Model predictive control of industrial processes. Vitali Vansovitš

Transcription

1 Model predictive control of industrial processes Vitali Vansovitš

2 Contents Industrial process (Iru Power Plant) Neural networ identification Process identification linear model Model predictive controller Results Future plans 2 (33)

3 Industrial process (Iru Power Plant) Three similar boilers in parallel Each boiler can wor in: basic mode (constant load) control mode (variable load) Control mode is used to control plant output temperature 3 (33)

4 Industrial process control Two cascade control loop Cascade control loop Control loop SP3+ SP2+ SP1+ PID 3 PID 2 PID 1 Process 1 Process 2 Process 3 fast slow slowest Output 4 (33)

5 Industrial process control (Iru Power Plant) C3: p = 0,25; ti = 20 C2: p = 0,9; ti = 240 C1: p = 0,5; ti = (33)

6 Industrial process (Iru Power Plant) :00 1:12 2:24 3:36 4:48 6:00 7:12 P. output SP P. output ME :00 1:12 2:24 3:36 4:48 6:00 7:12 Setpoint Measurement Water flow :00 1:12 2:24 3:36 4:48 6:00 7:12 6 (33)

7 Neural networ model Recursive prediction 7 (33) y output temperature prediction u vector of water, air and gas flows

8 Neural networ 5 min prediction Temperature, deg Temperature, deg Predicted temperature, deg Time, min 8 (33)

9 Neural networ first results 5 minutes predictions were good Simulation was not possible After 10 cycles model output was not close enough to real process output After 100 cycles model output was already somewhere in outer space So, it was decided to start from simple things linear model identification with conventional methods. 9 (33)

10 Process identification Process is simple, but nonlinear: Q Q r m c m fuel water T T r m c m fuel water As water flow is more or less constant during normal operation, so mainly it can be seen as linear. Matlab Identification Toolbox was used for identification. Most suitable results were acquired from polynomial and state space models. 10 (33)

11 Polynomial model identification 11 (33)

12 State-space model 12 (33)

13 Process model State space model with 4 states (ss2) was selected as: it is simpler than oe221 (6 states in state space representation) shows better results then ss1 (1 state) 4 state model showed better fit among all state space models (2, 3, 5 etc. states) 13 (33)

14 MPC (Model predictive controller) Model identification To avoid perfect theoretical results model for MPC was identified from the data acquired one year later at the time when boiler load was different (~1/8 of previous example) and nonconstant. 14 (33)

15 MPC structure 15 (33)

16 MPC observer 16 (33) 1 ˆ 1 ˆ ˆ 1 ˆ 1 ˆ 1 ˆ ˆ Cx y Bu Ax x y y L x x AL y Bu x L C I A x 1 ˆ 1 ˆ 1 ˆ x x e e LC A e 1 Observer is stable - estimation error converges to zero

17 MPC design (1) There is a cost function: where Z() predicted process output T() reference trajectory U() process input changes Q, R weight matrices 2 T a a Aa A Z xu1 U V xu1 Z T U 2 2 R Q Tracing error Free response with U = 0 17 (33)

18 MPC design (2) From this function optimal input changes for unconstrained case are found: U H G where G T 2 QE H T Q R 18 (33)

19 MPC constraints Constraints are in the form: U E 1 U Z 0, F 1 0, G 1 0 Which can be transformed to: WU w So, we solve constrained optimization problem: T T minimize U HU G U subject to inequality constraint. Quadratic programming problem 19 (33)

20 MPC for water boiler 1 manipulated process input (gas flow) 2 measured process disturbances (water & air flows) 1 measured process output Prediction horizon 10 steps Control horizon 2 steps Gas flow constraints (m 3 /h): min = 0 max = max down rate = 2000 max up rate = 2000 Gas flow rate weight = 0,01 Process output weight = (33)

21 MPC for water boiler (Simulin) 21 (33)

22 Outputs comparison 22 (33)

23 Control quality 23 (33)

24 Gas consumption 24 (33)

25 Earn some money Same control quality, but less raw materials 25 (33)

26 Setpoint decreased 0,6 (1) Output comparison 26 (33)

27 Setpoint decreased 0,6 (2) Gas consumption difference ~8000 m 3 27 (33)

28 Setpoint decreased 0,6 (3) Sum of errors 28 (33)

29 Very rough estimation Gas price 400 / 1000 m 3 Difference 8000 m 3 Period 16 hours Season length 50 days Economy = 50 * (24/16) * 8000 * 400 / 1000 = / season 29 (33)

30 Some results With MPC control became better: Sum of errors of output are twice lower MPC with bad model is better than PI cascade Raw material consumption is on the same level If we change setpoint then we can decrease raw material consumption with the same control quality as PI loops have. 30 (33)

31 Future plans Compare MPC with simulated PI loop Minimize raw material consumption with MPC (not setpoint change) Find better way of identification Identify all parts of the process (including actuators) Mae model based control closer to reality Try controller on real plant some day Etc. 31 (33)

32 References Oliver Nelles, Nonlinear System Identification, Springer, Berlin, 2001 J.M.Maciejowsi, Predictive Control with Constraints, pdf boo, 2000 Real life 32 (33)

33 Than you! Questions???