CN114879504B - Self-adaptive nonlinear control method of four-degree-of-freedom marine rotary crane - Google Patents
Self-adaptive nonlinear control method of four-degree-of-freedom marine rotary crane Download PDFInfo
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Abstract
The application discloses a self-adaptive nonlinear control method of a four-degree-of-freedom marine rotary crane, which comprises the steps of establishing a four-degree-of-freedom marine rotary crane mathematical model based on a Lagrange dynamics equation and analyzing characteristics; establishing an energy function of a mathematical model of the marine rotary crane according to the characteristics, and establishing a self-adaptive controller based on the energy function of the mathematical model of the marine rotary crane so as to inhibit external interference and regulate and control the swing inhibition of the marine rotary crane in real time; according to the application, the external disturbance of a crane system can be well restrained by coupling the disturbance generated by the measurable continuous yaw and roll of the ship and combining the self-adaptive control, and meanwhile, the method has a good compensation effect on parameter uncertainty caused by reciprocating transportation in actual operation, and finally, efficient track tracking and swing restraining can be realized, so that the control effect is achieved.
Description
Technical Field
The application relates to the technical field of under-actuated crane system motion control, in particular to a self-adaptive nonlinear control method of a four-degree-of-freedom marine rotary crane.
Background
Most practical physical systems in real life are nonlinear systems. For nonlinear systems, there is currently no viable general processing method. An underactuated system is a special nonlinear system. In particular, under-actuated systems generally have a simpler structure than full-drive systems, which further provides the advantages of greater flexibility, lower manufacturing costs, and lower energy consumption.
With the development of international trade, marine rotary cranes have also been increasingly used. As with land cranes, marine rotary cranes need to ensure positioning accuracy and eliminate the swing angle during transportation. However, unlike land cranes, marine rotary cranes operate under a non-inertial coordinate system. The marine rotating crane is subjected to various disturbances during operation, such as waves, wind directions, etc. In particular, we divide the variables caused by the disturbance of the vessel into roll, pitch, yaw, heave, etc. Because the marine rotary crane has a complex working environment, it is difficult to design a practical controller. Currently, most control methods are only applicable to land-based cranes, and the complexity of the vessel's movements at sea makes it more difficult to stabilize the load. Second, most control algorithms are based on a linearization model of the crane, and once the equilibrium point is deviated, the control performance of the system is severely degraded. At present, the rapid suppression of the swinging of the load becomes a very challenging problem while achieving accurate positioning of the cantilever and the load.
The existing under-actuated crane positioning and swing eliminating control is more aimed at a bridge crane system, even though the multi-degree-of-freedom bridge crane moving in a three-dimensional space still has linear force as the dynamic property of a driving mechanism, the dynamic property is still simple, and the control is convenient, when rotating torque appears in a crane conveying task, for example, the control is aimed at a shipborne rotating crane, which is researched by the application, one direction is the torque in the cantilever amplitude direction, and the other direction is the rotating torque in the cantilever horizontal rotating direction; at this time, due to the participation of centrifugal motion, the dynamic characteristics of the system become very complex, meanwhile, due to the interference of sea wave motion, the load swing characteristics of the crane system are more complex, and in addition, due to the unavoidable occurrence of parameter uncertainty in the process of repeated reciprocating transportation, the designed controller is invalid; for the traditional controller, on one hand, the crane dynamics equation needs to be linearized, so that positioning can be realized only under normal conditions, and once the system is far away from the balance position, the swing inhibition effect cannot reach the expected effect; in addition, the friction force is used as an unavoidable influence factor in the motion, and the feedforward friction model is applied to eliminate the adverse influence, so that the embodiment mainly aims at the problems of track tracking and swing suppression of the four-degree-of-freedom marine rotary crane and provides an adaptive control algorithm; specifically, the energy design self-adaptive controller of the underactuated marine rotary crane system is researched to effectively inhibit the interference of continuous yaw and roll disturbance and the influence of parameter uncertainty of the ship, and finally, efficient track tracking and swing inhibition can be realized.
Disclosure of Invention
This section is intended to outline some aspects of embodiments of the application and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section as well as in the description of the application and in the title of the application, which may not be used to limit the scope of the application.
The present application has been made in view of the above-described problems occurring in the prior art.
Therefore, the application solves the technical problems that: when the continuous yaw and roll disturbance of the ship are received, the load swing characteristic of the ship rotary crane becomes very complex, and in multiple transportation, the problem of uncertain model parameters can be generated, so that a system dynamics model becomes more complex, and the swing of the load can not be quickly restrained while the accurate positioning of a cantilever and the load is realized.
In order to solve the technical problems, the application provides a self-adaptive nonlinear control method of a four-degree-of-freedom marine rotary crane, which comprises the following steps:
establishing a four-degree-of-freedom marine rotary crane mathematical model based on a Lagrangian dynamics equation and analyzing dynamics characteristics of the model;
establishing an energy function of the model according to the mathematical model characteristics of the marine rotary crane, and establishing an adaptive controller and an adaptive law of the marine rotary crane based on the energy function;
and planning a target tracking track of the cantilever based on the self-adaptive law, wherein the target tracking track is used for verifying the effect of the self-adaptive controller on inhibiting the swing angle.
As a preferable mode of the swing suppressing control method of the marine rotary crane according to the present application, wherein: the mathematical model of the marine rotary crane comprises the following steps of The mathematical model of the marine rotary crane has the expression as follows:
G(q)＝[g 1 g 2 g 3 g 4 ] T
τ＝[τ 1 τ 2 0 0] T
τ f ＝[τ 1f τ 2f 0 0] T
q 1 ＝θ 1 -α,q 2 ＝θ 2 -β,q 3 ＝θ 3 -α,q 4 ＝θ 4 -β
wherein ：Ms (q) is an inertial matrix of the marine rotating crane system,is centripetal-Coriolis Li Juzhen, G (q) is a gravity vector, τ is a control input vector, τ f And D is the mechanical friction and wind resistance of the marine rotary crane system respectively, and the amplitude-changing angle and the rotation angle of the cantilever are respectively theta 1 and θ2 The roll angle and yaw angle of the ship are alpha and beta respectively, and the radial swing angle and tangential swing angle of the load are theta respectively 3 and θ4 Q is a new state variable of the system after coupling, q 1 and q2 Q is the amplitude and rotation angle of the coupled cantilever 3 and q4 For the radial and tangential pivot angles of the coupled load, < >>Is the first derivative, +>Is its second derivative; m and M are the mass of the cantilever and the load respectively, L and L are the length of the cantilever and the length of the lifting rope respectively, g is the gravitational acceleration, and tau is the driving force/torque 1 Driving torsion for cantilever amplitude directionMoment τ 2 For driving torque in horizontal rotation direction of cantilever, tau 1f and τ2f Mechanical friction forces in the cantilever amplitude direction and the horizontal rotation direction respectively, d ι (1..4) is an air friction parameter.
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps: its dynamic characteristics include cantilever positioning characteristics and yaw swing characteristics.
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps: the mathematical model of the marine rotary crane further comprises the steps of establishing a friction force feedforward compensation model for eliminating friction force generated by a driving mechanism of the marine rotary crane, and reducing positioning errors caused by the friction force by compensating disturbance generated by the friction force to the system in a forward passage of the system, wherein the friction force feedforward compensation model is expressed as follows:
wherein ,f11 、f 12 、f 21 、f 22 And epsilon is a parameter of a friction force feedforward compensation model, f 11 and f12 The value of (f) corresponds to the maximum static friction force, f 21 and f22 Is the viscous coefficient of friction and epsilon is the static coefficient of friction.
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps: the energy function of the mathematical model of the marine rotating crane comprises,
wherein ：speed signals representing the boom amplitude, horizontal rotation angle, radial and tangential load swing angle, respectively, after coupling, +.>Mgl (1-C) 3 C 4 ) For its load potential energy portion.
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps: the adaptive controller comprises following the dynamics rules of a rotary crane model, designing an error variable and designing the following Lyapunov equation based on the energy function of the marine rotary crane mathematical model:
wherein ：error of cantilever amplitude angle +.>Error of cantilever amplitude rotation angular velocity e 2 ＝q 2 -q 2d Is the error of the rotation angle of the cantilever in the horizontal direction,is the rotation angular velocity error of the cantilever in the horizontal direction.
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps:
also includes applying the equation V to the Lyapunov 1 And (3) conducting derivation:
wherein ：ζ1 T and ζ2 T Is a separate state quantity related term, ψ 1 and ψ2 To be evaluated for uncertain parameter-related items, W 1 and W2 Is an angle-related term;
as a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps:
the adaptive controller is designed as follows:
wherein ,kp1 、k d1 、k p2 and kd2 For adaptive controller gain, τ 1 For cantilever amplitude direction rotation torque τ 2 Is the rotation torque of the cantilever in the horizontal direction,is an uncertainty parameter ψ 1 Is used for the estimation of the estimated value of (a).
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps: the design of the adaptive law of the adaptive controller is as follows:
γ 1 ＝diag{γ 11 γ 12 γ 13 γ 14 γ 15 γ 16 }∈R 6×6
γ 2 ＝diag{γ 21 γ 22 γ 23 γ 24 γ 25 γ 26 γ 27 }∈R 7×7 wherein ,is an uncertainty parameter ψ 1 Estimate of +.>The first derivative of time is achieved by coupling the system state variables +.>The variation of (1) is such that->Can update in real time according to the change condition of system parameters, and gamma 1 and γ2 For positive diagonal matrices, the elements inside are adjustable.
As a preferable scheme of the self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane, the application comprises the following steps: the self-adaptive controller also comprises a step of tracking and controlling a marine rotating crane system by utilizing the reference track of the cantilever, and an S-shaped track for verifying the action of the self-adaptive controller is planned, wherein the S-shaped track is expressed as:
wherein x represents the cantilever amplitude angle q after coupling 1 Or the coupled horizontal rotation angle q 2 ；q(χ) d ，q(χ) 0 and tq(χ)d The boom rise angle and the rotation target angle/position, the initial angle/position and the arrival time, respectively.
The application has the beneficial effects that: according to the application, by coupling measurable ship yaw and roll disturbance and combining self-adaptive control, external disturbance of a crane system can be well restrained, and meanwhile, the method has a good compensation effect on parameter uncertainty caused by reciprocating transportation in actual operation, and finally, efficient track tracking and swing restraining can be realized, so that a control effect is achieved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art. Wherein:
FIG. 1 is an overall flow chart of an adaptive nonlinear control method of a four-degree-of-freedom marine rotary crane according to an embodiment of the present application;
fig. 2 is a schematic diagram of a mathematical model of a rotary crane for a ship according to a first embodiment of the present application;
fig. 3 is a schematic diagram of experimental results of a swing suppression control method of a marine rotary crane according to a second embodiment of the present application;
fig. 4 is a schematic diagram showing experimental results of a comparison controller LQR (linear-hydraulic-regulator) of a swing suppression control method of a marine rotary crane according to a second embodiment of the present application;
fig. 5 is a schematic diagram of an experimental platform of a swing suppression control method for a marine rotary crane according to a second embodiment of the application.
Detailed Description
So that the manner in which the above recited objects, features and advantages of the present application can be understood in detail, a more particular description of the application, briefly summarized above, may be had by reference to the embodiments, some of which are illustrated in the appended drawings. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments of the present application without making any inventive effort, shall fall within the scope of the present application.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application, but the present application may be practiced in other ways other than those described herein, and persons skilled in the art will readily appreciate that the present application is not limited to the specific embodiments disclosed below.
Further, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic can be included in at least one implementation of the application. 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.
While the embodiments of the present application have been illustrated and described in detail in the drawings, the cross-sectional view of the device structure is not to scale in the general sense for ease of illustration, and the drawings are merely exemplary and should not be construed as limiting the scope of the application. In addition, the three-dimensional dimensions of length, width and depth should be included in actual fabrication.
Also in the description of the present application, it should be noted that the orientation or positional relationship indicated by the terms "upper, lower, inner and outer", etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of describing the present application and simplifying the description, and do not indicate or imply that the apparatus or elements 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 application. 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 coupled" should be construed broadly in this disclosure unless otherwise specifically indicated and defined, such as: can be fixed connection, detachable connection or integral connection; it may also be a mechanical connection, an electrical connection, or a direct connection, or may be indirectly connected through an intermediate medium, or may be a communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
Example 1
Referring to fig. 1 and 2, a swing suppressing control method of a marine rotary crane according to a first embodiment of the present application is provided, including:
s1: and establishing a four-degree-of-freedom marine rotary crane mathematical model based on the Lagrangian dynamics equation and analyzing the dynamics characteristics of the model.
Order theEstablishing a mathematical model of the shipborne rotary crane:
G(q)＝[g 1 g 2 g 3 g 4 ] T
τ＝[τ 1 τ 2 0 0] T
τ f ＝[τ 1f τ 2f 0 0] T
q 1 ＝θ 1 -α,q 2 ＝θ 2 -β,q 3 ＝θ 3 -α,q 4 ＝θ 4 -β
wherein ：Ms (q) is an inertial matrix of the marine rotating crane system,is centripetal-Coriolis Li Juzhen, G (q) is a gravity vector, τ is a control input vector, τ f And D is the mechanical friction and wind resistance of the marine rotary crane system respectively, and the amplitude-changing angle and the rotation angle of the cantilever are respectively theta 1 and θ2 The roll angle and yaw angle of the ship are alpha and beta respectively, and the radial swing angle and tangential swing angle of the load are theta respectively 3 and θ4 Q is a new state variable of the system after coupling, q 1 and q2 Q is the amplitude and rotation angle of the coupled cantilever 3 and q4 For the radial and tangential pivot angles of the coupled load, < >>Is the first derivative, +>Is its second derivative; m and M are the mass of the cantilever and the load respectively, L and L are the length of the cantilever and the length of the lifting rope respectively, g is the gravitational acceleration, and tau is the driving force/torque 1 For driving torque in the cantilever amplitude direction, tau 2 For driving torque in horizontal rotation direction of cantilever, tau 1f and τ2f Mechanical friction forces in the cantilever amplitude direction and the horizontal rotation direction respectively, d ι (1..4) is an air friction parameter.
Still further, the mathematical model of the marine rotary crane further comprises the step of establishing a friction force feedforward compensation model for eliminating friction force generated by a driving mechanism of the marine rotary crane, and reducing positioning errors caused by the friction force by compensating disturbance generated by the friction force to the system in a forward passage of the system, wherein the friction force feedforward compensation model is expressed as follows:
wherein ,f11 、f 12 、f 21 、f 22 And epsilon is a parameter of a friction force feedforward compensation model, f 11 and f12 The value of (f) corresponds to the maximum static friction force, f 21 and f22 Is the viscous coefficient of friction and epsilon is the static coefficient of friction.
The inertial matrix of the marine rotary crane system is as follows:
m 12 ＝mLlS 1 S 4
m 13 ＝-mLlS 1-3 C 4
m 14 ＝mLlC 1-3 S 4
m 21 ＝mLlS 1 S 4
m 23 ＝-ml 2 C 3 S 4 C 4 ,
m 24 ＝ml 2 S 3 +mLlC 1 C 4
m 31 ＝-mLlS 1-3 C 4
m 32 ＝-ml 2 C 3 S 4 C 4
m 33 ＝ml 2 C 4 2
m 34 ＝0,
m 41 ＝mLlC 1-3 S 4
m 42 ＝ml 2 S 3 +mLlC 1 C 4
m 43 ＝0
m 44 ＝ml 2
wherein ,mij Representing matrix coordinates, i=1, … 4,j =1, 2 … 4.
Centripetal coriolis Li JuzhenThe following are provided:
c 11 ＝0
c 44 ＝0
wherein cij Representing matrix coordinates, i=1, … 4,j =1, 2 … 4.
Further, according to the mathematical model analysis characteristics of the marine rotary crane, the characteristics specifically include swing characteristics (simple pendulum system), load (rod translation characteristics) and the like.
S2: establishing an energy function of the model according to the mathematical model characteristics of the marine rotary crane, and establishing an adaptive controller and an adaptive law of the marine rotary crane based on the energy function;
the energy function of the mathematical model of the marine rotary crane is as follows:
wherein ：speed signals representing the boom amplitude, horizontal rotation angle, radial and tangential load swing angle, respectively, after coupling, +.>Mgl (1-C) 3 C 4 ) For its load potential energy portion.
The derivation of the energy function in the mathematical model of the marine rotating crane can be simplified as follows:
wherein ,for the amplitude angular rotation speed of the coupled cantilever, < >>For the horizontal rotation speed of the coupled cantilever, < >>For the angular velocity of its load.
Further, following the dynamics rules of the rotary crane model, and designing the following Lyapunov equation based on the energy function of the mathematical model of the marine rotary crane:
wherein ：error of cantilever amplitude angle +.>Error of cantilever amplitude rotation angular velocity e 2 ＝q 2 -q 2d Is the error of the rotation angle of the cantilever in the horizontal direction,is the rotation angular velocity error of the cantilever in the horizontal direction; the Lyapunov equation is an energy-like equation designed based on error variables, and is designed into a positive definite equation, and the first derivative of the equation is proved to be semi-negative through deduction in combination with the positioning requirement of a control system and the control target of desynchronization in order to ensure the stability of the system.
For the Lyapunov equation V 1 The derivation can be carried out:
wherein ：ζ1 T and ζ2 T Is a separate state quantity related term, ψ 1 and ψ2 To be evaluated for uncertain parameter-related items, W 1 and W2 Is an angle-related term;
the adaptive controller is designed on the basis:
wherein ,kp1 、k d1 、k p2 and kd2 For adaptive controller gain, τ 1 For cantilever amplitude direction rotation torque τ 2 Is the rotation torque of the cantilever in the horizontal direction,is an uncertainty parameter ψ 1 Is used for the estimation of the estimated value of (a).
The design of the adaptive law is as follows:
γ 1 ＝diag{γ 11 γ 12 γ 13 γ 14 γ 15 γ 16 }∈R 6×6
γ 2 ＝diag{γ 21 γ 22 γ 23 γ 24 γ 25 γ 26 γ 27 }∈R 7×7 wherein ,is an uncertainty parameter ψ 1 Estimate of +.>First derivative of time by couplingSystem state variable implementation->The variation of (1) is such that->Can update in real time according to the change condition of system parameters, and gamma 1 and γ2 For positive diagonal matrices, the elements inside are adjustable.
Specifically, the gain (k p1 ，k d1 ，k p2 and kd2 ) All positive gain, k p1 ，k d1 ，k p2 and kd2 The initial values of (1) are respectively 150, 90, 110 and 70, and the values can be adjusted according to actual conditions; it should be noted that adjusting k p1 and kp2 Positioning speed can be improved, but excessive adjustment usually generates super-harmonic oscillation phenomenon; k (k) d1 and kd2 Will be opposite due to too large k p1 and kp1 The generated bad output response plays a certain damping effect; second, for the adaptive term, the diagonal matrix γ is positive due to the presence of the integral part 1 and γ2 Has a great influence on the adaptive law. When gamma is 1 and γ2 The smaller the adaptation term update speed of the controller is, the faster the adaptation parameter is, and the closer the adaptation parameter is to the actual parameter. According to trial and error, gamma is adjusted for many times 1 and γ2 Element value of 0.01; finally, the relevant parameter f of the feedforward friction model 11 、f 12 、f 21 、f 22 After the off-line identification, the value of epsilon static friction coefficient is selected to be 0.01 without changing the selection of the value.
S3: and planning a target tracking track of the cantilever based on the self-adaptive law, wherein the target tracking track is used for verifying the effect of the self-adaptive controller on inhibiting the swing angle.
Tracking control of the marine rotary crane system is performed by using the following reference track to verify the positioning and swing eliminating functions, wherein the reference track is an S-shaped track:
wherein χ represents the boom amplitude angle q after coupling 1 Or the coupled horizontal rotation angle q 2 ；q(χ) d ，q(χ) 0 and tq(χ)d The boom rise angle and the rotation target angle/position, the initial angle/position and the arrival time, respectively.
In practice, the choice of a viable reference trajectory is arbitrary as long as the trajectory meets the positioning start and end constraint requirements. The following tracks are generally available, such as a step track, an S-track, and an input shaping track. However, the stepped track is a discontinuous track, which may cause excessive initial output of the system actuator, affect the control effect, and are not beneficial to long-term operation of the actuator. For an input shaping trajectory, a change in system rope length will result in a corresponding change in natural frequency of the vibrating system. The input shaping trajectory must then be redesigned at any time before use, which is very inconvenient. In the present application we choose the trajectory shown above, which has the following advantages: 1) The curve is continuous with respect to time, so the desired system state may be uninterrupted; 2) The track contains a sinusoidal function portion with a smoothing effect; 3) The arrival time can be manually adjusted according to actual requirements.
In the actual application occasion, under the condition of being disturbed by continuous yaw and roll of the ship, the swing characteristic of the crane is more obvious, so that the realization of a safe positioning task while the swing angle is restrained has more challenging and practical engineering significance; therefore, the application mainly aims at the problems of track tracking and swing inhibition of the marine rotating crane, firstly establishes a mathematical model of the marine rotating crane with particle load based on Lagrange dynamics 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 inhibit the problems of external disturbance (wind resistance, mechanical friction, disturbance generated by continuous yaw and roll of the ship, and the like) and uncertainty of model parameters; the crane can be operated to a certain extent (quick positioning and effective swing elimination). The self-adaptive controller uses a friction force feedforward compensation model as feedforward compensation mode, and finally, the self-adaptive controller is tracked through an S-shaped track which is given to meet the condition to verify the advantages of the self-adaptive controller; the method is mainly characterized in that the track tracking and load swing angle suppression of the marine rotary crane can be realized rapidly and effectively.
On the other hand, in the aspect of parameter selection, the platform adopts adaptive control to adjust the given value of the basic parameter and the proportional gain value of the parameter; the method has simple process, the gains and the number of parameters are not too much limited by the model and the physical conditions, and the response effect corresponding to each gain is clear, so that the parameter adjusting process is not complex in practical application, 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 movement of the drivable mechanism on the control effect is effectively avoided, and the swing caused by positioning lag/lead is greatly increased to eliminate the swing control difficulty.
Example 2
Referring to fig. 3-5, in order to better verify the technical effects of the method according to the present application, a conventional controller LQR is selected for testing, and the test results are compared by means of scientific demonstration to verify the true effects of the method.
Referring to fig. 4, an experimental platform was set up for the experiment in this example. Specifically, the hardware portion includes an angle encoder, an electronic governor, a motor, a PC, and a motor power supply. The PC comprises a motion control board for transmitting the angle signal collected by the angle encoder. After calculation in Matlab\Simulink, compiling generated codes, transmitting control signals to an electronic speed regulator through a motion control board to further control a motor, and then carrying out real-time monitoring and recording on experimental data on the motion control board through serial port communication, wherein position signals of a drivable part are counted from an encoder; the load/hook swing angle information is from an angle encoder whose voltage signal is transmitted to the control board via an a/D converter. In order to accurately simulate the actual situation, the rotation of the boom amplitude angle is realized through a steel rope.
Experiments are carried out by using the controller LQR and the controller using the control method, and the control formula of the controller LQR is as follows:
for LQR controllers, state vectorsAnd the Q matrix and the R matrix are set to q=diag {250,50,250,50,15,5,15,5}, r= [1,1 ]] T Finally, the gain of the controller is k 11 ＝45，k 12 ＝24，k 13 ＝4.5，k 14 ＝-0.1，k 21 ＝45，k 22 ＝31，k 23 ＝3.9，k 24 The amplitudes of the methods used for the present method and the LQR controller were calculated using the experimental platform constructed as described above, with the results shown in table 1 below=5.5:
table 1: maximum amplitude experiment compares results.
Meanwhile, referring to fig. 2 and 3, 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, the LQR controller cannot realize positioning in the cantilever amplitude direction, and the tracking and positioning process of the method is smoother. Using the proposed controller method, the crane is luffingAnd the arrival time of the rotation direction is 5.00 s]In the LQR method, the above parameters are 7.43 s, respectively]And 6.36[ s ]]. Compared to the proposed controller, the LQR positioning time in the pick-up and rotation directions is increased by 48.6% and 27.2%, respectively. For the swing suppression aspect, the amplitude of the load caused by the controller of the method is not large and does not exceed 1.00 deg]While the amplitude of the load caused by the controller of the traditional LQR method is too large and is not lower than 1[ deg ]]And up to approximately 3.1[ deg ]]Q, compared to LQR method 3 and q4 The maximum amplitude of (c) is reduced by 75% and 45%, respectively. The swing of the method can be completely eliminated within 2-4 seconds after the positioning of the driving mechanism is finished, the inhibiting effect of the traditional method is particularly poor, and residual swing still does not exist after the traditional method is subjected to a plurality of times of intense oscillations until 10 seconds, so that the swing inhibiting efficiency of the method is extremely high, the positioning is accurate, and overshoot and steady state errors are avoided.
It should be noted that the above embodiments are only for illustrating the technical solution of the present application and not for limiting the same, and although the present application has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present application may be modified or substituted without departing from the spirit and scope of the technical solution of the present application, which is intended to be covered in the scope of the claims of the present application.
Claims (7)
1. The self-adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane is characterized by comprising the following steps of:
establishing a four-degree-of-freedom marine rotary crane mathematical model based on a Lagrangian dynamics equation and analyzing dynamics characteristics of the model;
the four-degree-of-freedom marine rotary crane mathematical model is expressed as:
order the
G(q)＝[g 1 g 2 g 3 g 4 ] T
τ＝[τ 1 τ 2 0 0] T
τ f ＝[τ 1f τ 2f 0 0] T
q 1 ＝θ 1 -α,q 2 ＝θ 2 -β,q 3 ＝θ 3 -α,q 4 ＝θ 4 -β
wherein ,Ms (q) is an inertial matrix of the marine rotating crane system,is centripetal-Coriolis Li Juzhen, G (q) is a gravity vector, τ is a control input vector, τ f And D is the mechanical friction and wind resistance of the marine rotary crane system respectively, and the amplitude-changing angle and the rotation angle of the cantilever are respectively theta 1 and θ2 The roll angle and yaw angle of the ship are alpha and beta respectively, and the radial swing angle and tangential swing angle of the load are theta respectively 3 and θ4 Q is a new state variable of the system after coupling, q 1 and q2 Q is the amplitude and rotation angle of the coupled cantilever 3 and q4 For the radial and tangential pivot angles of the coupled load, < >>Is the first derivative, +>Is its second derivative; m and M are the mass of the cantilever and the load respectively, L and L are the length of the cantilever and the length of the lifting rope respectively, g is the gravitational acceleration, and tau is the driving force/torque 1 For driving torque in the cantilever amplitude direction, tau 2 Is cantilever waterDrive torque in the direction of flat rotation, τ 1f and τ2f Mechanical friction forces in the cantilever amplitude direction and the horizontal rotation direction respectively, d ι (1..4) is an air friction parameter;
the dynamic characteristics comprise cantilever positioning characteristics and swing angle swinging characteristics;
the four-degree-of-freedom marine rotary crane mathematical model further comprises:
establishing a friction force feedforward compensation model, which is expressed as:
wherein ,f11 、f 12 、f 21 、f 22 And epsilon is a parameter of a friction force feedforward compensation model, f 11 and f12 The value of (f) corresponds to the maximum static friction force, f 21 and f22 Is the viscous coefficient of friction, ε is the static coefficient of friction;
establishing an energy function of the model according to the mathematical model characteristics of the marine rotary crane, and establishing an adaptive controller and an adaptive law of the marine rotary crane based on the energy function;
and planning a target tracking track of the cantilever based on the self-adaptive law, wherein the target tracking track is used for verifying the effect of the self-adaptive controller on inhibiting the swing angle.
2. The adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane according to claim 1, wherein: the energy function of the four-degree-of-freedom marine rotary crane mathematical model:
wherein ：speed signals representing the boom amplitude, horizontal rotation angle, radial and tangential load swing angle, respectively, after coupling, +.>Mgl (1-C) 3 C 4 ) For its load potential energy portion.
3. The adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane according to claim 2, wherein: the adaptive controller includes:
and designing an error variable and designing the following Lyapunov equation based on an energy function of the mathematical model of the marine rotary crane:
wherein ,error of cantilever amplitude angle +.>Error of cantilever amplitude rotation angular velocity e 2 ＝q 2 -q 2d Is the error of the rotation angle of the cantilever in the horizontal direction,is the rotation angular velocity error of the cantilever in the horizontal direction.
4. The adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane according to claim 3, wherein: also includes applying the equation to the Lyapunov equationV 1 And (3) conducting derivation:
wherein ,ζ1 T and ζ2 T Is a separate state quantity related term, ψ 1 and ψ2 To be evaluated for uncertain parameter-related items, W 1 and W2 Is an angle-dependent term.
5. The adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane according to claim 4, wherein: the adaptive controller is designed on the basis of Lyapunov equation:
wherein ,kp1 、k d1 、k p2 and kd2 For adaptive controller gain, τ 1 For cantilever amplitude direction rotation torque τ 2 Is the rotation torque of the cantilever in the horizontal direction,is an estimate of the uncertainty parameter ψ.
6. The adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane according to claim 5, wherein: the following adaptive law is designed based on the adaptive controller:
γ 1 ＝diag{γ 11 γ 12 γ 13 γ 14 γ 15 γ 16 }∈R 6×6
γ 2 ＝diag{γ 21 γ 22 γ 23 γ 24 γ 25 γ 26 γ 27 }∈R 7×7
wherein ,is an uncertainty parameter ψ 1 Estimate of +.>The first derivative of time is achieved by coupling the system state variables +.>The variation of (1) is such that->Can update in real time according to the change condition of system parameters, and gamma 1 and γ2 For positive diagonal matrices, the elements inside are adjustable.
7. The adaptive nonlinear control method of the four-degree-of-freedom marine rotary crane according to claim 5 or 6, wherein: the target tracking track is an S-shaped track, and is expressed as:
q(χ d ).t∈[t q(χ)d ,+∞)
wherein χ represents the boom amplitude angle q after coupling 1 Or the coupled horizontal rotation angle q 2 ；q(χ) d ，q(χ) 0 and tq(χ)d The boom rise angle and the rotation target angle/position, the initial angle/position and the arrival time, respectively.
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