Patent ID: 11886200
Assignee: TOPCON POSITIONING SYSTEMS, INC.
Field: Control (Instruments)
Classification: CPC G | IPC G

Claim 6:
7. The system of claim 6, wherein the function V(z) is defined by, V
    ⁡
    (
    z
    )
   
   =
   
    
     
      z
      T
     
     ⁢
     Pz
    
    +
    
     θ
     ⁢
     
      
       ∫
       0
       
        
         c
         T
        
        ⁢
        z
       
      
      
       
        Φ
        ⁡
        (
        
         
          z
          2
         
         ,
         σ
        
        )
       
       ⁢
       d
       ⁢
       σ
      
     
    
   
  
  ,
 

where P is a 2 by 2 matrix
zT is (z1, z2)T, T stands for transposition,
θ is a scalar coefficient,
Φ is a control function defined by:, Φ
    ⁡
    (
    
     
      z
      2
     
     ,
     σ
    
    )
   
   =
   
    
     
      s
      
       u
       _
      
     
     (
     
      σ
      
       
        (
        
         1
         +
         
          z
          2
          2
         
        
        )
       
       
        3
        2
       
      
     
     )
    
    ⁢
    
     
      (
      
       1
       +
       
        z
        2
        2
       
      
      )
     
     
      3
      2
     
    
   
  
  ,
 

 
  
   
    s
    
     u
     _
    
   
   (
   u
   )
  
  =
  
   {
   
    
     
      
       
        
         
          -
          
           u
           _
          
         
         ⁢
            
         for
         ⁢
            
         u
        
        ≤
        
         -
         
          u
          _
         
        
       
       ,
      
     
    
    
     
      
       
        
         u
         ⁢
            
         for
         ⁢
            
         
          
           ❘
           "\[LeftBracketingBar]"
          
          u
          
           ❘
           "\[RightBracketingBar]"
          
         
        
        <
        u
       
       ,
      
     
    
    
     
      
       
        
         
          u
          _
         
         ⁢
            
         for
         ⁢
            
         u
        
        ≥
        
         u
         _
        
       
       ,
      
     
    
   
  
 

 
  
   σ
   =
   
    
     
      λ
      2
     
     ⁢
     
      z
      1
     
    
    +
    
     2
     ⁢
     λ
     ⁢
     
      z
      2
     
    
   
  
  ,
 

λ is a desired rate of exponential decrease of lateral displacement.