LU102696B1

LU102696B1 - Active heave compensation control and control system for offshore crane

Info

Publication number: LU102696B1
Application number: LU102696A
Authority: LU
Inventors: Rui Song; Yibin Li; Xin Ma; Xuewen Rong; Zhi Li
Original assignee: Univ Shandong
Priority date: 2019-07-25
Filing date: 2020-07-09
Publication date: 2021-04-02
Also published as: CN110426954A; WO2021012962A1; CN110426954B

Abstract

The present disclosure provides an active heave compensation control and control system for an offshore crane. The active heave compensation control for the offshore crane has a double-loop control structure, wherein the outer-loop control structure is an active disturbance rejection control, which is used to compensate for external disturbances and generate a desired angle for the inner loop; and the inner-loop control structure is an equivalent saturation model predictive control, which is used to compensate for input saturation and dead zone characteristics of an electro-hydraulic servo winch to ensure that the electro-hydraulic servo winch quickly and accurately tracks the desired angle.

Description

ACTIVE HEAVE COMPENSATION CONTROL AND CONTROL SYSTEM FOR LU102696

OFFSHORE CRANE Field of the Invention The present disclosure belongs to the field of compensation control design, and particularly relates to an active heave compensation control and control system for an offshore crane. Background of the Invention The statement of this section merely provides background art information related to the present disclosure, and does not necessarily constitute the prior art. Offshore cranes are one of the core equipment of marine engineering, mainly used for the hoisting and transportation of underwater equipment. Because the offshore crane is installed on a ship, during the offshore operation, due to the influence of waves, ocean currents and sea breeze, the ship itself performing the offshore operation heaves to enable the underwater load to move with the ship, which poses a great threat to the safety of marine operators and equipment. Therefore, the research and design of heave compensation systems is of great significance for improving the operation efficiency of offshore cranes and ensuring the safety of hoisting systems. There are two main types of heave compensation systems, that is, a passive heave compensation system (PHC system) and an active heave compensation system (AHC system). The passive heave compensation system is simple in structure, which is a hydraulic spring structure usually composed of an accumulator and hydraulic cylinders. For example, Hstleskog et al. designed a crown drilling platform heave compensation system. In this system, the load is connected to two compensating hydraulic cylinders through a pulley block. The positions of pistons of the hydraulic cylinders are adjusted by the accumulator. Driscoll et al. proposed a one-dimensional finite element total mass model. This model can predict the elastic load of a cable and reproduce the characteristics of the elastic load accordingly. Based on this model, a passive compensation system was designed, and its equivalent stiffness and damping characteristics were determined by a secondary optimization algorithm. It can be seen from the above research that the passive heave compensation system can be easily assembled into existing equipment and does not require additional energy input. However, | the inventors found that the passive heave compensation system was an open-loop system, and the compensation accuracy of the passive heave compensation system varied greatly under different working conditions. In addition, the passive heave compensation system cannot be applied in soH102696 scenarios, such as cargo transportation between two ships and wave matching when cargoes enter water from the air. Another heave compensation method is active heave compensation. Unlike the PHC system, the active heave compensation system is a closed-loop control system, and its compensation efficiency is much higher than that of the PHC system. Neupert and Küchler et al. designed a heave compensation control strategy for an offshore crane based on an electro-hydraulic servo winch. This control strategy considers the delay between a sensor and an actuator. This delay is processed by Fast Fourier transform in the article. The working conditions of offshore cranes are usually harsh, so external disturbances such as unmodeled characteristics, nonlinear friction, and system vibration are inevitable. In order to solve this problem, Do et al. designed a disturbance observer to compensate for external disturbances and designed an active heave compensation control using a back stepping method. However, the design process of the control requires prior information of the system, such as equivalent mass and cable stiffness, and it is difficult to obtain these parameters.

Aiming at the problem of unknown model parameters, Li et al. designed an extended disturbance observer to compensate for external disturbances and designed an adaptive sliding mode control to improve the robustness of an active heave compensation system. Sun et al. proposed an active heave system contro} without model parameters using an energy function and the Lyapunov theory. Li et al. designed an active-passive hybrid heave compensation system and designed an active | 20 disturbance rejection control (ADRC). The existing AHC system can achieve a better compensation | effect. However, there is still a problem with the AHC system: in the AHC system, an electro-hydraulic servo winch is usually used as an actuator, and the winch has excellent low-speed performance, high accuracy and good frequency response. However, the electro-hydraulic servo winch has obvious nonlinear characteristics, such as input saturation, dead zone, and nonlinear gain.

In view of the problems such as dead zone and nonlinear gain, Galuppini et al. added an initial compensation voltage to a servo valve control signal to avoid the dead zone, and designed an active model predictive control (MPC).

The inventors found that the current heave compensation control cannot well compensate for external disturbances such as deep ocean currents undergone by the underwater load and the nonlinear characteristics of the actuator, resulting in that the offshore crane control system is incapable of achieving satisfactory heave compensation effects.

Summary of the Invention In order to solve the above problems, the first aspect of the present disclosure provides an active heave compensation control for an offshore crane, which has a double-loop structure, wherein the outer-loop control system uses the advantages of an active disturbance rejection control, such as simple structure, no need for model parameters, and strong robustness, and the inner loop is an electro-hydraulic servo winch control loop, which uses an equivalent saturation model predictive control to ensure that the electro-hydraulic servo winch can quickly and accurately track a desired angle.

In order to achieve the above objectives, the present disclosure adopts the following technical solutions: An active heave compensation control for an offshore crane has a double-loop control structure, wherein the outer-loop control structure is an active disturbance rejection control, which is used to compensate for external disturbances undergone by an underwater load, and generate a desired angle for the inner loop; and the inner-loop control structure is an equivalent saturation model predictive control, which is used to compensate for input saturation and dead zone characteristics of an electro-hydraulic servo winch to ensure that the electro-hydraulic servo winch quickly and accurately tracks the desired angle.

Further, the active disturbance rejection control includes: a differential tracker, which is used to calculate a differential value of an input signal, wherein the input signal is a desired position of the underwater load; the output signal is a desired speed of the underwater load; an extended state observer, which is used to estimate the speed of the underwater load and the disturbance undergone by the underwater load; and anonlinear feedback combination module, which is: u =k fal(e,a,,0)+k fal(e,,a,,,6) | 0,=u, —z,/b, i le, |" sign (e) le] >0 fen.) a. ele le|< 6 where i=1, 2; er is a position error of the underwater load; ez is a speed error of the underwater load;

73 is an estimate of the disturbances undergone by the underwater load and an unmodeled dyndidi®2696 …… k a, § | a, . . quantity; 7, 7e, and bo are all control constants; and ~¢ is an output of the active disturbance rejection control, that is, a desired angle trajectory of the electro-hydraulic servo winch system.

In this embodiment, the active disturbance rejection control is used to compensate for the external disturbances undergone by the underwater load and generate the desired angle information for the inner loop subsystem, and the equivalent saturation model predictive control can ensure that the electro-hydraulic servo winch quickly and accurately track the desired angle.

Further, a differential equation of the differential tracker is: x (+1) =X (*) + hx, (k) X, (k+1) =x, (x) + hfst(x, —Z; (k),%,,7,,h) d, =r,h",a,=hx,,y=x 7, +4 5, =(sin(y+d,)-sign(y-d,))/2 a =jd, (a, + 8») a, =a, +sign(y)(a —d,)/2 a={a,+y-a,)s, +a, | 5, =(sign(a+d,)-sign(a-d,)}/2 fit(x—z, (k),x,,r,,h) =r, (a /d,— sign(a))s, —r,sign(a) where “4 is a desired position of the underwater load, and the parameter ra determines a tracking speed of the differential tracker; # is a filtering parameter; and the state variables x: and x2 respectively track a desired position signal and a desired speed signal of the underwater load.

Further, a construction equation of the extended state observer is: e,=z,(k)- z(k) z(k+1)=z(k)+ h(z, (k) - Pe, ) z, (k + 1) =z, (F) + h(z, (k) - PB. fal (e,.a,,5)) z,(k+1)=z,(k)- B fal(e,,a,,5)

, _, LU102696 ef sign(e) Je]> fal(e,,a,6)= 2 ele le, | <8 where i=1, 2; j=1, 2, 3; Z is the position of the underwater load, z1 is an estimate of the position of the underwater load, z2 is an estimate of the speed of the underwater load, and z3 is an estimate of the disturbances undergone by the underwater load and the unmodeled dynamic quantity; 4 is the 5 filtering parameter, % and p / are both control constants, and k represents a discrete time point.

Further, the expression of feedback information about the position of the underwater load in a continuous time domain is: z(t) =1(0)+r0(t) + w(t) + Al (1) 1 (0) .. | . ch 6) . where © is an initial length of a cable, 7 is a radius of the winch, is an angle of rotation of the electro-hydraulic servo winch, (1) is a heave displacement of the floating crane under the Alt) . . . . action of waves, is an estimated value of elongation of the cable, and the elongation of the cable is estimated by the state observer.

Further, the heave displacement of the floating crane under the action of waves is: X 2; œ(t) = £2 sin — 2 7 where # is a proportional coefficient between the amplitude of the heave displacement of the floating crane and the wave height, X is the amplitude of the wave height, and T is a wave period.

Further, the control law of the equivalent saturation model predictive control is obtained by quadratic minimization of a cost function; and the cost function is: N, N.

N, J=> x, 0x, + > u' Pu + > Au” RAu i=0 i=0 i=0 X Amin < X ti < X Mmax -V+HC<H<V—C N,N p where i=1, 2; Q, R and P are weight parameters; xx is a variable error; # is a control input; À u is a change rate of the control input; N, is a prediction domain; N° is a control domain; ¢ and v are both positive constants; Xam» is a minimum value of the variable error, and X»mmax is a maximum value of the variable error. LU102696 After the implementation example is equivalent, the system can equate complex nonlinear characteristics to simple bounded characteristics, which greatly simplifies the complexity of calculation. In this way, the prediction domain of model predictive control can be increased to further improve the control effect. The second aspect of the present disclosure provides an active heave compensation control system for an offshore crane. An active heave compensation control system for an offshore crane includes the aforementioned active heave compensation control for the offshore crane.

Further, the active heave compensation control for the offshore crane is connected to the offshore crane, the offshore crane includes an electro-hydraulic servo winch, and the winch is connected to an underwater load through a cable.

Further, the cable and the underwater load form a spring-mass-damper system. The system is used to quickly construct a load dynamics model and an electro-hydraulic servo winch dynamics model in the offshore crane to improve the accuracy of heave compensation. The beneficial effects of the present disclosure are: The active heave compensation control for an offshore crane according to the present disclosure has a double-loop structure, wherein the outer-loop control system uses the advantages of an active disturbance rejection control, such as simple structure, no need for model parameters, and strong robustness, to compensate for the disturbances such as underwater ocean currents, friction and model uncertainty in the outer loop system, the input is a desired position of the underwater load, and the output is a desired angle of the electro-hydraulic servo winch; the inner loop is an electro-hydraulic servo winch control loop, which considers that the electro-hydraulic servo winch system has nonlinear characteristics such as input saturation and dead zone; the input of the ' 25 equivalent saturation model predictive control is used as the desired angle, and the output is the | actual rotation angle of the electro-hydraulic servo winch, which ensures that the electro-hydraulic servo winch can quickly and accurately track the desired angle.

Brief Description of the Drawings The accompanying drawings constituting a part of the present disclosure are used for providing a further understanding of the present disclosure, and the schematic embodiments of the present disclosure and the descriptions thereof are used for interpreting the present disclosure, rather|thap2696 constituting improper limitations to the present disclosure.

Fig. 1 is a schematic diagram of an offshore crane system according to an embodiment of the present disclosure.

Fig. 2 is a schematic diagram of an electro-hydraulic servo winch according to an embodiment of the present disclosure.

Fig. 3 is a schematic structural diagram of an active heave compensation control for a offshore crane according to an embodiment of the present disclosure.

Fig. 4 is a schematic structural diagram of an active disturbance rejection control according to an embodiment of the present disclosure.

Fig. 5 is a schematic diagram of a saturated and dead zone series system according to an embodiment of the present disclosure.

Fig. 6 is a schematic structural diagram of an equivalent saturation model predictive control according to an embodiment of the present disclosure.

Fig. 7 shows the motion and displacement of a floating crane and an underwater load according to an embodiment of the present disclosure.

Fig. 8 shows the tension of a cable and the output of an observer according to an embodiment of the present disclosure.

Fig. 9 shows compensation effects of the controls according to an embodiment of the present disclosure.

Fig. 10 shows a result of heave compensation under the influence of disturbances according to an embodiment of the present disclosure.

Fig. 11{a) is a comparison diagram of heave compensation effects before compensation and after œ=2.5sin 27, compensation when 5 according to an embodiment of the present disclosure.

Fig. 11(b) is a comparison diagram of heave compensation effects before compensation and after w=4 sin; compensation when 6 according to an embodiment of the present disclosure.

Fig. 11(c) is a comparison diagram of heave compensation effects before compensation and after @ = 6sin 27, compensation when 7 according to an embodiment of the present disclosure.

Detailed Description of Embodiments The present disclosure will be further illustrated below in conjunction with the accompanying drawings and embodiments.

It should be noted that the following detailed descriptions are exemplary and are intended to provide further descriptions of the present disclosure. All technical and scientific terms used in the embodiments have the same meanings as commonly understood by those of ordinary skill in the technical field to which the present disclosure belongs, unless otherwise indicated.

It should be noted that the terms used here are merely used for describing specific embodiments, but are not intended to limit the exemplary embodiments of the present invention. As used herein, the singular form is also intended to include the plural form uniess otherwise indicated in the context. In addition, it should be understood that when the terms “contain” and/or “include” are used in the description, they are intended to indicate the presence of features, steps, operations, devices, components and/or combinations thereof. Explanation of terms: ADRC: Active Disturbance Rejection Control; ESMPC: Equivalent Saturation Model Predictive Control; ADRC-ESMPC: Active Disturbance Rejection Control-Equivalent Saturation Model Predictive Control. The structure of an offshore crane is analyzed below: The structure of the offshore crane is shown in Fig. 1 and Fig. 2. An underwater load is connected to an electro-hydraulic servo winch through a cable. In the embodiment 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-damper system. In addition, it is assumed that the mass of the underwater load is a multiple of the mass of a hull at a level of 10? or below, and the motion of the underwater load does not affect the motion of the hull.

This embodiment focuses on heave compensation control of the underwater load in the vertical direction, so the lateral force of the underwater load is not considered in the design process of a control.

Since the load is submerged in water, the hydrodynamic force needs to be considered. The

. m . . Ce LU102696 equivalent mass “ of the load submerged in water in the vertical direction is expressed as: m, =Mam+m, Where M is the mass of the load and a hook in the air. is an additional mass, expressed in the following form: m=p CF (2) Where Aw is a water density, Ca is an additional mass coefficient, and V is a volume of the load submerged in water. 1 m,=—mJ, m ] 3 is an equivalent mass of the cable. ““e is the mass of the cable per meter, and “« is a nominal length of the cable and can be expressed in the following form: 1 (0) =1(0)+r0() 5

1. (0) is an initial length of the cable, r is a radius of the winch, and Of) is the rotation angle of the winch. According to the Newton's formula, a dynamic equation of the load can be expressed in the following form: 2» 1 1 N | m, (ré(t) ++ Al) = (m + mE — 7P.C,2f — P,gY — KA (4) | —_—— Where Ü(#) is an angular acceleration of rotation of the winch. @ is a heave displacement of a floating crane under the action of waves, and @ is an acceleration of the heave displacement of the floating crane. Al, is a dynamic elongation of the cable. Al is a dynamic elongation acceleration of the cable. z represents a position of the underwater load. Z and = respectively represent a speed and an acceleration of the underwater load. g is a gravity acceleration. C, is a water damping coefficient. V is the volume of the load submerged in water. Al = AI, + Al, is an elongation of the cable, wherein Al, is a static elongation, and the sum of static tension and buoyancy is equal to the gravity of the load and the cable, that is,

(m+—ml)g=KAl + P,8Y 2 (5) K is a stiffness coefficient of the cable, and the cable follows the Hooke's law:

E A K==r—r L © Where E, and 4, represent the Young's modulus and the cross-sectional area of the cable. The motion of the floating crane under regular waves can be estimated by the wave height and period. The heave displacement of the floating crane is directiy proportional to the height of waves. It is assumed that the proportional coefficient is H | the amplitude of the wave height is X, and the wave period is T, then the heave displacement of the floating crane can be expressed by the | following formula: | x (2 a(t) = EL sin — 7 KT) The active heave compensation system generally uses the electro-hydraulic servo winch as an actuator, and its structure is shown in Fig. 2. The angle output of the electro-hydraulic servo winch can be expressed as the following transfer function: K u “e ) = a, s(s / @, +2€,/w, +1) (8) Where, K, is the proportional coefficient. # is the control input. @ is the natural frequency of the hydraulic winch. Sn is the damping coefficient. Through the above analysis: The control objective of the heave compensation system can be described as enabling the underwater load z(f) = (0) + ré(t) + (1) + Al(1) to quickly and accurately track a desired trajectory under the influence of waves. In order to achieve the control objective, this embodiment designs a nonlinear control with a dual-loop structure. The structure of the control is shown in Fig. 3. For the outer loop system, an ADRC is designed to compensate for external disturbances, nonlinear friction, and model uncertainty, and to generate a desired angle for the inner loop. For the inner loop system, an

ESMPC is designed to ensure that the electro-hydraulic servo winch can accurately track the detiped2696 angle in the cases of bounded input and dead zones. (1) Design of an outer loop control An active disturbance rejection control has strong robustness, does not require model parameter information, and is currently widely used in the field of automatic control.

The structure of the active disturbance rejection control is shown in Fig. 4. A differential tracker is used to obtain a differential value of an input signal.

The differential form is designed as follows: x (k+1) =x, (k)+ hx, (k) (5 (k+1) =x, (k)+hfst(x —z, (E)xroh) 5) The function f$H x, — Z, (k),x,,7,,h) is defined as: d, =r,h°,a =h,y =x —z, +a, s, =(sign(y+d,) —sign(y—d, )) /2 a =Jd,(d, +8) fit(x —2,(k),x"ph;) =14=% +sign(y)(a —d/) /2 a=(a, +y-a)s, +a, 5, =(sign(a+d,)-sign(a-d,)) /2 At(x—z,(k),x,.7,,h) =—v,(a/d, —sign(a))s, —r,sign( a) (10) Where “4 is a desired position of the underwater load, and the parameter rs determines a tracking speed of the differential tracker; À is a filtering parameter; the state variables x; and x; respectively track a desired position signal of the underwater load and a differential signal thereof.

An extended state observer is constructed as follows: e,=2,(k)-2(t) 1,(k+1)=7(k)+h(z,(k)- Be,) z,(k+1)=z,(k)+h(z,(k)- B fal(e,,a,6)) z,(k+1)=z,(k)- A,fal(e,,a,,6) (11) The nonlinear function Fe al(e,.a, > ö) (i=1, 2) is defined as:

a, . LU102696 of signe) le/>6 fal(e,,a,6)= 4 ele, | 6 1) À nonlinear feedback combination module is designed as follows: e=z,-z2 e,=zZ,—2 27 “yg (13) u, =k fal(e,a.,6)+k fal(e,,a,,,5) 0,=u, — 7, / Where, i=1, 2; eı is a position error of the underwater load; e2 is a speed error of the underwater load; z3 is an estimate of the disturbances undergone by the underwater load and an unmodeled dynamic quantity; k, , a. , 0 and bo are all control constants; and 0, is an output of the active disturbance rejection control, that is, a desired angle trajectory of the winch.

Z and Z are a position and a speed of the underwater load respectively, z4 and Z, are a desired position and a desired speed of the underwater load respectively, # is the filtering parameter, 4, and B / are both control constants, i=1,2, j=1,2,3; and k represents a discrete time point.

Considering that the elongation of the cable cannot be directly measured, the position of the underwater load cannot be directly measured. To solve this problem, a state observer is designed to estimate the elongation of the cable. State variables of the observer are defined as: 7 D=[ Al AT] ; Then the state observer is designed as follows: d=AD+Bu,+C,(F,-F,) a4) Where: 0 1 A=| K 0 0 r . Mey .B,=[0 1] : D and ® are estimated values of the state variables ® and & respectively, and u, = rl — à is the input of the observer: Co is a feedback compensation matrix, and the matrix can be obtained by a pole assignment method; Fa is an elastic force of the cable; F is an estimated value of the elastic force of the cable; Ÿ is the output of the state observer, which is defined in the following form: LU102696 A A 1 5 y= =m + md. |a+kai 2 (15) Where, Al is an estimated value of the elongation Al of the cable.

At this time, the position of the underwater load can be approximated as: ; z(t)=1(0)+r0(t)+æ(t)+ Al (1) (16) (2) Design of an inner loop control In actual engineering, most electro-hydraulic servo systems have nonlinear characteristics, such as bounded input and dead zone.

In response to this problem, an equivalent saturation model predictive control (ESMPC) is proposed below, as shown in Fig. 5. Before the control is designed, the dead zone and the bounded input should be analyzed and defined.

The characteristics of the dead zone can be expressed as: u(t)=c if u(t)zc ug. =, (u(t) = 0 if —c<u(t)<c ult)+c if ult)é-c (Je Fu()<< an Where, c is a positive constant; and u(#) is an input signal.

The right inverse of the dead zone can be expressed as: u(t)te if u(t)>0 ofu(r))=10 if u()=0 u(t)—c if u(lt)<OÔ The bounded input can be expressed as: V if u(t)zv u, =sat,(u(t))=qu(t) if -v<u(t)<v —v if u(t}s-v if ( ) (19) Where, v is a positive constant.

For the system shown in Fig. 5, if the nonlinear function vb) is equal to the right inverse of the ms + . dead zone, that is, y) = Pa ( ) then for any u(r) eL [0,%) , whenV > €,

ve if u(t)2v-c LU102696 P,. (sat, (A (u()))) =sat, (u(t))= a if —v+e<u(t)<v-c —v+e if ult)sv+c 20) According to the above equivalent bounded theory, the control structure diagram of ESMPC is shown in Fig. 6. It can be seen that the system can equate complex nonlinear characteristics to simple bounded characteristics after equivalence. In this way, the complexity of calculation is greatly simplified, and the prediction domain of the model predictive control can be enlarged to further improve the control effect. The control law of the equivalent saturation model predictive control is obtained by quadratic minimization of a cost function. The cost function is defined as: Np Ne N, J=Y x1,.0x,, + > uw Pu + > Au” RAU i=0 i=0 i=0 Xitmin < Xi < Xa —v+ec<u<v-—c N.<N p @1) Where, i=1, 2; 0, R and P are weight parameters; x is a variable error; # is a control input; Au is a change rate of the control input; N, represents a prediction domain; Ne is a control domain; c and v are both positive constants; Xam» is a minimum value of the variable error, and XAmax is à maximum value of the variable error.

Simulation analysis will be performed below on the ADRC-ESMPC strategy proposed in the embodiments of the present disclosure. The effectiveness of ADRC-ESMPC strategy is proved by comparing the control effect of the ADRC-ESMPC strategy with the control effects of the PID control, the ADRC and the MPC.

In the simulation experiment, the model parameters of the offshore crane system are shown in Table 1, and the parameters of the control are shown in Table 2.

The inputs of the PID control, the ADRC and the MPC are the heave displacement of the floating crane. The gain of the PID control is obtained through a PID tuner module in Simulink, and its form is as follows:

(5) =k, (bo, -0@)+k, (0, -w)+k,—(co, - o) LU102696 U nid =K, d sc d 1 d 1+N— § (22) Where, kp, ki, and ka are a proportional parameter, an integral parameter and a differential parameter of the PID control respectively; b, c, and N are control parameters of the PID control; Cd is a desired heave displacement of the offshore crane.

Table 1 Model parameters LU102696 Parameter Value Parameter #3 Value i M 42006Kg V m, 7.26Ke /m c, R 0.5m EA Pu 1025Kg ' m’ C, Table 2 Control parameters Control Control parameter k, =35.86 [b=0.99 PID k =3,27 4e=1.06 k;=-154 [N =22.02 B =[0.1, 40.1] b=1 h=0.01 ADRC k=[100.70] 46=01 T =0.001 a=[0.5.1.5] |r=20 =2.23 N, =10 © MPC P=0 N =2 ‘ R=0.045 B=|1.20.3} {b, =4 h=0.01 k=[20.5] <6=01 T =0.001 a=[0.5.1.5] (r= 20 ADRC-ESMPC =1.90 N,=10 2 P=0 N =2 € R=0.053 -_— °°°... The motion of a hull is obtained according to formula (7). The heave motion of the underwater load is calculated by formula (4). After the initial length of the cable is preset, poles of the state obsenye52696 are assigned to be -150 and -100 respectively. The motion of the hull and the motion of the underwater load without control are shown in Fig. 7. The output of the state observer and the tension of the cable are shown in Fig. 8. The heave compensation control effect of each control is shown in Fig. 9. It can be seen from Fig. 7 that the amplitude of the heave displacement of the underwater load is

3.13 m, which is much larger than that of the floating crane. The dynamic amplification coefficient is 2.5, which greatly exceeds the safety factor of 1.9, so heave compensation has to be carried out for the underwater load.

It can be seen from Fig. 8 that the state observer has fast convergence speed and observation accuracy. Compared with the true value, the average error of the observed values is 42.31 (from

0.09 second to 20 seconds), and the standard deviation of errors is 18.42. This shows that the output of the state observer can well estimate the elastic force of the cable, and the position of the underwater load can be calculated by formula (16).

It can be seen from Fig. 9 that, compared with the PID control, the ADRC has smaller overshoot and higher compensation accuracy. However, due to the limited abilities of the PID control and the ADRC in processing the characteristics of bounded input and dead zone, their compensation accuracy is much lower than that of MPC and ADRC-ESMPC. The tracking error ranges of the above four controls are respectively +£0.78 m, +0.63 m, 0.071 m and +0.076 m. Then, the compensation percentages of heave displacements are respectively: (313-0.78)/3.13x100% = (PID control) ) # (ADRC) (313—0.63)/3.13x100% = 7.0/7 \AUKC | (MPC) (313—0.071)/3. 13x100% =97.73% (MPC (ADRC-ESMPC) It can be seen from the above calculation that the ADRC-ESMPC can better compensate the heave motion of the underwater load in the case of nonlinear characteristics of the actuator. In order to further verify the robustness of the ADRC-ESMPC, it is assumed that the underwater load is suddenly interfered during 15-20 seconds. The external interference is defined as follows:

d=d, +d, 0» | LU102696 Where, Gh =2000sin0.4¢(N)(0<t), d,=1x10°sin Zr(N) The control gain and initial state of the control and the parameters of the crane remain unchanged.

It can be seen from Fig. 10 that, when t<15 s, the two controls can better compensate the heave displacement of the underwater load to be within a range of +0.1 m, and the compensation percentage is more than 96.81%. When d begins to act on the system, under the control of MPC, the underwater load fluctuates greatly, and the amplitude of the heave displacement reaches 0.6 m.

The reason for this phenomenon is that the input of the MPC is the heave displacement of the crane, and the deep-water ocean current has less influence on the motion of the hull and greater influence on the motion of the load.

In contrast, the ADRC-ESMPC strategy can always maintain the efficient heave compensation effect, and can limit the heave displacement of the load to be +0.1 m whether it is affected by dz or not.

Considering that the offshore crane may work in different sea conditions, the heave compensation effects of ADRC-ESMPC under different sea conditions will be verified.

The parameters of the control, the system parameters of the offshore crane and the initial state remain unchanged.

The disturbance is d = 2000sin 0.4t(N)(0 << 50) From Fig. 11 (a)-Fig. 11 (c), it can be seen that under different sea conditions, ADRC-ESMPC can ensure that the heave displacement of the underwater load is limited to a very small range.

The compensation percentages are respectively: (4.09 —0.78)23/ 4.09 x 100% = (Sea condition (a)) (Sea condition (b)) (AAA _NAOY/ A AA XTAMA= 07 ata 18 (7.60—1.09)/ 7.60% 100% = 85 (Sea condition (c)) The above simulation results prove that the ADRC-ESMPC proposed in this embodiment not only can effectively compensate the heave motion of the underwater load, but also has strong robustness to external disturbances.

In addition, due to the optimization capability of ESMPC, the nonlinear characteristics of the actuator such as bounded input and dead zone are better compensated.

The control strategy has an outer-inner loop structure.

In the outer loop, the active disturbance rejection control is used to compensate for the external disturbances and generate desired angle

| 19 information for the inner loop subsystem.

For the inner loop system, considering that {hep2696 electro-hydraulic servo winch system has nonlinear characteristics such as bounded input and dead zone, this embodiment designs an equivalent saturation model predictive control to compensate for the nonlinear characteristics, thereby ensuring that the winch can quickly and accurately track the desired angle.

The simulation results prove that the ADRC-ESMPC proposed in this embodiment has strong robustness to external disturbances, and has good compensation accuracy under different sea conditions.

Described above are merely preferred embodiments of the present application, and the present application is not limited thereto.

Various modifications and variations may be made to the present application for those skilled in the art.

Any modification, equivalent substitution, improvement or the like made within the spirit and principle of the present application shall fall into the protection scope of the present application.

Claims

CLAIMS LU102696

1. An active heave compensation control for an offshore crane, wherein the active heave compensation control for the offshore crane has a double-loop control structure;, the outer-loop control structure is an active disturbance rejection control, which is used to compensate for external disturbances and generate a desired angle for the inner loop; and the inner-loop control structure is an equivalent saturation model predictive control, which is used to compensate for input saturation and dead zone characteristics of an electro-hydraulic servo winch to ensure that the electro-hydraulic servo winch quickly and accurately tracks the desired angle.

2. The active heave compensation control for the offshore crane according to claim 1, wherein the active disturbance rejection control comprises: a differential tracker, which is used to calculate a differential value of an input signal, wherein the input signal is the position of an underwater load; the differential value of the input signal is a speed of the underwater load; an extended state observer, which is used to estimate the position and speed of the underwater load and the disturbances and unmodeled dynamic quantity in a load dynamics model; and a nonlinear feedback combination module, which is: u, = k fal (e,,a,,,8) +k, fal(e,,a.,,0) 0,=u, —z,/b _ * |" sign(e,) le |> 6 fal(e,a,;,0)= ele le|<é where i=1, 2; eı is a position error of the underwater load; e is a speed error of the underwater load; z3 is an observed quantity of the disturbances undergone by the underwater load and the unmodeled dynamic quantity; k, , Ya, Ô and bo are all control constants; and Ca is an output of the active disturbance rejection control, that is, a desired angle trajectory of the winch.

3. The active heave compensation control for the offshore crane according to claim 2, wherein a differential equation of the differential tracker is: x, (k+1) = x, (k) + hx, (k) A (k+1)= x, (k) + hfst(x — zu (&),x2,7,h)

d,=rh’,ay=hx,y=x-2,+a, LU102696 s, =(sign(y+d,)-sign(y-d,))/2 a = /d,(d, +8|»]) a, =a, +sign(y)(a, —d,)/2 a=(a,+y-a,)s, +a, 5, = (sign(a +d,)- sign(a— d,)}/2 {x zu (k), x fs h)=-5, (a ld, - sign(a))s, —r,sign(a) where “4 is a desired position of the underwater load, and the parameter r4 determines a tracking speed of the differential tracker; h is a filtering parameter; and the state variables x1 and x2 respectively track a desired position signal and a desired speed signal of the underwater load.

4. The active heave compensation control for the offshore crane according to claim 2, wherein a construction equation of the extended state observer is: e, =z (k) — z(k) z,(k+1)=z,(k)+h(z,(k)- Be,) z,(k+1)=z,(k) + h(z, (k) - B, fal (e,.a,,5)) z,(k+1)=z,(k)- 8,fal(e,,a,,6) e,|” sign(e e|>0 fal(e,,a,,6)= | | (e.) | | ele © le. | <ô where i=1, 2; j=1, 2, 3; Z is the position of the underwater load, zi is an estimate of the position of the underwater load, z2 is an estimate of the speed of the underwater load, and z3 is an estimate of the disturbances undergone by the underwater load and the unmodeled dynamic quantity; A is the filtering parameter, 4; and p / are both control constants, and k represents a discrete time point.

5. The active heave compensation control for the offshore crane according to claim 1, wherein the expression of the position of the underwater load in a continuous time domain is: 1, Z(1)=1(0)+r0(1)+œ(t)+ where I(0) is an initial length of a cable, r is a radius of the winch, O(t) is an angle of rotation

| 22 a(t) . | | LU102696 of the electro-hydraulic servo winch, is a heave motion of the floating crane under the action of waves, Al (7) is an estimated value of elongation of the cable, and the elongation of the cable is estimated by the state observer.

6. The active heave compensation control for the offshore crane according to claim 5, wherein the expression of the heave displacement a(t) of the floating crane under the action of waves is: o(t)= MX sin (2 7 7 where is a proportional coefficient between the amplitude of the heave displacement of the floating crane and the wave height, X is the amplitude of the wave height, and 7 is a wave period.

7. The active heave compensation control for the offshore crane according to claim 1, wherein the control law of the equivalent saturation model predictive control is obtained by quadratic minimization of a cost function; and the cost function is: N, Ne N. J=> x,,0x,, + Su" Pu + > Au" RAU i=0 i=0 i=0 X Mmin < Xs < X Mmax -V+HC<U<V-C N.<N p where i=1, 2; J, R and P are weight parameters; xx is a variable error; u is a control input; À u is a change rate of the control input; Np is a prediction domain; Ne is a control domain; c and v are both positive constants; XMmin 15 a minimum value of the variable error, and Xumax 1s a maximum value of the variable error.

8. An active heave compensation control system for an offshore crane, comprising the active heave compensation control for the offshore crane according to any one of claims 1-7.

9. The active heave compensation control system for the offshore crane according to claim 8, wherein the active heave compensation control for the offshore crane is connected to the offshore crane, the offshore crane comprises an electro-hydraulic servo winch, and the winch is connected to an underwater load through a cable.

10. The active heave compensation control system for the offshore crane according to claim 9, wherein the cable and the underwater load form a spring-mass-damper system.