Model Identification and Predictive Control of a Laboratory Binary Distillation Column

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1 Model Identification and Predictive Control of a Laboratory Binary Distillation Column Ján Drgoňa, Martin Klaučo, Richard Valo, Jakub Bendžala, and Miroslav Fikar Slovak University of Technology in Bratislava, Slovakia June 12, 2015 I AM Ján Drgoňa (STU) Distillation Control June 12, / 19

2 Motivation Ján Drgoňa (STU) Distillation Control June 12, / 19

3 Motivation Ján Drgoňa (STU) Distillation Control June 12, / 19

4 Distillation Ján Drgoňa (STU) Distillation Control June 12, / 19

5 Distillation Ján Drgoňa (STU) Distillation Control June 12, / 19

6 Distillation Ján Drgoňa (STU) Distillation Control June 12, / 19

7 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

8 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

9 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

10 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

11 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

12 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

13 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

14 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

15 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

16 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

17 Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

18 Distillation Column Control Aims Concentration via temperature control T [ C] y x x, y [] Ján Drgoňa (STU) Distillation Control June 12, / 19

19 Distillation Column Control Aims Concentration via temperature control Challenges Hardware setup Nonlinearities Disturbances Plant-model mismatch Ján Drgoňa (STU) Distillation Control June 12, / 19

20 Distillation Column Control Aims Concentration via temperature control Challenges Tools Hardware setup Nonlinearities Disturbances Plant-model mismatch Model identification Model predictive control Ján Drgoňa (STU) Distillation Control June 12, / 19

21 Distillation Column Variables condenser reflux valve accumulator 1 Process variable: Temperature at top of the column pre-heater feed 2 Manipulated variable: Reflux ratio waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

22 Control Challenges Hardware condenser reflux valve accumulator 1 Oversized condenser 2 PWM signal pre-heater feed 3 Feed temperature control waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

23 Control Challenges Hardware condenser reflux valve accumulator 1 Oversized condenser 2 PWM signal pre-heater feed 3 Feed temperature control waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

24 Control Challenges Hardware condenser reflux valve accumulator 1 Oversized condenser 2 PWM signal pre-heater feed 3 Feed temperature control waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

25 Control Challenges Hardware condenser reflux valve accumulator 1 Oversized condenser 2 PWM signal pre-heater feed 3 Feed temperature control waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, / 19

26 Model Identification Step changes Responses Reflux Ratio [%] Time [s] 3 Identified model 84 x k+1 = Ax k + Bu k y k = Cx k T1 [ C] Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

27 Model Identification Step changes Responses Reflux Ratio [%] Time [s] 3 Identified model 84 x k+1 = Ax k + Bu k y k = Cx k T1 [ C] Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

28 Model Identification Step changes Responses Reflux Ratio [%] Time [s] 3 Identified model x k+1 = Ax k + Bu k y k = Cx k T1 [ C] Measurement Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

29 Model Identification Step changes Responses Reflux Ratio [%] Time [s] 3 Identified model x k+1 = Ax k + Bu k y k = Cx k T1 [ C] Measurement Identification Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

30 Common Assumption Design model is equal Plant Ján Drgoňa (STU) Distillation Control June 12, / 19

31 Reality Design model is equal Plant Ján Drgoňa (STU) Distillation Control June 12, / 19

32 Reality Plant-model mismatch Design model is equal Plant Ján Drgoňa (STU) Distillation Control June 12, / 19

33 Origins of Offset in Control 1 Plant-model mismatch 2 Unmeasured disturbances 3 Incomplete state information Ján Drgoňa (STU) Distillation Control June 12, / 19

34 Offset-free Control Tools 1 Disturbance modelling 2 Estimation of variables 3 Model predictive control Ján Drgoňa (STU) Distillation Control June 12, / 19

35 Disturbance Modelling Design model: x k+1 = Ax k + Bu k d k+1 = d k Luenberger observer: [ˆxˆd] [ ] ] A 0 = 0 I [ˆxˆd k+1 k [ ] [ˆx ] ŷ k = C I ˆd k y k = Cx k +d k + [ ] B u 0 k + L(y m,k ŷ k ) Ján Drgoňa (STU) Distillation Control June 12, / 19

36 Disturbance Modelling Augmented design model: x k+1 = Ax k + Bu k d k+1 = d k Luenberger observer: [ˆxˆd] [ ] ] A 0 = 0 I [ˆxˆd k+1 k [ ] [ˆx ] ŷ k = C I ˆd k y k = Cx k + d k + [ ] B u 0 k + L(y m,k ŷ k ) Ján Drgoňa (STU) Distillation Control June 12, / 19

37 Estimation of Variables Augmented design model: x k+1 = Ax k + Bu k d k+1 = d k Luenberger observer: [ˆxˆd] [ ] ] A 0 = 0 I [ˆxˆd k+1 k [ ] [ˆx ] ŷ k = C I ˆd k y k = Cx k + d k + [ ] B u 0 k + L(y m,k ŷ k ) Ján Drgoňa (STU) Distillation Control June 12, / 19

38 Model Predictive Control Reference tracking MPC: min N 1 k=0 ((y k+1 r) 2 + λ( u k ) 2) s.t. x k+1 = Ax k + Bu k k = 0,..., N 1 y k = Cx k + d 0 u k = u k u k 1 u min u k u max x 0 = ˆx(t) d 0 = ˆd(t) k = 0,..., N Ján Drgoňa (STU) Distillation Control June 12, / 19

39 Offset-free Control Tools 1 Disturbance modelling 2 Estimation of variables 3 Model predictive control Ján Drgoňa (STU) Distillation Control June 12, / 19

40 Control Scheme d r Distillation MPC u x Column Ján Drgoňa (STU) Distillation Control June 12, / 19

41 Control Scheme d r u Distillation y m MPC Column ˆx, ˆd Observer Ján Drgoňa (STU) Distillation Control June 12, / 19

42 Control Scheme d r u Distillation y m MPC Column ˆx, ˆd Observer Filter Ján Drgoňa (STU) Distillation Control June 12, / 19

43 Control Scheme d r u Distillation y m MPC PWM Column ˆx, ˆd Observer Filter Ján Drgoňa (STU) Distillation Control June 12, / 19

44 Experimental Results T s = 5 seconds, N = 50 samples, λ = 10 2 T1 [ C] Reflux Ratio [%] Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

45 Experimental Results T s = 5 seconds, N = 50 samples, λ = 10 2 T1 [ C] Reflux Ratio [%] Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

46 Experimental Results T s = 5 seconds, N = 50 samples, λ = 10 2 xd [-] Reflux Ratio [%] Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19

47 Conclusions 1 Identification of laboratory distillation column 2 Disturbance modelling 3 State and disturbance estimation 4 Model predictive control design 5 Experimental verification of control on laboratory device Ján Drgoňa (STU) Distillation Control June 12, / 19

48 Conclusions 1 Identification of laboratory distillation column 2 Disturbance modelling 3 State and disturbance estimation 4 Model predictive control design 5 Experimental verification of control on laboratory device Ján Drgoňa (STU) Distillation Control June 12, / 19

49 Conclusions 1 Identification of laboratory distillation column 2 Disturbance modelling 3 State and disturbance estimation 4 Model predictive control design 5 Experimental verification of control on laboratory device Ján Drgoňa (STU) Distillation Control June 12, / 19

50 Conclusions 1 Identification of laboratory distillation column 2 Disturbance modelling 3 State and disturbance estimation 4 Model predictive control design 5 Experimental verification of control on laboratory device Ján Drgoňa (STU) Distillation Control June 12, / 19

51 Conclusions 1 Identification of laboratory distillation column 2 Disturbance modelling 3 State and disturbance estimation 4 Model predictive control design 5 Experimental verification of control on laboratory device Ján Drgoňa (STU) Distillation Control June 12, / 19

52 Conclusions 1 Identification of laboratory distillation column 2 Disturbance modelling 3 State and disturbance estimation 4 Model predictive control design 5 Experimental verification of control on laboratory device Ján Drgoňa (STU) Distillation Control June 12, / 19

53 Backup: Distillation Column Hardware Solution Ján Drgoňa (STU) Distillation Control June 12, / 19

54 Backup: Effect of Diturbances Feed Temp. [ C] Trays Temp. [ C] Time [s] T 2 T 3 T 4 T 5 T Time [s] Ján Drgoňa (STU) Distillation Control June 12, / 19