Motivation Stochastic MPC based River Control River Simulations Conclusions A Control Engineering Perspective on Efficient Management of Rivers with Uncertain In-flows Hasan Arshad Nasir1 Collaborators: Prof. Erik Weyer2 Algo Car`e3 1School of Electrical Engineering and Computer Science, National University of Sciences and Technology 2Department of Electrical and Electronic Engineering, The University of Melbourne 3Department of Information Engineering, The University of Brescia October 13, 2018 Motivation Stochastic MPC based River Control River Simulations Conclusions 1 Motivation 2 Stochastic MPC based River Control 3 River Simulations 4 Conclusions Motivation Stochastic MPC based River Control River Simulations Conclusions Motivation - Efficient River Management To prevent water from getting wasted. To avoid flooding. To ensure satisfaction of environmental needs. Hume Dam, Australia www.wikipedia.org/wiki/Hume Dam Motivation Stochastic MPC based River Control River Simulations Conclusions Motivation - Talking about Pakistan Floods: 2010 (2; 000 died, 20 million affected) 2011 (361 died, 5:3 million affected) upload.wikimedia.org/wikipedia/commons/thumb/5/57/ Indus˙flooding_2010_en.svg/2000px-Indus˙flooding_2010_en.svg.png Motivation Stochastic MPC based River Control River Simulations Conclusions Motivation - Talking about Australia Australia is described as the driest continent on Earth. 1However, due to flooding, between 1852 and 2011, At least 951 people were killed, and 1326 were injured. The cost of damage reached an estimated $4:76 billion dollars. http://www.holidayaustralia.co.uk/html/google-map.html 1http://www.australiangeographic.com.au/topics/history-culture/2012/03/floods-10-of-the-deadliest-in-australian- history/ Motivation Stochastic MPC based River Control River Simulations Conclusions Upper part of Murray River, Australia Hume Reservoir Mulwala Canal Murray River Howlong Heywoods Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Motivation Stochastic MPC based River Control River Simulations Conclusions Upper part of Murray River, Australia Identify the output, control input and disturbance variables. Hume Reservoir Mulwala Canal Murray River Howlong Heywoods Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Variable to Control/Output Control Input Uncontrolled Input/Disturbance Water level: yLM Flows: uC = QH Flows: wU = [QB QP QDY W QYMC QMC ] Motivation Stochastic MPC based River Control River Simulations Conclusions Upper part of Murray River, Australia Control challenges. 1. Constraints Hume Reservoir Mulwala Canal Murray River Howlong Heywoods Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Variable to Control/Output Control Input Uncontrolled Input/Disturbance Water level: yLM Flows: uC = QH Flows: wU = [QB QP QDY W QYMC QMC ] Motivation Stochastic MPC based River Control River Simulations Conclusions Upper part of Murray River, Australia Control challenges. 1. Constraints 2. Time Delays Hume Reservoir Mulwala Canal Murray River Howlong Heywoods Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Variable to Control/Output Control Input Uncontrolled Input/Disturbance Water level: yLM Flows: uC = QH Flows: wU = [QB QP QDY W QYMC QMC ] Motivation Stochastic MPC based River Control River Simulations Conclusions Upper part of Murray River, Australia Control challenges. 1. Constraints 2. Time Delays Hume Reservoir Mulwala Canal Murray River Howlong Heywoods Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Variable to Control/Output Control Input Uncontrolled Input/Disturbance Water level: yLM Flows: uC = QH Flows: wU = [QB QP QDY W QYMC QMC ] 3. Unregulated In- and Out-flows Motivation Stochastic MPC based River Control River Simulations Conclusions A suitable control strategy for rivers with uncertain in-flows The one that can incorporate: Constraints on1. water Constraints levels and flow releases. Time delays. 2. Time Delays Forecast of unregulated in- and out-flows, andHume the Reservoir Mulwala Canal Murray River Howlong Heywoods uncertainties within.Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Variable to Control/Output Control Input Uncontrolled Input/Disturbance Water level: yLM Flows: uC = QH Flows: wU = [QB QP QDY W QYMC QMC ] 3. Unregulated In- and Out-flows Motivation Stochastic MPC based River Control River Simulations Conclusions A suitable control strategy for rivers with uncertain in-flows Stochastic1. Model Constraints Predictive2. Time Control Delays (Stochastic MPC)Hume Reservoir Mulwala Canal Murray River Howlong Heywoods Corowa Albury Lake Mulwala Yarrawonga Weir Doctors Point Hume Weir Bandiana Peechelba Downstream YW Weir Yarrawonga Main Channel Ovens River Kiewa River Measuring Station Hydraulic Structure Flow Direction Variable to Control/Output Control Input Uncontrolled Input/Disturbance Water level: yLM Flows: uC = QH Flows: wU = [QB QP QDY W QYMC QMC ] 3. Unregulated In- and Out-flows Motivation Stochastic MPC based River Control River Simulations Conclusions 1 Motivation 2 Stochastic MPC based River Control 3 River Simulations 4 Conclusions Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes k Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes u yˆj+1 = f(ˆyj,Qj τ ,Qj ), j = k, .., k + M − k k + M Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes u y^j+1 = f(^yj;Qj−τ ;Qj ), j = k; ::; k + M k+M 2 min. Pi=k (yi − ydes) s.t. yLL ≤ y ≤ yUL QLL ≤ Q ≤ QUL k k + M Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes k k + M Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes k + 1 Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes k + 1 k + M + 1 Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes u y^j+1 = f(^yj;Qj−τ ;Qj ), j = k + 1; ::; k + M + 1 k+M+1 2 min. Pi=k+1 (yi − ydes) s.t. yLL ≤ y ≤ yUL QLL ≤ Q ≤ QUL k + 1 k + M + 1 Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes k + 1 k + M + 1 Time Motivation Stochastic MPC based River Control River Simulations Conclusions Model Predictive Control (MPC) y Q ydes k + 2 Time Motivation Stochastic MPC based River Control River Simulations Conclusions River control problem in an MPC set-up The following optimisation problem is solved in a receding horizon fashion. k+M X 2 min. (yi ydes ) Qk ;Qk+1;:::;Qk+M−1 − i=k+1 u s.t. yi+1 = f (yi ; Qi τ ; Qi ) − u y yi (Q; Q ) y ; LL ≤ ≤ HL QLL Qi 1 QHL; ≤ − ≤ i = k + 1;:::; k + M: Motivation Stochastic MPC based River Control River Simulations Conclusions Water level constraints Water level should stay within two limits. y: water level Q: regulated inflows and outflows Qu: unregulated inflows and outflows yUL yset y yLL y y(Q, Qu) y LL ≤ ≤ UL Motivation Stochastic MPC based River Control River Simulations Conclusions Water level constraints Due to uncertainties in unregulated flows (Qu), we soften the constraint as below, y: Water level Q: regulated inflows and outflows Qu: unregulated inflows and outflows yUL yset y yLL P y y(Q, Qu) y 1 ǫ, { LL ≤ ≤ UL} ≥ − 2 e.g. ǫ = 10− . Motivation Stochastic MPC based River Control River Simulations Conclusions River control problem in a Stochastic MPC set-up k+M X 2 min. (yi ydes ) Qk ;Qk+1;:::;Qk+M−1 − i=k+1 u s.t. yi+1 = f (yi ; Qi τ ; Qi ) − u P y yi (Q; Q ) y 1 , f LL ≤ ≤ HLg ≥ − QLL Qi 1 QHL; ≤ − ≤ i = k + 1;:::; k + M: This is a Chance-Constrained optimisation Problem (CCP), and it is generally non-solvable. We employ the Scenario Approach to find an approximate solution to a CCP. Motivation Stochastic MPC based River Control River Simulations Conclusions River control problem in a Scenario-based Stochastic MPC set-up The following optimisation problem is solved in a receding horizon fashion. k+M X 2 min. (yi ydes ) Qk ;Qk+1;:::;Qk+M−1 − i=k+1 u s.t. yi+1 = f (yi ; Qi τ ; Qi ) − u;(j) y yi (Q; Q ) y ; LL ≤ ≤ HL QLL Qi 1 QHL; ≤ − ≤ i = k + 1; : : :; k + M; j = 1;:::; N: Motivation Stochastic MPC based River Control River Simulations Conclusions River control in the context of flooding Is the aforementioned formulation scale-able to accommodate flood mitigation? Motivation Stochastic MPC based River Control River Simulations Conclusions River control in the context of flooding Is the aforementioned formulation scale-able to accommodate flood mitigation? Yes! Motivation Stochastic MPC based River Control River Simulations Conclusions Water level constraints (revisiting) Water level should stay within two limits. y: water level Q: regulated inflows and outflows Qu: unregulated inflows and outflows yUL yset y yLL y y(Q, Qu) y LL ≤ ≤ UL Motivation Stochastic MPC based River Control River Simulations Conclusions Water level constraints (revisiting) Due to uncertainties in unregulated flows, we want water level to stay within two limits most of the time. y: Water level Q: regulated inflows and outflows Qu: unregulated inflows and outflows yUL yset y yLL P y y(Q, Qu) y 1 ǫ, { LL ≤ ≤ UL} ≥ − 2 e.g.