Ramesh R. Rao Isermann Department of Chemical Engineering Rensselaer Polytechnic Institute Applications of Model Predictive Control Glass Forehearth Control Drug Infusion Control

Chemical Process Control Group at RPI Kevin Schott: Multiple model adaptive control (MMAC) Manoel de Carvalho: CVD reactor modeling and control Ramesh Rao: Drug infusion control, multiple model predictive control (MMPC), gain scheduling Vinay Prasad: batch operability/safety, multirate estimation and control Brian Aufderheide: Drug infusion and MMPC Deepak Nagrath: optimization of chromatographic separations, run-to-run control Sandra Lynch: insulin infusion control Vikas Saraf: Autotuning for unstable cascade processes

Chemical Process Control Group at RPI Fundamental process control theory and applications to practical problems, with a focus on the effect of nonlinearity on control and the interaction of process design and control. Biomedical systems: regulation of hemodynamic variables of patients in critical care or surgery. Automated infusion of insulin for diabetics. Optimization of chromatographic separations: off- line and run-to-run optimization of protein separations. Batch reactor operability and safety, multirate nonlinear model predictive control.

Control of a Glass Cooling Forehearth Motivation u Downstream product quality dependent on temperature u Open-loop unstable process u Requires tight regulation of temperature Illustration source: (

Glass Cooling Forehearth T0T0 T6T6 T c1 T c3 T c5 T2T2 T4T4

Steady-State Energy Balance

Steady-States & Eigen Values

Control System Description Control of temperature in 3 zones of the forehearth [T 2, T 4, T 6 ] by manipulating [T c1, T c3, T c5 ] Need to operate at open-loop unstable steady state operating point Existence of model mismatch between plant and model in addition to unmeasured disturbances and measurement noise EKF based nonlinear MPC is used for state estimation and control u explicit handling of constraints u inferential control

Estimation and Control Strategy Extended Kalman filtering (EKF) is used to obtain current estimates of model states. Disturbances are modeled as integrated white noise states augmented to the original model. Nonlinear MPC algorithm uses EKF state estimates to predict future values of states and controlled outputs, which are then used to calculate the optimal manipulated variable action. Both the EKF and the nonlinear MPC algorithms are based on successive linearization of nonlinear model.

Estimation using EKF

EKF Equations Model prediction Kalman filter gain and covariance Measurement correction

Interaction of Estimation and Control

Setpoint tracking Parameter estimation  Viscosity parameter  Unmeasured disturbance u fluctuations in flow rate M 0 Bias in heating circuit [T c1, T c3, T c5 ] Bias in output measurements [T 2, T 4, T 6 ] Control parameters: u sample time 10 minutes u constraints on inputs 5 deg. C per 10 min u prediction horizon P = 20, control horizon N = 3, output weights Q 1:1:5, input weights R 1:1:1, Gaussian noise 0.1 deg. C Results

Summary of Glass Forehearth Control A first principles model was developed and parameters were identified from plant data EKF based NLMPC was developed and tested in simulation studies Setpoint tracking and regulatory control in the presence of disturbances was achieved

Motivation For Drug Infusion Control Patients in critical care or surgery u require regulation of vital states Typical clinical practice u manual regulation with drip IV u programmable pumps (open loop) State of the art u clinical trials of closed loop control of mean arterial pressure (MAP) Control objective u automated regulation of hemodynamic variables with physician “in the loop” u free-up physician to monitor difficult-to-measure variables

Problem Overview Multivariable, nonlinear system u regulation of mean arterial pressure (MAP), cardiac output (CO) using sodium nitroprusside (SNP), phenylephrine (PNP) and dopamine (DPM) Inter- and intra-patient variability u requires on-line adaptation to patient conditions Interactions from anesthetics Presence of constraint specifications u inputs: drug dosage u outputs: setpoint specified as range, min or max Use model predictive control (MPC) to handle constraints explicitly u model should encompass drug responses

Controller Design Challenges Lack of models that encompass the wide variety of patient responses to drugs Models from first principles u fairly cumbersome u requires online parameter estimation/adaptation u not viable for real-time applications Empirical model fitting u step response tests u pseudo random binary sequence (PRBS) tests

Optimization Prediction r(k) Reference Model Plant 1 2 m Model Bank  u(k) y(k)  i (k) y(k) ^ w i (k) Weight Computation Constrained MPC X X X y i (k) ^ y(k+1:P) ^ Multiple-Model Predictive Control (MMPC)

Model Bank Parameters

MENNEN BAXTER ANESTHESIA ROTARY PUMPS DRUGS MAP CO Experimental Setup

MAP Regulation (SISO)

MAP and CO Regulation (MIMO)

Weighted-Model Tracking

MAP and CO Regulation (MIMO)

Summary of Drug Infusion Control Multiple-model predictive control approach u weighted model bank provides a flexible and bounded prediction model to handle inter- and intra-patient variability u handling constraints Controller issues u controller tuning u choice of model banks (model types, number of models) Future work u develop weighting scheme more conducive to blending u more experiments

Acknowledgements B. Wayne Bequette The Whitaker Foundation, NSF, Merck, P&G David M. Koenig, Corning Inc. Animal Research Facility – Albany Medical Center Vinay Prasad, Brian Aufderheide AspenTech