The text below is a brief description of the master topics supervised by professor Lars Imsland. Contact lars.imsland@itk.ntnu.no for further information.

1. Updating simple hydraulic model for MPD using PWD and Kalman Filter Pressure While Drilling (PWD) measured close to the drill bit are available topside with up to 30 seconds delay during circulation above a minimum flow rate. After a connection when the rig pumps are stopped, minimum, average and maximum downhole pressure are pumped up. A hydraulic model is used to estimate the downhole pressure in real time based on topside measurements only. The task is to utilize the delayed downhole measurements to update this hydraulic model. Kalman Filter is proposed for estimation. I suggests to have 3 KF objects running simultaneously; one KF1 in real time, one temporary KF2 and one KF3 in standby waiting for a new measurement. When a new PWD is received, then a) integrate KF3 (xhat(k+1)=xhat(k)+f(xhat,u)) up to time stamp for new PWD and correct with this measurement (xhat=xhat+K*(y-yhat)), b) replace KF2 with this KF3 and integrate KF2 up to real time, c) replace KF1 with KF2.
   
   1) Short literature study on MPD, hydraulic models, Kalman Filtering
   2) Select a simple model, e.g. ESD = MW + constant1, ECD = ESD + constant2*circulation rate. Constant1= compression factor + cuttings load. Constant2=friction factor
   3) Develop a KF to update constant 1&2 and test on your own generated data
   a. First assume PWD available in real time for all flow rates, PWD updated every 10 seconds
   b. Assume PWD delayed by 10 seconds for all flow rates. Develop a solution updating 10 seconds old model, then use this information to update real time model
   c. Assume PWD delayed by 10 seconds for high flow rates and min/avg/max after connections. Develop a solution updating 10 seconds old model, then use this information to update real time model
   d. Show how uncertainty/covariance increases with time if PWD is unavailable for a period of time
   4) Test on real data set provided by Statoil
   
   ESD=Equivalent Static Density=Downhole pressure without circulation/vertical depth
   ECD=Equivalent Circulating Density=Downhole pressure with circulation/vertical depth
   
   Co-supervisors: John-Morten Godhavn and Henrik Manum, Statoil.
2. Områdebasert frekvenskontroll i kraftsystemet Statnett bruker automatisk sekundærregulering til å sørge for balanse mellom produksjon og forbruk. I dag er dette én PI-regulator som styrer hele Norden. Vi ønsker at studenten(e) skal designe en alternativ reguleringsstruktur med flere autonome regulatorer som samhandler ved hjelp av pris- og kapasitetssignaler. Studenten kan ta utgangspunkt i et eksisterende rammeverk av modell og regulatorer i Simulink. Oppgave gitt i samarbeid med Statnett.
3. Robust linear model predictive control This project will investigate methods for computation of (robust) reachable sets, based on existing software, and how to use this for construction of different robust linear MPC schemes. This should be tested and compared on simple examples. This problem will fit best for «theoretically inclined» students with fondness for optimization and Matlab programming.