Figure FDA0003520425630000029
is the sliding mode surface vector χ and the first derivative of the state vector
Figure FDA00035204256300000210
The sum of (a) and (b),
Figure FDA00035204256300000211
as the first derivative of the sliding-mode surface vector
Figure FDA00035204256300000212
Second derivative of sum state vector
Figure FDA00035204256300000213
Of sliding mode surface vector χ is [ s 00 ]]TS is a Terminal slip form surface, KpEta is positive control gain, KiFor the controller gain, Λ is [ 100 ]]T。
7. The PI type Terminal sliding mode controller for the double-pendulum bridge crane as claimed in claim 6, wherein the Terminal sliding mode surface is specifically as follows:
Figure FDA00035204256300000214
wherein s (t) is a Terminal sliding mode surface, ζ is a PI type deviation signal,
Figure FDA00035204256300000215
is the first derivative of ζ, γ1And gamma2Is a positive constant, q and p are odd numbers, and 0<p<2q；
The PI type deviation signal is specifically:
Figure FDA0003520425630000031
where ζ (t) is a PI type deviation signal, pd(t) is the expected track of the trolley, and delta (t) is a composite signal;
the composite signal is specifically:
Figure FDA0003520425630000032
wherein, delta (t) is a composite signal, alpha and beta are positive controller gains, x is trolley displacement, theta is a swing angle of a lifting hook,
Figure FDA0003520425630000033
is the load swing angle.
8. The utility model provides a bridge crane double pendulum PI type Terminal sliding mode controller design system which characterized in that includes:
at least one processor; and the number of the first and second groups,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the bridge crane double pendulum PI type Terminal sliding mode controller design method of any one of claims 1 to 5.
9. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the method of designing a double-pendulum PI Terminal sliding-mode controller for a bridge crane according to any one of claims 1 to 5.
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