Patent ID: 11971690
Assignee: UNIVERSITY OF NEW BRUNSWICK
Field: Control (Instruments)
Classification: CPC G  B | IPC G

Claim 1:
2. The computer-implemented method of claim 1, wherein the step of computing the control parameters further comprises computing the variables:
Variables:, ⁢
    
      s
      ⁢
      
        
      
      ⁢
      LaPlace
      ⁢
      
        
      
      ⁢
      frequency
      ⁢
      
        
      
      ⁢
      variable
    
  

  
    
      
    
    ⁢
    
      Δ
      ⁢
      
        
      
      ⁢
      t
      ⁢
      
        
      
      ⁢
      Controller
      ⁢
      
        
      
      ⁢
      sample
      ⁢
      
        
      
      ⁢
      time
    
  

  
    
      
    
    ⁢
    
      
        d
        1
      
      =
      
        
          
            d
            ^
          
          1
        
        ⁡
        
          (
          1
          )
        
      
    
  

  
    
      
    
    ⁢
    
      
        d
        
          2
          ⁢
          i
        
      
      =
      
        
          
            d
            ^
          
          
            2
            ⁢
            i
          
        
        ⁡
        
          (
          1
          )
        
      
    
  

  
    
      
    
    ⁢
    
      
        d
        3
      
      =
      
        
          ∑
          
            i
            =
            1
          
          
            n
            a
          
        
        ⁢
        
          
            k
            i
          
          ⁢
          
            d
            
              2
              ⁢
              i
            
          
        
      
    
  

  
    
      
    
    ⁢
    
      
        
          d
          ^
        
        1
      
      =
      
        
          M
          
            -
            1
          
        
        ⁢
        
          
            A
            T
          
          ⁡
          
            [
            
              
                
                  1
                
              
              
                
                  1
                
              
              
                
                  ⋮
                
              
              
                
                  1
                
              
            
            ]
          
        
      
    
  

  
    
      
    
    ⁢
    
      
        
          d
          ^
        
        
          2
          ⁢
          i
        
      
      =
      
        
          M
          
            -
            1
          
        
        ⁢
        
          
            A
            T
          
          ⁡
          
            [
            
              
                
                  
                    (
                    
                      1
                      -
                      
                        α
                        i
                      
                    
                    )
                  
                
              
              
                
                  
                    (
                    
                      1
                      -
                      
                        α
                        i
                        2
                      
                    
                    )
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    (
                    
                      1
                      -
                      
                        α
                        i
                        N
                      
                    
                    )
                  
                
              
            
            ]
          
        
      
    
  

  
    
      
    
    ⁢
    
      A
      =
      
        [
        
          
            
              
                
                  c
                  ^
                
                1
              
            
            
              0
            
            
              …
            
            
              0
            
          
          
            
              
                
                  c
                  ^
                
                2
              
            
            
              
                
                  c
                  ^
                
                1
              
            
            
              …
            
            
              0
            
          
          
            
              ⋮
            
            
              ⋮
            
            
              ⋱
            
            
              ⋮
            
          
          
            
              
                
                  c
                  ^
                
                N
              
            
            
              
                
                  c
                  ^
                
                
                  N
                  -
                  1
                
              
            
            
              …
            
            
              
                
                  c
                  ^
                
                
                  N
                  -
                  
                    n
                    a
                  
                  +
                  1
                
              
            
          
        
        ]
      
    
  

  
    M
    =
    
      

    
    ⁢
    
      [
      
        
          
            
              λ
              ⁢
              
                
                  ∑
                  
                    j
                    =
                    1
                  
                  N
                
                ⁢
                
                  
                    (
                    
                      
                        c
                        ^
                      
                      j
                    
                    )
                  
                  2
                
              
            
          
          
            
              
                ∑
                
                  j
                  =
                  1
                
                
                  N
                  -
                  1
                
              
              ⁢
              
                
                  (
                  
                    
                      c
                      ^
                    
                    j
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      c
                      ^
                    
                    
                      j
                      +
                      1
                    
                  
                  )
                
              
            
          
          
            …
          
          
            
              
                ∑
                
                  j
                  =
                  1
                
                
                  N
                  -
                  
                    n
                    u
                  
                  +
                  1
                
              
              ⁢
              
                
                  (
                  
                    
                      c
                      ^
                    
                    j
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      c
                      ^
                    
                    
                      j
                      +
                      
                        n
                        u
                      
                      -
                      1
                    
                  
                  )
                
              
            
          
        
        
          
            
              
                ∑
                
                  j
                  =
                  1
                
                
                  N
                  -
                  1
                
              
              ⁢
              
                
                  (
                  
                    
                      c
                      ^
                    
                    j
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      c
                      ^
                    
                    
                      j
                      +
                      1
                    
                  
                  )
                
              
            
          
          
            
              λ
              ⁢
              
                
                  ∑
                  
                    j
                    =
                    1
                  
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                    (
                    
                      
                        c
                        ^
                      
                      j
                    
                    )
                  
                  2
                
              
            
          
          
            …
          
          
            
              
                ∑
                
                  j
                  =
                  1
                
                
                  N
                  -
                  
                    n
                    u
                  
                  +
                  1
                
              
              ⁢
              
                
                  (
                  
                    
                      c
                      ^
                    
                    jj
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      c
                      ^
                    
                    
                      j
                      +
                      
                        n
                        u
                      
                      -
                      2
                    
                  
                  )
                
              
            
          
        
        
          
            ⋮
          
          
            ⋮
          
          
            ⋱
          
          
            ⋮
          
        
        
          
            
              
                ∑
                
                  j
                  =
                  1
                
                
                  N
                  -
                  
                    n
                    u
                  
                  +
                  1
                
              
              ⁢
              
                
                  (
                  
                    
                      c
                      ^
                    
                    j
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      c
                      ^
                    
                    
                      j
                      +
                      
                        n
                        u
                      
                      -
                      1
                    
                  
                  )
                
              
            
          
          
            
              
                ∑
                
                  j
                  =
                  1
                
                
                  N
                  -
                  
                    n
                    u
                  
                  +
                  1
                
              
              ⁢
              
                
                  (
                  
                    
                      c
                      ^
                    
                    j
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      c
                      ^
                    
                    
                      j
                      +
                      
                        n
                        u
                      
                      -
                      2
                    
                  
                  )
                
              
            
          
          
            …
          
          
            
              λ
              ⁢
              
                
                  ∑
                  
                    j
                    =
                    1
                  
                  
                    N
                    -
                    
                      n
                      u
                    
                    +
                    1
                  
                
                ⁢
                
                  
                    (
                    
                      
                        c
                        ^
                      
                      j
                    
                    )
                  
                  2
                
              
            
          
        
      
      ]
    
  

  
    
      
    
    ⁢
    
      
        
          c
          ^
        
        j
      
      =
      
        
          ∑
          
            i
            =
            1
          
          
            n
            a
          
        
        ⁢
        
          
            k
            i
          
          ⁡
          
            (
            
              1
              -
              
                α
                i
                j
              
            
            )
          
        
      
    
  

  
    
      
    
    ⁢
    
      
        α
        i
      
      ⁢
      
        
      
      ⁢
      Constant
      ⁢
      
        
      
      ⁢
      
        (
        
          e
          
            
              
                -
                Δ
              
              ⁢
              
                
              
              ⁢
              t
            
            
              τ
              i
            
          
        
        )
      
    
  

Tunning Parameters:
N Prediction horizon length
nu Control horizon length
λ Move suppression factor

where the model of the dynamic system is defined by the equation:, Y
      ⁡
      
        (
        s
        )
      
    
    
      U
      ⁡
      
        (
        s
        )
      
    
  
  =
  
    
      ∑
      
        i
        =
        1
      
      
        n
        a
      
    
    ⁢
    
      
        k
        i
      
      
        
          
            τ
            i
          
          ⁢
          s
        
        +
        1
      
    
  

System Constants:
na Order of the system
τi ith order time constant
ki ith order gain

and where:
Y(s) is a control output,
U(s) is an input.