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Control of Irrigation Channels

VIEWS: 57 PAGES: 36

Water is becoming scarce, and it is therefore important to manage the water resources well This is particularly important in networks of irrigation channels where water is transported under the power of gravity alone The two most common control strategies are decentralized PI control and centralized LQ or predictive control

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									Control of Irrigation Channels




                                 1
             OVERVIEW
   Introduction
   Part of Haughton Main Channel
   Control Objectives
   Models for HMC
   Decentralized PI Control
   Centralized LQ Control
   Field Test Results
   Conclusion                      2
             INTRODUCTION
   Water is becoming scarce, and it is therefore
    important to manage the water resources well
   This is particularly important in networks of irrigation
    channels where water is transported under the power
    of gravity alone
   The two most common control strategies are
    decentralized PI control and centralized LQ or
    predictive control




                                                           3
SIDE VIEW OF A PART OF HAUGHTON
         MAIN CHANNEL




                                  4
TOPVIEW OF IRRIGATION CHANNEL
WITH FARMS AND SECONDARY
CHANNELS




                                5
    CONTROL OBJECTIVES
  Setpoint Regulation of Water Levels
  (control water levels y9, y10 and y11)
 Rejection of Load Disturbances

  (disturbances due to off takes in Pool 8, 9, and 10.)
 Setpoint Regulation of the Flow Over the Last Gate

   (control the head h11)
 Limit the Gate Movements

 (keep the movements of Gate 8, 9, 10, and 11 small )



                                                          6
MODELS FOR CONTROL OF THE
HMC

   Continuous Time Models
   Discrete Time Models
   State Space Model




                             7
CONTINUOUS TIME MODELS
Basic volume balance of a pool gives
    dV ( t )
             Qin ( t )  Qout ( t )                    ……………….. (1)
      dt
    where      Q( t )  ch 3 2 ( t )

 For pool 8

y 9 ( t )  cin h8         ( t   )  cout h9         ( t )  v9 ( t ) ......(2)
                     3 2                         3 2



Approximately
     
    y 9 ( t )  cin h8 ( t   )  cout h9 ( t )  v9 ( t ) …………….. (3)             8
POOL LENGTHS, DOMINANT WAVE
FREQUENCY, AND MODEL
PARAMETERS
POOL   LENGTH      WAVE       Cin     Cout      τ
         (m)    FREQUENCY(                    (min)
                  rad/min)

 8      1600       0.42      0.014   -0.017    6


 9      900        0.72      0.046   -0.042    3

 10     3200       0.20      0.009   -0.010    16
                  TABLE 1


                                                    9
         DISCRETE TIME MODELS
        For pool 8
    
    y 9 ( t  1 )  y9 ( t )  c8 ,1 h8         ( t  k 8 )  c8 ,1 h9         ( t )  v9 ( t )
                                          3 2                            3 2
                                                                                                  (4)


        For pool 9

y 10 ( t  1 )  y10 ( t )  c9 ,1 h9         ( t  k 9 )  c9 ,1 h10          ( t )  v10 ( t ) (5)
                                        3 2                              3 2




                                                                                                        10
MODEL PARAMETERS FOR
DISCRETE TIME MODELS
POOL   C   i,1    C   i,2    C   i,3   C   i,4   Ki(samples)



 8     0.042     -0.055                              4



 9     0.148     -0.134                              3



 10    0.254     -0.153     -0.238     0.133         8



                 TABLE 2                                   11
STATE SPACE MODELS
   Introduce the state variables
    xi ,0 ( t )  y i ( t )  y i ,setp ( t ) i = 8,9, 10
    x j ,i ( t )  h3 2 i ( t  i )  u j ( t  i )     ……..(6)
    Introduce the input variables
      u11 ( t )  h 3       2
                                11   ( t )  h3   2
                                                      11,setp   (t )
     u8 ( t )  h 3     2
                            8   ( t ), u 9 ( t )  h 3           2
                                                                     9   (t )
      u10 ( t )  h 3   2
                            10   (t )                                           ..……(7)


                                                                                          12
STATE SPACE
MODELS(Continued)
For pool 8 , equation (4) can be written as
x8 ,1 ( t  1 )  u8 ( t )
x8 ,i 1 ( t  1 )  x8 ,i ( t )
x9,0 ( t  1 )  x9,0 ( t )  c8,1 x8,4 ( t )  c8,2u9 ( t )  v9,0 ( t )  vsc ,9 ( t )
                                       ……………….(8)
So model of each pool can be written as
  x( t  1 )  A x( t )  B u ( t )  v( t ) …………..(9)



                                                                                       13
DECENTRALIZED CONTROL

   The water levels are controlled using overshot gates
    located along the channel, and the output of the
    controllers is the head over gate.

   Pure Decentralized control
     The flow over gate i is controlled on the basis of the
    water level yi+1, measured at gate i+1, relative to the
    set point for pool i+1.
      
      y 9 ( t )  cin h8 ( t   )  v9 ( t ) ……………….(10)
                                     

     v9 ( t )  cout h9 ( t )  v9 ( t ) …………………….(a)
     

                                                              14
DECENTRALIZED CONTROL
(Continued)
   For Pool 8
    h8 ( s )  C ( s )( y9, setp ( s )  y9 ( s )) …………………..(11)


   Gate position is given by
    p8 (t )  y8 (t )  h8 (t ) ………………………………..(11.a)

   PI controller with a first order filter is given by
     K (1  Ti s) ………………..……………………….. (12)
    Ti s(1  T f s)

                                                                   15
DECENTRALIZED CONTROL
(Continued)
    Decentralized control with feed forward
   The flow over gate i is controlled on the basis of the
    measured water level yi+1 , relative to the set point for
    pool i+1, in addition to information about the flow over
    gate i+1
   A controller structure which utilizes this information is
    given by                               
      h8 ( s )  C( s )( y 9 ,setp ( s )  y 9 ( s ))  F ( s )h9 ( s ) (13)
                               cin
       F ( s )  K ff FB ( s )
                               c out …………………………. (14)
                                                                         16
TUNING OF PI CONTROLLERS
              Feed forward compensator
   Cutoff frequency -1/2(wave frequency in the
    pool)
   Kff =0.75
                Feedback compensator
   Tuned using standard frequency response
    methods
   Phase margin- between 300 and 500
   Gain between -8dB and-12 dB
                                                  17
CENTRALIZED CONTROLLERS
   Implemented at a central computer and
    required communication between all
    gates and the computer.

   Linear Quadratic Controller is used



                                          18
DESIGN OF LQ CONTROLLER
    To reject the load disturbances introduce integral of
     set point errors
                                     y9 ( t )  y9 ,setp ( t ) 
                                     y (t ) y             (t ) 
    xint ( t  1 )  xint ( t )  T                             
                                         10        10 ,setp
                                                                   (15)
                                     y11 ( t )  y11,setp ( t ) 
                                     3 2                        
                                      h11 ( t )  h11,setp ( t )
                                                           3 2
                                    
                                                                

    Where T=2 min is sampling interval



                                                                          19
DESIGN OF LQ
CONTROLLER(Continued)
   In order to avoid exciting wave dynamics
    filter is introduced
      x f ,i ( t  1 )  A f ,i x f ,i ( t )  B f ,i u i ( t )

       y f ,i ( t )  C f ,i x f ,i ( t )  D f ,i u i ( t )      (16)

   So model of each pool can be written as
       x( t  1 )  A x( t )  B u ( t )  v( t ) (17)


                                                                         20
DESIGN OF LQ
CONTROLLER(Continued)
   Criteria Function
   The criterion to be minimized is
           
     J   x T ( t )Qx ( t )  u T ( t )Ru( t )  2 x T Nu( t )   (18)
          t 0




    R is a positive definite matrix and
Q      N
N T    R
               is a positive semi definite matrix.
                                                                         21
  LQ Controller Equations
  The LQ controller is given by (ignoring the disturbances
    v(t) for the moment)
             u( t )   Kx( t )             (19)
  The gain matrix K is given by
     K  ( B T SB  R ) 1 ( B T SA  N T ) (20)

  where S is the positive definite solution to the steady
     state Riccati equation
S  AT SA  ( AT SB  N )( B T SB  R )1  ( B T SA  N T )  Q
                                                          (21)

                                                                   22
LQ Controller
Equations(Continued)
   Feed forward From Setpoint Changes
    and Off takes
   The controller is given by
    u( t )   Kx( t )  K v d ( t )                     (22)
    K  ( B T SB  R ) 1 B T                              (23)
    d ( t )  ( A  BK )T d ( t  1 )  ( A  BK )T Sv( t ) (24)




                                                                   23
FIELD TEST (PI CONTROLLERS)-
EXPERIMENTAL PARAMETERS
  Time    Head over Gate 11   Setpoint in pool 9
  (min)         (m)               (mAHD)
   0            0.12                23.80

   270          0.30                23.80
   520          0.30                23.75

   600          0.12                23.75



             TABLE 3
                                              24
FIELD TEST (PI CONTROLLERS)-
RESULTS




                               25
FIELD TEST (PI CONTROLLERS)-
RESULTS (Continued)




                     After time 0, h11
                        is reduced
                        from 0.30 m
                        to 0.12 m




                                    26
FIELD TEST (PI CONTROLLERS)-
RESULTS (Continued)




                               27
FIELD TEST (PI CONTROLLERS)-
RESULTS (Continued)




                               28
FIELD TEST (PI CONTROLLERS)-
RESULTS (Continued)




                               29
FIELD TEST (LQ CONTROLLERS)-
RESULTS


                    Setpoints
                     (mAHD)
                    Pool 8: 26.45
                    Pool 9: 23.75
                    Pool 10: 21.15



                                      30
FIELD TEST (LQ CONTROLLERS)-
RESULTS (Continued)




                           31
 PI VERSUS LQ
                  PI                 LQ
Performance       Not so good as     Better.
                  LQ.                Disturbances
                                     are quickly
                                     attenuated
Robustness to     sensor failure     failure can have
Sensor and        are localized to   widespread
Actuator Faults   the pool           effects
Tuning            Easy, straight     difficult
                  forward
Implementation    Less effort.       More effort
                                                        32
PI VERSUS LQ (Continued)




                           33
CONCLUSION
   Control of irrigation channels using decentralized PI
    controller and centralized LQ controller are discussed
   The designed controllers showed very good
    performance in field tests
   LQ controller gave better performance than the PI
    controllers, but it also required more design effort
   for longer channels distributed or multivariable
    designs based on H∞ loopshaping techniques may
    provide attractive alternatives



                                                        34
            REFERENCES
[1] E.Weyer, “Control of irrigation channels,” IEEE Transactions on Control Systems
    Technology, Volume 16, No.4 July 2008

[2] M. Cantoni, et al, “Control of large-scale irrigation networks,” Proceedings. IEEE,
   Special Issue on the Emerging Technology of Networked Control Systems, Volume.
   95, No.1, 2007.

[3] E.Weyer, “Multivariable control of an irrigation channel: Experimental results and
    robustness analysis,” in Proceedings. 45th IEEE Conference. Decision and Control
    (CDC’06), San Diego, CA, December. 2006.

[4] E. Weyer, “LQ control of an irrigation channel,” in Proceedings. 42nd
   IEEEConference. Decision and Control (CDC’03), Maui, HI, December. 2003

 [5] X. Litrico, “Robust IMC flow control of SIMO dam-river open-channel systems,”
   IEEE Transactions on Control Systems Technology, Volume 10,No. 3, May 2002. 5   3
Thank You


            36

								
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