CN110426954B - Active heave compensation controller and control system for deep sea crane - Google Patents

Active heave compensation controller and control system for deep sea crane Download PDF

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CN110426954B
CN110426954B CN201910677156.6A CN201910677156A CN110426954B CN 110426954 B CN110426954 B CN 110426954B CN 201910677156 A CN201910677156 A CN 201910677156A CN 110426954 B CN110426954 B CN 110426954B
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controller
deep sea
heave compensation
active
crane
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CN110426954A (en
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马昕
李轾
宋锐
荣学文
李贻斌
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Shandong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C23/00—Cranes comprising essentially a beam, boom, or triangular structure acting as a cantilever and mounted for translatory of swinging movements in vertical or horizontal planes or a combination of such movements, e.g. jib-cranes, derricks, tower cranes
    • B66C23/18—Cranes comprising essentially a beam, boom, or triangular structure acting as a cantilever and mounted for translatory of swinging movements in vertical or horizontal planes or a combination of such movements, e.g. jib-cranes, derricks, tower cranes specially adapted for use in particular purposes
    • B66C23/36—Cranes comprising essentially a beam, boom, or triangular structure acting as a cantilever and mounted for translatory of swinging movements in vertical or horizontal planes or a combination of such movements, e.g. jib-cranes, derricks, tower cranes specially adapted for use in particular purposes mounted on road or rail vehicles; Manually-movable jib-cranes for use in workshops; Floating cranes
    • B66C23/52—Floating cranes
    • B66C23/53—Floating cranes including counterweight or means to compensate for list, trim, or skew of the vessel or platform
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B66—HOISTING; LIFTING; HAULING
    • B66C—CRANES; LOAD-ENGAGING ELEMENTS OR DEVICES FOR CRANES, CAPSTANS, WINCHES, OR TACKLES
    • B66C13/00—Other constructional features or details
    • B66C13/02—Devices for facilitating retrieval of floating objects, e.g. for recovering crafts from water
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The disclosure provides an active heave compensation controller and a control system for a deep sea crane. The active heave compensation controller of the deep sea crane has a double-ring control structure; the outer ring control structure is an active disturbance rejection controller which is used for compensating external disturbance and generating a desired angle for the inner ring; the inner ring control structure is an equivalent saturation model prediction controller and is used for compensating the input saturation and dead zone characteristics of the hydraulic motor and ensuring that the hydraulic motor drives the winch to track the expected angle quickly and accurately.

Description

Active heave compensation controller and control system for deep sea crane
Technical Field
The disclosure belongs to the field of design of compensation controllers, and particularly relates to an active heave compensation controller and an active heave compensation control system for a deep sea crane.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The deep sea crane is one of the core equipment of ocean engineering, and is mainly used for hoisting, transporting and the like of underwater equipment. Because the deep sea crane is installed on a ship, in the deep sea operation process, due to the influence of sea waves, ocean currents and sea winds, the deep sea operation ship can generate heave motion, so that underwater loads can move along with the ship, and great threat is caused to the safety of offshore operation personnel and equipment. Therefore, the research and design of the heave compensation system have important significance for improving the operation efficiency of the deep sea crane and ensuring the safety of the hoisting system.
Heave Compensation systems can be mainly divided into two types, namely Passive Heave Compensation (PHC System) and Active Heave Compensation (AHCsystem). The passive heave compensation has a simple structure, and a hydraulic spring structure is usually formed by an energy accumulator and a hydraulic cylinder. For example, Hstleskog et al have devised a heave compensation system for a coronary vessel. In this system, the load is connected to two compensating cylinders by means of a pulley block. The position of the piston of the hydraulic cylinder is adjusted by an accumulator. Driscoll et al propose a one-dimensional finite element total mass model. The model can predict the elastic load of the cable and accurately reproduce the elastic load characteristic. Based on the model, a passive compensation system is designed, and the equivalent stiffness and damping characteristics of the passive compensation system are determined by a quadratic optimization algorithm. It can be seen from the above document that the passive heave compensation system can be easily fitted into existing equipment and does not require additional energy input. However, the inventor finds that the passive heave compensation system is an open-loop system, and the compensation accuracy of the passive heave compensation system can be greatly changed under different working conditions. Furthermore, passive heave compensation systems cannot be applied in certain scenarios, such as cargo transport between two vessels and wave matching during cargo entry into the water from the air.
The other heave compensation mode is active heave compensation or active-passive hybrid (HAHC) unlike PHC systems, which are closed-loop control systems with much higher compensation efficiency than PHC systems, Neupert and K ü chler et al have designed a deep sea crane heave compensation control strategy based on hydraulically driven winches, which considers the delay between sensors and actuators.
For the problem of unknown model parameters, Li et al design an extended disturbance observer to compensate external disturbances and a self-adaptive sliding mode controller to improve the robustness of the active heave compensation system. Sun et al propose an active heave system controller without model parameters using energy functions and Lyapunov theory. Li et al designed an Active-passive hybrid heave compensation system and an Active Disturbance Rejection Control (ADRC). The existing AHC system can obtain a better compensation effect. However, one problem still exists with AHC systems: in the AHC system, an electro-hydraulic servo motor or the like having excellent low-speed performance, high accuracy, and good frequency response is generally used as an actuator. However, electro-hydraulic servomotors have significant non-linear characteristics such as input saturation, dead band, and non-linear gain. Aiming at the problems of dead zones, nonlinear gains and the like, an initial compensation voltage is added into an artificial servo valve control signal of Galuppini and the like to avoid the dead zones, and an active Model predictive controller (MPC for short) is designed.
The inventor has found that the heave compensation controller does not take into account both external disturbances and the non-linear characteristics of the actuator at the same time, resulting in the inability of the winch of a deep sea crane to quickly and accurately track the desired angle.
Disclosure of Invention
In order to solve the above problems, a first aspect of the present disclosure provides an active heave compensation controller for a deep sea crane, which has a dual-loop structure, wherein an outer loop control system utilizes advantages of a simple structure of an active disturbance rejection controller, no need of model parameters, strong robustness, and the like, an inner loop is a hydraulic winch control loop, and an equivalent saturated model prediction controller ensures that the hydraulic winch can quickly and accurately track an expected angle.
In order to achieve the purpose, the following technical scheme is adopted in the disclosure:
an active heave compensation controller of a deep sea crane is provided with a double-ring control structure; the outer ring control structure is an active disturbance rejection controller which is used for compensating external disturbance and generating a desired angle for the inner ring; the inner ring control structure is an equivalent saturation model prediction controller and is used for compensating input saturation and dead zone characteristics of the hydraulic motor and ensuring that the hydraulic motor drives the winch to track an expected angle quickly and accurately.
Further, the active disturbance rejection controller includes:
a differential tracker for calculating a differential value of the input signal; wherein the input signal is an underwater load position; the differential value of the input signal is the underwater load speed;
the extended state observer is used for estimating the underwater load position, the underwater load speed and disturbance and unmodeled dynamic quantity in the hanging object dynamic model;
a nonlinear feedback combining module that:
u0＝k1fal(e1，ac1，δ)+k2fal(e2，ac2，δ)
u＝u0-z3/b0
Figure GDA0002418845540000041
wherein i is 1, 2; e.g. of the type1Is the underwater load position deviation; e.g. of the type2Is the underwater load speed deviation; z is a radical of3The observed quantities of disturbance and unmodeled dynamic quantities in the crane dynamics model are obtained; k is a radical ofi、aciδ and b0Are all controller constants; u is the output of the active disturbance rejection controller.
In the embodiment, the active disturbance rejection control is used for compensating the external disturbance and generating the expected angle information for the inner ring subsystem, and the equivalent saturated model prediction controller can ensure that the winch can track the expected angle quickly and accurately.
Further, the differential equation of the differential tracker is:
Figure GDA0002418845540000042
Figure GDA0002418845540000043
wherein the parameter rdDetermining the tracking speed of the differentiator; h is a filtering parameter; state variable x1And x2The input signal and its differential signal are tracked separately.
Further, the structural equation of the extended state observer is as follows:
es＝z1(k)-z(k)
z1(k+1)＝z1(k)+h(z2(k)-β1es)
z2(k+1)＝z2(k)+h(z3(k)-β2fal(u，a1，δ))
z3(k+1)＝z3(k)-hβ3fal(u，a2，δ)
Figure GDA0002418845540000051
wherein z is the underwater load position, z1As an observation of the position of the load underwater, z2Is the observed quantity of the underwater load speed, h is a filtering parameter, aiAnd βiAre all controller constants, j is 1, 2, 3; k represents a discrete time point.
Further, the expression of the feedback information of the underwater load position in the continuous time domain is as follows:
Figure GDA0002418845540000052
wherein l (0) is the initial length of the cable, r is the radius of the winch, theta (t) is the rotation angle of the winch, omega (t) is the heave motion of the crane ship under the action of sea waves,
Figure GDA0002418845540000053
is an estimate of the elongation of the cable,
Figure GDA0002418845540000054
the cable elongation is estimated by a state observer.
Further, the expression of the heave motion ω (t) of the crane vessel under the action of the sea waves is:
Figure GDA0002418845540000055
wherein mu is a direct ratio coefficient of the amplitude of the heave motion of the crane ship and the height of the sea waves, X is the maximum value of the wave height, and T is the wave period.
Further, the control law of the equivalent saturated model predictive controller is obtained by quadratic minimization of a cost function; the cost function is:
Figure GDA0002418845540000056
xmin＜xi＜xmax
-v+c＜ui＜v-c
Nc≤Np
wherein Q, R and P are weight parameters; x is the number ofiIs the model variable error; u. ofiIs a control input; Δ uiTo control the rate of change of the input; n is a radical ofpRepresenting a prediction domain; n is a radical ofcIs a control domain; c and v are both positive constants; x is the number ofminIs the minimum value of the error of the model variable, xmaxIs the maximum value of the error of the model variable.
After the system is subjected to equivalence, the complex nonlinear characteristic can be equivalent to the simple bounded characteristic, so that the complexity of calculation is greatly simplified, and the prediction domain of model predictive control can be increased to further improve the control effect.
A second aspect of the present disclosure provides an active heave compensation control system for a deep sea crane.
An active heave compensation control system of a deep sea crane comprises the active heave compensation controller of the deep sea crane.
Further, the deep sea crane active heave compensation controller is connected with a deep sea crane, the deep sea crane comprises a winch driven by a hydraulic motor, and the winch is connected with an underwater load through a cable.
Further, the cable and the underwater load are a spring-mass-damping system.
The method is used for quickly constructing a hoisting object dynamic model and a hydraulic winch dynamic model in the deep sea crane so as to improve the heave compensation precision.
The beneficial effects of this disclosure are:
the active heave compensation controller of the deep sea crane has a double-ring structure, wherein an outer ring control system compensates disturbance, friction, model uncertainty and the like in an outer ring system by using the advantages of simple structure, no need of model parameters, strong robustness and the like of an active disturbance rejection controller, the input is an underwater load position, and the output is an expected angle of a hydraulic winch; the inner ring is a hydraulic winch control ring, the nonlinear characteristics of input saturation, dead zones and the like of a hydraulic winch system are considered, the input of the equivalent saturation model prediction controller is an expected angle, the output of the equivalent saturation model prediction controller is an actual rotation angle of the winch, and the hydraulic winch can be enabled to track the expected angle quickly and accurately.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.
Fig. 1 is a schematic view of a deep sea crane system provided in an embodiment of the present disclosure.
FIG. 2 is a schematic view of a hydraulically driven drawworks provided by an embodiment of the present disclosure.
Fig. 3 is a schematic structural diagram of an active heave compensation controller of a deep sea crane according to an embodiment of the disclosure.
Fig. 4 is a schematic structural diagram of an active disturbance rejection controller provided in an embodiment of the present disclosure.
Fig. 5 is a schematic diagram of a saturation, dead-band series system provided by an embodiment of the present disclosure.
Fig. 6 is a schematic structural diagram of an equivalent saturation model predictive controller provided in an embodiment of the present disclosure.
Fig. 7 illustrates a crane vessel and underwater crane motion provided by an embodiment of the present disclosure.
FIG. 8 is a cable pull and observer output provided by embodiments of the disclosure.
Fig. 9 is a controller compensation effect provided by an embodiment of the present disclosure.
FIG. 10 is a heave compensation result under the influence of a disturbance provided by an embodiment of the disclosure.
FIG. 11(a) is a schematic representation of an embodiment of the disclosure
Figure GDA0002418845540000071
The heave compensation effect is compared with the heave compensation effect without compensation and after compensation.
FIG. 11(b) is a schematic diagram of an embodiment of the present disclosure
Figure GDA0002418845540000072
The heave compensation effect is compared with the heave compensation effect without compensation and after compensation.
FIG. 11(c) is a schematic diagram of an embodiment of the present disclosure
Figure GDA0002418845540000073
The heave compensation effect is compared with the heave compensation effect without compensation and after compensation.
Detailed Description
The present disclosure is further described with reference to the following drawings and examples.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Interpretation of terms:
ADRC: active Disturbance Rejection Control;
ESMPC: equivalent validation Model Predictive Control, Equivalent bounded Model Predictive Control;
ADRC-ESMPC: active Disturbance Rejection Control-Equivalent creation model Predictive Control strategy.
The deep sea crane structure was analyzed as follows:
the structure of the deep sea crane is shown in figures 1 and 2, and the underwater load is connected with a winch driven by a hydraulic motor through a cable. In the embodiments of the present disclosure, it is assumed that the crane is a rigid body. The cable and the load can be regarded as a spring-mass-damping system, and furthermore, it is assumed that the mass of the underwater load is 10 of the mass of the hull-2By a multiple of the following scale, the motion of the underwater load does not affect the motion of the hull.
The embodiment focuses on heave compensation control in the vertical direction of the underwater load, so that the transverse stress of the underwater load is not considered in the design process of the controller.
Since the load is submerged, hydrodynamic forces need to be considered. Equivalent mass m in the vertical direction of a load submerged under watereqExpressed as:
meq＝M+m1+m2(1)
wherein M is the mass of the hoisted object and the lifting hook in the air. m is1For added mass, this is expressed in the form:
m1＝ρwCAV (2)
where ρ iswIs water density, CAFor additional mass coefficient, V is the volume of the suspended object under water.
Figure GDA0002418845540000081
Is the equivalent mass of the cable. m iscMass per meter of cable, /)cIs the nominal length of the cable and can be expressed in the form:
lc(t)＝lc(0)+rθ(t) (3)
lc(0) the initial length of the cable, r the radius of the winch, and θ (t) the arc of winch rotation.
According to newton's equation, the dynamic equation of the load can be expressed in the form:
Figure GDA0002418845540000091
wherein the content of the first and second substances,
Figure GDA0002418845540000092
is the angular acceleration of the winch rotation. Omega is the heave movement of the crane ship under the action of sea waves,
Figure GDA0002418845540000093
the acceleration of the heave motion of the crane vessel. Δ ldIs the dynamic elongation of the cable.
Figure GDA0002418845540000094
Is the cable dynamic elongation acceleration. z represents the position of the underwater load.
Figure GDA0002418845540000095
And
Figure GDA0002418845540000096
representing the velocity and acceleration of the underwater load, respectively. g is the acceleration of gravity. CwIs the water damping coefficient. V is the volume of the underwater hanging object. Δ l ═ Δ ls+ΔldIs the elongation of the cable, where Δ lsIs static elongation and the sum of static tension and buoyancy is equal to the gravity of the suspended object, i.e.
Figure GDA0002418845540000097
K is the stiffness coefficient of the cable, and the cable follows hooke's law:
Figure GDA0002418845540000098
wherein ErAnd ArRepresenting the young's modulus and the cross-sectional area of the cable.
The motion of the crane vessel under linear waves can be estimated by wave height and period. The amplitude of the heave motion of the crane ship is proportional to the height of the sea wave, μ, and assuming that the proportional coefficient is, the maximum value of the wave height is X, and the period of the sea wave is T, the heave motion of the crane ship can be represented by the following formula:
Figure GDA0002418845540000099
the active heave compensation system generally adopts a hydraulic motor to drive a winch as an actuator, and the structure of the active heave compensation system is shown in fig. 2.
The angular output of a hydraulically driven drawworks can be expressed in the form of a transfer function as follows:
Figure GDA00024188455400000910
wherein, KnIs a scaling factor. U is the proportional valve input voltage. Omeganξ for natural frequency of hydraulic motornIs the damping coefficient.
By the above analysis:
the control objective of the heave compensation system can be described as making the submerged lifting object z (t) l under the influence of sea wavesc(0) + r θ (t) + ω (t) + Δ l (t) enables the desired trajectory to be tracked quickly and accurately.
To achieve this control objective, the present embodiment designs a nonlinear controller with a dual-loop structure, and the controller structure is shown in fig. 3. For the outer loop system, the ADRC controller is designed to compensate for external disturbances, non-linear friction, and model uncertainty and generate the desired angle for the inner loop. For the inner loop system, the ESMPC controller is designed to ensure that the drawworks can accurately track the desired angle with bounded inputs and dead zones.
(1) Outer loop controller design
The active disturbance rejection control has strong robustness, does not need model parameter information, and is widely applied to the field of automatic control at present. The active disturbance rejection control structure is shown in fig. 4.
The differential tracker is used to obtain the differential value of the input signal ξ.
Figure GDA0002418845540000101
Where the function fst (-) is defined as:
Figure GDA0002418845540000102
u is the input signal, i.e. the signal that needs to be differentiated. Parameter rdDetermines the tracking speed of the differentiator. h is a filtering parameter. State variable x1And x2The input signal and its differential signal are tracked separately.
The extended state observer is constructed as follows:
es＝z1(k)-z(k)
z1(k+1)＝z1(k)+h(z2(k)-β1es)
z2(k+1)＝z2(k)+h(z3(k)-β2fal(u，a1，δ))
z3(k+1)＝z3(k)-hβ3fal(u，a2，δ) (11)
wherein the nonlinear function fal (-) is defined as:
Figure GDA0002418845540000111
the nonlinear feedback combination module is designed as follows:
e1＝z-z1
Figure GDA0002418845540000112
u0＝k1fal(e1，ac1，δ)+k2fal(e2，ac2，δ)
u＝u0-z3/b0(13)
wherein i is 1, 2; e.g. of the type1Is the underwater load position deviation; e.g. of the type2Is the underwater load speed deviation; z is a radical of3For disturbance in the model of crane dynamics and observation of unmodeled dynamic quantityAn amount; k is a radical ofi、aciδ and b0Are all controller constants; and u is the output quantity of the active disturbance rejection controller, namely the position of the underwater load after the active disturbance rejection control.
z is the position of the underwater load, z1As an observation of the position of the load underwater, z2Is the observed quantity of the underwater load speed, h is a filtering parameter, aiAnd βjAre all controller constants, j is 1, 2, 3; k represents a discrete time point.
Considering that the elongation of the cable cannot be measured directly, the position of the underwater load cannot therefore be measured directly. To solve this problem, a state observer is designed to estimate the elongation of the cable. Defining the observer state variables as:
Φ＝[Δl Δi]T；
the state observer is then designed as follows:
Figure GDA0002418845540000121
wherein:
Figure GDA0002418845540000122
Bo＝[0 1]T；
Figure GDA0002418845540000123
and
Figure GDA0002418845540000124
respectively, the state variables phi and
Figure GDA0002418845540000125
is determined by the estimated value of (c),
Figure GDA0002418845540000126
is the observer input; l is0For feedback compensation matrix, the matrix can be obtained by pole allocation method; fdIs the elastic force of the cable;
Figure GDA0002418845540000127
is the state observer output, which is defined as follows:
Figure GDA0002418845540000128
wherein the content of the first and second substances,
Figure GDA0002418845540000129
is an estimate of cable elongation Δ l.
At this point, the position of the underwater load may be approximated as:
Figure GDA00024188455400001210
(2) inner loop controller design
In actual engineering, most hydraulic systems have non-linear characteristics, such as input-bound, dead band, hysteresis, and backlash. To address this problem, an Equivalent Saturation Model Predictive Controller (ESMPC) is proposed below, as shown in fig. 5.
The controller design is preceded by an analytical definition of dead band and input-bounded. Wherein the dead zone characteristic may be expressed as:
Figure GDA00024188455400001211
wherein c is a positive constant; u (t) is the input signal.
The right inverse of the dead zone can be expressed as:
Figure GDA0002418845540000131
the input is bounded and can be represented as:
Figure GDA0002418845540000132
where v is a positive constant.
For the system shown in FIG. 5, if notThe linear function psi (-) is equal to the right inverse of the dead zone, i.e.
Figure GDA0002418845540000133
At this time
Figure GDA0002418845540000134
Then for any un∈L2[0, ∞), in v > c, there are:
Figure GDA0002418845540000135
the control structure diagram of the ESMPC is shown in FIG. 6 according to the above equivalent bounded theory. It can be seen that after the equivalence, the system can equate the complex nonlinear characteristic to the simple bounded characteristic. This greatly simplifies the computational complexity so that the prediction domain of model predictive control can be increased to further improve the control effect.
The control law of the equivalent bounded model predictive control is obtained by quadratic minimization of a cost function. The cost function is defined as:
Figure GDA0002418845540000136
xmin＜xi＜xmax
-v+c＜ui＜v-c
Nc≤Np(21)
wherein Q, R and P are weight parameters; x is the number ofiIs the model variable error; u. ofiIs a control input; Δ uiTo control the rate of change of the input; n is a radical ofpRepresenting a prediction domain; n is a radical ofcIs a control domain; c and v are both positive constants; x is the number ofminIs the minimum value of the error of the model variable, xmaxIs the maximum value of the error of the model variable.
The ADRC-ESMPC control strategy proposed by the embodiment of the present disclosure is subjected to simulation analysis. The effectiveness of the ADRC-ESMPC control strategy is proved by comparing the control effect of the ADRC-ESMPC control strategy and the PID controller, ADRC controller MPC controller.
In the simulation experiment, the parameters of the deep sea crane system model are shown in table 1, and the parameters of the controller are shown in table 2.
Wherein, the input of the PID controller, the ADRC controller and the MPC controller is the heave movement of the crane ship. The PID controller gain is obtained by the PID tuner module in Simulink, which is of the form:
Figure GDA0002418845540000141
wherein k isp、ki、kdProportional parameters, integral parameters and differential parameters of the PID controller are respectively;
b. c and N are control parameters of a PID controller;
ωdis the input signal, i.e. the heave movement of the crane vessel.
TABLE 1 model parameters
Figure GDA0002418845540000142
TABLE 2 controller parameters
Figure GDA0002418845540000151
The hull motion is obtained according to equation (7). The deep movement of the underwater hanging object is obtained by the calculation of the formula (4). After the initial length of cable is preset, the poles of the state observer are configured to-150 and-100, respectively.
The movement of the hull and the underwater hoists without control is shown in figure 7. The state observer output and cable pull are shown in FIG. 8. The heave compensation control effect of each controller is shown in fig. 9.
As can be seen from fig. 7, the amplitude of the heave motion of the underwater suspended object is 3.13m, which is much larger than that of the crane ship. The dynamic amplification factor is 2.5, which greatly exceeds the safety factor of 1.9, so that the underwater suspended object must be subjected to heave compensation.
As can be seen from fig. 8, the state observer has a faster convergence speed and observation accuracy. The observed values compared to the true values had an average error of 42.31 (from 0.09 seconds to 20 seconds) and a standard deviation of 18.42. This indicates that the state observer output can better estimate the cable elastic force, and the position of the submerged suspended object can be calculated by equation (16).
As can be seen from fig. 9, the overshoot amount of the ADRC controller is smaller and the compensation accuracy is also higher compared to the PID controller. However, due to the bounded processing inputs of PID and ADRC controllers and the limited ability of the ADRC controllers to handle dead band characteristics, the compensation accuracy is much lower than that of MPC and ADRC-ESMPC controllers. The tracking error ranges of the four controllers are +/-0.78 m, + -0.63 m, + -0.071 m and +/-0.076 m respectively. Then, the heave motion compensation percentages are:
(3.13-0.78)/3.13 × 100 (75.08% (PID controller)
(3.13-0.63)/3.13 × 100 ═ 79.87% (ADRC controller)
(3.13-0.071)/3.13 × 100%
(3.13-0.076)/3.13 × 100%
From the above calculations, it can be seen that the ADRC-ESMPC controller is able to better compensate for underwater adhesion heave motions in the presence of actuator non-linearity.
To further verify the robustness of the ADRC-ESMPC controller, assume that the underwater lifting is suddenly affected by interference between 15 seconds and 20 seconds. External interference is defined as follows:
d＝d1+d2(23)
wherein the content of the first and second substances,
Figure GDA0002418845540000161
the control gain, initial state and crane parameters of the controller are all kept unchanged.
As can be seen from fig. 10, at t < 15s, both controllers can better compensate the heave motion of the underwater suspended object and can limit the heave motion to be less than ± 0.1m, and the compensation percentage is greater than 96.81%. When d is2Start ofWhen acting on the system, under the control action of the MPC, the underwater adhesion generates large fluctuation, and the amplitude of the heave motion reaches 0.6m once. This occurs because the input to the MPC controller is the crane vessel heave motion, while deep water currents have little effect on the hull motion and a greater effect on the suspended load motion. In contrast, the ADRC-ESMPC control strategy can maintain an efficient heave compensation effect at all times, whether or not subject to d2The effect is to limit the heave motion of the suspended load to ± 0.1 m.
Considering that a deep sea crane may work under different sea conditions, the heave compensation effect of the ADRC-ESMPC controller under different sea conditions will be verified below. The parameters of the controller, the system parameters of the deep sea crane, the initial state and the like are kept unchanged. The perturbation d is 2000sin0.4t (N) (0. ltoreq. t.ltoreq.50).
As can be seen from fig. 11(a) -11 (c), ADRC-ESMPC can ensure that the heave motion of the underwater suspended object is limited to a very small range under different sea conditions. The compensation percentages are respectively:
(4.09-0.78)23/4.09 × 100% ═ 94.38% (sea state (a))
(6.44-0.49)/6.44 × 100 (92.40% (sea state (b))
(7.60-1.09)/7.60 × 100 (85.66% (sea state (c))
The simulation results prove that the ADRC-ESMPC controller provided by the embodiment not only can effectively compensate the heave motion of the underwater suspended object, but also has strong robustness to external disturbance. In addition, the nonlinear characteristics of the actuator, such as input-bounded and dead-band, are better compensated for by the optimization capability of the ESMPC.
The control strategy has an outer-inner loop structure. In the outer loop, the external disturbances are compensated for and desired angle information is generated for the inner loop subsystems using active disturbance rejection control. For the inner loop system, considering that the hydraulic drive winch system has nonlinear characteristics such as input bounded and dead zone, the embodiment designs equivalent bounded model predictive control to compensate the nonlinear characteristics, and ensures that the winch can track the expected angle quickly and accurately. Simulation results prove that the ADRC-ESMPC controller provided by the embodiment has strong robustness to external disturbance and has better compensation accuracy under different sea conditions.
The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.

Claims (8)

1. The active heave compensation controller of the deep sea crane is characterized by having a double-ring control structure; the outer ring control structure is an active disturbance rejection controller which is used for compensating external disturbance and generating a desired angle for the inner ring; the inner ring control structure is an equivalent saturation model prediction controller which is used for compensating the input saturation and dead zone characteristics of the hydraulic motor and ensuring that the winch driven by the hydraulic motor can quickly and accurately track the expected angle;
the active disturbance rejection controller includes:
a differential tracker for calculating a differential value of the input signal; wherein the input signal is an underwater load position; the differential value of the input signal is the underwater load speed;
the extended state observer is used for estimating the underwater load position, the underwater load speed and disturbance and unmodeled dynamic quantity in the hanging object dynamic model;
a nonlinear feedback combining module that:
u0＝k1fal(e1，acl，δ)+k2fal(e2，ac2，δ)
u＝u0-z3/b0
Figure FDA0002418845530000011
wherein i is 1, 2; e.g. of the type1Is the underwater load position deviation; e.g. of the type2Is the underwater load speed deviation; z is a radical of3To hang thingsDisturbance in the dynamic model and observation of unmodeled dynamic quantity; k is a radical ofi、aciδ and b0Are all controller constants; u is the output quantity of the active disturbance rejection controller;
the control law of the equivalent saturation model predictive controller is obtained by quadratic minimization of a cost function; the cost function is:
Figure FDA0002418845530000012
xmin＜xi＜xmax
-v+c＜ui＜v-c
Nc≤Np
wherein Q, R and P are weight parameters; x is the number ofiIs the model variable error; u. ofiIs a control input; Δ uiTo control the rate of change of the input; n is a radical ofpRepresenting a prediction domain; n is a radical ofcIs a control domain; c and v are both positive constants; x is the number ofminIs the minimum value of the error of the model variable, xmaxIs the maximum value of the error of the model variable.
2. The active heave compensation controller for a deep sea crane according to claim 1, wherein the differential tracker has a differential equation:
Figure FDA0002418845530000021
Figure FDA0002418845530000022
wherein the parameter rdDetermining the tracking speed of the differentiator; h is a filtering parameter; state variable x1And x2The input signal and its differential signal are tracked separately.
3. The deep sea crane active heave compensation controller of claim 2, wherein the extended state observer has the structural equation:
es＝z1(k)-z(k)
z1(k+1)＝z1(k)+h(z2(k)-βles)
z2(k+1)＝z2(k)+h(z3(k)-β2fal(u，a1，δ))
z3(k+1)＝z3(k)-hβ3fal(u，a2，δ)
Figure FDA0002418845530000023
wherein z is the underwater load position number, z1As an observation of the position of the load underwater, z2Is the observed quantity of the underwater load speed, h is a filtering parameter, aiAnd βjAre all controller constants, j is 1, 2, 3; k represents a discrete time point.
4. The active heave compensation controller for a deep sea crane according to claim 1, wherein the expression of the underwater load position in a continuous time domain is:
Figure FDA0002418845530000024
wherein l (0) is the initial length of the cable, r is the radius of the winch, theta (t) is the rotation angle of the winch, omega (t) is the heave motion of the crane ship under the action of sea waves,
Figure FDA0002418845530000031
is an estimate of the elongation of the cable,
Figure FDA0002418845530000032
the cable elongation is estimated by a state observer.
5. Active heave compensation controller for a deep sea crane according to claim 4, wherein the heave motion ω (t) of the crane vessel under the action of sea waves is expressed by:
Figure FDA0002418845530000033
wherein mu is a direct ratio coefficient of the amplitude of the heave motion of the crane ship and the height of the sea waves, X is the maximum value of the wave height, and T is the wave period.
6. An active heave compensation control system for a deep sea crane, comprising an active heave compensation controller for a deep sea crane according to any of claims 1-5.
7. The active heave compensation control system for a deep sea crane according to claim 6, wherein the active heave compensation controller is connected to the deep sea crane, the deep sea crane comprising a winch driven by a hydraulic motor, the winch being connected to the subsea load by a cable.
8. The deep sea crane active heave compensation control system of claim 7, wherein the line and the underwater load are spring-mass-damper systems.
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