Patent ID: 11970357
Assignee: TAIYUAN UNIVERSITY OF TECHNOLOGY
Field: Control (Instruments)
Classification: CPC B  G | IPC B  G

Claim 0:
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
   ⁡
   (
   s
   )
  
  =
  
   
    
     
      G
      a
     
     (
     s
     )
    
    ⁢
    
     
      G
      b
     
     (
     s
     )
    
   
   =
   
    
     a
     
      
       bs
       a
      
      +
      1
     
    
    ·
    
     c
     
      s
      σ
     
    
   
  
 

in the formula, Ga(s) is a fractional order transfer function of an unwinding roll module of a tension control system, Gh(s) is a fractional order transfer function of a swing rod module of the tension control system,, a
   =
   
    
     K
     1
    
    
     BR
     +
     
      
       K
       e
      
      ⁢
      
       K
       t
      
     
    
   
  
  ,, Kt 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, Ke is a back electromotive force coefficient,, b
  =
  
   JR
   
    BR
    +
    
     
      K
      e
     
     ⁢
     
      K
      t, J is a total rotational inertia,, c
   =
   
    1
    
     2
     ⁢
     
      L
      B
     
    
   
  
  ,, LB is a half of a length of the swing rod, α is an introduced differential operator and 0<α<2, and σ is an introduced integral operator and 0<σ<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 Gk(s) of the time-varying fractional order PID controller is:, G
    k
   
   (
   s
   )
  
  =
  
   
    K
    p
   
   +
   
    
     K
     i
    
    
     s
     λ
    
   
   +
   
    
     K
     d
    
    ⁢
    
     s
     μ
    
   
  
 

in the formula, Kp is a proportionality coefficient of the time-varying fractional order PID controller, Ki is an integral coefficient of the time-varying fractional order PID controller, Kd is a differential coefficient of the time-varying fractional order PID controller, λ is an integral operator of the time-varying fractional order PID controller and 0<λ<2, and μ is a differential operator of the time-varying fractional order PID controller and 0<μ<2,
a setting rule of the proportionality coefficient Kp, the integral coefficient Ki and the differential coefficient Kd of the time-varying fractional order PID controller is as follows:

Kp=m·f2(t), Ki=n·f3(t), Kd=p·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)=ζ·(1−e−t)

in the formula, ζ is determined according to a time behavior of a controlled system and has a value range of (1<ζ<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 Δd 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 uSC by the time-varying fractional order PID controller;
S5: inputting an output value uSC of the controller and the unknown external interference Δd 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).