Standards Certification Education & Training Publishing Conferences & Exhibits Automation Connections ISA EXPO 2006

Standards Certification Education & Training Publishing Conferences & Exhibits New Directions in Bioprocess Modeling and Control Gregory K McMillan CDI - Process & Industrial

Key Points –Opportunities –Process Dynamics –Basic Feedback Control (PID) –Model Predictive Control (MPC) –Virtual Plant (VP) –Multivariate Statistical Process Control (MSPC) –Unification of Controller Tuning Rules

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Opportunities - Bioreactor Inputs and Outputs for No Feedback Control Reagent Air Optimum DO Optimum pH Optimum Biomass Optimum Product Feeds Concentrations pH DO Product Biomass Optimum Substrate Time

Opportunities - Bioreactor Inputs and Outputs for Basic PID Control Air Optimum DO Optimum pH Optimum Biomass Optimum Product Feeds Concentrations pH DO Product Biomass Reagent Substrate Optimum Substrate Time

Opportunities - Bioreactor Inputs and Outputs for Advanced Control Air Optimum DO Optimum pH Optimum Biomass Optimum Product Feeds Concentrations pH DO Product Biomass Reagent Optimum Substrate Time

Opportunities - Variation in Optimum DO and Glucose DO Glucose Product max Product min Glucose max Glucose min DO max DO min Biomass max Biomass min Region of feasible solutions Optimal solution is in one of the vertexes

Opportunities - Inferential Measurements and Profiles from an Adapted Virtual Plant Actual Plant Optimization Dissolved Oxygen Set Point Substrate Set Point Virtual Plant Online KPI: Yield and Capacity Inferential Measurements: Biomass Growth and Production Rates Adaptation Key Actual Process Variables Key Virtual Process Variables Model Parameters Error between virtual and actual process variables are minimized by correction of model parameters Model Predictive Control and LP For Optimization of Actual Plant Model Predictive Control and Neural Network For Adaptation of Virtual Plant Optimum and Reference Batch Profiles Actual Batch Profiles Super Model Based Principal Component Analysis

Process Dynamics - Self-Regulating Response Time (seconds) Process Variable or Controller Output (%)  CO  CV dd oo K p =  CV  CO  CV CO CV Dead time Time Constant Open loop gain (%/%) (process gain)

Process Dynamics - Integrating Response Variable (%) Time (seconds) dd K i = { [  CV 2  T 2 ]  CV 1  T 1 ] }  CO  CO ramp rate is  CV 1  T 1 ramp rate is  CV 2  T 2 CO CV Dead time Integrating process gain (%/sec/%)

PID - Closed Loop Time Constant CO Time Signal (%) 0 dd Dead Time (Time Delay) cc Open Loop Error E o (%) 0.63  E o Closed Loop Time Constant (Time Lag) CV SP Controller is in Automatic

PID - Limit Cycle in Cascade Loop from Final Element Resolution Limit Secondary PV Secondary CO Primary PV

PID - Slowly Decaying Oscillation in Cascade Loop from an Integrating Loop Secondary SP Secondary CO Primary PV Primary controller reset time decreased from 1000 to 100 sec/rep Primary controller gain decreased from 1.0 to 0.1 Secondary SP Secondary CO Primary PV

PID - Interacting Oscillations in Cascade Loop from Slow Secondary Loop Secondary loop slowed down by a factor of 5 Secondary SP Secondary CO Primary PV Secondary SP Primary PV Secondary CO

PID - The Effect of Load Disturbance Speed on Process Recovery Periodic load disturbance time constant increased by factor of 10 Adaptive loop Baseline loop Adaptive loop Baseline loop

PID - Batch Set Point Performance of an Integrating Loop Practice 1 Practice 2Practice 4 PV CO PV

MPC - Identified Responses for Batch Profile Control

MPC - Optimization of Growth Rate and Product Formation Rate Product Formation Rate Biomass Growth rate Substrate Dissolved Oxygen

MPC - Optimization of Antibiotic Batch Profiles Batch Basic Fed-Batch APC Fed-Batch Batch Inoculation Dissolved Oxygen (AT6-2) pH (AT6-1) Estimated Substrate Concentration (AT6-4) Estimated Biomass Concentration (AT6-5) Estimated Product Concentration (AT6-6) Estimated Net Production Rate (AY6-12) Estimated Biomass Growth Rate (AY6-11) MPC in Auto

MPC - Improvement in Penicillin Key Performance Parameters Current Product Yield (AY6-10D) Current Batch Time (AY6-10A) Predicted Batch Cycle Time (AY6-10B) Predicted Cycle Time Improvement (AY6-10C) Predicted Final Product Yield (AY6-10E) Predicted Yield Improvement (AY6-10F) Batch Basic Fed-Batch APC Fed-Batch Batch Inoculation MPC in Auto Predicted Final Product Yield (AY6-10E) Predicted Batch Cycle Time (AY6-10B)

Virtual Plant - Imported Configuration and Embedded Process Simulation

Virtual Plant - Adaptation of Henry Coefficient to Match Plant Pressures Henry coefficient for oxygen transfer in actual plant was changed from 7770 (77%) to 7500 (50%) CV1 - Virtual Plant Pressure (kPa) MV1 - Virtual Plant Henry Coefficient (%) SP1 - Actual Plant Pressure (kPa) Batch Cycle

Virtual Plant - Adaptation of Henry Coefficient to Match Plant Pressures Henry coefficient for oxygen transfer in actual plant was changed from 7770 (77%) to 7500 (50%) CV1 - Virtual Plant Pressure (kPa) MV1 - Virtual Plant Henry Coefficient (%) SP1 - Actual Plant Pressure (kPa) Batch Cycle

Golden Batch Based PCA Fault and PLS Error Detection Actual Plant  PCA (with delays) Logic PLS Golden Batch Profiles Differences In Profiles Scores Latent Variables Inputs The “golden batch” profile is an average of the best batches for a fixed set of inputs from previous runs of the actual plant Qualitative Faults Quantitative Errors Faults (errors) in concentrations (seed and glucose), measurements (pH, DO, and glucose), and kinetic parameters (max specific growth and product formation rates and oxygen limitations constants) X space Y space

Model Based PCA Fault and PLS Error Detection Actual Plant Virtual Plant  PCA (with delays) Logic PLS Profiles Differences In Profiles Scores Latent Variables Inputs Qualitative Faults Quantitative Errors Note that the virtual plant is more than just a first principal model. Faults (errors) in concentrations (seed and glucose), measurements (pH, DO, and glucose), and kinetic parameters (max specific growth and product formation rates and oxygen limitations constants) X space Y space

Super Model Based PCA Fault and PLS Error Detection Actual Plant Virtual Plant  Profiles Differences In Profiles Inputs Dynamic Error Model Errors in Profiles  PCA (with delays) Logic PLS Scores Latent Variables Qualitative Faults Quantitative Faults Note that the virtual plant is more than just a first principal model. Faults (errors) in concentrations (seed and glucose), measurements (pH, DO, and glucose), and kinetic parameters (max specific growth and product formation rates and oxygen limitations constants) X space Y space

Virtual Plant - Summary of Uses Testing of configuration and process interactions Process control education of operators, technicians, and engineers Experimentation for exploration of optimums and “what if” scenarios Rapid prototyping of innovative and advanced controls Evaluation of tuning settings Identification of MPC models Training of NN Development of latent variables and reference trajectories for PCA Development of logic for fault analysis by PCA Online prediction of abnormal situations Inferential real time measurements of important concentrations Optimization of batch profiles Online prediction of batch KPI, such as cycle time and yield

Unification of PID Controller Tuning Rules The equation for the integrated absolute error (IAE) as a function of controller gain and reset time derived from the PI controller’s response to a load upset is: reset time scan time open loop error (PID in manual) controller gain process gain

Unification of PID Controller Tuning Rules The Lambda tuning equation to set a degree of transfer of variability in terms of an original dead time is: Lambda factor process time constant original dead time

Unification of PID Controller Tuning Rules The Simplified Internal Model Control (SIMCA) and Ziegler Nichols (ZN) reaction curve tuning equation (with controller gain cur in half per industrial practice to increase smoothness and robustness) for max disturbance rejection (transfer of variability) is: new dead time

Unification of PID Controller Tuning Rules A detuned controller (e.g. lower controller gain) has the same load rejection capability as a loop with more dead time. The capability for a given dead time is suggested by using the SIMC/ZN tuning for max controller gain in equation for the IAE. Thus, we can find out how much dead time is implied in a detuned controller by setting the detuned controller gain equal to the SIMC/ZN controller gain. If you set Lambda equation equal to the SIMC/ZN equation, set the reset time equal to the time constant, and cancel terms, then you end up with the following equation for the new dead time as a function of the Lambda factor, the time constant, and the original dead time.

Unification of PID Controller Tuning Rules If we take the worst case where the load upset arrives just after the analog input block reads the measurement, all of the scan time is dead time. In this case, the new dead time is equal to the original dead time plus the scan time. If you set the last two equations equal, then the scan time is:

Summary Transfer of variability by different levels of control profoundly affects choice of inputs for NN and MSPC Most primary and upper level loops have an integrating response Biomass and product concentration are one sided integrators and require translation to a rate of change (slope of batch profile) for a MPC Virtual Plant can generate optimum and reference profiles Virtual plant can generate inferential measurements Controller tuning rules reduce to Ziegler Nichols reaction curve rule Controller tuning settings determine IAE Dead time from process dead time, control execution interval, scan time, or wireless communication time interval has little effect if it is less than what is the dead time implied from controller tuning

Questions and Discussion

Related Resources from ISA Phone: (919) Address: McMillan, Gregory and Cameron, Robert, Advanced pH Measurement and Control, 3rd edition, Instrumentation, Automations, and Systems (ISA), McMillan, Gregory, Good Tuning – a Pocket Guide, 2nd edition, Instrumentation, Automations, and Systems (ISA), 2005.