Click to edit Master title style Fast Model Predictive Control Trevor Slade Reza Asgharzadeh John Hedengren Brigham Young University 3 Apr 2012
Discussion Overview Models for Fast Model Predictive Control (MPC) Selecting a Model for MPC Subspace Identification (Linear model) Parameter Estimation (Nonlinear model) Fast MPC Demonstrations with a 4 Tank Process PID Control Fast Linear MPC Fast Nonlinear MPC Comparison of Control Performance Next Generation Modeling and Control Platform
Selecting a Model for Predictive Control Many model forms Linear vs. Non-linear Steady state vs. Dynamic Empirical vs. First Principles Select the simplest model Accuracy requirements Steady State Gain Dynamics Time to Steady State Speed requirements PID < Linear MPC < Nonlinear MPC Continuous Form (SS x Ax Bu y Cx Du Discrete Form (SS x[ k y[ k] C Nonlinear Model 0 f 1] A x, x, u, p, d 0 g( x, u, p, d) 0 h( x, u, p, d) d d d ) x[ k] B x[ k] D u[ k] d c ) d u[ k]
Control Technology Overview Soderstrom, Hedengren, and Yang, Advanced Process Control in ExxonMobil Chemical Company: Successes and Challenges, AIChE 2010.
Discussion Overview Models for Fast Model Predictive Control (MPC) Selecting a Model for MPC Subspace Identification (Linear model) Parameter Estimation (Nonlinear model) Fast MPC Demonstrations with a 4 Tank Process PID Control Fast Linear MPC Fast Nonlinear MPC Comparison of Control Performance Next Generation Modeling and Control Platform
Multivariate 4 Tank Process Multiple Inputs (2) Pump 1 and Pump 2 Voltages Multiple Outputs (2) Height in Lower Tanks (1-2) Measured Characteristics Highly coupled system May exhibit inverse response Split fractions ( 1-2 ) drastically change system dynamics and steady state behavior
Capture Essential Dynamics with State Space Models SS Cont (5 states) SS Disc (5 states) FIR (120 states)
Determine Number of States Indicates that 5 states are sufficient for this Reduced Order Model (ROM)
Discussion Overview Models for Fast Model Predictive Control (MPC) Selecting a Model for MPC Subspace Identification (Linear model) Parameter Estimation (Nonlinear model) Fast MPC Demonstrations with a 4 Tank Process PID Control Fast Linear MPC Fast Nonlinear MPC Comparison of Control Performance Next Generation Modeling and Control Platform
Linear Model Identification Linear Empirical Model (ARX) 4 2 Observed data vs predictions of model: Output 1 Data Prediction 0-2 -4 0 50 100 150 200 250 300 350 400 Time (s) Observed data vs predictions of model: Output 2 4 Data 2 0-2 Prediction -4 0 50 100 150 200 250 300 350 400 Time (s)
Correlation of Residuals Residual Whiteness Correlation 1 0.5 Residual Correlation + Confidence Interval: Output 1 Residual Correlation 99% Confidence on Whiteness 0-0.5 0 5 10 15 20 25 Lag Residual Correlation + Confidence Interval: Output 2 1 0.5 Residual Correlation 99% Confidence on Whiteness 0-0.5 0 5 10 15 20 25 Lag
Model Step Response 8 Pump 1 Voltage Step Pump 2 Voltage Step Step Response 6 Height 1 4 2 0 8 6 Height 2 4 2 0 0 100 200 300 400 500 600 700 Time (seconds) 0 100 200 300 400 500 600 700
Discussion Overview Models for Fast Model Predictive Control (MPC) Selecting a Model for MPC Subspace Identification (Linear model) Parameter Estimation (Nonlinear model) Fast MPC Demonstrations with a 4 Tank Process PID Control Fast Linear MPC Fast Nonlinear MPC Comparison of Control Performance Next Generation Modeling and Control Platform
Nonlinear Parameter Estimation First Principles Model (DAE System) Determine valve characterization, split fractions, outlet flow constants (6 parameters) using PRBS generated data
Discussion Overview Models for Fast Model Predictive Control (MPC) Selecting a Model for MPC Subspace Identification (Linear model) Parameter Estimation (Nonlinear model) Fast MPC Demonstrations with a 4 Tank Process PID Control Fast Linear MPC Fast Nonlinear MPC Comparison of Control Performance Next Generation Modeling and Control Platform
Nonlinear Control in Simulink Implemented APMonitor controller into a Simulink plant simulation The controller runs at 5 Hz
Nonlinear Control in Simulink APM Simulink Interface 1000 500 Tank 1 Tank 2 0 1 2-500 Tank 3 Tank 4-1000 -1000-500 0 500 1000
NLC (Nonlinear) Control Performance Reverse doublet test results from Simulink simulation: Tank 1 system response using NLC Tank 2 system response using NLC
Discussion Overview Models for Fast Model Predictive Control (MPC) Selecting a Model for MPC Subspace Identification (Linear model) Parameter Estimation (Nonlinear model) Fast MPC Demonstrations with a 4 Tank Process PID Control Fast Linear MPC Fast Nonlinear MPC Comparison of Control Performance Next Generation Modeling and Control Platform
PID Control Performance Disturbance 1 =0.8 Set point changes Inlet flows
MPC (Linear) Control Performance Disturbance 1 =0.8 Set point changes Inlet flows
Trends of state variables and disturbances
NLC (Nonlinear) Control Performance Disturbance 1 =0.8 Set point changes Inlet flows
CPU Performance Traditional MPC CPUTime (sec) 1.4 1.2 1 0.8 0.6 0.4 Summary of Solution Times Windows 7, Intel i7, 8 CPU SSHD, gcc Compiler PID MPC Solve MPC Total NLC Solve NLC Total 0.2 0 0 10 20 30 40 50 60 70 Cycle 1 0.9 0.8 0.7 CentOS Linux, AMD, 64 CPU 15k RPM HD, Intel Compiler PID MPC Solve MPC Total NLC Solve NLC Total CPUTime(sec) 0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 Cycle
CPU Performance Optimized 0.35 0.3 0.25 CPUTime (sec) 0.2 0.15 0.1 Windows 7, Intel i7, 8 CPU SSHD, gcc Compiler PID MPC Solve MPC Total NLC Solve NLC Total 0.05 0 0 10 20 30 40 50 60 70 Cycle 0.2 0.18 0.16 CPUTime (sec) 0.14 0.12 0.1 0.08 0.06 CentOS Linux, AMD, 64 CPU 15k RPM HD, Intel Compiler PID MPC Solve MPC Total NLC Solve NLC Total 0.04 0.02 0 0 10 20 30 40 50 60 70 Cycle
Next Generation Control Next Generation Modeling and Control Platform? Address usability issues Integrated with Distributed Control System (DCS) Operate efficiently and reliably Use in base control as a replacement for PID control Does storage and retrieval have a place? APM Software