Patent ID: 11874672
Assignee: HARBIN INSTITUTE OF TECHNOLOGY
Field: Control (Instruments)
Classification: CPC G  Y | IPC G

Claim 0:
1. A method for controlling a vehicle using an active disturbance rejection roll controller under disturbance of complex sea conditions, the method comprising:
step 1: acquiring a plurality of parameters of the vehicle, the plurality of parameters comprising a moment of inertia of the vehicle along an x axis, additional mass of the vehicle along the x axis, density of an environment where the vehicle is located, a velocity of the vehicle, a characteristic area of the vehicle, a characteristic length of the vehicle, a roll moment damping constant of the vehicle, an angular velocity in roll of the vehicle, a relative derivative of a roll control moment of the vehicle, an equivalent roll rudder deflection angle of the vehicle, and a disturbance moment caused by the complex sea conditions around the vehicle;
step 2: establishing a vehicle roll attitude control model based on the plurality of parameters;
step 3: designing an active disturbance rejection controller (LADRC) on the basis of the control model in step 2 and a pole placement method; and
step 4: controlling the vehicle by using the active disturbance rejection controller in step 3,
wherein
in step 2, according to a theorem of momentum and moment of momentum, an equation of the roll motion is obtained as follows:, {
     
      
       
        
         
          
           
            J
            x
           
           ⁢
           
            
             w
             .
            
            x
           
          
          +
          
           
            (
            
             
              J
              z
             
             -
             
              J
              y
             
            
            )
           
           ⁢
           
            w
            y
           
           ⁢
           
            w
            x
           
          
         
         =
         
          
           
            A
            
             m
             x
            
            β
           
           ⁢
           
            v
            2
           
           ⁢
           β
          
          -
          
           
            A
            
             m
             x
            
            δ
           
           ⁢
           
            v
            2
           
           ⁢
           
            δ
            d
           
          
          -
          
           
            A
            
             m
             x
            
            w
           
           ⁢
           
            v
            2
           
           ⁢
           
            w
            x
           
          
          +
          
           
            A
            
             m
             xp
            
           
           ⁢
           
            v
            2
           
          
          -
          
           
            λ
            
             4
             ⁢
             4
            
           
           ⁢
           
            
             w
             .
            
            x
           
          
          -
          

                                                                             
          
           
            B
            ⁡
            (
            
             
              
               z
               b
              
              ⁢
                
              cos
              ⁢
                
              φ
             
             +
             
              h
              ⁢
                
              sin
              ⁢
                
              φ
             
            
            )
           
           ⁢
             
           cos
           ⁢
             
           θ
          
          +
          
           M
           d
          
         
        
       
      
      
       
        
         φ
         =
         
          
           w
           x
          
          -
          
           
            (
            
             
              
               w
               y
              
              ⁢
                
              cos
              ⁢
                
              φ
             
             -
             
              
               w
               z
              
              ⁢
                
              sin
              ⁢
                
              φ
             
            
            )
           
           ⁢
             
           tan
           ⁢
             
           θ
          
         
        
       
      
      
       
        
         
          cos
          ⁢
            
          Θ
          ⁢
            
          sin
          ⁢
            
          Φ
         
         =
         
          
           cos
           ⁢
             
           β
           ⁢
             
           cos
           ⁢
             
           θ
           ⁢
             
           sin
           ⁢
             
           φ
          
          -
          
           sin
           ⁢
             
           α
           ⁢
             
           sin
           ⁢
             
           β
           ⁢
             
           cos
           ⁢
             
           θ
           ⁢
             
           cos
           ⁢
             
           φ
          
          +
          
           cos
           ⁢
             
           α
           ⁢
             
           sin
           ⁢
             
           β
           ⁢
             
           sin
           ⁢
             
           θ
          
         
        
       
      
     
    
   
   
    
     (
     1
     )
    
   
  
 

wherein, a simplifying assumption is made on the equation according to a typical trajectory, that is, the equation is simplified under three conditions of linearization, horizontal straight trajectory and axial symmetry of the vehicle, and the simplified equation of roll motion is as follows:, (
        
         
          J
          x
         
         +
         
          λ
          
           4
           ⁢
           4
          
         
        
        )
       
       ⁢
       
        
         d
         ⁢
         
          w
          x
         
        
        
         d
         ⁢
         t
        
       
      
      +
      
       
        1
        2
       
       ⁢
       ρ
       ⁢
       
        v
        2
       
       ⁢
       S
       ⁢
       L
       ⁢
       
        m
        x
        
         w
         ⁢
         x
        
       
       ⁢
       
        w
        
         x
         1
        
       
      
     
     =
     
      
       
        1
        2
       
       ⁢
       ρ
       ⁢
       
        v
        2
       
       ⁢
       S
       ⁢
       L
       ⁢
       
        m
        x
        
         δ
         d
        
       
       ⁢
       
        δ
        d
       
      
      +
      
       M
       d
      
     
    
   
   
    
     (
     2
     )
    
   
  
 

where Jx is the moment of inertia of the vehicle along the x axis, λ44 is the additional mass of the vehicle along the x axis, ρ is the density of the environment where the vehicle is located, v is the velocity of the vehicle, S is the characteristic area of the vehicle, L is the characteristic length of the vehicle, mxwx is the roll moment damping constant of the vehicle, wx is the angular velocity in roll of the vehicle, mxδd is the relative derivative of the roll control moment of the vehicle, δd is the equivalent roll rudder deflection angle of the vehicle, and Md is the disturbance moment caused by the complex sea conditions around the vehicle; and
a transfer function of a roll angle to a roll rudder deflection angle is as follows:, G
        φ
       
       (
       s
       )
      
      =
      
       
        
         
          1
          2
         
         ⁢
         ρ
         ⁢
         
          v
          2
         
         ⁢
         S
         ⁢
         L
         ⁢
         
          m
          x
          
           δ
           d
          
         
        
        
         
          
           (
           
            
             J
             x
            
            +
            
             λ
             
              4
              ⁢
              4
             
            
           
           )
          
          ⁢
          s
         
         -
         
          
           1
           2
          
          ⁢
          ρ
          ⁢
          
           v
           2
          
          ⁢
          S
          ⁢
          L
          ⁢
          
           m
           x
           
            w
            ⁢
            x
           
          
         
        
       
       ⁢
       
        1
        s
       
      
     
     ;
    
   
   
    
     (
     3
     )
    
   
  
 

in step 3, designing the active disturbance rejection controller comprises:
step 3.1: designing a linear extended state observer (LESO) without an object model;
step 3.2: designing a linear state error feedback (LSEF) controller;
step 3.3: performing a simulation analysis on the LESO in step 3.1 and the LSEF controller in step 3.2; and
step 3.4: verifying performance of the active disturbance rejection controller (LADRC);
in step 3.1, with making y→φ and w representing total disturbance, a vehicle roll control system is described as follows:

ÿ−a1{dot over (y)}−a0y+w+bu   (4)

wherein, y is a roll angle, {dot over (y)} is an angular velocity in roll, ÿ is an acceleration of the roll angle, u is an input of control quantity, b is a relative coefficient of control, a0 is a relative coefficient of the roll angle, and a1 is a relative coefficient of the angular velocity in roll;
the total disturbance is set as follows:

f(y, {dot over (y)}, w, t)=−a1{dot over (y)}−a0y+w+(b−b0)u   (5)

formula (4) is rewritten as follows:

ÿ=f+b0u   (6)

by setting state variables as follows: x1=y, x2={dot over (y)}, and x3=f, a continuous extended state observer is obtained as follows:

{dot over (x)}=Ax+Bu+E{dot over (f)}  (7), A
   =
   
    [
    
     
      
       0
      
      
       1
      
      
       0
      
     
     
      
       0
      
      
       0
      
      
       1
      
     
     
      
       0
      
      
       0
      
      
       0
      
     
    
    ]
   
  
  ,
  
   B
   =
   
    [
    
     
      
       0
      
     
     
      
       
        b
        0
       
      
     
     
      
       0
      
     
    
    ]
   
  
  ,
    
  
   
    
     and
     ⁢
        
     E
    
    =
    
     [
     
      
       
        0
       
      
      
       
        0
       
      
      
       
        1
       
      
     
     ]
    
   
   ;
  
 

wherein,
a corresponding LESO is:, {
     
      
       
        
         
          z
          .
         
         =
         
          Ax
          +
          
           B
           ⁢
           u
          
          +
          
           L
           ⁡
           (
           
            y
            -
            
             y
             ˆ
            
           
           )
          
         
        
       
      
      
       
        
         
          y
          ˆ
         
         =
         
          C
          ⁢
          z
         
        
       
      
     
    
   
   
    
     (
     8
     )
    
   
  
 

wherein, C=[1 0 0], and L=[L1L2 L3]T is an error feedback control gain matrix of the observer;
a characteristic equation of the formula (8) is:

λ(s)=|sI−(A−LC)|  (9)

after parameterization, a pole of the characteristic equation is designed as follows:

λ(s)=(s+w0)(s+k0w0)(s+k2w0)   (10)

where wo is a pole of a designed extended state observer, and k1 and k2 are pole placement coefficients of the extended state observer; and
a gain matrix of the extended state observer is obtained as follows:, L
      =
      
       [
       
        
         
          
           
            (
            
             
              k
              1
             
             +
             
              k
              2
             
             +
             1
            
            )
           
           ⁢
           
            w
            0
           
          
         
        
        
         
          
           
            (
            
             
              k
              1
             
             +
             
              k
              2
             
             +
             
              
               k
               1
              
              ⁢
              
               k
               2
              
             
            
            )
           
           ⁢
           
            w
            0
            2
           
          
         
        
        
         
          
           
            (
            
             
              k
              1
             
             ⁢
             
              k
              2
             
            
            )
           
           ⁢
           
            w
            0
            3
           
          
         
        
       
       ]
      
     
     ;
    
   
   
    
     (
     11
     )
    
   
  
 

in step 3.2, the LSEF adopts a controller of a linear proportional and derivative (PD) combination, z1→y, z2→{dot over (y)}; and
a control law is:

u0=kp(zc−z1)−kdz2   (12)

where, u0 is a final control output, zc is an expected roll angle, z1 is a roll angle of the vehicle in a current state, and z2 is an angular velocity in roll of the vehicle in the current state;
a closed-loop transfer function is:, G
      ⁡
      (
      s
      )
     
     =
     
      
       k
       p
      
      
       
        s
        2
       
       +
       
        
         k
         d
        
        ⁢
        s
       
       +
       
        k
        p
       
      
     
    
   
   
    
     (
     13
     )
    
   
  
 

where kp and kd are controller parameters needing to be designed, and, by selecting the pole of the transfer function of the controller and placing the pole at different positions wc and k3wc, wc>1, k3>1, the controller parameters are obtained as follows:

kp=k3wc2 

kd=(k3+1)wc   (14)

after parametric design, six parameters to be adjusted in the LADRC are w0, wc, b0, k1, k2, k3wherein w0 is the pole of the extended state observer, wc is a pole of the controller, b0 is a control coefficient, k1 and k2 are the pole placement coefficients of the extended state observer, and k3 is a pole placement coefficient of the controller.