1. Model-based Predictive Control (MPC)
IA3112 Automatiseringsteknikk Høsten 2018
Model-based Predictive Control (MPC)
Finn Aakre Haugen
IA3112 Aut. MPC. Haugen. 2018

2. J. M. Maciejowski in Predictive Control with Constraints (2002).
"MPC is the only advanced control technique that is more advanced than standard PID to have a significant and widespread impact on industrial process control."
J. M. Maciejowski in Predictive Control with Constraints (2002).
IA3112 Aut. MPC. Haugen. 2018

3. History
Cutler and Ramaker (Shell Oil), 1973: DMC (Dynamic Matrix Control). 1983: QDMC (Quadratic DMC). Application to furnace temperature control.
Richalet et al., 1976: Algorithm: MPHC (Model predictive heuristic control). Software: IDCOM (Identification and Command). Applied to a fluid catalytic cracking unit and a PVC plant.
Lot of development since then. MPC is the dominating model-based controller in control-oriented conferences and journals.
IA3112 Aut. MPC. Haugen. 2018

4. Some MPC products DeltaV (Emerson Process Partner) 800xA APC (ABB)
Matlab MPC Toolbox, also for Simulink
LabVIEW Predictive Control palette in Control Design toolkit
Septic (Statoil, no external use) .
IA3112 Aut. MPC. Haugen. 2018

5. What is MPC?
IA3112 Aut. MPC. Haugen. 2018

6. (typical from Euler forward discretization)
Process model
(typical from Euler forward discretization)
IA3112 Aut. MPC. Haugen. 2018

7. MPC as an optimization problem: Cost-coefficients (tuned by user)
Prediction horizon
Control error
= Setpoint - Meas
Control signal change
min U
Compactly expressed:
t = time now!
min U
Cost-coefficients (tuned by user)
U (to be calculated as the optimal solution) in detail:
IA3112 Aut. MPC. Haugen. 2018

8. Summary of MPC:
The MPC is a model-based controller that continuously predicts the optimal future control sequence using the following information:
An optimization criterion that typically consists of a sum of future (predicted) squared control errors and quadratic control signal changes.
A process model
The current process state obtained from measurements and/or state estimates from a state estimator which typically is in the form of a Kalman filter.
Current, and, if available, future setpoint values and process disturbance values.
Constraints (max and min values) of the control signal and the process variable.
From the optimal future control sequence, the first element is picked out and applied as control signal to the process.
Some versions of the MPC assume linear process models, while others are based on nonlinear process models. The models may be multivariable and contain time delays.
IA3112 Aut. MPC. Haugen. 2018

9. Application: MPC temperature control of a simulated air heater
IA3112 Aut. MPC. Haugen. 2018

10. Example: Temperature control of air heater
IA3112 Aut. MPC. Haugen. 2018

11. Mathematical model (time-constant with time-delay):
IA3112 Aut. MPC. Haugen. 2018

12. Front panel of the simulator:
Teacher runs simulations (link will not work for students)
IA3112 Aut. MPC. Haugen. 2018

13. Experimental results:
PID
MPC
Which is better?
IA3112 Aut. MPC. Haugen. 2018

14. Application: MPC for position control of a simulated pendulum
IA3112 Aut. MPC. Haugen. 2018

15. Front panel of the simulator:
Teacher runs simulations (link will not work for students)
IA3112 Aut. MPC. Haugen. 2018

16. Application: MPC for averaging level control of the inlet magazine upstreams the VEAS wrrf (water resource recovery facility), Slemmestad, Norway
IA3112 Aut. MPC. Haugen. 2018

17. Combined sewage system of Oslo and surroundings:
Slemmestad
IA3112 Aut. MPC. Haugen. 2018

18. The WWTP in Slemmestad (in the Bjerkås mountain):
IA3112 Aut. MPC. Haugen. 2018

19. Facts about VEAS
VEAS is Norway's largest wastewater treatment plant (WWTP)
Serves approx pe (person equivalents).
Average: 3,5 m³/s.
Retention time in the WWTP: 3 – 4 hours.
IA3112 Aut. MPC. Haugen. 2018

20. The inlet magazine: Inflow to WWTP Tunnel Inlet basin Controller20
The inlet magazine:
Inflow to WWTP
Tunnel
Inlet basin
Controller
(PI, MPC)
IA3112 Aut. MPC. Haugen. 2018

21. Compliant level control @ Normally low load (tunnel flow)
Operation mode #1
Compliant level Normally low load (tunnel flow) 21
Constraints in this mode:
1. Smooth pump flow. Specifically, d(F_in)/dt <= 20 (L/s)/min
2. Pump flow, F_in, between 8000 and 0 L/s.
3. Level between soft limits of 1.5 m and 2.5 m, with 1.8 m as the nominal level setpoint. (Lately, these limits have been changed to 1.6 m and 2.8 m, respectively, with setpoint 2.3 m. Both the above sets of specifications are used in this article.)
IA3112 Aut. MPC. Haugen. 2018

22. Mathematical model of liquid level of inlet basin22
Mathematical model of
liquid level of inlet basin
(needed in simulator, PI tuning, MPC and Kalman Filter):
(material balance)
IA3112 Aut. MPC. Haugen. 2018

23. PI controller Skogestad tuning:
Process model:
PI settings:
IA3112 Aut. MPC. Haugen. 2018

24. MPC including KF (Kalman Filter):
(impl. with
fmincon in
MATLAB)
Model used in KF:
IA3112 Aut. MPC. Haugen. 2018

25. Let's look at real results of three various level control solutions
PI control with original PI settings
PI control with Skogestad (or optimized) PI settings (cf. previous lecture)
MPC
IA3112 Aut. MPC. Haugen. 2018

26. Computer implementation PC with LabVIEW and MATLAB:
LabVIEW for implementation of main program and GUI, and - in case of real experiments - IO (voltages for measurement and control).
Matlab in Matlab Script Node in LabVIEW for running the MPC based on fmincon() incl. the observer.
IA3112 Aut. MPC. Haugen. 2018

27. Experimental results on the real plant (VEAS) (time interval = 21 h)27
MPC
(preliminary results)
Original PI settings
(Kc = 8.0 , Ti = 1000 s)
Skogestad PI settings (Kc = 3.1 , Ti = 3240 s)
Level
Pump flow
Rate of change
of pump flow
IA3112 Aut. MPC. Haugen. 2018

28. PI control with Skogestad settings (Tc = 1000 s), and MPC
Simulations:
PI control with Skogestad settings (Tc = 1000 s), and MPC
Level:
Pump flow:
Rate of change
of pump flow:
MPC: Blue.
PI: Magenta
IA3112 Aut. MPC. Haugen. 2018