Model Identification and Predictive Control of a Laboratory Binary Distillation Column

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, 2015 1 / 19

Motivation Ján Drgoňa (STU) Distillation Control June 12, 2015 2 / 19

Distillation Ján Drgoňa (STU) Distillation Control June 12, 2015 3 / 19

Distillation Column Process Unit condenser reflux valve accumulator pre-heater feed waste valve reboiler Ján Drgoňa (STU) Distillation Control June 12, 2015 4 / 19

Distillation Column Control Aims Concentration via temperature control 100 90 T [ C] 80 70 60 y x 0 0.2 0.4 0.6 0.8 1 x, y [] Ján Drgoňa (STU) Distillation Control June 12, 2015 5 / 19

Distillation Column Control Aims Concentration via temperature control Challenges Hardware setup Nonlinearities Disturbances Plant-model mismatch Ján Drgoňa (STU) Distillation Control June 12, 2015 5 / 19

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, 2015 5 / 19

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, 2015 6 / 19

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, 2015 7 / 19

Model Identification 100 1 2 Step changes Responses Reflux Ratio [%] 80 60 40 20 0 0 1000 2000 3000 4000 Time [s] 3 Identified model 84 x k+1 = Ax k + Bu k y k = Cx k T1 [ C] 79 74 69 64 0 1000 2000 3000 4000 Time [s] Ján Drgoňa (STU) Distillation Control June 12, 2015 8 / 19

Model Identification 100 1 2 Step changes Responses Reflux Ratio [%] 80 60 40 20 0 0 1000 2000 3000 4000 Time [s] 3 Identified model x k+1 = Ax k + Bu k y k = Cx k T1 [ C] 84 79 74 69 Measurement 64 0 1000 2000 3000 4000 Time [s] Ján Drgoňa (STU) Distillation Control June 12, 2015 8 / 19

Model Identification 100 1 2 Step changes Responses Reflux Ratio [%] 80 60 40 20 0 0 1000 2000 3000 4000 Time [s] 3 Identified model x k+1 = Ax k + Bu k y k = Cx k T1 [ C] 84 79 74 69 Measurement Identification 64 0 1000 2000 3000 4000 Time [s] Ján Drgoňa (STU) Distillation Control June 12, 2015 8 / 19

Common Assumption Design model is equal Plant Ján Drgoňa (STU) Distillation Control June 12, 2015 9 / 19

Reality Design model is equal Plant Ján Drgoňa (STU) Distillation Control June 12, 2015 10 / 19

Reality Plant-model mismatch Design model is equal Plant Ján Drgoňa (STU) Distillation Control June 12, 2015 10 / 19

Origins of Offset in Control 1 Plant-model mismatch 2 Unmeasured disturbances 3 Incomplete state information Ján Drgoňa (STU) Distillation Control June 12, 2015 11 / 19

Offset-free Control Tools 1 Disturbance modelling 2 Estimation of variables 3 Model predictive control Ján Drgoňa (STU) Distillation Control June 12, 2015 12 / 19

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, 2015 13 / 19

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, 2015 13 / 19

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, 2015 14 / 19

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, 2015 15 / 19

Offset-free Control Tools 1 Disturbance modelling 2 Estimation of variables 3 Model predictive control Ján Drgoňa (STU) Distillation Control June 12, 2015 16 / 19

Control Scheme d r Distillation MPC u x Column Ján Drgoňa (STU) Distillation Control June 12, 2015 17 / 19

Control Scheme d r u Distillation y m MPC Column ˆx, ˆd Observer Ján Drgoňa (STU) Distillation Control June 12, 2015 17 / 19

Control Scheme d r u Distillation y m MPC Column ˆx, ˆd Observer Filter Ján Drgoňa (STU) Distillation Control June 12, 2015 17 / 19

Control Scheme d r u Distillation y m MPC PWM Column ˆx, ˆd Observer Filter Ján Drgoňa (STU) Distillation Control June 12, 2015 17 / 19

Experimental Results T s = 5 seconds, N = 50 samples, λ = 10 2 T1 [ C] Reflux Ratio [%] 67.5 67 66.5 66 65.5 65 64.5 100 80 60 40 20 0 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 Time [s] Ján Drgoňa (STU) Distillation Control June 12, 2015 18 / 19

Experimental Results T s = 5 seconds, N = 50 samples, λ = 10 2 xd [-] Reflux Ratio [%] 1 0.99 0.98 0.97 0.96 0.95 100 80 60 40 20 0 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 Time [s] Ján Drgoňa (STU) Distillation Control June 12, 2015 18 / 19

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, 2015 19 / 19

Backup: Distillation Column Hardware Solution Ján Drgoňa (STU) Distillation Control June 12, 2015 19 / 19

Backup: Effect of Diturbances Feed Temp. [ C] Trays Temp. [ C] 76 74 72 100 95 90 85 80 75 70 65 60 0 100 200 300 400 500 600 700 Time [s] T 2 T 3 T 4 T 5 T 6 0 100 200 300 400 500 600 700 Time [s] Ján Drgoňa (STU) Distillation Control June 12, 2015 19 / 19