HOISTING CONTAINER POSE CONTROL METHOD OF DOUBLE-ROPE WINDING TYPE ULTRA-DEEP VERTICAL SHAFT HOISTING SYSTEM

Abstract

The present invention discloses a hoisting container pose control method of a double-rope winding type ultra-deep vertical shaft hoisting system. The method comprises the following steps of step 1, building a mathematical model of a double-rope winding type ultra-deep vertical shaft hoisting subsystem; step 2, building a position closed-loop mathematical model of an electrohydraulic servo subsystem; step 3, outputting a flatness characteristics of a nonlinear system; step 4, designing a pose leveling flatness controller of a double-rope winding type ultra-deep vertical shaft hoisting subsystem; and step 5, designing a position closed-loop flatness controller of the electrohydraulic servo subsystem. The present invention has the advantages that a system state variable derivation process is omitted, so that a design process of the controllers is greatly simplified. The response time of the controllers can be shortened, and a hoisting container can fast reach a leveling state. In an application process of the system, sensor measurement noise and system non-modeling characteristics can be amplified through state variable derivation, so that tracking errors can be reduced through design of the flatness controller. A control process is more precise, and good control performance is ensured.

Claims

1. A hoisting container pose control method of a double-rope winding type ultra-deep vertical shaft hoisting system, comprising: step 1, building a mathematical model of the double-rope winding type ultra-deep vertical shaft hoisting subsystem; step 2, building a position closed-loop mathematical model of an electrohydraulic servo subsystem; step 3, outputting flatness characteristics of a nonlinear system; step 4, designing a flatness controller of the double-rope winding type ultra-deep vertical shaft hoisting subsystem; and step 5, designing a position closed-loop flatness controller of the electrohydraulic servo subsystem.

2. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 1, wherein the mathematical model of the double-rope winding type ultra-deep vertical shaft hoisting subsystem in step 1 is as follows:
M{umlaut over (q)}+C{dot over (q)}+Kq=F, wherein in the formula, {umlaut over (q)}, {dot over (q)} and q are respectively a generalized acceleration, speed and displacement, q=[x.sub.c,y.sub.c,], x.sub.c and y.sub.c are respectively a vertical displacement and a horizontal displacement of a gravity center of a hoisting container, .sub.c is an anticlockwise rotation angle of the hoisting container, and M, C, K and F are respectively a mass matrix, a damping matrix, a stiffness matrix and a non-potential force of the hoisting subsystem, wherein $M = [\begin{matrix} m_{c} + \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 1} + \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 2} & 0 & - \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 1} .Math. a_{1} + \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 2} .Math. a_{2} \\ 0 & m_{c} & 0 \\ - \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 1} .Math. a_{1} + \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 2} .Math. a_{2} & 0 & I_{c} - \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 1} .Math. a_{1}^{2} + \frac{1}{3} .Math. .Math. .Math. l_{h .Math. .Math. 2} .Math. a_{2}^{2} \end{matrix}], .Math. C = [\begin{matrix} c_{h .Math. .Math. 1} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 1} + c_{h .Math. .Math. 2} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 2} & 0 & - (c_{h .Math. .Math. 1} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 1}) .Math. a_{1} + (c_{h .Math. .Math. 2} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 2}) .Math. a_{2} \\ 0 & c_{s .Math. .Math. 1} + c_{s .Math. .Math. 2} + c_{s .Math. .Math. 3} + c_{s .Math. .Math. 4} & - c_{s .Math. .Math. 1} .Math. b_{1} + c_{s .Math. .Math. 2} .Math. b_{2} - c_{s .Math. .Math. 3} .Math. b_{1} + c_{s .Math. .Math. 4} .Math. b_{2} \\ - (c_{h .Math. .Math. 1} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 1}) .Math. a_{1} + (c_{h .Math. .Math. 2} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 2}) .Math. a_{2} & - c_{s .Math. .Math. 1} .Math. b_{1} + c_{s .Math. .Math. 2} .Math. b_{2} - c_{s .Math. .Math. 3} .Math. b_{1} + c_{s .Math. .Math. 4} .Math. b_{2} & (c_{h .Math. .Math. 1} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 1}) .Math. a_{1}^{2} + (c_{h .Math. .Math. 2} + \frac{1}{3} .Math. .Math. {\dot{l}}_{h .Math. .Math. 2}) .Math. a_{2}^{2} + b_{1}^{2} .Math. c_{s .Math. .Math. 1} + b_{2}^{2} .Math. c_{s .Math. .Math. 2} + b_{1}^{2} .Math. c_{s .Math. .Math. 3} + b_{2}^{2} .Math. c_{s .Math. .Math. 4} \end{matrix}], .Math. K = [\begin{matrix} k_{h .Math. .Math. 1} + k_{h .Math. .Math. 2} & 0 & - k_{h .Math. .Math. 1} .Math. a_{1} + k_{h .Math. .Math. 2} .Math. a_{2} \\ 0 & k_{s .Math. .Math. 1} + k_{s .Math. .Math. 2} + k_{s .Math. .Math. 3} + k_{s .Math. .Math. 4} & - k_{s .Math. .Math. 1} .Math. b_{1} + k_{s .Math. .Math. 2} .Math. b_{2} - k_{s .Math. .Math. 3} .Math. b_{1} + k_{s .Math. .Math. 4} .Math. b_{2} \\ - k_{h .Math. .Math. 1} .Math. a_{1} + k_{h .Math. .Math. 2} .Math. a_{2} & - k_{s .Math. .Math. 1} .Math. b_{1} + k_{s .Math. .Math. 2} .Math. b_{2} - k_{s .Math. .Math. 3} .Math. b_{1} + k_{s .Math. .Math. 4} .Math. b_{2} & k_{h .Math. .Math. 1} .Math. a_{1}^{2} + k_{h .Math. .Math. 2} .Math. a_{2}^{2} + b_{1}^{2} .Math. k_{s .Math. .Math. 1} + b_{2}^{2} .Math. k_{s .Math. .Math. 2} + b_{1}^{2} .Math. k_{s .Math. .Math. 3} + b_{2}^{2} .Math. k_{s .Math. .Math. 4} \end{matrix}], and$ $F = [\begin{matrix} - \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 1} [{\overset{.Math.}{l}}_{r .Math. .Math. 1} + {\overset{.Math.}{u}}_{1} (1 + \sin .Math. .Math._{1})] - \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 2} [{\overset{.Math.}{l}}_{r .Math. .Math. 2} + {\overset{.Math.}{u}}_{2} (1 + \sin .Math. .Math._{2})] + (- \frac{1}{6} .Math. .Math. .Math. {\dot{l}}_{h .Math. .Math. 1} + c_{h .Math. .Math. 1}) [{\dot{l}}_{r .Math. .Math. 1} + {\dot{u}}_{1} (1 + \sin .Math. .Math._{1})] + \\ (- \frac{1}{6} .Math. .Math. .Math. {\dot{l}}_{h .Math. .Math. 2} + c_{h .Math. .Math. 2}) [{\dot{l}}_{r .Math. .Math. 2} + {\dot{u}}_{2} (1 + \sin .Math. .Math._{2})] + k_{h .Math. .Math. 1} [l_{r .Math. .Math. 1} + u_{1} (l + \sin .Math. .Math._{1})] + k_{h .Math. .Math. 2} [l_{r .Math. .Math. 2} + u_{2} (1 + \sin .Math. .Math._{2})] - m_{c} .Math. g - \frac{1}{2} .Math. .Math. .Math. {gl}_{h .Math. .Math. 1} - \frac{1}{2} .Math. .Math. .Math. {gl}_{h .Math. .Math. 2} \\ 0 \\ \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 1} .Math. a_{1} [{\overset{.Math.}{l}}_{r .Math. .Math. 1} + {\overset{.Math.}{u}}_{1} (1 + \sin .Math. .Math._{1})] - \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 2} .Math. a_{2} [{\overset{.Math.}{l}}_{r .Math. .Math. 2} + {\overset{.Math.}{u}}_{2} (1 + \sin .Math. .Math._{2})] + (- \frac{1}{6} .Math. .Math. .Math. {\dot{l}}_{h .Math. .Math. 1} + c_{h .Math. .Math. 1}) .Math. a_{1} [{\dot{l}}_{r .Math. .Math. 1} + {\dot{u}}_{1} (1 + \sin .Math. .Math._{1})] - \\ (- \frac{1}{6} .Math. .Math. .Math. {\dot{l}}_{h .Math. .Math. 2} + c_{h .Math. .Math. 2}) .Math. a_{2} [{\dot{l}}_{r .Math. .Math. 2} + {\dot{u}}_{2} (1 + \sin .Math. .Math._{2})] + k_{h .Math. .Math. 1} .Math. a_{1} [l_{r .Math. .Math. 1} + u_{1} (l + \sin .Math. .Math._{1})] - k_{h .Math. .Math. 2} .Math. a_{2} [l_{r .Math. .Math. 2} + u_{2} (1 + \sin .Math. .Math._{2})] + \frac{1}{2} .Math. .Math. .Math. {gl}_{h .Math. .Math. 1} .Math. a_{1} - \frac{1}{2} .Math. .Math. .Math. {gl}_{h .Math. .Math. 2} .Math. a_{2} \end{matrix}] .$

3. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 2, wherein in the modeling process of the hoisting subsystem, if it is assumed that no offset load condition exists, i.e., a .sub.1=a.sub.2, and when the anticlockwise rotation angle of the hoisting container is 0, the tension of two steel wire ropes is consistent; and therefore, the mathematical model of the double-rope winding type ultra-deep vertical shaft hoisting subsystem is simplified as:
(M.sub.31{umlaut over (x)}.sub.c+M.sub.33{umlaut over ()})+(C.sub.31{dot over (x)}.sub.c+C.sub.33{dot over ()})+(K.sub.31x.sub.c+K.sub.33)=F.sub.31, wherein in the formula, M.sub.ij, C.sub.ij, K.sub.ij and F.sub.ij are respectively elements of the mass matrix, the damping matrix, the stiffness matrix and the non-potential force, i=1,2,3, and j=1,2,3.

4. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 3, wherein a pose leveling of the hoisting container is regulated by two hydraulic executors, so that u.sub.1=u=u.sub.2, an inclination angle of the hoisting container is a controlled variable, and the mathematical model of the double-rope winding type ultra-deep vertical shaft hoisting subsystem is further simplified as:
A{umlaut over ()}+B{dot over ()}+C=Q+W{dot over (u)}+Ru+F.sub.0, wherein in the formula, ${\begin{matrix} A = M_{33} \\ B = C_{33} \\ C = K_{33} \\ Q = \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 1} .Math. a_{1} (1 + \sin (_{1})) + \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 2} .Math. a_{2} (1 + \sin (_{2})) \\ W = (- \frac{1}{6} .Math. .Math. {\dot{l}}_{h .Math. .Math. 1} + c_{h .Math. .Math. 1}) .Math. a_{1} (1 + \sin (_{1})) + (- \frac{1}{6} .Math. .Math. {\dot{l}}_{h .Math. .Math. 2} + c_{h .Math. .Math. 2}) .Math. a_{1} (1 + \sin (_{2})) \\ R = k_{h .Math. .Math. 1} .Math. a_{1} (1 + \sin (_{1})) + k_{h .Math. .Math. 2} .Math. a_{2} (1 + \sin (_{2})) \\ F_{0} = \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 1} .Math. a_{1} .Math. {\overset{.Math.}{l}}_{r .Math. .Math. 1} - \frac{1}{6} .Math. .Math. .Math. l_{h .Math. .Math. 2} .Math. a_{2} .Math. {\overset{.Math.}{l}}_{r .Math. .Math. 2} + (- \frac{1}{6} .Math. .Math. .Math. {\dot{l}}_{h .Math. .Math. 1} + c_{h .Math. .Math. 1}) .Math. a_{1} .Math. {\dot{l}}_{r .Math. .Math. 1} - \\ (- \frac{1}{6} .Math. .Math. {\dot{l}}_{h .Math. .Math. 2} + c_{h .Math. .Math. 2}) .Math. a_{2} .Math. {\dot{l}}_{r .Math. .Math. 2} + k_{h .Math. .Math. 1} .Math. a_{1} .Math. l_{r .Math. .Math. 1} - k_{h .Math. .Math. 2} .Math. a_{2} .Math. l_{r .Math. .Math. 2} - \\ M_{31} .Math. {\overset{.Math.}{x}}_{c} - C_{31} .Math. {\dot{x}}_{c} - K_{31} .Math. x_{c} + \frac{1}{2} .Math. .Math. .Math. {gl}_{h .Math. .Math. 1} .Math. a_{1} - \frac{1}{2} .Math. .Math. .Math. {gl}_{h .Math. .Math. 2} .Math. a_{2} \end{matrix};$ and k.sub.h1 and k.sub.h2 are much greater than c.sub.h1 and c.sub.h2, so that the formula is further simplified as:
A{umlaut over ()}+B{dot over ()}+C=Ru+F.sub.0.

5. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 3, wherein a state variable is selected to be x.sub.1=[x.sub.1, x.sub.2].sup.T=[, {dot over ()}].sup.T, so that a dynamic model of the hoisting subsystem may be converted into a state space form: ${\begin{matrix} {\dot{x}}_{1} = x_{2} \\ {\dot{x}}_{2} = - h_{1} .Math. x_{2} - h_{2} .Math. x_{1} + h_{3} .Math. x_{3} + f \end{matrix},$ and y.sub.1=x.sub.1, wherein in the formula, h.sub.1=B/A, h.sub.2=C/A, h.sub.3=R/A, and f=F.sub.0/A.

6. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 1, wherein the mathematical model of the electrohydraulic servo subsystem in step 2 is as follows: $A_{p} .Math. {\dot{x}}_{p} + C_{tl} .Math. P_{L} + \frac{V_{t}}{4 .Math._{e}} .Math. {\dot{P}}_{L} = Q_{L},$ wherein in the formula, A.sub.p is an effective acting area of a hydraulic cylinder piston, C.sub.t1 is a total leakage coefficient of a hydraulic cylinder, x.sub.p is a displacement of a hydraulic cylinder piston rod, V.sub.t is a total volume of an oil inlet cavity and an oil return cavity of the hydraulic cylinder, and .sub.e is an effective volume elasticity modulus of oil liquid in the hydraulic cylinder; and according to the Newton's second law, a load force balance equation of an electrohydraulic servo system is as follows:
m{umlaut over (x)}.sub.pB.sub.p{dot over (x)}.sub.p+A.sub.pP.sub.L=F.sub.L, wherein F.sub.L is a force acting on floating hoisting sheaves by the hydraulic cylinder, m is a total mass of the floating hoisting sheaves, and B.sub.p is a viscous damping coefficient of the hydraulic cylinder.

7. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 5, wherein a state variable is selected to be x.sub.2=[x.sub.3, x.sub.4, x.sub.5].sup.T=[x.sub.p, {dot over (x)}.sub.p, P.sub.hL].sup.T, so that a kinetic model of the electrohydraulic servo subsystem may be converted into a state space form: ${\begin{matrix} {\dot{x}}_{3} = x_{4} \\ {\dot{x}}_{4} = a_{1} .Math. x_{5} - a_{2} .Math. x_{4} - a_{3} .Math. F_{g} \\ {\dot{x}}_{5} = - a_{4} .Math. x_{4} - a_{5} .Math. x_{5} + a_{6} .Math. Q_{L} \end{matrix},$ and y.sub.2=x.sub.3, wherein in the formula, a.sub.1=A.sub.p/m, a.sub.2=B.sub.p/m, a.sub.3=1/m, a.sub.4=4.sub.eA.sub.p/V.sub.t, a.sub.5=4.sub.eC.sub.tl/V.sub.t, and a.sub.6=4.sub.e/V.sub.t.

8. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 1, wherein a concrete design of outputting the flatness characteristics of the nonlinear system in step 3 is as follows:
{dot over (x)}=f(x,u), wherein in the formula, x is a system state variable, and u is a system control input with a same dimension as system output y; if the following system output y exists:
y=P(x, {dot over (u)}, , . . . , u.sup.(p)), the system state variable x and the system control input u may be expressed as equation forms of the system output and finite differential thereof:
x=P(y, {dot over (y)}, , . . . , y.sup.(q)), and
u=Q(y, {dot over (y)}, , . . . , y.sup.(q+1)).

9. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 1, wherein a concrete design of the post leveling flatness controller of the double-rope winding type ultra-deep vertical shaft hoisting subsystem in step 4 is as follows: ${\begin{matrix} x_{1 .Math. d} = y_{1 .Math. d} \\ x_{2 .Math. d} = {\dot{y}}_{1 .Math. d} \\ u_{hd} = (h_{1} .Math. {\dot{y}}_{1 .Math. d} + h_{2} .Math. y_{1 .Math. d} - f + {\dot{x}}_{2 .Math. d}) / h_{3} \\ z_{1} = x_{1 .Math. d} - x_{1} \\ z_{2} = x_{2 .Math. d} - x_{2} \\ u_{h} = u_{hd} + \frac{1}{h_{3}} .Math. K_{1} .Math. z_{1} \end{matrix} .$

10. The hoisting container pose control method of the double-rope winding type ultra-deep vertical shaft hoisting system according to claim 1, wherein a design of the position closed-loop flatness controller of the electrohydraulic servo subsystem in step 5 is as follows: ${\begin{matrix} x_{3 .Math. d} = y_{2 .Math. d} \\ x_{4 .Math. d} = {\dot{y}}_{2 .Math. d} \\ x_{5 .Math. d} = \frac{1}{a_{6}} .Math. ({\overset{.Math.}{y}}_{2 .Math. d} + a_{4} .Math. {\dot{y}}_{2 .Math. d} + a_{5} .Math. y_{2 .Math. d} - a_{3} .Math. F_{g}) \\ u_{Ld} = \frac{1}{a_{6}} .Math. (a_{4} .Math. x_{4 .Math. d} + a_{5} .Math. x_{5 .Math. d} + {\dot{x}}_{5 .Math. d}) \\ z_{3} = x_{3 .Math. d} - x_{3} \\ z_{4} = x_{4 .Math. d} - x_{4} \\ z_{5} = x_{5 .Math. d} - x_{5} \\ u_{L} = u_{Ld} + \frac{1}{a_{6}} .Math. K_{2} .Math. z_{2} \end{matrix} .$

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0099] FIG. 1 is a schematic structural diagram of a hoisting system of the present invention.

[0100] FIG. 2 is a kinetic model diagram of a double-outlet-rod hydraulic cylinder.

[0101] FIG. 3 is a structural block diagram of a control system of the present invention.

[0102] FIG. 4 is a comparison diagram of angle tracking signals of a hoisting container of a flatness controller in a concrete embodiment of the present invention.

[0103] FIG. 5 is a partial enlarged diagram of the angle tracking signals of the hoisting container of the flatness controller in the concrete embodiment of the present invention.

[0104] FIG. 6 is a comparison diagram of tracking signals of a hydraulic cylinder 1 of the flatness controller in the concrete embodiment of the present invention.

[0105] FIG. 7 is a tracking error diagram of the hydraulic cylinder 1 of the flatness controller in the concrete embodiment of the present invention.

[0106] FIG. 8 is a comparison diagram of tracking signals of a hydraulic cylinder 2 of the flatness controller in the concrete embodiment of the present invention.

[0107] FIG. 9 is a tracking error diagram of the hydraulic cylinder 2 of the flatness controller in the concrete embodiment of the present invention.

[0108] FIG. 10 is a comparison diagram of angle tracking signals of a hoisting container of a backstepping controller in the concrete embodiment of the present invention.

[0109] FIG. 11 is a partial enlarged diagram of the angle tracking signals of the hoisting container of the backstepping controller in the concrete embodiment.

[0110] FIG. 12 is a comparison diagram of tracking signals of a hydraulic cylinder 1 of the backstepping controller in the concrete embodiment.

[0111] FIG. 13 is a tracking error diagram of the hydraulic cylinder 1 of a backstepping controller in the concrete embodiment.

[0112] FIG. 14 is a comparison diagram of tracking signals of a hydraulic cylinder 2 of the backstepping controller in the concrete embodiment.

[0113] FIG. 15 is a tracking error diagram of the hydraulic cylinder 2 of the backstepping controller in the concrete embodiment.

[0114] Numerals in the figures indicate: 1, duplex winding drum; 2, string rope; 3, floating hoisting sheave; 4, double-outlet-rod hydraulic cylinder; 5, vertical section steel wire rope; and 6, hoisting container.

DETAILED DESCRIPTION OF THE INVENTION

[0115] The present invention will be described in detail with reference to the accompanying drawings and a concrete embodiment.

[0116] As shown in FIG. 1 and FIG. 2, for an oil source pressure P.sub.s of a hydraulic system, P.sub.s=15*10.sup.6 Pa. For an effective acting area A.sub.p of a double-outlet-rod hydraulic cylinder 4, A.sub.p=1.88*10.sup.3 m.sup.2. For a load mass m of the hydraulic system, m=200 kg. For a viscous damping coefficient B.sub.p of the hydraulic system, B.sub.p=25000 N(m/s). For a total volume V.sub.t of an oil inlet cavity and an oil return cavity of the hydraulic cylinder, V.sub.t=0.96*10.sup.3 m.sup.3. For a total leakage coefficient C.sub.t1 of the hydraulic system, C.sub.t1=9.2*10.sup.13 m.sup.3/(s/Pa). For a volume elasticity modulus .sub.e of hydraulic oil, .sub.e=6.9*10.sup.8 Pa. For vertical distances b.sub.1 and b.sub.2 from upper and lower surfaces of a hoisting container 6 to a gravity center of the hoisting container, b.sub.1=b.sub.2=0.0625 m. For horizontal distances a.sub.1 and a.sub.2 from connecting points of two vertical section steel wire ropes 5 on the hoisting container 6 to the gravity center of the hoisting container, a.sub.1=a.sub.2=0.1575 m. For initial lengths l.sub.h20 and l.sub.h20 of the vertical section steel wire ropes 5, l.sub.h20=l.sub.h20=6 m. For a rotational inertia I.sub.c of the hoisting container 6, I.sub.c=3.307 kg.Math.m.sup.2. For a unit length mass of the steel wire rope, =0.417 kg/m. For inclination angles a.sub.1 and a.sub.2 of left and right string ropes 2, a.sub.1=a.sub.2=64.5. For radii r.sub.1 and r.sub.2 of two floating hoisting sheaves 3, r.sub.1=r.sub.2=0.2 m. For masses m.sub.1 and m.sub.2 of the two floating hoisting sheaves 3, m.sub.1=m.sub.2=10 kg. For a mass m.sub.c of the hoisting container 6, m.sub.c=120 kg. For transverse equivalent damping coefficients c.sub.s1, c.sub.s2, c.sub.s3 and c.sub.s4 of four pairs of spring-damping models, c.sub.s1=c.sub.s2=c.sub.s3=c.sub.s4=10 N/(m/s). For transverse equivalent stiffness k.sub.s1, k.sub.s2, k.sub.s3 and k.sub.s4 of the four pairs of spring-damping models, k.sub.s1=k.sub.s2=k.sub.s3=k.sub.s4=1000 Pa.

[0117] For control parameters of a flatness controller, K.sub.1=[k.sub.1,k.sub.2]=[20,10], and K.sub.2=[k.sub.3,k.sub.4,k.sub.5]=[3*10.sup.14,2*10.sup.12,2].

[0118] For control parameters of a backstepping controller, k.sub.1=20, k.sub.2=20, k.sub.3=300, k.sub.4=280, and k.sub.5=260.

[0119] An initial angle of the hoisting container is set to be 5.

[0120] As shown in FIG. 3, the steps of leveling the hoisting container of the flatness controller are as follows:

[0121] 1) A state space form of a kinetic model of a hoisting subsystem is:

[00031] $\begin{matrix} {\begin{matrix} {\dot{x}}_{1} = x_{2} \\ {\dot{x}}_{2} = - h_{1} .Math. x_{2} - h_{2} .Math. x_{1} + h_{3} .Math. x_{3} + f \end{matrix}, & (34) \end{matrix}$

and

[0122] y.sub.1=x.sub.1, wherein

[0123] in the formula, h.sub.1=B/A, h.sub.2=C/A, h.sub.3=R/A, and f=F.sub.0/A.

[0124] 2) A state space form of a kinetic model of an electrohydraulic servo subsystem is:

[00032] $\begin{matrix} {\begin{matrix} {\dot{x}}_{3} = x_{4} \\ {\dot{x}}_{4} = a_{1} .Math. x_{5} - a_{2} .Math. x_{4} - a_{3} .Math. F_{g} \\ {\dot{x}}_{5} = - a_{4} .Math. x_{4} - a_{5} .Math. x_{5} + a_{6} .Math. Q_{L} \end{matrix}, & (36) \end{matrix}$

and

[0125] y.sub.2=x.sub.3, wherein

[0126] in the formula, a.sub.1=A.sub.p/m, a.sub.2=B.sub.p/m, a.sub.3=1/m, a.sub.4=4.sub.eA.sub.p/V.sub.t, a.sub.5=4.sub.eC.sub.tl/V.sub.t and a.sub.6=4.sub.e/V.sub.t.

[0127] 3) A system state variable x and a system control input u may be expressed as the following equation form of the system flatness characteristic output and a finite differential thereof:

x=P(y, {dot over (y)}, , . . . , y.sup.(q)), (39), and

u=Q(y, {dot over (y)}, , . . . , y.sup.(q+1)), (40).

[0128] 4) A concrete design of a pose leveling flatness controller of a double-rope winding type ultra-deep vertical shaft hoisting subsystem is as follows:

[00033] $\begin{matrix} {\begin{matrix} x_{1 .Math. d} = y_{1 .Math. d} \\ x_{2 .Math. d} = {\dot{y}}_{1 .Math. d} \\ u_{hd} = (h_{1} .Math. {\dot{y}}_{1 .Math. d} + h_{2} .Math. y_{1 .Math. d} - f + {\dot{x}}_{2 .Math. d}) / h_{3} \\ z_{1} = x_{1 .Math. d} - x_{1} \\ z_{2} = x_{2 .Math. d} - x_{2} \\ u_{h} = u_{hd} + \frac{1}{h_{3}} .Math. K_{1} .Math. z_{1} \end{matrix} . & (47) \end{matrix}$

[0129] 5) A design of a position closed-loop flatness controller of the electrohydraulic servo subsystem is as follows:

[00034] $\begin{matrix} {\begin{matrix} x_{3 .Math. d} = y_{2 .Math. d} \\ x_{4 .Math. d} = {\dot{y}}_{2 .Math. d} \\ x_{5 .Math. d} = \frac{1}{a_{6}} .Math. ({\overset{.Math.}{y}}_{2 .Math. d} + a_{4} .Math. {\dot{y}}_{2 .Math. d} + a_{5} .Math. y_{2 .Math. d} - a_{3} .Math. F_{g}) \\ u_{Ld} = \frac{1}{a_{6}} .Math. (a_{4} .Math. x_{4 .Math. d} + a_{5} .Math. x_{5 .Math. d} + {\dot{x}}_{5 .Math. d}) \\ z_{3} = x_{3 .Math. d} - x_{3} \\ z_{4} = x_{4 .Math. d} - x_{4} \\ z_{5} = x_{5 .Math. d} - x_{5} \\ u_{L} = u_{Ld} + \frac{1}{a_{6}} .Math. K_{2} .Math. z_{2} \end{matrix} . & (57) \end{matrix}$

[0130] According to parameter input of the concrete embodiment, the obtained leveling performance of the hoisting container of the flatness controller is shown in FIG. 4 to FIG. 9.

[0131] A pose leveling control design of the hoisting container of the backstepping controller is as follows:

[00035] $\begin{matrix} {\begin{matrix} z_{1} = x_{1 .Math. d} - x_{1 .Math. r} \\ z_{2} = x_{2 .Math. d} -_{1} \\ _{1} = k_{1} .Math. z_{1} + {\dot{x}}_{1 .Math. r} \\ u_{h} = \frac{1}{h_{3}} .Math. (h_{1} .Math. x_{2} + h_{2} .Math. x_{1} - f + {\dot{}}_{1} - k_{2} .Math. z_{2} + z_{1}) \end{matrix} . & (48) \end{matrix}$

[0132] A position closed-loop control process of the electrohydraulic servo subsystem of the backstepping controller is as follows:

[00036] $\begin{matrix} {\begin{matrix} z_{3} = x_{3 .Math. d} - x_{3} \\ z_{4} =_{3} - x_{4} \\ z_{5} =_{4} - x_{5} \\ _{3} = - k_{3} .Math. z_{3} + {\dot{x}}_{3 .Math. d} \\ _{4} = \frac{1}{a_{1}} .Math. (z_{3} + a_{2} .Math. x_{2} - \frac{F_{g}}{a_{3}} + {\dot{}}_{3} + k_{4} .Math. z_{4}) \\ u_{L} = \frac{1}{a_{6}} .Math. (k_{5} .Math. z_{5} + {\dot{}}_{4} + a_{4} .Math. x_{2} + a_{5} .Math. x_{3} + a_{1} .Math. z_{4}) \end{matrix} . & (58) \end{matrix}$

[0133] According to parameter input in the concrete embodiment, leveling performance of the hoisting container of the backstepping controller is shown in FIG. 10 to FIG. 15.

[0134] From the angle tracking performance of the hoisting containers of the two controllers, the hoisting containers may both reach a leveling state in a certain time, but the flatness controller enables the hoisting container to reach the leveling state in 70 ms, and the backstepping controller enables the hoisting container to reach a stable state in 450 ms. From the position tracking performance of two hydraulic cylinders, the tracking error of the backstepping controller is greater than that of the flatness controller. Based on the above, the control performance of the flatness controller is superior to that of the backstepping controller.

HOISTING CONTAINER POSE CONTROL METHOD OF DOUBLE-ROPE WINDING TYPE ULTRA-DEEP VERTICAL SHAFT HOISTING SYSTEM

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Cpc classification

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F15B15/00

MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING

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B66B1/28

PERFORMING OPERATIONS; TRANSPORTING

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G05B13/042

PHYSICS

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G06F2111/10

PHYSICS

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B66B19/00

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

G06F30/17

PHYSICS

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G06F30/23

PHYSICS

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G06F2113/06

PHYSICS

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B66B7/10

PERFORMING OPERATIONS; TRANSPORTING

International classification

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B66B1/28

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

B66B19/00

PERFORMING OPERATIONS; TRANSPORTING

Classification Explorer

F15B15/00

MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING

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G05B13/04

PHYSICS

Classification Explorer

G06F30/23

PHYSICS

Abstract

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