Tension control method of multi-bundle winding equipment combined driving system

Abstract

The present application relates to the technical field of fiber winding control, and provides a tension control method of a multi-bundle winding equipment combined driving system, which solves the problem that the tension fluctuates greatly and cannot be output constantly in the fiber winding process. The method includes: establishing a tension control system fractional order mathematical model; establishing a time-varying fractional order PID controller; inputting a target tension value and an unknown external interference to the tension control system fractional order mathematical model, and outputting a real-time tension value; and calculating a difference between the target tension value and the real-time tension value and then inputting the difference into the time-varying fractional order PID controller, inputting an output value of the time-varying fractional order PID controller and the unknown external interference into the tension control system fractional order mathematical model, and outputting a real-time tension value until the real-time tension value output by the tension control system fractional order mathematical model approaches the target tension value. The tension value output by the control system according to the present application can be well stabilized near the target tension value; and the system has high robustness when the tension changes suddenly.

Claims

1. A tension control method of a multi-bundle winding equipment combined driving system, comprising the following steps: S1: establishing a tension control system fractional order mathematical model according to an unwinding roll moment equation, a swing rod speed difference equation and a circuit equation, wherein a transfer function G(s) of the tension control system fractional order mathematical model is: $G\left(s\right)=G_a\left(s\right)G_b\left(s\right)=\frac{a}{{\mathrm{bs}}^a+1}.Math.\frac{c}{s^{?}}$ in the formula, G.sub.a(s) is a fractional order transfer function of an unwinding roll module of a tension control system, G.sub.h(s) is a fractional order transfer function of a swing rod module of the tension control system, $a=\frac{K_1}{\mathrm{BR}+K_e{K}_t},$ K.sub.t is a torque constant of a tension servo motor, B is a total friction coefficient converted to a motor shaft of the tension servo motor R is an equivalent resistance, K.sub.e is a back electromotive force coefficient, $b=\frac{\mathrm{JR}}{\mathrm{BR}+K_e{K}_t}$ J is a total rotational inertia, $c=\frac{1}{2L_B},$ L.sub.B is a half of a length of the swing rod, ? is an introduced differential operator and 0<?<2, and ? is an introduced integral operator and 0<?<2; S2: introducing a time-varying parameter into fractional order PD control, and establishing a time-varying fractional order PID controller, wherein a transfer function G.sub.k(s) of the time-varying fractional order PID controller is: $G_k\left(s\right)=K_p+\frac{K_i}{s^{?}}+K_d{s}^{?}$ in the formula, K.sub.p is a proportionality coefficient of the time-varying fractional order PID controller, K.sub.i is an integral coefficient of the time-varying fractional order PID controller, K.sub.d is a differential coefficient of the time-varying fractional order PID controller, ? is an integral operator of the time-varying fractional order PID controller and 0<?<2, and ? is a differential operator of the time-varying fractional order PID controller and 0<?<2, a setting rule of the proportionality coefficient K.sub.p, the integral coefficient K.sub.i and the differential coefficient K.sub.d of the time-varying fractional order PID controller is as follows:
K.sub.p=m.Math.f.sup.2(t), K.sub.i=n.Math.f.sup.3(t), K.sub.d=p.Math.f(t) in the formula, m, n and p are adjustable parameters and m, n, p?[0, 100], f(t) is an adjustment formula, and an expression of the adjustment formula f(t) is as follows:
f(t)=?.Math.(1?e.sup.?t) in the formula, ? is determined according to a time behavior of a controlled system and has a value range of (1<?<100), and e is a natural constant; S3: setting a target tension value r(t), inputting the target tension value r(t) and an unknown external interference ?d into the tension control system fractional order mathematical model, and outputting a real-time tension value y(t); S4: calculating a difference between the target tension value r(t) and the real-time tension value y(t) and then inputting the difference into the time-varying fractional order PID controller, and outputting u.sub.SC by the time-varying fractional order PID controller; S5: inputting an output value u.sub.SC of the controller and the unknown external interference ?d into the tension control system fractional order mathematical model, and outputting a real-time tension value y(t); and S6: repeating steps S4 and S5 until the real-time tension value y(t) output by the tension control system fractional order mathematical model approaches the target tension value r(t).

Description

(1) FIG. 1 is a main control function module diagram of a combined driving system according to the present application;

(2) FIG. 2 is an equipment schematic diagram of a combined driving system according to the present application;

(3) FIG. 3 is a control flowchart of a tension control system according to the present application;

(4) FIG. 4 is a control schematic diagram of a tension control system according to the present application;

(5) FIG. 5 is an output curve diagram of a tension control system according to the present application;

(6) FIG. 6 is a schematic diagram of a multi-bundle equipment combined driving control system according to the present application; and

(7) FIG. 7 is a program design flowchart of a whole control system according to the present application.

(8) In the drawings: 1. six-degree-of-freedom mechanical arm; 2. spiral winding device; 3. hoop winding device; 4. carrying cart; 5. movable sliding rail; 6. wound piece.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(9) The technical solutions in the embodiments of the present application are described clearly and completely with reference to the accompanying drawings in the embodiments of the present application. Apparently, the described embodiments are merely some rather than all of the embodiments of the present application. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present application without creative efforts should fall within the protection scope of the present application.

(10) It should be noted that the structure, scale, size and the like shown in the drawings of the specification are only used to cooperatively describe the content disclosed by the specification for those skilled in the art to understand and read, and are not intended to limit the implementation of the present application. Therefore, it has no technical substantive significance. Any structural modification, change of a scale relationship or adjustment of size should still fall within the scope which can be covered by the technical content disclosed by the present application without affecting the effects and the objective achieved by the present application. It should be noted that in this specification, relationship terms such as first and second are only used to distinguish one entity from several other entities, and do not necessarily require or imply the presence of any such actual relationship or sequence between these entities.

(11) The present application provides an embodiment: as shown in FIG. 1 and FIG. 2, a multi-bundle winding equipment combined driving system includes a six-degree-of-freedom mechanical arm 1, a spiral winding device 2, a hoop winding device 3, a controller, an upper computer, a wound piece 6, a tension control system, a carrying cart 4 and a movable sliding rail 5, where the six-degree-of-freedom mechanical arm 1 is configured to grab, clamp, feed and return the wound piece 6; the spiral winding device 2 is configured to spirally wind the wound piece 6; the hoop winding device 3 is configured to perform hoop winding on the wound piece 6; the controller is configured to receive a control instruction sent by the upper computer and transmit the control instruction to a corresponding performing mechanism; the upper computer is configured to set a parameter of the performing mechanism, set a target tension value and perform analogue simulation on a tension control system model; the carrying cart 4 is configured to transport the wound piece 6; the movable sliding rail 5 is configured to horizontally slide the spiral winding device 2 or the hoop winding device 3; upper computer software is Matlab, CADWIND, Abaqus and other simulation systems; the tension control system includes an unwinding roll module, a swing rod module, a tension detection roll, a tension servo motor, a tension sensor and a time-varying fractional order PID controller; the tension sensor is configured to perform real-time detection on the tension; and the unwinding roll module, the swing rod module and the time-varying fractional order PID controller are configured to compensate an output moment of the tension servo motor according to a deviation value of the tension to stably output the tension.

(12) As shown in FIG. 6 and FIG. 7, the control system software adopts modular program structure design, and the written program communicates with other modules through interfaces; and spiral and hoop winding parameters are designed according to the size of the wound piece 6, and the function of the program is realized through communication and mutual call between the modules.

(13) The combined driving control system has two control modes: a manual control mode and an automatic control mode. In the manual mode, each device system controls operation independently; and in the automatic working mode, each device system cooperates with each other to complete the transportation, spiral winding and hoop winding of the wound piece 6. In this process, the tension control system ensures that the tension of the winding yarn tends to be constant, and adjusts the yarn feeding and returning actions, thereby avoiding yarn twisting in the winding process and the yarn slippage and breakage caused by the fluctuation and sudden change of the tension. Meanwhile, the controller may control the movement of the corresponding servo motor to adjust the winding line type and angle.

(14) After the controller is powered on, the internal program is automatically executed, each degree-of-freedom rotating shaft of the multi-bundle winding equipment is initialized according to the set rotating shaft parameter of the upper computer, and communication connection with the upper computer is established after the program of the operation equipment is initialized. However, the system will display an error when connection is unsuccessful, and the manual or automatic control model may be selected for winding after communication connection is successful.

(15) In the automatic control mode, the winding motion is started, the system variable is initialized, and motion parameter information is recorded at the same time in the automatic winding process. Then, the upper computer checks whether the currently executed code file is consistent with the preset parameter of the winding software of the upper computer. If the currently executed code file is inconsistent with the preset parameter of the winding software of the upper computer, the upper computer is returned and an error is reported. If the currently executed code file is consistent with the preset parameter of the winding software of the upper computer, the code file is opened and read for cyclic determination of statements. When a terminator is read, the program is read, and the read code information is converted into a motion instruction. In combination with the input product size and position parameter, the motion instruction is transmitted to the six-degree-of-freedom mechanical arm 1, the spiral winding device 2, the hoop winding device 3, the carrying cart 4 and the movable sliding rail 5 to control the motion of the combined driving system to complete the winding action of the wound piece 6.

(16) Different winding tensions are applied to different winding sections according to the process requirements, and different spiral and hooping winding modes require different applied tensions. In this embodiment, the target tension value r(t) is related to the winding mode of the fiber and the position of a spinning nozzle on the surface of the wound piece 6. When the winding mode is the spiral winding, the target tension value r(t) corresponding to a seal head section of the wound piece 6 wound by the spinning nozzle is a first preset value, the target tension value r(t) corresponding to a cylinder body section of the wound piece 6 wound by the spinning nozzle is a second preset section, and the first preset value is greater than the second preset value. When the winding mode is the hoop winding, the target tension value r(t) corresponding to the cylinder body section of the wound piece 6 wound by the spinning nozzle is a third preset value.

(17) Specifically, according to the trajectory coordinates of the spinning nozzle on the surface of the wound piece 6, it is determined that the winding position is at the seal head section or the cylinder body section by determining the real-time trajectory point and in combination with the position coordinates of the wound piece 6, so that the corresponding target tension value is given. This kind of positioning method is the prior art, which is not elaborated herein.

(18) As shown in FIG. 3 and FIG. 4, the present application provides a tension control method of a multi-bundle winding equipment combined driving system, depending on the multi-bundle winding equipment combined driving system and including the following steps: S1: establish a tension control system fractional order mathematical model according to an unwinding roll moment equation, a swing rod speed difference equation and a circuit equation, S2: introduce a time-varying parameter into fractional order PID control, and establish a time-varying fractional order PID controller; S3: set a target tension value r(t), input the target tension value r(t) and an unknown external interference ?d into the tension control system fractional order mathematical model, and output a real-time tension value y(t); S4: calculate a difference between the target tension value r(t) and the real-time tension value y(t) and then input the difference into the time-varying fractional order PID controller, and output u.sub.SC by the time-varying fractional order PID controller; S5: input an output value u.sub.SC of the controller and the unknown external interference ?d into the tension control system fractional order mathematical model, and output a real-time tension value y(t); and S6: repeat steps S4 and S5 until the real-time tension value y(t) output by the tension control system fractional order mathematical model approaches the target tension value r(t).

(19) In step S1, the establish a tension control system fractional order mathematical model includes: the mechanical property of the unwinding roll and the swing in the fiber winding process is analyzed, where the tension model has non-linearity and multi-parameter time variation in the fiber winding process; and a transfer function of the tension control system fractional order mathematical model is obtained according to an unwinding dynamic roll moment equation, a tension servo motor circuit equation and the swing rod speed difference equation, where the unwinding roll dynamic moment balance equation is shown in a formula (1):

(20) $\begin{array}{cc}M\left(t\right)-T\left(t\right)R\left(t\right)=J\left(t\right)\frac{d^{?}?\left(t\right)}{d{t}^{?}}+B?\left(t\right)& \left(1\right)\end{array}$ the servo motor circuit equation is shown in a formula (2):

(21) $\begin{array}{cc}{u}_c\left(t\right)=R{i}_c+L\frac{d^{?}{i}_c\left(t\right)}{d{t}^{?}}+K_e.Math.?\left(t\right)& \left(2\right)\end{array}$ the swing rod speed difference equation is shown in a formula (3):

(22) $\begin{array}{cc}?=\frac{1}{2L_B}{D}^{-?}\left(v_2-v_1\right)=\frac{1}{2L_B}{?}_0^{t_0}{}^{\left(?\right)}\left(v_2-v_1\right)\mathrm{dt}& \left(3\right)\end{array}$

(23) In the formulas (1), (2) and (3), M(t) is an output moment of the tension servo motor and M(t)=K.sub.i.Math.i.sub.c(t); R(t) is a coil radius of the unwinding roll; ?(t) is a rotational angle speed of the tension servo motor; K.sub.t is a torque constant of the tension servo motor; e.sub.v is a back electromotive force of the tension servo motor; K.sub.e is a back electromotive force coefficient; B is a total friction coefficient converted to a motor shaft of the tension servo motor; J is a total rotational inertia; u.sub.c is an armature voltage; R is an equivalent resistance; i.sub.c is an armature current; L is an inductance coefficient; T(t) is a real-time tension; L.sub.B is a half of a length of the swing rod; ? is a swing angle of the swing rod; and ?.sub.1 is a fiber input speed of a yarn feeding end; ?.sub.2 is a fiber output speed of a yarn outlet end. To approximate the actual physical process, differential operators ? and ?, and an integral operator ? are introduced, and 0<?<2, 0<?<2, and 0<?<2, where ?, ? and ? may be valued according to the characteristic (non-linearity) of the actual physical system.

(24) The formula (1) and the formula (2) are combined for Laplace change to obtain a formula (4):

(25) $\begin{array}{cc}W\left(s\right)=\frac{K_t}{\left(J{s}^{?}+B\right)\left(L{s}^{?}+R\right)+K_e{K}_t}{U}_c\left(s\right)& \left(4\right)\end{array}$

(26) The formula (3) is subjected to Laplace change to obtain a formula (5):

(27) 0$\begin{array}{cc}?\left(s\right)=\frac{1}{2L_B}.Math.\frac{1}{s^{?}}v\left(s\right)& \left(5\right)\end{array}$

(28) In the formula, ?(s)=?.sub.2??.sub.1.

(29) In a case that dry friction and viscous friction are omitted, the unit of the inductance coefficient L is milliampere, the influence of the inductance coefficient (L?0) may be omitted, and fractional order transfer functions of the unwinding roll module and the swing rod module of the tension control system are obtained and shown in a formula (6) and a formula (7):

(30) $\begin{array}{cc}{G}_a\left(s\right)=\frac{W\left(s\right)}{U_c\left(s\right)}=\frac{K_t}{JR{s}^{?}+BR+K_e{K}_t}& \left(6\right)\end{array}$$\begin{array}{cc}{G}_b\left(s\right)=\frac{?\left(s\right)}{v\left(s\right)}=\frac{1}{2L_B}.Math.\frac{1}{s^{?}}& \left(7\right)\end{array}$

(31) The tension control system fractional order mathematical model includes the unwinding roll module and the swing rod module which are connected in series. A transfer function of the tension control system fractional order mathematical model is shown in a formula (8):

(32) $\begin{array}{cc}G\left(s\right)=G_a\left(s\right)G_b\left(s\right)=\frac{a}{b{s}^{?}+1}.Math.\frac{c}{s^{?}}& \left(8\right)\end{array}$ where

(33) $a=\frac{K_t}{BR+K_e{K}_t},b=\frac{JR}{BR+K_e{K}_t}\mathrm{and}c=\frac{1}{2L_B}.$

(34) The obtained transfer function of the tension control system fractional order mathematical model is simulated by a FOMCON toolbox in matlab or simulink to obtain a system tension output curve under the setting of constant tension input, as shown in FIG. 5.

(35) A nominal model of the system is obtained by a system identification method, the fractional order integral-differential operator is introduced into the tension control system mathematical model, and a tension control mathematical model with the non-linear characteristic is established, thereby fitting a tension output curve and representing the actual tension process more accurately.

(36) In step S2, by adoption of a method for introducing a time-varying parameter in the fractional order PID control, in the tension control system, a relationship among parameters ?, ?, Kp, Ki and Kd is established for the fractional order PID controller, and a time-varying fractional order PID controller is provided.

(37) Taking a tension roll sensor in a winding tension control system as a feedback object, the principle of adjusting the tension is as follows: a real-time tension value y(t) is compared with a target tension value r(t); and when a deviation value occurs, torque compensation is performed after time-varying fractional order PID control adjustment, and the tension is adjusted by the torque of the tension servo motor.

(38) A transfer function G.sub.k(s) of the time-varying fractional order PID controller is:

(39) $\begin{array}{cc}{G}_k\left(s\right)=K_p+\frac{K_i}{s^{?}}+K_d{s}^{?}& \left(9\right)\end{array}$

(40) In the formula, K.sub.p is a proportionality coefficient of the time-varying fractional order PID controller, K.sub.i is an integration coefficient of the time-varying fractional order PID controller, K.sub.d is a differential coefficient of the time-varying fractional order PID controller, ? is an integral operator of the time-varying fractional order PID controller and 0<?<2, ? is a differential operator of the time-varying fractional order PID controller and 0<?<2.

(41) The output of the time-varying fractional order PID controller is shown in a formula (10):

(42) $\begin{array}{cc}{u}_{SC}\left(t\right)=K_p{e}_1\left(t\right)+K_i\frac{d^{-?}{e}_1\left(t\right)}{d{t}^{-?}}+K_d\frac{d^{?}{e}_1\left(t\right)}{d{t}^{?}}& \left(10\right)\end{array}$

(43) The input of the time-varying fractional order PID controller is shown in formula (11):
e.sub.1(t)=r(t)?y(t)(11)

(44) A setting rule of three parameters such as the proportionality coefficient K.sub.p, the integral coefficient K.sub.i and the differential coefficient K.sub.d of the time-varying fractional order PID controller is shown in a formula (12):
K.sub.p=m.Math.f.sup.2(t), K.sub.i=n.Math.f.sup.3(t) and K.sub.d=p.Math.f(t)(12)

(45) An adjustment formula f(t) is shown in a formula (13):
f(t)=?.Math.(1?e.sup.t)(13)

(46) In the formulas (10), (11), (12) and (13), r(t) is a target tension value; y(t) is a real-time value; e.sub.1(t) is a real-time tension deviation value; u.sub.SC (t) is a controller output; m, n and p are adjustable parameters, and m, n, p?[0,100]; and ? is determined by a time behavior of a controlled system, and has a value range is (1<?<100).

(47) In steps S3, S4 and S5, the tension control principle is as follows: under the condition that the target tension value r(t) is given, the parameters m, n and p are selected by the time-varying fractional order PID controller, so that the real-time tension value y(t) output by the tension control system gradually approaches the target tension value r(t), that is,

(48) $\underset{l.fwdarw.?}{\lim }{e}_1\left(t\right)=r\left(t\right)-y\left(t\right)=0,$
the shorter the adjusting time t is, the higher the control dynamic response performance is, and the better the control effect is.

(49) The state space expression of the tension control system fractional order under a time domain is shown in a formula (14):

(50) $\begin{array}{cc}\{\begin{array}{c}\frac{d^{?}{y}_1\left(t\right)}{d{t}^{?}}=\frac{a}{b}{u}_{sc}\left(t\right)-\frac{1}{b}{y}_1\left(t\right)+?d\left(t\right)\\ \frac{d^{?}{y}_2\left(t\right)}{d{t}^{?}}=c{y}_1\left(t\right)\\ y\left(t\right)=y_2\left(t\right)\end{array}& \left(14\right)\end{array}$ where u.sub.SC(t) is a controller output; y(t) is a real-time tension value; ?d is an unknown external interference;

(51) $a=\frac{K_t}{BR+K_e{K}_t},b=\frac{JR}{BR+K_e{K}_t},\mathrm{and}c=\frac{1}{2L_B};$
y.sub.1(t) is an output of the unwinding roll module of the tension control system; and y.sub.2(t) is an output of the swing rod module of the tension control system, that is, a real-time tension value.

(52) The formula (10) and the formula (12) are combined to obtain a formula (15):

(53) $\begin{array}{cc}{u}_{SC}\left(t\right)=m.Math.f^2\left(t\right).Math.e_1\left(t\right)+n.Math.f^3\left(t\right).Math.\frac{d^{-?}{e}_1\left(t\right)}{d{t}^{-?}}+p.Math.f\left(t\right).Math.\frac{d^{?}{e}_1\left(t\right)}{d{t}^{?}}& \left(15\right)\end{array}$

(54) The formula (15) is put into the formula (14) to obtain:

(55) 0$\frac{d^{?+?}y\left(t\right)}{d{t}^{?+?}}=\frac{a.Math.c}{b}\left[m.Math.f^2\left(t\right).Math.e_1\left(t\right)+n.Math.f^3\left(t\right).Math.\frac{d^{-?}{e}_1\left(t\right)}{d{t}^{-?}}+p.Math.f\left(t\right).Math.\frac{d^{?}{e}_1\left(t\right)}{{\mathrm{dt}}^{?}}\right]-\frac{1}{b}\frac{d^{?}y\left(t\right)}{d{t}^{?}}+c.Math.?d\left(t\right)$ the time-varying fractional order PID controller is designed for the tension control of the fiber bundle, and f(t) is added to the parameter setting of the controller, so that the system has higher dynamic response performance and robustness, the tension output precision can be improved, and the tension output stability can be ensured.

(56) In FIG. 7, r(t) is a reference input (a target tension value), and y(t) is a system output (a real-time tension value), where the real-time tension deviation value is e.sub.1(t)=r(t)?y(t), the error integral is

(57) $e_0=\frac{d^{-?}{e}_1\left(t\right)}{d{t}^{-?}},$
and the error differential is

(58) $e_2=\frac{d^{?}{e}_1\left(t\right)}{d{t}^{?}},0<?<2\mathrm{and}0<?<2.$

(59) u.sub.SC(t) is a controller output. When there is an interference ?d in the system, as shown in dotted lines in FIG. 5, when the set target tension value is 20 N, a large vibration phenomenon occurs in the tension output of the original tension control system firstly, and after 20 s, the tension output is stabilized within a certain range, and vibration is performed according to a certain frequency. When the target tension value is suddenly changed from 20 N to 30 N, a large vibration phenomenon occurs in the original tension control system, it takes a long time for the system to recover to a stable state, and the system robustness and recovery capability are low.

(60) As shown in solid lines in FIG. 5, under the action of the time-varying fractional order PID controller, the performance of the tension control system is greatly improved, the vibration amplitude of the tension output value is obviously reduced, the system can recover to a stable state rapidly, the final tension value can be stabilized near the target tension value well, and when the tension is suddenly changed, the system has high robustness, so that the response time of tension recovery is shortened.

(61) The above is only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited to this. Any changes or substitutions that may be easily conceived by those skilled in the art within the technical scope disclosed by the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subjected to the protection scope of the claims.