VIEWS: 57 PAGES: 36 CATEGORY: Engineering POSTED ON: 7/7/2010
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
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