Outline • Motivation • Water networks : A CPS / IoT perspective • Open channel hydraulics: physical models • System identification : theory to experiments • Sensing: building telemetry networks • Control: putting it all together • Conclusions and outlook
Model Learning for Control Data Driven Models Physical Models dy ( ) t 3 3 i 1 c h 2 ( t ) c h 2 ( ). t i in , i i 1, out i 1 dt Abstraction
(Lumped) Volume Balance Model dV Q t Q t ( ) ( ). 3 Q c h 2 , in out dt in in 3 Q c h 2 . out out dy ( ) t 3 3 i 1 c h 2 ( t ) c h 2 ( ). t i in , i i 1, out i 1 dt
Plant Model • Declare ℎ 3/2 𝑢 = 𝑣 𝑢 . • W.r.t. inflow, a linear transfer function emerges:
System Identification Idea prototyped in a LUMS MS Thesis 2011.
System Identification contd. 3 3 2 2 y ( t ) c h ( t ) c h ( t ). i i 1 i , in i 1 , out i 1
Date extracted Pool 1 2 3 Time delay 2 3 1 (min) Wave Period 8 13 7 (min) Ci,in 0.1090 0.1010 0.2340 Ci+1,out 0.1460 0.0910 0.2010
System ID: Experiments System Identification Location: – KHAIRA Distributory – Length 87000 feet – Width 10 feet – Max height 4 feet – 3 Minors – Discharge 87 cusecs Tested in a LUMS FYP 2013 !
System ID: Experiments System Identification Procedure: – Water level sensors are placed at appropriate sites along the canal and communicate through mobile or other networks. – At the Upstream, Gate is closed and then subsequently opened to generate a step input. – The readings are recorded and then used as empirical output, in conjunction with the input, to perform System Identification.
System ID: Gate Modeling System Identification Wat ater Flo low: Ov Overshot Gat ate Wat ater Flo low: Und Undershot Gat ate
System ID: Parametric Equation for the given channel System Identification • The parameters in 𝜄 matrix are estimated by the minimization of a least-squares criterion.
System ID: Experiment
System ID: Least Squares Estimation System Identification • Experimental Setup – Upstream Gate was closed and then opened – The water level was measured at 50m, 350m and 550m, every 10s. – The corresponding data was processed and interpolated to obtain a uniformly sampled and synchronized set. • Estimation – A model was fit to the observed response at 350m and 550m sensors by linear regression. – As mentioned earlier, y u was assumed to be constant and p 2 [k] was taken to be zero to model an „ always opened – hypothetical – downstream gate’ . – In addition, y d [k] was taken to be the values of 50m sensor. – The response delay were inspected from the raw data, which came out be approximately 200s and 350s for the 50m, 350m and 550m sensors respectively. – Using the above conditions, the response for the sensors at 350m and 550m was estimated
System ID: Least Squares Estimation
System ID: Least Squares Estimation
System ID: Least Squares Estimation System Identification • Results – For 350m the estimated parameters were: • θ = [0.0160 -0.3271]x10 -3 – For 550m the estimated parameters were: • θ = [0.0152 -0.2737]x10 -3 • The estimated parameter values make sense from a physical point of view. – θ 1 is positive. It is associated with the inflow of water – θ 2 is negative. It is associated with the outflow of water – θ 2 has a greater magnitude than θ 1 because there exists no hydraulic structure at the downstream sensor position, and there is always an outflow at the hypothetical downstream end.
System ID: Model Validation System Identification • Simulation of Model • Average Squared Prediction Error • Comparison of predicted water level with the measured one
System ID: Model Validation
Outline • Motivation • Water networks : A CPS / IoT perspective • Open channel hydraulics: physical models • System identification : theory to experiments • Sensing: building telemetry networks • Control: putting it all together • Conclusions and outlook
Hydrometry for Open Channel Flows Objective: Measure flows in distributary canal networks
Hydrometry for Open Channel Flows • Outdated infrastructure • Gaps in monitoring expertise • Objective: To develop a low-cost low-power robust flow gauge
Challenges • Power / energy autarky • Communication mode • Physical security • Cost / scalability • Calibration / maintenance • Data dissemination / services Solution: A smart metering like approach
Smart Water Grid : LUMS-IWMI collaboration Goal: To install a network of 20+ sensors at a real site (distributary network on Hakra Branch, Bahawalnagar)
Smart Water Grid in Bahawalnagar Ref. Ahmad, Muhammad. IECON 2013
Hakra Branch Distributaries
Packaging / Assembly Circuitry Enclosure Material die cast Aluminum IP 67 Enclosures Connectors for external antenna and temperature sensors are also IP67 standard Prototyped in a LUMS FYP 2012 !
Stilling well / Civil Infrastructure 60cm x 90cm To secure electronics High strength PCC concrete No steel reinforcement for good GSM reception
Ultrasonic Sensor • Maxbotix MB7380 Ultra Sonic Sensor • 1mm resolution, 1% accuracy
Block diagram of Smart Water Meter
Unit Performance • 10 months data of a field deployed unit (5R) with 10 minutes sampling interval. • Average signal level -69dBm • 42,187 samples
Flow Calibration • Level to flow calibration • Hydraulic rating equation (Manning equation) • “Calibrating” flow from level measurements
Model based Filtering for Sensor Data • Physical models for – Pipe blockage – False ultrasound returns – Sensor failures
Installation at LUMS
End of Lecture 2
Outline • Motivation • Water networks : A CPS / IoT perspective • Open channel hydraulics: physical models • System identification : theory to experiments • Sensing: building telemetry networks • Control: putting it all together • Conclusions and outlook
Low level downstream control
Controller Design • Model
Controller Design • Model • Root locus (with 2 nd order Pade approx. of delay)
Controller Design • Model • Root locus (with 4 th order Pade approx. of delay)
Model Refinement • Wave excitations in the channel: damped oscillations. • Model is approximate. There are higher-order invisible modes.
Model Refinement • Model is approximate. There are higher-order invisible modes. Introduce damping / friction
Model Refinement • Model is approximate. There are higher-order invisible modes. Oscillatory mode + damping
How to choose a Controller? • Water off-takes from channel act as disturbances – Therefore, Integral action needed for disturbance rejection (PI control) • At some higher frequencies, waves in channels may get excited. – Therefore, controller should have “low gain” at wave frequency. (LPF with roll-off) • Both plant and controller (PI) introduce integrators. – Therefore, need lead compensation.
Controller Design • Model • PI-control + low-pass + lead compensator K ( 1 T s ) i 1 C ( s ) ( K ). p s ( 1 T s ) 2 PI control LPF Phase Lead
Level regulation (physical simulation)
Closed Loop On-Off Control Gate Controller: Prototyped in a LUMS FYP 2014 ! (Farwa Akhtar, Shibal Ibrahim, Muhammad Soban, Usama Munir)
Downstream Control in Other Parts of the World • Australia, Europe, USA, China
Networked Control Issues • So far, plant is single pool • Control problem is downstream water level regulation for one pool. • But irrigation networks are extremely complex, specially in the Indus basin • Control effects propagate • Enters Networked Control Systems !
Network effects TOP VIEW SIDEVIEW Controller of last gate sends signal of water scarcity
Network effects TOP VIEW SIDEVIEW Controller of a gate sends signal of water scarcity
Network effects TOP VIEW SIDEVIEW Controller of a gate sends signal of water scarcity
Network effects TOP VIEW SIDEVIEW Water starts entering the canal
Network effects TOP VIEW SIDEVIEW After reaching the set value controller sends signal to close upstream gate
Network effects TOP VIEW SIDEVIEW After reaching the set value controller sends signal to close upstream gate
Network effects TOP VIEW SIDEVIEW Off take creates water scarcity in a pool
Network effects TOP VIEW SIDEVIEW Controller sends signal of water scarcity
Network effects TOP VIEW SIDEVIEW Controller sends signal of water scarcity
Network effects TOP VIEW SIDEVIEW After reaching set value gates are closed
Network effects TOP VIEW SIDEVIEW All gates closed
Irrigation Networked Control Models • Multiple pools, multiple inputs, multiple outputs • What about control? Ref. Cantoni et al . “Control of Large-Scale Irrigation Networks,” IEEE proceedings 2007.
Irrigation Networked Control Models • Distributed control • Local controller for each pool
Irrigation Networked Control Models • Distributed control with feed-forward paths • Local controller for each pool + comm. with neighbors
Irrigation Networked Control Models • Centralized control • All feedback loops closed via a “central processor”.
Irrigation Networked Control Models • Centralized Vs Distributed control – which is better? Solid (distributed), dashed (centralized), dotted (with feedfoward) Ref. Cantoni et al. IEEE proceedings 2007.
CPS Security • Physical security + Network security = CPS security • Can we detect – Illegal dumps? – Breaches? – Seepages? – Non-technical losses? – covert misappropriations?
Nominal Networked Control System • LTI plant • Measurements • Actuation • Closed loop response where, Ref. . Roy. IEEE Control Systems Magazine, 2015.
Compromised System : Covert Agent • LTI plant • Measurements • Offsets • Closed loop response Impossible to detect if cover agent‟s model ∏ u = reality P u Ref. . Roy. IEEE Control Systems Magazine, 2015.
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