US 3921818 A Abstract A system for controlling a suspension type crane which moves transversely while suspending a load by a rope. The crane is accelerated at least two times to a predetermined maximum speed during an acceleration period, the swing of the rope is minimized when a predetermined maximum speed is reached, the crane is moved at the predetermined maximum speed for a predetermined interval, the crane is decelerated from the maximum speed at least two times during the deceleration period, and the crane is stopped when the swing of the rope is reduced to a minimum, and the areas of the acceleration and deceleration periods of the crane are made equal.
Claims available in Description (OCR text may contain errors) United States Patent 1191 Yamagishi 1 1 CRANE SUSPENSION CONTROL APPARATUS [75] Inventor: Toshio Yamagishi, Chofu, Japan [73] Assignee: Tokyo Shibaura Denki Kabushiki Kaisha, Japan 22 Filed: Mar. 28, 1974 [211 App]. No.: 455,906 [30] Foreign Application Priority Data [4 1 Nov. 25, 1975 6/1970 Virkkala 212/132 11/1974 Meyeret a1 212/132 [57] ABSTRACT A system for controlling a suspension type crane which moves transversely while suspending a load by a Apr. 2 1973 Japan 48-37665 rope- The crane is accglerated least two times to a predetermined maximum speed during an acceleration 52 U.S. c1 212/132- 212/39 R- 212/86' PeYiOdthCSwingofthempeisminimized Whenaprede' 3:18/384. 340/267 termined maximum speed is reached, the crane is 51 1m.c1. ..1366c 19/00 mved Predetermined maximum Speed for a [58] Field of Search 318/384. 212/39 R 132 predetermined interval, the crane is decelerated from 212/39 MS 86; 340/267 6 282 the maximum speed at least two times during the deceleration period, and the crane is stopped when the [56] References Cited swing of the rope is reduced to a minimum, and the areas of the acceleration and deceleration periods of UNITED STATES PATENTS the crane are made equal. 2,806,610 9/1957 Goertz 212/132 X 3,351,213 11/1967 Newman et a1. 212/39 R 10 Clams, 20 Drawing Flgures LLI a Lu (f) D 2 LL! LLI [I D. l- (f) S L1J Z t Z z Vmox 0: 3 1- 0: 1 l1 1 1: t5 t t T|ME US. Patent Nov. 25, 1975 Sheet1of13 3,921,818 85 FIG. 312 Vmox EE K to t [2 113 [14 T5116 t7 "*TIME FIG. 2 X TROLLEY ROPE US. Patent Nov. 25, 1975 Sheet3of 13 3,921,818 FIG. 7 FIG. 8 RUNNING SPEED V TROLLEY TRANSVERSE US. Patent Nov. 25, 1975 Sheet4ofl3 3,921,818 FIG. 9 FIG. IO ammaw OZEZDE mmmw mZ mP m Owtl FIG.|I US. Patent Nov.25, 1975 Sheet5ofl3 3,921,818 ON Q (1-'1) EIWLL QNIHQLIMS US. Patent Nov. 25, 1975 Sheet7of 13 3,921,818 u a J U m o 3296 P5235228 050m 20 US. Patent Nov. 25, 1975 Sheet 8 of 13 3,921,818 US. Patent Nov. 25, 1975 Sheet 10 Of13 3,921,818 ON BOARD (SWITCHING TIME COMPUTOR STOP OFF BOARD i I0 r SIGNAL I VARIATION v. DETECTOR IVI Val KX RyOG I00 1 O HOLDING lymcIxl @Xig CIRCUIT ABSOLUTE H ADDITION v,- VALUE "F 5, RELAY-AMP. ADDITION L1@7 CIRCUIT RELAY i y; A2 ADDITION z ylzu Rylb CIRCUIT A4 53 INTEGRATOR i p y zu Ry2cI O RyA ADDITION CIRCUIT RY4G INTEGRATOR U.S. Patent Nov. 25, 1975 shw 11 0f 13 3,921,818 FIG. l8 U.S. Patent Nov. 25, 1975 Sheet 12 Of 13 3,921,818 FIG. l9 ON BOARD STOP SPEED REFERENCE GENERATOR /OFF BOARD IOO VI ADDITION CIRCUIT 1 I LFVZI 1 TG V2 RyAs D1 D2 RELAY-AMP S RyAe (9 Ry5Cl A6 R yl3u @LtZ- l y 2u RH3 Ry6O y ADDITION CIRCUIT INTEGRATOR US. Patent Nov. 25, 1975 Sheet 13 01 13 3,921,818 F l G. 20 o CLOSE ix/ OPEN- CLOSE Ry6c1 OPEN CLOSE Rylaq OPEN- 1; CLOSE y zo OPEN L CLOSE 7 OPEN 3 6 P A6 OUTPUT IaOUTPUT' to 1l t2 13 t4 t5 117 This invention relates to a method and system for controlling the positioning of a suspension type crane and more particularly to an improved method and system for suppressing swinging motions of a suspension rope of a trolley of the crane and for stopping the trolley at a correct target position when the swing of the rope is reduced to zero or substantially to zero When a suspension type crane is accelerated or decelerated during its transverse running, the rope suspending a load undergoes a pendulum motion. Such pendulum motion or swinging motion can be suppressed by the operation of the operator of the crane. Thus, when such swinging motion occurs the operator operates the controller of the crane for adjusting the transverse running speed to suppress the swinging motion However, such adjustment cannot be made other than by a skilled crane operator and in most cases the adjustment of the transverse running speed becomes excessive or insufficient whereby a long time is required until the swinging motion is perfectly suppressed thus decreasing the cargo efficiency. To obviate this difficulty, there has been proposed a method wherein the swinging angle of the rope and the angular velocity 6 of the swinging motion are detected and signals corresponding to angle 6 and angular velocity are negatively fed back to a transverse speed controller through a feedback circuit having a suitable gain for attenuating the swinging motion of the rope. With such a feedback system, if the gain of the feedback circuit were decreased for sufficiently suppressing the swinging motion the average transverse running speed would be decreased. Accordingly, a compromise method has been proposed in which an insensitive zone is provided for the feedback circuit for preventing the cargo efficiency from decreasing at the sacrifice of the accuracy of the swing suppression. Accordingly, such method is not satisfactory for such an application as a container crane which requires an extremely accurate swing suppression for the purpose of precisely lowering the load at a predetermined position. In order to have a better understanding of this invention, the problem involved in the control system for effecting suppression of the swinging motion in a shortest time will be analyzed hereunder. In a diagram shown in FIG. 2, let m represents the mass of a load, T the tension ofa suspension rope, g the acceleration due to gravity. Under a balanced condition of the horizontal component and the vertical component of the force acting upon the load, the following equations of motion hold: m Fmg- TcosO There are the following relations among x, y, 1 (length of the rope), 0 (angle of swing) and X (distance between the origin and the trolley) x X l sin 0 y 1 cos 0 2 By differentiating both sides of equations 3 and 4 with respect to time t. we obtain 5 7 T d! sin 0 l Ttos 0 5. dy dl d9 d1 cos 6 l Tsm 9 6. 10 By additionally differentiating both sides of equations 5 and 6 with respect to time, we obtain rf x (FX 41'"! 11/ d9 11 (l9 15 d1 (11 d! 0 (I! 111 9 d1 m (1 0 d6 2 cos0+l TcosG-l d! sinfl 1 x [r 1 {110V} m2 d? l T sin 0 7 d1 116 (F0 T 1 [T2 cos 9 7. Jy (F! d! d6 d1 d6 TcosB- TSIIIB- T Ts|n0+l d0 d0 T5"! 0 l cos 0 d"! d9 1 d1 d6 dfl dr m d: +1 (#0 F sin 8 8. Substituting equations 7 and 8 for the lefthand sides of equations 1 and 2, respectively, (PX d'-'l im m T2 m T2 I T sin 0 40 3 dl d0 d'-0 m d! T I dig cos 0 i sin 6 9. if! d0. 7 11! d6 m T, l T cos 0 m d! d l sin 0 =mg-Tcos0 When an equation equation 9 X cos 0 equation 10 X sin 9 is operated, the second term in the lefthand side of equation 9 and the first term in the lefthand side of equation 10 cancel with each other, and the righthand side of equation 9 and the second term in the righthand B putting the following relation can be obtained d.\' v. 16" d d1 5 0 d9 +w=e+ l -0 m. e Obtdm When the both sides of equation l6 are integrated with respect to 0, under an assumption that the acceleration d' x dV 1 '11 10 a of the trolley constant, the following equation Wl d! 11! Y be obtained Where 0 is small, then cos 0 e l and sin 0 e 0, so that equation 12 can be rewritten as follows 1k (2+ 1MB 02 a: C0 174 15 (IV +7 dl :10 +1 1 0 0 l3 d1 d1 g where Co represents an integration constant. By multiplying the both sides of equation 17 by 2, Thus, equation 13 expresses the pendulum motion of the rope and the load. 20 If We assume that, the length 1 of the rope is constant, (W (w a 2C0 then 11 By modifying the term in the bracket and by substitutd! 0 5 ing the result of the following equation l9 into equation l8, we obtain equation 20. and equation 13 can be rewritten as follows. 2 When the length l of the rope is constant, the rela- 7 g a 32 tionship between (00 and 0 or the phase plane locus cor responds to a circular motion rotating in the clockwise direction at a constant angular velocity on on a circle Since there is a relation: having a center at da 1 L do d do a d! d! d: d1 d0 d! F by putting as shown in FIG. 3. The speed of the motion around the circle can be ob- 10 d (EL) L tained as follows. As shown in FIG. 4, since d: d0 d1 d1 and by substituting this relation in equation 14, we oban a 21' tam I (a) 0+ 12 46 (IV 15 tan" 6 tan" 7 22 I6 g9=- L do d! w 6 w l By dividing the both sides of equation 15 by l and by where putting z= a dv w 0 2 ho of a point (106, 6) can be expressed as follows 5 dd: d2 (1 I r= r F (1(1) o 2 0((u0+ 'r 01(0) x 9 z a 0 0 u6+ rms) I where d0 0 dr From equation 14 '6 i-0+ )=(m 0+ -T) By substituting equation 24 into equation 23 the following equation can be derived This equation shows that the point (m6, 9) rotates on a circle in the clockwise direction at a constant angular velocity (u, as has been pointed out hereinabove. It can be readily understood that, during acceleration since a 0, the center of the circle lies on the negative side of axis on 0, whereas during decelration since a 0, the center of the circle lies on the positive side, as shown by FIGS. 3a and 3b. Where the trolley is running transversely at a constant speed, 0: =0 so that the center of the circle coincides with the origin 0 as shown in FIG. 30. Further, the radius of the circle'is determined by the initial conditions. Assume now that the trolley is started from standstill at a constant acceleration, decelerated at a constant deceleration during an interval r, t and thereafter again accelerated at a constant acceleration during an interval t t until a maximum speed is reached, as shown in FIG. 1. Under these conditions, the relationship between the swing angle 0 and the angular velocity 0 of the swinging motion will now be considered with reference to the phase phane locus described above. Since the initial conditions are: t t 0 0 and 9 0, the phase plane locus starts from the origin 0 as shown in I I C I. 5 so that the initial radius of the circle is equal to 0,0. When the position ofa state point ((00, 9) at t= t, is denoted by P,, the time required for the point P, to move from O to P, is equal to (t, t and since the angular velocity of the circular motion of the state joint P, about the center 0, is expressed by w, the following relation holds During a period t expressed by t, s: t s t a 0 so that the phase plane locus becomes a circle having a center at 0 At an instant I t,, are PTP intersects arc UP, at point P, so that the radius of the latter circle will be By denoting the position of a state point (000, (i) at t r by P the time required for the state point to move from point P, to point P will be (1 r,) and since the angular velocity of the circular motion about the center 0 is w, the following relation holds, During an interval expressed by a relation I t since a O, the phase plane locus again assurn es the circle with its center at 0,. At t =1 since arc P P, intersects arc PTP, at point P the radius of the circle having a center at point 0, is equal to Further, since the time required for the state point to move from point P to state point P is equal to (l t and the angular velocity of the circular motion about center 0, is w, the following relation holds P 0,P w (r, 1,) During an interval wherein t, 2 t as a 0, the phase surface locus takes the form of a circle having its center at the origin and a radius From the foregoing description, it will be clear that the phase surface locus varies when the time instants r, and t FIG. 1, at which the acceleration is switched to deceleration or vice versa are varied. For example, when state point P is made to coincide with the origin 0 as shown in FIG. 6 by a suitable selection of acceleration-deceleration switching points 2, and 1 when the state point P is reached or when the trolley attains the maximum running speed, both swing angle 0 and angular velocity of the swinging motion become zero so that it will be clear that during the succeeding interval in which the trolley runs at a constant speed the swing angle of the rope is always maintained zero. Let us now consider a case wherein the trolley running at the maximum speed is to be stopped. Consider now a speed pattern as shown in FIG. 7 wherein the deceleration of the trolley is commenced at time acceleration is commenced at time t and thereafter deceleration is commenced again at time t,,. The phase plane locus in this case is shown in FIG. 8. As has been pointed out hereinabove, as it is possible to make zero both the swing angle 6 and the angular velocity of the swinging motion (5 during the interval in which the trolley is running at a constant speed, if the state point co- 7 incides with the origin at t t the phase plane locus shown in FIG. 8 would originate from the origin 0. Since a during an interval 1 s t s the phase plane locus will become a circle having its center at point 0 and a radius oft DIG Further, since a 0 during an interval s I s i the phase plane locus will become a circle having its center at'point O, and a radius of (T 5 During an interval i g i I in which a 0, the phase plane locus will again become the circle having its center at point 0 and a radius as determined by the intersecting condition of the locus at state point P At a time r= t the trolley stops and thereafter since a O, the phase surface locus would be a circle having its center at the origin 0 and a radius offilz. In this manner, by the suitable selection of the acceleration-deceleration switching points 1 and I it is possible to make the phase plane locus as that shown in FIG. 9. At a time I 1 at which the trolley stops, since both the swing angle 0 of the rope and the angular velocity (i of the swinging motion are zero and since a 0 during the period t 2 t the rope will be maintained in a condition in which its swing is zero. For this reason, where the speed pattern from start to stop of the trolley is selected to be equal to that shown in FIG. and where the switching points 11, Ir s r determined such that a phase plane locus as shown in FIG. 11 can be provided, it is possible to make zero the swing of the rope both during the period 1 in which the trolley runs at a constant running speed and at time at which the trolley stops. It will thus be clear that it would not be necessary to vary the speed pattern during the intervals t,, t and t t, in accordance with the transverse running distance or stroke of the trolley if the interval 2 in which the trolley runs at the constant speed were varied in accordance with the transverse stroke of the trolley when it is controlled by the speed pattern as shown in FIG. 10. The fact that the swing angle 0 of the rope is kept at zero during the interval 1 t of the constant speed running is advantageous from the standpoint of safeness of the cargo operation. The locus P P P P shown in FIG. 11 can be obtained by tracing the locus O P, P P in the opposite direction. Consequently, following equations hold. With reference to an arc D P shown in FIG. 11 since '66. sin OOIPI) sin 35. with reference to an arc P,P having a center at 0 By substituting equation 37 into equation 36, we obtain By the concurrent solution of equations 32, 34 and 39, (t,- t (t 1,) and (t can be obtained. From the foregoing description, it can be noted that it is possible to make zero the swing of the rope at the time of stopping the trolley when the trolley is controlled according to the speed pattern shown in FIG. 10 and when the acceleration-deceleration switching points which satisfy equations 32, 34 and 39 are selected. However, as equation 39 is a complicated equation in terms of implicit functions including complicated trigonometrical functions, a complicated and expensive electronic computor is necessary for the simultaneous solution of equations 32, 34 and 39. Incorporation of such an expensive computer into the control system of a crane increases the cost thereof so that at present the control system is not provided with such computer but merely depends upon a mathematical analysis. The inventor has solved equations 32, 34 and 39 with an electronic computer utilizing the data regarding the rope length and the transverse running speed of the trolley and found that a high accuracy sufficient for the practical use can be obtained from the following equation 40 in which interval (t, t,,) is approximated as the explicit functions of Vmax, and 1. r, 1., =a Vmax |+b1 6 40. where a, b, and 0 represent constants. Accordingly, t t, and t 2 can be obtained as follows from equations 32 and 34. As can be noticed from FIG. 10, time t (or 1 represents an instant at which the transverse running speed of the trolley reaches a predetermined ultimate value and at which the difference between the ultimate speed commanded by the trolley controller and the actual running speed of the trolley reduces to substantially zero. Accordingly, by terminating the acceleration or deceleration by detecting this condition it will be not necessary to calculate t by using equation 42. In other words, it is sufficient to calculate (t t and (t I alone by using equations 40 and 41. The straight lines shown in FIG. 12 show the relationship between the switching time t and the rope length obtained by solving equations 32, 34 and 39 for the rope length of from 7.5m to 22.5m and the trolley running speed of from 31.25 m/min. to lm/min. Straight lines shown in FIG. 12 show the solution of equation 40. Thus, FIG. 12 shows that even when the switching time is calculated according to equation 40 of approximation, it is possible to realize sufficiently high practical accuracy for the ranges of the rope length variation and the trolley speed variation encounted in the actual use. Equations 29, and 31 also show that the stroke of the trolley (the area of the lefthand shaded portion in FIG. 1) during interval t t in which the trolley has accelerated to a maximum speed Vmax after starting is equal to the stroke (the area of the righthand shaded portion in FIG. 1) during interval t t, in which the trolley has decelerated from Vmax to standstill. This method of operation is the result of approximation of the above described analysis in terms of the maximum speed and the length of the rope. From this it can be understood that it is possible to terminate the swinging motion of the rope when the trolley stops by measuring or calculating the distance S over which the trolley travels from starting until the maximum speed is reached and by issuing a deceleration initiation command signal when the trolley reaches a point spaced from a target stopping position by a required distance. From the foregoing description, it will be clear that according to the control system described hereinabove, it is possible to substantially reduce to zero the swing of the rope when the trolley is accelerated to a predetermined maximum speed Vmax and when the trolley is brought to stop. With this system, however, as no signal is given as to when the deceleration should be commenced at time t.,, the crane operator must determine by himself such time by relying upon his skill. Accordingly, it is not always possible to correctly stop the trolley at the target position at time t SUMMARY OF THE INVENTION It is an object of this invention to provide a novel method and system for controlling a suspension type crane capable of suppressing to substantially zero the swing of the load suspending rope while the crane is running at a constant speed. Another object of this invention is to provide a novel method and system for controlling a suspension type crane capable of initiating the deceleration at a correct 10 time for stopping it at a predetermined target position without any swinging motion of the rope. Still another object of this invention is to provide a novel method and system of controlling a suspension type crane capable of operating the same with a minumum time without permitting any swing to the rope while the crane is running at a constant speed and when the crane is stopped, thereby increasing the cargo efficiency. A further object of this invention is to provide a novel acceleration-dcce[eration pattern signal generating circuit suitable for use in this invention. According to one aspect of this invention there is provided a method of controlling a suspension type crane which is moved transversely while suspending a load by means of a rope wherein the crane is accelerated at least two times at spaced points to a predetermined maximum speed during the acceleration period, the swing of the rope is minimized when the predetermined maximum speed is reached, the crane is run at the predetermined maximum speed for a predetermined interval, the crane is decelerated from the maximum speed at least two times at spaced points during the deceleration period, and the crane is stopped when the swing of the rope is reduced to a minimum, characterized in that the areas of the acceleration and deceleration periods of the crane are made equal. According to another aspect of this invention there is provided a control system for a suspension type crane running in the transverse direction, characterized by comprising means for providing a start command signal, means responsive to the start command signal for determining a maximum transverse running speed of the crane corresponding to the starting position and a predetermined target position of the crane, means for providing a deceleration command signal when the crane reaches a point a predetermined distance before the target position, which is determined by the maximum transverse running speed, means for generating a deceleration command signal, and means responsive to the start command signal or the deceleration command signal for providing a predetermined accelerationdeceleration pattern signal corresponding to the maximum transverse running speed, whereby the running speed of the crane is controlled so as to stop the crane at the target position. BRIEF DESCRIPTION OF THE DRAWINGS In the accompanying drawings: FIG. 1 is a diagram showing a typical transverse running speed pattern of the trolley of a suspension type crane which can be realized by the control system of this invention; FIGS. 2 to 11 inclusive are diagrams useful to explain the principle of this invention; FIG. 12 is a graph showing the relationship between the switching time and the rope length calculated for various rope lengths and trolley speeds which are used actually; FIG. 13 is a block diagram of one embodiment of the novel control system of this invention; FIG. 14 is a block diagram ofa modified embodiment of this invention; FIG. 15 shows a modified speed pattern; FIG. 16 is a block diagram of a crane control system; FIG. 17 is a block diagram showing one example of the acceleration-deceleration switching time operating circuit utilized in this invention; FIG. 18 is a diagram for explaining the operation of the operating circuit shown in FIG. 17; FIG. 19 shows a block diagram of the speed reference generating circuit controlled by the operating circuit shown in FIG. 17; and FIG. is a diagram for explaining the operation of the speed reference generating circuit shown in FIG. 19. DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 13 shows the construction of one embodiment of the control system of this invention which comprises a deceleration command signal generator A which generates a deceleration commandsignal in accordance with the deviation A L of the present position L from the target position L0 for providing a transverse running speed pattern as shown in FIG. 1, a maximum transverse running speed determining unit B which determines the maximum transverse running speed Vmax in accordance with a deviation A L corresponding to the distance L0 to the target position and rope length 1 (for the reason to be described later, rope length is not taken into consideration at the present stage of the description). an acceleration-deceleration pattern generator C connected to receive the output from the maximum transverse running speed determining unit B when the deceleration command signal generator A operates for forming the transverse running speed pattern shown in FIG. 1, and a speed controller D for controlling the speed ofa motor M for driving the trolley in accordance with the output from the acceleration-deceleration pattern generator C. These component elements will be described in detail in the following. The deceleration command signal generator A will firstly be described. The distance S over which the trolley which has been running at the maximum speed Vmax should travel before it is stopped in accordance with the speed pattern shown in FIG. 1 can be derived out from equations 29, and 31, thus S= A vmax{2u,-r,,)+(1,r,)} 42. Intervals (t, t and (t can be obtained from the following equations. and Vmax Instead of using equation 41, an approximate value of distance s can be derived out from equations 42, 44 and the following equation 45 which is an equation of approximation expressed by an explicit function of the maximum speed Vmax and the rope length l t,-r,,=a|Vmaxl+bl +c 45. where a, b and c are constants. This also corresponds to the distance of running during interval t shown in FIG. 1 but this distance of running can be obtained by storing the running distance during interval 2 -1 This is because the running distances during intervals t and t, are equal as has been mentioned hereinbefore. In any way, the dis- 12 tance S required to stop the trolley has already been determincd by the time at which the trolley attains its maximum speed Vmax. Such measurement or calculation is'requircd to be made only once during the operation of'the crane, and the result is given to the deceleration command signal generator A. Thus, the deceleration command signal generator A stores a signal corresponding to distance S and operates to compare the deviation AL L0 L) of the present position L of the trolley from the target postion L0, with signal S for producing a deceleration command signal when AL becomes equal to S. The deceleration command signal can be generated by switching the speed command for the acce[eration-deceleration pattern generator C from Vmax to 0, as shown in FIG. 13. The maximum transverse running speed determining unit B will now be described. While in the foregoing description it was explained that the maximum transverse running speed Vmax is prescribed, as can be noted, from equation 43 where the maximum speed Vmax and rope length 1 are given it is possible to determine acceleration and decleration intervals 1 t r, t t t t t t and 1 r Accordingly, where the values of Vmax and l are given, the distance over which the trolley runs between starting and completion of acceleration, and the distance over which the trolley runs from the maximum speed until it stops will also be determined. For this reason, even when a deceleration command signal is generated at an instant I at which acceleration has been completed thus making t t the trolley runs a ddistance 28, that is, the sum of the distance 5 from start to the completion of acceleration and the distance S from the maximum speed to the stop. Accordingly, the run ning distance L0 is shorter than 25, so that it is necessary to suitably decrease the maximum speed. The purpose of the maximum transverse running speed determining unit B is to determine such an optimum maximum transverse running speed. The maximum speed Vmax can be derived from equations 42, 43 and 44 by putting (In lieu of equation 44, equation 45 can also be used). For this reason, in FIG. 12 the distance between the starting position and the target position is designated by Lo/2. As shown in FIG. 12, since the maximum speed Vmax does not vary so much with the rope length 1, it is possible to simplify the control device by ignoring the effect of length 1. FIG. 13 shows such simplified construction wherein a signal representing 1 is not applied to the maximum transverse running speed determining unit B. Turning now to the acceleration-deceleration pattern generator C, it is comprised essentially of integrators and is constructed and operated to generate a predetermined acceleration-deceleration pattern signal as will be described later in detail in connection with FIGS. 17 to 20. At this stage of description, it is merely pointed out that the deceleration command signal generator A switches the input to the acceleration-deceleration pat tern generator C from signal Vmax to a reference signal 0 at time 2 Further, a signal representing the rope length l is also applied to the pattern generator C for Patent Citations
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