Crane controller with division of a kinematically constrained quantity of the hoisting gear

Abstract

The present disclosure relates to a crane controller for a crane which includes a hoisting gear for lifting a load hanging on a cable, with an active heave compensation which by actuating the hoisting gear at least partly compensates the movement of the cable suspension point and/or of a load deposition point due to the heave, and an operator control which actuates the hoisting gear with reference to specifications of the operator, wherein the division of at least one kinematically constrained quantity of the hoisting gear is adjustable between heave compensation and operator control.

Claims

1. A crane controller for a crane which includes a hoisting gear for lifting a load hanging on a cable, comprising: an active heave compensation which by actuating the hoisting gear at least partly compensates a movement of a cable suspension point and/or a load deposition point due to a heave; and an operator control which actuates the hoisting gear with reference to specifications of an operator, wherein a division of at least one kinematically constrained quantity of the hoisting gear is adjustable between the heave compensation and the operator control, wherein the division of the at least one kinematically constrained quantity is effected via at least one weighting factor, via which a maximum available power and/or velocity and/or acceleration of the hoisting gear is split up between the heave compensation and the operator control.

2. The crane controller according to claim 1, wherein the division of the at least one kinematically constrained quantity of the hoisting gear comprises a division of the maximum available power and/or maximum available velocity and/or maximum available acceleration of the hoisting gear.

3. The crane controller according to claim 1, wherein the division is steplessly adjustable at least over a partial region and/or wherein the heave compensation is switched off by assigning an entire at least one kinematically constrained quantity to the operator control.

4. A crane controller for a crane which includes a hoisting gear for lifting a load hanging on a cable, comprising: an active heave compensation which by actuating the hoisting gear at least partly compensates movement of a cable suspension point and/or a load deposition point due to heave; and an operator control which actuates the hoisting gear with reference to specifications of an operator, wherein the controller includes two separate path planning modules via which trajectories for the heave compensation and for the operator control are calculated separate from each other, wherein the trajectories specified by the two separate path planning modules are added up and serve as setpoint values for control and/or regulation of the hoisting gear, wherein the control of the hoisting gear feeds back measured values to a position and/or velocity of a hoisting winch of the hoisting gear and/or takes account of dynamics of a drive of the hoisting winch.

5. The crane controller according to claim 4, wherein the heave compensation includes an optimization function which calculates a trajectory with reference to a predicted movement of the cable suspension point and/or the load deposition point and takes into account at least one kinematically constrained quantity available for the heave compensation, wherein the operator control calculates a trajectory with reference to specifications of the operator and takes into account at least one kinematically constrained quantity available for the operator control.

6. The crane controller according to claim 5, wherein a division of the at least one kinematically constrained quantity is changed during a lifting operation.

7. The crane controller according to claim 4, further comprising a calculation function which calculates a currently available at least one kinematically constrained quantity, wherein the calculation function takes account of a length of unwound cable and/or a cable force and/or a power available for driving the hoisting gear.

8. The crane controller according to claim 6, wherein the optimization function of the heave compensation initially includes a change in the division of the at least one kinematically constrained quantity of the hoisting gear and/or a change of an available at least one kinematically constrained quantity of the hoisting gear during lifting only at an end of a prediction horizon and then pushes the at least one kinematically constrained quantity to a beginning with progressing time.

9. The crane controller according to claim 8, wherein the optimization function of the heave compensation determines a target trajectory which is included in the control of the hoisting gear, wherein optimization can be effected at each time step on the basis of an updated prediction of movement of a load lifting point.

10. The crane controller according to claim 8, wherein the optimization function of the heave compensation determines a target trajectory which is included in the control of the hoisting gear, wherein the optimization function works with a greater scan time than the control.

11. The crane controller according to claim 8, wherein the optimization function of the heave compensation determines a target trajectory which is included in the control of the hoisting gear, wherein the optimization function makes use of an emergency trajectory planning when no valid solution is found.

12. The crane controller according to claim 8, wherein the operator control calculates a velocity desired by the operator with reference to a signal specified by an operator through an input device.

13. A crane controller for a crane which includes a hoisting gear for lifting a load hanging on a cable, comprising: an active heave compensation which by actuating the hoisting gear at least partly compensates movement of a cable suspension point and/or a load deposition point due to heave; and an operator control which actuates the hoisting gear with reference to specifications of an operator, wherein the controller includes two separate path planning modules via which trajectories for the heave compensation and for the operator control are calculated separate from each other, wherein the heave compensation includes an optimization function which calculates a trajectory with reference to a predicted movement of the cable suspension point and/or the load deposition point and takes into account at least one kinematically constrained quantity available for the heave compensation, wherein the operator control calculates a trajectory with reference to specifications of the operator and takes into account at least one kinematically constrained quantity available for the operator control, wherein a division of the at least one kinematically constrained quantity is changed during a lifting operation, wherein the optimization function of the heave compensation initially includes a change in the division of the at least one kinematically constrained quantity of the hoisting gear and/or a change of an available at least one kinematically constrained quantity of the hoisting gear during lifting only at an end of a prediction horizon and then pushes the at least one kinematically constrained quantity to a beginning with progressing time, wherein the operator control calculates a velocity desired by the operator with reference to a signal specified by an operator through an input device, and wherein path planning of the operator control generates the trajectory by integration of a maximum admissible positive jerk, until a maximum acceleration is achieved, and thereupon is achieved by integration of the maximum acceleration, until the desired velocity can be achieved by adding a maximum negative jerk.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) FIG. 1 shows a crane according to the present disclosure arranged on a pontoon.

(2) FIG. 2 shows the structure of a separate trajectory planning for the heave compensation and the operator control.

(3) FIG. 3 shows a fourth order integrator chain for planning trajectories with steady jerk.

(4) FIG. 4 shows a non-equidistant discretization for trajectory planning, which towards the end of the time horizon uses larger distances than at the beginning of the time horizon.

(5) FIG. 5 shows how changing constraints first are taken into account at the end of the time horizon using the example of velocity.

(6) FIG. 6 shows the third order integrator chain used for the trajectory planning of the operator control, which works with reference to a jerk addition.

(7) FIG. 7 shows the structure of the path planning of the operator control, which takes account of constraints of the drive.

(8) FIG. 8 shows an exemplary jerk profile with associated switching times, from which a trajectory for the position and/or velocity and/or acceleration of the hoisting gear is calculated with reference to the path planning.

(9) FIG. 9 shows a course of a velocity and acceleration trajectory generated with the jerk addition.

(10) FIG. 10 shows an overview of the actuation concept with an active heave compensation and a target force mode, here referred to as constant tension mode.

(11) FIG. 11 shows a block circuit diagram of the actuation for the active heave compensation.

(12) FIG. 12 shows a block circuit diagram of the actuation for the target force mode.

DETAILED DESCRIPTION

(13) FIG. 1 shows an exemplary embodiment of a crane 1 with a crane controller according to the present disclosure for actuating the hoisting gear 5. The hoisting gear 5 includes a hoisting winch which moves the cable 4. The cable 4 is guided over a cable suspension point 2, in the exemplary embodiment a deflection pulley at the end of the crane boom, at the crane. By moving the cable 4, a load 3 hanging on the cable can be lifted or lowered.

(14) There can be provided at least one sensor which measures the position and/or velocity of the hoisting gear and transmits corresponding signals to the crane controller.

(15) Furthermore, at least one sensor can be provided, which measures the cable force and transmits corresponding signals to the crane controller. The sensor can be arranged in the region of the crane body, in particular in a mount of the winch 5 and/or in a mount of the cable pulley 2.

(16) In the exemplary embodiment, the crane 1 is arranged on a pontoon 6, here a ship. As is likewise shown in FIG. 1, the pontoon 6 moves about its six degrees of freedom due to the heave, the heaving including heaving motion. The crane 1 arranged on the pontoon 6 as well as the cable suspension point 2 also are moved thereby.

(17) The crane controller may be a microcomputer including: a microprocessor unit, input/output ports, read-only memory, random access memory, keep alive memory, and a data bus. As noted above, software with code for carrying out the methods according to the present disclosure may be stored on a machine-readable data carrier in the controller. Advantageously, a crane controller according to the present disclosure can be implemented by installing the software according to the present disclosure on a crane controller. The crane controller may receive various signals from sensors coupled to the crane and/or pontoon. In one example, the software may include various programs (including control and estimation routines, operating in real-time), such as heave compensation, as described herein. The specific routines described herein may represent one or more of any number of processing strategies such as event-driven, interrupt-driven, multi-tasking, multi-threading, and the like. Thus, the described methods may represent code to be programmed into the computer readable storage medium in the crane control system.

(18) In one example, the crane controller according to the present disclosure can include an active heave compensation which by actuating the hoisting gear at least partly compensates the movement of the cable suspension point 2 due to the heave. In particular, the vertical movement of the cable suspension point due to the heave is at least partly compensated.

(19) The heave compensation can comprise a measuring device which determines a current heave movement from sensor data. The measuring device can comprise sensors which are arranged at the crane foundation. In particular, this can be gyroscopes and/or tilt angle sensors. Particularly, three gyroscopes and three tilt angle sensors are provided.

(20) Furthermore a prediction device can be provided, which predicts a future movement of the cable suspension point 2 with reference to the determined heave movement and a model of the heave movement. In particular, the prediction device solely predicts the vertical movement of the cable suspension point. In connection with the measuring and/or prediction device, a movement of the ship at the point of the sensors of the measuring device possibly can be converted into a movement of the cable suspension point.

(21) The prediction device and the measuring device advantageously are configured such as is described in more detail in DE 10 2008 024513 A1.

(22) Alternatively, the crane according to the present disclosure also might be a crane which is used for lifting and/or lowering a load from or to a load deposition point arranged on a pontoon, which therefore moves with the heave. In this case, the prediction device must predict the future movement of the load deposition point. This can be effected analogous to the procedure described above, wherein the sensors of the measuring device are arranged on the pontoon of the load deposition point. The crane for example can be a harbor crane, an offshore crane or a cable excavator.

(23) In the exemplary embodiment, the hoisting winch of the hoisting gear 5 is driven hydraulically. In particular, a hydraulic circuit of hydraulic pump and hydraulic motor is provided, via which the hoisting winch is driven. In one example, a hydraulic accumulator can be provided, via which energy is stored on lowering the load, so that this energy is available when lifting the load.

(24) Alternatively, an electric drive might be used. The same might also be connected with an energy accumulator.

(25) In the following, an exemplary embodiment of the present disclosure will now be shown, in which a multitude of aspects of the present disclosure are jointly realized. The individual aspects can, however, also each be used separately for developing the embodiment of the present disclosure as described in the general part of the present application.

(26) 1 Planning of Reference Trajectories

(27) For implementing the required predictive behavior of the active heave compensation, a sequential control comprising a pilot control and a feedback in the form of a structure of two degrees of freedom is employed. The pilot control is calculated by a differential parameterization and requires reference trajectories steadily differentiable two times.

(28) For planning it is decisive that the drive can follow the specified trajectories. Thus, constraints of the hoisting gear are also taken into account. Starting point for the consideration are the vertical position and/or velocity of the cable suspension point {tilde over (z)}.sub.a.sup.h and {tilde over (ż)}.sub.a.sup.h, which are predicted e.g. by the algorithm described in DE 10 2008 024 513 over a fixed time horizon. In addition, the hand lever signal of the crane operator, by which he moves the load in the inertial coordinate system, also is included in the trajectory planning.

(29) For safety reasons it is necessary that the winch also can still be moved via the hand lever signal in the case of a failure of the active heave compensation. With the used concept for trajectory planning, a separation between the planning of the reference trajectories for the compensation movement and those as a result of a hand lever signal therefore is effected, as is shown in FIG. 1.

(30) In the Figure, y.sub.a*, {dot over (y)}.sub.a* and ÿ.sub.a* designate the position, velocity and acceleration planned for the compensation, and y.sub.l*, {dot over (y)}.sub.l* and ÿ.sub.l* the position, velocity and acceleration for the superimposed unwinding or winding of the cable as planned on the basis of the hand lever signal. In the further course of the execution, planned reference trajectories for the movement of the hoisting winch always are designated with y*, {dot over (y)}* and ÿ*, respectively, since they serve as reference for the system output of the drive dynamics.

(31) Due to the separate trajectory planning it is possible to use the same trajectory planning and the same sequential controller with the heave compensation switched off or in the case of a complete failure of the heave compensation (e.g. due to failure of the IMU) for the hand lever control in manual operation and thereby generate an identical operating behavior with the heave compensation switched on.

(32) In order not to violate the given constraints in velocity v.sub.max and acceleration a.sub.max despite the completely independent planning, v.sub.max and a.sub.max are split up by a weighting factor 0≦k.sub.l≦1 (cf. FIG. 1). The same is specified by the crane operator and hence provides for individually splitting up the power which is available for the compensation and/or for moving the load. Thus, the maximum velocity and acceleration of the compensation movement are (1−k.sub.l)v.sub.max and (1−k.sub.l)a.sub.max and the trajectories for the superimposed unwinding and winding of the cable are k.sub.lv.sub.max and k.sub.la.sub.max.

(33) A change of k.sub.l can be performed during operation. Since the maximum possible traveling speed and acceleration are dependent on the total mass of cable and load, v.sub.max and a.sub.max also can change in operation. Therefore, the respectively applicable values likewise are handed over to the trajectory planning.

(34) By splitting up the power, the control variable constraints possibly are not utilized completely, but the crane operator can easily and intuitively adjust the influence of the active heave compensation.

(35) A weighting of k.sub.l=1 is equal to switching off the active heave compensation, whereby a smooth transition between a compensation switched on and switched off becomes possible.

(36) The first part of the chapter initially explains the generation of the reference trajectories y.sub.a*, {dot over (y)}.sub.a* and ÿ.sub.a* for compensating the vertical movement of the cable suspension point. The essential aspect here is that with the planned trajectories the vertical movement is compensated as far as is possible due to the given constraints set by k.sub.l.

(37) Therefore, by the vertical positions and velocities of the cable suspension point {tilde over (z)}.sub.a.sup.h=[{tilde over (z)}.sub.a.sup.h(t.sub.k+T.sub.p,l) . . . {tilde over (z)}.sub.a.sup.h(t.sub.k+T.sub.p,K.sub.p)].sup.T and {tilde over (ż)}.sub.a.sup.h=[{tilde over (ż)}.sub.a.sup.h(t.sub.k+T.sub.p,l) . . . {tilde over (ż)}.sub.a.sup.h(t.sub.k+T.sub.p,K.sub.p)].sup.T predicted over a complete time horizon, an optimal control problem therefore is formulated, which is solved cyclically, wherein K.sub.p designates the number of the predicted time steps. The associated numerical solution and implementation will be discussed subsequently.

(38) The second part of the chapter deals with the planning of the trajectories y.sub.l*, {dot over (y)}.sub.l* and ÿ.sub.l* for traveling the load. The same are generated directly from the hand lever signal of the crane operator w.sub.hh. The calculation is effected by an addition of the maximum admissible jerk.

(39) 1.1 Reference Trajectories for the Compensation

(40) In the trajectory planning for the compensation movement of the hoisting winch, sufficiently smooth trajectories must be generated from the predicted vertical positions and velocities of the cable suspension point taking into account the valid drive constraints. This task subsequently is regarded as constrained optimization problem, which can be solved online at each time step. Therefore, the approach resembles the draft of a model-predictive control, although in the sense of a model-predictive trajectory generation.

(41) As references or setpoint values for the optimization the vertical positions and velocities of the cable suspension point {tilde over (z)}.sub.a.sup.h=[{tilde over (z)}.sub.a.sup.h(t.sub.k+T.sub.p,l) . . . {tilde over (z)}.sub.a.sup.h(t.sub.k+T.sub.p,K.sub.p)].sup.T and {tilde over (ż)}.sub.a.sup.h=[{tilde over (ż)}.sub.a.sup.h(t.sub.k+T.sub.p,l) . . . {tilde over (ż)}.sub.a.sup.h(t.sub.k+T.sub.p,K.sub.p)].sup.T are used, which are predicted at the time t.sub.k over a complete time horizon with K.sub.p time steps and are calculated with the corresponding prediction time, e.g. by the algorithm described in DE 10 2008 024 513.

(42) Considering the constraints valid by k.sub.l, v.sub.max and a.sub.max an optimum time sequence thereupon can be determined for the compensation movement.

(43) However, analogous to the model-predictive control only the first value of the trajectory calculated thereby is used for the subsequent control. In the next time step, the optimization is repeated with an updated and therefore more accurate prediction of the vertical position and velocity of the cable suspension point.

(44) The advantage of the model-predictive trajectory generation with successive control as compared to a classical model-predictive control on the one hand consists in that the control part and the related stabilization can be calculated with a higher scan time as compared to the trajectory generation. Therefore, the calculation-intensive optimization can be shifted into a slower task.

(45) In this concept, on the other hand, an emergency function can be realized independent of the control for the case that the optimization does not find a valid solution. It includes a simplified trajectory planning which the control relies upon in such emergency situation and further actuates the winch.

(46) 1.1.1 System Model for Planning the Compensation Movement

(47) To satisfy the requirements of the steadiness of the reference trajectories for the compensation movement, its third derivative at the earliest can be regarded as jump-capable. However, jumps in the jerk should be avoided in the compensation movement with regard to the winch life, whereby only the fourth derivative y.sub.a.sup.(4)* can be regarded as jump-capable.

(48) Thus, the jerk must at least be planned steady and the trajectory generation for the compensation movement is effected with reference to the fourth order integrator chain illustrated in FIG. 2. In the optimization, the same serves as system model and can be expressed as

(49) $\begin{array}{cc}{\stackrel{.}{x}}_a=\underset{\underset{A_a}{︸}}{\left[\begin{array}{cccc}0& 1& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\\ 0& 0& 0& 0\end{array}\right]}{x}_a+\underset{\underset{B_a}{︸}}{\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]}{u}_a,x_a\left(0\right)=x_{a,0},y_a=x_a& \left(1.1\right)\end{array}$
in the state space. Here, the output y.sub.a=[y.sub.a*,{dot over (y)}.sub.y*,ÿ.sub.a*,].sup.T includes the planned trajectories for the compensation movement. For formulating the optimal control problem and with regard to the future implementation, this time-continuous model initially is discretized on the lattice
τ.sub.0<τ.sub.1< . . . <τ.sub.K.sub.p.sub.−1<τ.sub.K.sub.p  (1.2)
wherein K.sub.p represents the number of the prediction steps for the prediction of the vertical movement of the cable suspension point. To distinguish the discrete time representation in the trajectory generation from the discrete system time t.sub.k, it is designated with τ.sub.k=kΔτ, wherein k=0, . . . , K.sub.p and Δτ is the discretization interval of the horizon K.sub.p used for the trajectory generation.

(50) FIG. 3 illustrates that the chosen lattice is non-equidistant, so that the number of the necessary supporting points on the horizon is reduced. Thus, it is possible to keep the dimension of the optimal control problem to be solved small. The influence of the rougher discretization towards the end of the horizon has no disadvantageous effects on the planned trajectory, since the prediction of the vertical position and velocity is less accurate towards the end of the prediction horizon.

(51) The time-discrete system representation valid for this lattice can be calculated exactly with reference to the analytical solution

(52) $\begin{array}{cc}{x}_a\left(t\right)=e^{A_{a}t}{x}_a\left(0\right)+{\int }_0^t{e}^{A_a\left(t-\tau \right)}{B}_a{u}_a\left(\tau \right)\mathrm{d\tau }& \left(1.3\right)\end{array}$

(53) For the integrator chain from FIG. 2 it follows to

(54) $\begin{array}{cc}{x}_a\left({\tau }_{k+1}\right)=\left[\begin{array}{cccc}1& \Delta {\tau }_k& \frac{\Delta {\tau }_k^2}{2}& \frac{\Delta {\tau }_k^3}{6}\\ 0& 1& \Delta {\tau }_k& \frac{\Delta {\tau }_k^2}{2}\\ 0& 0& 1& \Delta {\tau }_k\\ 0& 0& 0& 1\end{array}\right]+\left[\begin{array}{c}\frac{\Delta {\tau }^{4k}}{24}\\ \frac{\Delta {\tau }_k^3}{6}\\ \frac{\Delta {\tau }_k^2}{2}\\ \Delta {\tau }_k\end{array}\right]u_a\left({\tau }_k\right),x_a\left(0\right)=x_{a,0},y_a\left({\tau }_k\right)=x_a\left({\tau }_k\right),k=0,\mathrm{.Math.},K_p-1,& \left(1.4\right)\end{array}$
wherein Δτ.sub.k=τ.sub.k+1−τ.sub.k describes the discretization step width valid for the respective time step.
1.1.2 Formulation and Solution of the Optimal Control Problem

(55) By solving the optimal control problem a trajectory will be planned, which as closely as possible follows the predicted vertical movement of the cable suspension point and at the same time satisfies the given constraints.

(56) To satisfy this requirement, the merit function reads as follows:

(57) $\begin{array}{cc}J=\frac{1}{2}\underset{k=1}{\overset{K_p}{.Math.}}\left\{\begin{array}{c}{\left[y_a\left({\tau }_k\right)-w_a\left({\tau }_k\right)\right]}^T{Q}_w\left({\tau }_k\right).Math.y_a\left({\tau }_k\right)-w_a\left({\tau }_k\right).Math.+\\ u_a\left({\tau }_{k-1}\right)r_u{u}_a\left({\tau }_{k-1}\right)\end{array}\right\}& \left(1.5\right)\end{array}$
wherein w.sub.a(τ.sub.k) designates the reference valid at the respective time step. Since only the predicted position {tilde over (z)}.sub.a.sup.h(t.sub.k+T.sub.p,k) and velocity {tilde over (ż)}.sub.a.sup.h(t.sub.k+T.sub.p,k) of the cable suspension point are available here, the associated acceleration and the jerk are set to zero. The influence of this inconsistent specification, however, can be kept small by a corresponding weighting of the acceleration and jerk deviation. Thus:
w.sub.a(τ.sub.k)=[{tilde over (z)}.sub.a.sup.h(t.sub.k+T.sub.p,k){tilde over (ż)}.sub.a.sup.h(t.sub.k+T.sub.p,k)00].sup.T,k=1, . . . ,K.sub.p.  (1.6)
Over the positively semidefinite diagonal matrix
Q.sub.w(τ.sub.k)=diag(q.sub.w,1(τ.sub.k),q.sub.w,2(τ.sub.k),q.sub.w,3,q.sub.w,4),k=1, . . . ,K.sub.p  (1.7)
deviations from the reference are weighted in the merit function. The scalar factor ru evaluates the correction effort. While r.sub.u, q.sub.w,3 and q.sub.w,4 are constant over the entire prediction horizon, q.sub.w,1 and q.sub.w,2 are chosen in dependence on the time step τ.sub.k. Reference values at the beginning of the prediction horizon therefore can be weighted more strongly than those at the end. Hence, the accuracy of the vertical movement prediction decreasing with increasing prediction time can be depicted in the merit function. Because of the non-existence of the references for the acceleration and the jerk, the weights q.sub.w,3 and q.sub.w,4 only punish deviations from zero, which is why they are chosen smaller than the weights for the position q.sub.w,1(τ.sub.k) and velocity q.sub.w,2(τ.sub.k).

(58) The associated constraints for the optimal control problem follow from the available power of the drive and the currently chosen weighting factor k.sub.l (cf. FIG. 1). Accordingly, it applies for the states of the system model from (1.4):
−δ.sub.a(τ.sub.k)(1−k.sub.l)v.sub.max≦x.sub.a,2(τ.sub.k)≦δ.sub.a(τ.sub.k)(1−k.sub.l)v.sub.max,
−δ.sub.a(τ.sub.k)(1−k.sub.l)a.sub.max≦x.sub.a,3(τ.sub.k)≦δ.sub.a(τ.sub.k)(1−k.sub.l)a.sub.max,k=1, . . . ,K.sub.p,
−δ.sub.a(τ.sub.k)j.sub.max≦x.sub.a,4(τ.sub.k)≦δ.sub.a(τ.sub.k)j.sub.max  (1.8)
and for the input:

(59) $\begin{array}{cc}-{\delta }_a\left({\tau }_k\right)\frac{d}{\mathrm{dt}}{j}_{\mathrm{ma}x}\le u_a\left({\tau }_k\right)\le {\delta }_a\left({\tau }_k\right)\frac{d}{\mathrm{dt}}{j}_{\mathrm{ma}x},k=0,\mathrm{.Math.},K_p-1.& \left(1.9\right)\end{array}$

(60) Here, δ.sub.a(τ.sub.k) represents a reduction factor which is chosen such that the respective constraint at the end of the horizon amounts to 95% of that at the beginning of the horizon. For the intermediate time steps, δ.sub.a(τ.sub.k) follows from a linear interpolation. The reduction of the constraints along the horizon increases the robustness of the method with respect to the existence of admissible solutions.

(61) While the velocity and acceleration constraints can change in operation, the constraints of the jerk j.sub.max and the derivative of the jerk d/dt j.sub.max are constant. To increase the useful life of the hoisting winch and the entire crane, they are chosen with regard to a maximum admissible shock load. For the positional state no constraints are applicable.

(62) Since the maximum velocity v.sub.max and acceleration a.sub.max as well as the weighting factor of the power k.sub.l in operation are determined externally, the velocity and acceleration constraints also are changed necessarily for the optimal control problem. The presented concept takes account of the related time-varying constraints as follows: As soon as a constraint is changed, the updated value first is taken into account only at the end of the prediction horizon for the time step τ.sub.K.sub.p. With progressing time, it is then pushed to the beginning of the prediction horizon.

(63) FIG. 4 illustrates this procedure with reference to the velocity constraint. When reducing a constraint, care should be taken in addition that it fits with its maximum admissible derivative. This means that for example the velocity constraint (1−k.sub.l)v.sub.max maximally can be reduced as fast as is allowed by the current acceleration constraint (1−k.sub.l)a.sub.max. Because the updated constraints are pushed through, there always exists a solution for an initial condition x.sub.a(τ.sub.0) present in the constraints, which in turn does not violate the updated constraints. However, it will take the complete prediction horizon, until a changed constraint finally influences the planned trajectories at the beginning of the horizon.

(64) Thus, the optimal control problem is completely given by the quadratic merit function (1.5) to be minimized, the system model (1.4) and the inequality constraints from (1.8) and (1.9) in the form of a linear-quadratic optimization problem (QP problem for Quadratic Programming Problem). When the optimization is carried out for the first time, the initial condition is chosen to be x.sub.a(τ.sub.0)=[0,0,0,0].sup.T. Subsequently, the value x.sub.a(τ.sub.1) calculated for the time step τ.sub.1 in the last optimization step is used as initial condition.

(65) At each time step, the calculation of the actual solution of the QP problem is effected via a numerical method which is referred to as QP solver.

(66) Due to the calculation effort for the optimization, the scan time for the trajectory planning of the compensation movement is greater than the discretization time of all remaining components of the active heave compensation; thus: Δτ>Δt.

(67) To ensure that the reference trajectories are available for the control at a faster rate, the simulation of the integrator chain from FIG. 2 takes place outside the optimization with the faster scan time Δt. As soon as new values are available from the optimization, the states x.sub.a(τ.sub.0) are used as initial condition for the simulation and the correcting variable at the beginning of the prediction horizon u.sub.a(τ.sub.0) is written on the integrator chain as constant input.

(68) 1.2 Reference Trajectories for Moving the Load

(69) Analogous to the compensation movement, two times steadily differentiable reference trajectories are necessary for the superimposed hand lever control (cf. FIG. 1). As with these movements specifiable by the crane operator, no fast changes in direction normally are to be expected for the winch, the minimum requirement of a steadily planned acceleration ÿ.sub.l* also was found to be sufficient with respect to the useful life of the winch. Thus, in contrast to the reference trajectories planned for the compensation movement, the third derivative , which corresponds to the jerk, already can be regarded as jump-capable.

(70) As shown in FIG. 5, it also serves as input of a third order integrator chain. Beside the requirements as to steadiness, the planned trajectories also must satisfy the currently valid velocity and acceleration constraints, which for the hand lever control are found to be k.sub.lv.sub.max and k.sub.la.sub.max.

(71) The hand lever signal of the crane operator −100≦w.sub.hh≦100 is interpreted as relative velocity specification with respect to the currently maximum admissible velocity k.sub.lv.sub.max. Thus, according to FIG. 6 the target velocity specified by the hand lever is

(72) $\begin{array}{cc}{v}_{\mathrm{hh}}^{*}=k_l{v}_{\mathrm{ma}x}\frac{w_{\mathrm{hh}}}{100}.& \left(1.10\right)\end{array}$

(73) As can be seen, the target velocity currently specified by the hand lever depends on the hand lever position w.sub.hh, the variable weighting factor k.sub.l and the current maximum admissible winch speed v.sub.max.

(74) The task of trajectory planning for the hand lever control now can be indicated as follows: From the target velocity specified by the hand lever, a steadily differentiable velocity profile can be generated, so that the acceleration has a steady course. As procedure for this task a so-called jerk addition is recommendable.

(75) The basic idea is that in a first phase the maximum admissible jerk j.sub.max acts on the input of the integrator chain, until the maximum admissible acceleration is reached. In the second phase, the speed is increased with constant acceleration; and in the last phase the maximum admissible negative jerk is added such that the desired final speed is achieved.

(76) Therefore, merely the switching times between the individual phases must be determined in the jerk addition. FIG. 7 shows an exemplary course of the jerk for a speed change together with the switching times. T.sub.l,0 designates the time at which replanning takes place. The times T.sub.l,1, T.sub.l,2 and T.sub.l,3 each refer to the calculated switching times between the individual phases. Their calculation is outlined in the following paragraph.

(77) As soon as a new situation occurs for the hand lever control, replanning of the generated trajectories takes place. A new situation occurs as soon as the target velocity v.sub.hh* or the currently valid maximum acceleration for the hand lever control k.sub.la.sub.max is changed. The target velocity can change due to a new hand lever position w.sub.hh or due to a new specification of k.sub.l or v.sub.max (cf. FIG. 6). Analogously, a variation of the maximum valid acceleration by k.sub.l or a.sub.max is possible.

(78) When replanning the trajectories, that velocity initially is calculated from the currently planned velocity {dot over (y)}.sub.l(T.sub.l,0) and the corresponding acceleration ÿ.sub.l*(T.sub.l,0) which is obtained with a reduction of the acceleration to zero:

(79) $\begin{array}{cc}\tilde{v}={\stackrel{.}{y}}_i^{*}\left(T_{l,0}\right)+\Delta {\tilde{T}}_1{\tilde{y}}_l^{*}\left(T_{l,0}\right)+\frac{1}{2}\Delta {\tilde{T}}_1^2{\tilde{u}}_{l,1},& \left(1.11\right)\end{array}$
wherein the minimum necessary time is given by

(80) $\begin{array}{cc}\Delta {\tilde{T}}_1=-\frac{{\tilde{y}}_l^{*}}{{\tilde{u}}_{l,1}},{\tilde{u}}_{l,1}\ne 0& \left(1.12\right)\end{array}$
and ũ.sub.l,1 designates the input of the integrator chain, i.e. the added jerk (cf. FIG. 5): In dependence on the currently planned acceleration ÿ.sub.l*(T.sub.l,0) it is found to be

(81) $\begin{array}{cc}{\tilde{u}}_{l,1}=\{\begin{array}{cc}{j}_{\mathrm{ma}x},& \mathrm{for}{\tilde{y}}_l^{*}<0\\ -j_{\mathrm{ma}x},& \mathrm{for}{\tilde{y}}_l^{*}>0\\ 0,& \mathrm{for}{\tilde{y}}_l^{*}=0.\end{array}& \left(1.13\right)\end{array}$

(82) In dependence on the theoretically calculated velocity and the desired target velocity, the course of the input now can be indicated. If v.sub.hh*>{tilde over (v)}, {tilde over (v)} does not reach the desired value v.sub.hh* and the acceleration can be increased further. However, if v.sub.hh*<{tilde over (v)}, {tilde over (v)} is too fast and the acceleration must be reduced immediately.

(83) From these considerations, the following switching sequences of the jerk can be derived for the three phases:

(84) 0$\begin{array}{cc}{u}_l=\{\begin{array}{cc}\left[\begin{array}{ccc}{j}_{\mathrm{ma}x}& 0& -j_{\mathrm{ma}x}\end{array}\right],& \mathrm{for}\tilde{v}\le v_{\mathrm{hh}}^{*}\\ \left[\begin{array}{ccc}-j_{\mathrm{ma}x}& 0& j_{m\mathrm{ax}}\end{array}\right],& \mathrm{for}\tilde{v}>v_{\mathrm{hh}}^{*}\end{array}& \left(1.14\right)\end{array}$
with u.sub.l=[u.sub.l,1,u.sub.l,2,u.sub.l,3] and the input signal u.sub.l,i added in the respective phase. The duration of a phase is found to be ΔT.sub.i=T.sub.l,i−T.sub.l,i−1 with i=1, 2, 3. Accordingly, the planned velocity and acceleration at the end of the first phase are:

(85) $\begin{array}{cc}{\stackrel{.}{y}}_l^{*}\left(T_{l,1}\right)={\stackrel{.}{y}}_l^{*}\left(T_{l,0}\right)+\Delta T_1{\stackrel{\_}{y}}_l^{*}\left(T_{l,0}\right)+\frac{1}{2}\Delta T_1^2{u}_{l,1},& \left(1.15\right)\\ {\stackrel{\_}{y}}_l^{*}\left(T_{l,1}\right)={\stackrel{\_}{y}}_l^{*}\left(T_{l,0}\right)=\Delta T_1{u}_{l,1}& \left(1.16\right)\end{array}$
and after the second phase:
{dot over (y)}.sub.l*(T.sub.l,2)={dot over (y)}.sub.l*(T.sub.l,1)+ΔT.sub.2ÿ.sub.l*(T.sub.l,3)  (1.17)
ÿ.sub.l*(T.sub.l,2)=ÿ.sub.l*(T.sub.l,1).  (1.18)
wherein u.sub.l,2 was assumed=0. After the third phase, finally, it follows:

(86) $\begin{array}{cc}{\stackrel{.}{y}}_l^{*}\left(T_{l,3}\right)={\stackrel{.}{y}}_l^{*}\left(T_{l,2}\right)+\Delta T_3{\stackrel{\_}{y}}_l^{*}\left(T_{l,2}\right)+\frac{1}{2}\Delta T_3^2{u}_{l,3},& \left(1.19\right)\\ {\stackrel{\_}{y}}_l^{*}\left(T_{l,3}\right)={\stackrel{\_}{y}}_l^{*}\left(T_{l,2}\right)+\Delta T_3{u}_{l,3}.& \left(1.20\right)\end{array}$

(87) For the exact calculation of the switching times T.sub.l,i the acceleration constraint initially is neglected, whereby ΔT.sub.2=0. Due to this simplification, the lengths of the two remaining time intervals can be indicated as follows:

(88) $\begin{array}{cc}\Delta T_1=\frac{\tilde{a}-{\stackrel{\_}{y}}_l^{*}\left(T_{l,0}\right)}{u_{l,1}},& \left(1.21\right)\\ \Delta T_3=\frac{0-\tilde{a}}{u_{l,3}},& \left(1.22\right)\end{array}$
wherein ã stands for the maximum acceleration achieved. By inserting (1.21) and (1.22) into (1.15), (1.16) and (1.19) a system of equations is obtained, which can be resolved for ã. Considering {dot over (y)}.sub.l*(T.sub.l,3)=v.sub.hh*, the following finally is obtained:

(89) $\begin{array}{cc}\tilde{a}=\pm \sqrt{\frac{u_{l,3}\left[2{\stackrel{.}{y}}_l^{*}\left(T_{l,0}\right)u_{l,1}-{{\stackrel{\mathrm{.Math.}}{y}}_l^{*}\left(T_{l,0}\right)}^2-2v_{\mathrm{hh}}^{*}{u}_{l,1}\right]}{u_{l,1}-u_{l,3}}}.& \left(1.23\right)\end{array}$

(90) The sign of ã follows from the condition that ΔT.sub.1 and ΔT.sub.3 in (1.21) and (1.22) must be positive.

(91) In a second step, ã and the maximum admissible acceleration k.sub.la.sub.max result in the actual maximum acceleration:
ā=ÿ.sub.l*(T.sub.l,1)=ÿ.sub.l*(T.sub.l,2)=min{k.sub.la.sub.max,max{−k.sub.la.sub.max,ā}}.  (1.24)

(92) With the same, the really occurring time intervals ΔT.sub.1 and ΔT.sub.3 finally can be calculated. They result from (1.21) and (1.22) with ã=ā. The yet unknown time interval ΔT.sub.2 now is determined from (1.17) and (1.19) with ΔT.sub.1 and ΔT.sub.3 from (1.21) and (1.22) to be

(93) $\begin{array}{cc}\Delta T_2=\frac{2v_{\mathrm{hh}}^{*}{u}_{l,3}+{\stackrel{\_}{a}}^2-2{\stackrel{.}{y}}_l^{*}\left(T_{l,1}\right)u_{l,3}}{2\stackrel{\_}{a}{u}_{l\mathrm{.3}}},& \left(1.25\right)\end{array}$
wherein {dot over (y)}.sub.l*(T.sub.l,1) follows from (1.15). The switching times can directly be taken from the time intervals:
T.sub.l,i=T.sub.l,i−1+ΔT.sub.i,i=1,2,3.  (1.26)

(94) The velocity and acceleration profiles {dot over (y)}.sub.l* and ÿ.sub.l* to be planned can be calculated analytically with the individual switching times. It should be mentioned that the trajectories planned by the switching times frequently are not traversed completely, since before reaching the switching time T.sub.l,3 a new situation occurs, replanning thereby takes place and new switching times must be calculated. As mentioned already, a new situation occurs by a change in w.sub.hh, v.sub.max, a.sub.max or k.sub.l.

(95) FIG. 8 shows a trajectory generated by the presented method by way of example. The course of the trajectories includes both cases which can occur due to (1.24). In the first case, the maximum admissible acceleration is reached at the time t=1 s, followed by a phase with constant acceleration. The second case occurs at the time t=3.5 s. Here, the maximum admissible acceleration is not reached completely due to the hand lever position. The consequence is that the first and the second switching time coincide, and ΔT.sub.2=0 applies. According to FIG. 5, the associated position course is calculated by integration of the velocity curve, wherein the position at system start is initialized by the cable length currently unwound from the hoisting winch.

(96) Actuation Concept for the Hoisting Winch

(97) In principle, the actuation includes two different operating modes: the active heave compensation for decoupling the vertical load movement from the ship movement with free-hanging load and the constant tension control for avoiding a slack cable, as soon as the load is deposited on the sea bed. During a deep-sea lift, the heave compensation initially is active. With reference to a detection of the depositing operation, switching to the constant tension control is effected automatically. FIG. 9 illustrates the overall concept with the associated reference and control variables.

(98) Each of the two different operating modes however might also be implemented each without the other operating mode. Furthermore, a constant tension mode as it will be described below can also be used independent of the use of the crane on a ship and independent of an active heave compensation.

(99) Due to the active heave compensation, the hoisting winch should be actuated such that the winch movement compensates the vertical movement of the cable suspension point z.sub.a.sup.h and the crane operator moves the load by the hand lever in the h coordinate system regarded as inertial. To ensure that the actuation has the required predictive behavior for minimizing the compensation error, it is implemented by a pilot control and stabilization part in the form of a structure of two degrees of freedom. The pilot control is calculated from a differential parameterization by the flat output of the winch dynamics and results from the planned trajectories for moving the load y.sub.l*, {dot over (y)}.sub.l* and ÿ.sub.l* as well as the negative trajectories for the compensation movement −y.sub.a*, −{dot over (y)}.sub.a* and −ÿ.sub.a* (cf. FIG. 9). The resulting target trajectories for the system output of the drive dynamics and the winch dynamics are designated with y.sub.h*, {dot over (y)}.sub.h* and ÿ.sub.h*. They represent the target position, velocity and acceleration for the winch movement and thereby for the winding and unwinding of the cable.

(100) During the constant tension phase, the cable force at the load F.sub.sl is to be controlled to a constant amount, in order to avoid a slack cable. The hand lever therefore is deactivated in this operating mode, and the trajectories planned on the basis of the hand lever signal no longer are added. The actuation of the winch in turn is effected by a structure of two degrees of freedom with pilot control and stabilization part.

(101) The exact load position z.sub.l and the cable force at the load F.sub.sl are not available as measured quantities for the control, since due to the long cable lengths and great depths the crane hook is not equipped with a sensor unit. Furthermore, no information exists on the kind and shape of the suspended load. Therefore, the individual load-specific parameters such as load mass m.sub.l, coefficient of the hydrodynamic increase in mass C.sub.a, coefficient of resistance C.sub.d and immersed volume ∇.sub.l, are not known in general, whereby a reliable estimation of the load position is almost impossible in practice.

(102) Thus, merely the unwound cable length l.sub.s and the associated velocity i.sub.s as well as the force at the cable suspension point F.sub.c are available as measured quantities for the control. The length l.sub.s is obtained indirectly from the winch angle φ.sub.h measured with an incremental encoder and the winch radius r.sub.h(j.sub.l) dependent on the winding layer j.sub.l. The associated cable velocity i.sub.s can be calculated by numerical differentiation with suitable low-pass filtering. The cable force F.sub.c applied to the cable suspension point is detected by a force measuring pin.

(103) 2.1 Actuation for the Active Heave Compensation

(104) FIG. 10 illustrates the actuation of the hoisting winch for the active heave compensation with a block circuit diagram in the frequency range. As can be seen, there is only effected a feedback of the cable length and velocity y.sub.h=l.sub.s and {dot over (y)}.sub.h=i.sub.s from the partial system of the drive G.sub.h(s). As a result, the compensation of the vertical movement of the cable suspension point Z.sub.a.sup.h(s) acting on the cable system G.sub.s,z(s) as input interference takes place purely as pilot control; cable and load dynamics are neglected. Due to a non-complete compensation of the input interference or a winch movement, the inherent cable dynamics is incited, but in practice it can be assumed that the resulting load movement is greatly attenuated in water and decays very fast.

(105) The transfer function of the drive system from the correcting variable U.sub.h(s) to the unwound cable length Y.sub.h(s) can be approximated as IT.sub.l system and results in

(106) $\begin{array}{cc}\begin{array}{c}{G}_h\left(s\right)=\frac{Y_h\left(s\right)}{U_h\left(s\right)}\\ =\frac{K_h{r}_h\left(j_l\right)}{T_h{s}^2+s}\end{array}& \left(2.1\right)\end{array}$
with the winch radius r.sub.h(j.sub.l). Since the system output Y.sub.h(s) at the same time represents a flat output, the inverting pilot control F(s) will be

(107) $\begin{array}{cc}\begin{array}{c}F\left(s\right)=\frac{U_{\mathrm{ff}}\left(s\right)}{Y_h^{*}\left(s\right)}\\ =\frac{1}{G_h\left(s\right)}\\ =\frac{T_h}{K_h{r}_h\left(j_l\right)}{s}^2+\frac{1}{K_h{r}_h\left(j_l\right)}s\end{array}& \left(2.2\right)\end{array}$
and can be written in the time domain in the form of a differential parameterization as

(108) $\begin{array}{cc}{u}_{\mathrm{ff}}\left(t\right)=\frac{T_h}{K_h{r}_h\left(j_l\right)}{\stackrel{\_}{y}}_h^{*}\left(t\right)+\frac{1}{K_h{r}_h\left(j_l\right)}{\stackrel{.}{y}}_h^{*}\left(t\right)& \left(2.3\right)\end{array}$
(2.3) shows that the reference trajectory for the pilot control must be steadily differentiable at least two times.

(109) The transfer function of the closed circuit, consisting of the stabilization K.sub.a(s) and the winch system G.sub.h(s), can be taken from FIG. 10 to be

(110) $\begin{array}{cc}{G}_{\mathrm{AHC}}\left(s\right)=\frac{K_a\left(s\right)G_h\left(s\right)}{1+K_a\left(s\right)G_h\left(s\right)}& \left(2.4\right)\end{array}$

(111) By neglecting the compensation movement Y.sub.a*(s), the reference variable Y.sub.h*(s) can be approximated as ramp-shaped signal with a constant or stationary hand lever deflection, as in such a case a constant target velocity v.sub.hh* exists. To avoid a stationary control deviation in such reference variable, the open chain K.sub.a(s)G.sub.h(s) therefore must show a I.sub.2 behavior [9]. This can be achieved for example by a PID controller with

(112) 0$\begin{array}{cc}{K}_a\left(s\right)=\frac{T_h}{K_h{r}_h\left(j_l\right)}\left(\frac{{\kappa }_{\mathrm{AHC},0}}{s}+{\kappa }_{\mathrm{AHC},1}+{\kappa }_{\mathrm{AHC},2}s\right),{\kappa }_{\mathrm{AHC},i}>0& \left(2.5\right)\end{array}$
Hence it follows for the closed circuit:

(113) $\begin{array}{cc}{G}_{\mathrm{AHC}}\left(s\right)=\frac{{\kappa }_{\mathrm{AHC},0}+{\kappa }_{\mathrm{AHC},1}s+{\kappa }_{\mathrm{AHC},2}{s}^2}{s^3+\left(\frac{1}{T_h}+{\kappa }_{\mathrm{AHC},2}\right)s^2+{\kappa }_{\mathrm{AHC},1}s+{\kappa }_{\mathrm{AHC},0}},& \left(2.6\right)\end{array}$

(114) wherein the exact values of κ.sub.AHC,i are chosen in dependence on the respective time constant T.sub.h.

(115) Detection of the Depositing Operation

(116) As soon as the load hits the sea bed, switching from the active heave compensation into the constant tension control should be effected. For this purpose, a detection of the depositing operation is necessary (cf. FIG. 9). For the same and the subsequent constant tension control, the cable is approximated as simple spring-mass element. Thus, the force acting at the cable suspension point approximately is calculated as follows
F.sub.c=k.sub.cΔl.sub.c,  (2.7)

(117) wherein k.sub.c and Δl.sub.c designate the spring constant equivalent to the elasticity of the cable and the deflection of the spring. For the latter, it applies:

(118) $\begin{array}{cc}\begin{array}{c}\Delta l_c={\int }_0^l{\mathrm{.Math.}}_s\left(\stackrel{\_}{s},t\right)d\stackrel{\_}{s}\\ ={\stackrel{\_}{z}}_{s,\mathrm{stat}}\left(1\right)-{\stackrel{\_}{z}}_{s,\mathrm{stat}}\left(0\right)-l_s\\ =\frac{{\mathrm{gl}}_s}{E_s{A}_s}\left(m_e+\frac{1}{2}{\mu }_s{l}_s\right).\end{array}& \left(2.8\right)\end{array}$

(119) The equivalent spring constant k.sub.c can be determined from the following stationary observation. For a spring loaded with the mass m.sub.f it applies in the stationary case:
k.sub.cΔl.sub.c=m.sub.jg.  (2.9)

(120) A transformation of (2.8) results in

(121) $\begin{array}{cc}\frac{E_s{A}_s}{l_s}\Delta l_c=\left(m_e+\frac{1}{2}{\mu }_s{l}_s\right)g.& \left(2.10\right)\end{array}$

(122) With reference to a coefficient comparison between (2.9) and (2.10) the equivalent spring constant can be read as

(123) $\begin{array}{cc}{k}_c=\frac{E_s{A}_s}{l_s}& \left(2.11\right)\end{array}$

(124) In (2.9) it can also be seen that the deflection of the spring Δl.sub.c in the stationary case is influenced by the effective load mass m.sub.e and half the cable mass

(125) $\frac{1}{2}{\mu }_s{l}_s.$
This is due to the fact that in a spring the suspended mass m.sub.f is assumed to be concentrated in one point. The cable mass, however, is uniformly distributed along the cable length and therefore does not fully load the spring. Nevertheless, the full weight force of the cable μ.sub.sl.sub.sg is included in the force measurement at the cable suspension point.

(126) With this approximation of the cable system, conditions for the detection of the depositing operation on the sea bed now can be derived. At rest, the force acting on the cable suspension point is composed of the weight force of the unwound cable μ.sub.sl.sub.sg and the effective weight force of the load mass m.sub.eg. Therefore, the measured force F.sub.c with a load located on the sea bed approximately is
F.sub.c=(m.sub.e+μ.sub.sl.sub.s)g+ΔF.sub.c  (2.12)
with
ΔF.sub.c=−k.sub.cΔl.sub.s,  (2.13)
wherein Δl.sub.s designates the cable unwound after reaching the sea bed. From (2.13) it follows that Δl.sub.s is proportional to the change of the measured force, since the load position is constant after reaching the ground. With reference to (2.12) and (2.13) the following conditions now can be derived for a detection, which must be satisfied at the same time:

(127) The decrease of the negative spring force must be smaller than a threshold value:
ΔF.sub.c<Δ{circumflex over (F)}.sub.c.  (2.14)

(128) The time derivative of the spring force must be smaller than a threshold value:
{dot over (F)}.sub.c<{circumflex over ({dot over (F)})}.sub.c.  (2.15)

(129) The crane operator must lower the load. This condition is checked with reference to the trajectory planned with the hand lever signal:
{dot over (y)}.sub.l*≧0.  (2.16)

(130) To avoid a wrong detection on immersion into the water, a minimum cable length is unwound as:
l.sub.s>l.sub.s,min.  (2.17)

(131) The decrease of the negative spring force ΔF.sub.c each is calculated with respect to the last high point F.sub.c in the measured force signal F.sub.c. To suppress measurement noise and high-frequency interferences, the force signal is preprocessed by a corresponding low-pass filter.

(132) Since the conditions (2.14) and (2.15) must be satisfied at the same time, a wrong detection as a result of a dynamic inherent cable oscillation is excluded: As a result of the dynamic inherent cable oscillation, the force signal F.sub.c oscillates, whereby the change of the spring force ΔF.sub.c with respect to the last high point F.sub.c and the time derivative of the spring force {dot over (F)}.sub.c have a shifted phase. Consequently, with a suitable choice of the threshold values Δ{circumflex over (F)}.sub.c and {circumflex over ({dot over (F)})}.sub.c in the case of a dynamic inherent cable oscillation, both conditions cannot be satisfied at the same time. For this purpose, the static part of the cable force must drop, as is the case on immersion into the water or on deposition on the sea bed. A wrong detection on immersion into the water, however, is prevented by condition (2.17).

(133) The threshold value for the change of the spring force is calculated in dependence on the last high point in the measured force signal as follows:
Δ{circumflex over (F)}.sub.c=min{−χ.sub.1F.sub.c,Δ{circumflex over (F)}.sub.c,max}.  (2.18)
wherein χ.sub.1<1 and the maximum value Δ{circumflex over (F)}.sub.c,max were determined experimentally. The threshold value for the derivative of the force signal {circumflex over ({dot over (F)})}.sub.c can be estimated from the time derivative of (2.7) and the maximum admissible hand lever velocity k.sub.lv.sub.max as follows
{circumflex over ({dot over (F)})}.sub.c=min{−χ.sub.2k.sub.ck.sub.lv.sub.max,{circumflex over ({dot over (F)})}.sub.c,max}  (2.19)
The two parameters χ.sub.2<1 and {circumflex over ({dot over (F)})}.sub.c,max likewise were determined experimentally.

(134) Since in the constant tension control a force control is applied instead of the position control, a target force F.sub.c* is specified as reference variable in dependence on the sum of all static forces F.sub.l,stat acting on the load. For this purpose F.sub.l,stat is calculated in the phase of the heave compensation in consideration of the known cable mass μ.sub.sl.sub.s:
F.sub.l,stat=F.sub.c,stat−μ.sub.sl.sub.sg.  (2.20)

(135) F.sub.c,stat designates the static force component of the measured force at the cable suspension point F.sub.c. It originates from a corresponding low-pass filtering of the measured force signal. The group delay obtained on filtering is no problem, as merely the static force component is of interest and a time delay has no significant influence thereon. From the sum of all static forces acting on the load, the target force is derived taking into account the weight force of the cable additionally acting on the cable suspension point, as follows:
F.sub.c*=p.sub.sF.sub.l,stat+μ.sub.sl.sub.sg.  (2.21)
wherein the resulting tension in the cable is specified by the crane operator with 0<p.sub.s<1. To avoid a setpoint jump in the reference variable, a ramp-shaped transition from the force currently measured on detection to the actual target force F.sub.c* is effected after a detection of the depositing operation.

(136) For picking up the load from the sea bed, the crane operator manually performs the change from the constant tension mode into the active heave compensation with free-hanging load.

(137) 2.3 Actuation for the Constant Tension Mode

(138) FIG. 11 shows the implemented actuation of the hoisting winch in the constant tension mode in a block circuit diagram in the frequency range. In contrast to the control structure illustrated in FIG. 10, the output of the cable system F.sub.c(s), i.e. the force measured at the cable suspension point, here is fed back instead of the output of the winch system Y.sub.h(s). According to (2.12), the measured force F.sub.c(s) is composed of the change in force ΔF.sub.c(s) and the static weight force m.sub.eg+μ.sub.sl.sub.sg, which in the Figure is designated with M(s). For the actual control, the cable system in turn is approximated as spring-mass system.

(139) The pilot control F(s) of the structure of two degrees of freedom is identical with the one for the active heave compensation and given by (2.2) and (2.3), respectively. In the constant tension mode, however, the hand lever signal is not added, which is why the reference trajectory only consists of the negative target velocity and acceleration −{dot over (y)}.sub.a* and −ÿ.sub.a* for the compensation movement. The pilot control part initially in turn compensates the vertical movement of the cable suspension point Z.sub.a.sup.h(s). However, a direct stabilization of the winch position is not effected by a feedback of Y.sub.h(s). This is effected indirectly by the feedback of the measured force signal.

(140) The measured output F.sub.c(s) is obtained from FIG. 11 as follows

(141) $\begin{array}{cc}{F}_c\left(s\right)=G_{\mathrm{CT},1}\left(s\right)\underset{\underset{E_a\left(s\right)}{︸}}{\left[Y_a^{*}\left(s\right)F\left(s\right)G_h\left(s\right)+Z_a^h\left(s\right)\right]}+G_{\mathrm{CT},2}\left(s\right)F_c^{*}\left(s\right)& \left(2.22\right)\end{array}$
with the two transfer functions

(142) $\begin{array}{cc}{G}_{\mathrm{CT},1}\left(s\right)=\frac{G_{s,F}\left(s\right)}{1+K_s\left(s\right)G_h\left(s\right)G_{s,F}\left(s\right)},& \left(2.23\right)\\ G_{\mathrm{CT},2}\left(s\right)=\frac{K_s\left(s\right)G_h\left(s\right)G_{s,F}\left(s\right)}{1+K_s\left(s\right)G_h\left(s\right)G_{s,F}\left(s\right)},& \left(2.24\right)\end{array}$
wherein the transfer function of the cable system for a load standing on the ground follows from (2.12):
G.sub.s,F(s)=−k.sub.c.  (2.25)

(143) As can be taken from (2.22), the compensation error E.sub.a(s) is corrected by a stable transfer function G.sub.CT,l(s) and the winch position is stabilized indirectly. In this case, too, the requirement of the controller K.sub.s(s) results from the expected reference signal F.sub.c*(s), which after a transition phase is given by the constant target force F.sub.c* from (2.21). To avoid a stationary control deviation with such constant reference variable, the open chain K.sub.s(s)G.sub.h(s)G.sub.s,F(s) must have an I behavior. Since the transfer function of the winch G.sub.h(s) already implicitly has such behavior, this requirement can be realized with a P feedback; thus, it applies:

(144) $\begin{array}{cc}{K}_s\left(s\right)=\frac{T_h}{K_h{r}_h\left(j_l\right)}{\kappa }_{\mathrm{CT}},{\kappa }_{\mathrm{CT}}>0.& \left(2.6\right)\end{array}$