Mathematical Models for Simulation, Control and Testing Nordisk drifts- og vedlikeholdsmøte Oslofjordmuseet, 14th - 15th September 2017 Mathematical Models for Simulation, Control and Testing Finn Aakre Haugen Finn Aakre Haugen, VEAS

Consultant at VEAS (part-time position) My background: Consultant at VEAS (part-time position) Docent at University College of Southeast Norway (Høgskolen i Sørøst-Norge), campus Porsgrunn MSc in Engineering Cybernetics PhD with thesis "Optimal design, operation and control of an anaerobic digestion reactor" Finn Aakre Haugen, VEAS

Finn Aakre Haugen, VEAS

Three applications of modelling at VEAS: Compliant level control of inlet basin (magazine) Temperature control of biogas reactor Control of combined tunnel system Finn Aakre Haugen, VEAS

Modeling and simulation of the inlet basin of the VEAS WWTP. Application 1: Modeling and simulation of the inlet basin of the VEAS WWTP. Aim: Smooth WWTP inflow with compliant level control of basin (PID/MPC). Finn Aakre Haugen, VEAS

Application 1 continued: The inlet basin (magazine): Finn Aakre Haugen, VEAS

Application 1 continued: Practical tests with suggested model-based "Skogestad" PI tuning (tested on simulator in LabVIEW): At present, with more or less "random" PI settings: Model-based PI settings = improvement! (Smoother pump flow) Finn Aakre Haugen, VEAS

Application 1 continued: Practical tests with suggested MPC (tested on simulator in LabVIEW+MATLAB): At present, with more or less "random" PI settings: MPC is also an improvement! Finn Aakre Haugen, VEAS

Application 1 continued: The mathematical model which is used for PI tuning, MPC, and simulation: A mechanistic model (a first order differential equation) based on material balance of the liquid, assumed as water, in the inlet basin: dh/dt = [Fin - Fpump]/A where the net unknown inflows are estimated with a Kalman Filter (which is a model-based soft sensor). Finn Aakre Haugen, VEAS

Application 1 continued: The principle of MPC: Continuously calculating the control signal (u_LC) as the solution to the following optimization problem: In this application, the fmincon optimization function in Matlab was used. Result: Smoother flow u_LC, and more compliant level h, is obtained with larger cost C2. Finn Aakre Haugen, VEAS

ySP ypred u Principle of MPC: The optimal control signal applied to the actuator. Calculated, but not applied to the process. ySP The optimal control sequence is calculated by the MPC. ypred u(2) u u(0) u(1) Now! Future For example: Np = 20 (samples) Finn Aakre Haugen, VEAS

Application 1 continued: Kc = 1/(2*Ki*Tc) og Ti = 2*Tc [s] PI controller tuning of the level controller with Skogestad's rules for "integrator without time-delay": Kc = 1/(2*Ki*Tc) og Ti = 2*Tc [s] where Ki = 1/A and Tc is the specified (adjustable) time-constant of the closed loop system. Result: Smoother flow u_LC, and more compliant level h, is obtained with larger Tc. Finn Aakre Haugen, VEAS

Application 2 (by PhD candidate Shadi Attar et al.): Model-based PI controller tuning and simulator-based testing of a new temperature control design of the biogas reactors at VEAS Finn Aakre Haugen, VEAS

The temperature control system where the controller TC must be tuned: Application 2: The temperature control system where the controller TC must be tuned: Finn Aakre Haugen, VEAS

Application 2 continued: Operation sequence of each reactor: Filling Phase (45 min): Pumping raw sludge to reactor from raw-sludge storage tank, and also pumping digested sludge through heat exchangers. Note: In the current reactor operation regime, heat can be added to the reactor only in the filling phase. Holding Phase (120 min): Circulating digested sludge and no new feed flow for sludge hygeinisation purposes. Reactor sludge is retained at minimum 55 °C for minimum of 2h. Emptying phase (15 min): Transferring the hygienised digested sludge to a buffer tank. Finn Aakre Haugen, VEAS

Application 2 continued: The following mathematical model is used for simulation of the biogas reactor: A mechanistic model (a first order differential equation) based on energy balance of liquid in the reactor (assuming homogeneous conditions and water): Finn Aakre Haugen, VEAS

Application 2 continued: Front panel of the LabVIEW-based simulator: Finn Aakre Haugen, VEAS

Application 2 continued: Small part of block diagram of the LabVIEW-based simulator: Finn Aakre Haugen, VEAS

Application 2 continued: For the controller tuning the following "integrator with time-delay" model is used: Skogestad PI settings: (These theoretically derived PI settings works well in practice.) Finn Aakre Haugen, VEAS

Application 3 (which is in its very beginning): Conceptual simulation and model-based predictive control (MPC) of the combined tunnel system of VEAS with these main aims: Reduction of overflow into the Oslo Fjord at large loads. Smoother inflow into the WWTP (WRRF) at normal loads. Finn Aakre Haugen, VEAS

Finn Aakre Haugen, VEAS

The preliminary model for the simulator and the MPC is based on: Application 3 cont.: The preliminary model for the simulator and the MPC is based on: Mass balance of each magazine Hydraulic transportation of liquid as transportation time (time delay) in series with time lags (critically damped or overdamped second-order transfer functions). The model must be adapted to real data. The model should - eventually - include predictions of tunnel inflows from precipitations sensors and sewage system model(s). Finn Aakre Haugen, VEAS

Final comments: Quite simple mechanistic mathematical models can be very useful in practical applications. Can we make more use of models in our plants? Finn Aakre Haugen, VEAS