Detection and Diagnosis of Plant-wide Oscillations: An Application Study

Detection and Diagnosis of Plant-wide Oscillations: An Application Study Vinay Kariwala M.A.A. Shoukat Choudhury, Sirish L. Shah, J. Fraser Forbes, Edward S. Meadows Department of Chemical and Materials Engineering University of Alberta Hisato Douke, Haruo Takada Mitsubishi Chemical Corporation, Mizushima, Japan

Outline • Problem Description • Detection • Theory (Autocorrelation function) • Application Results • Diagnosis • Theory (Valve Stiction) • Application Results • Future Directions

Problem Description Condenser Feed Reflux Drum Top Product Stripper Side Stripper Bottom Product Oscillations in Condenser Level Distillation Column

Problem Description • Condenser Level • Oscillations with Large amplitude • Back-off from Optimal operating point • Economic Potential 1% increase in set points ~ 20M Yen/year • Previous attempts • PID tuning, MPC model • Not successful

Plant-wide Oscillation Detection

Heat Exchanger Chain Column 2 FC 4 FC 3 LC 10 LC 9 LC 8 LC 7 FC 8 TC 2 FC 7 FC 5 FC 6 LI 5 LI 4 LI 1 LC 3 LC 6 LC 11 PC 1 FI 2 LC 2 AC 2 TI 1 TI 4 TI 5 PC 4 PC 5 PC 2 TC 1 PC 3 LC 1 LC 5 LI 3 LC 4 LI 2 FC 1 FI 1 Compressor SI 1 FC 2 FI 3 AC 1 Column 1 TI 3 TI 6 TI 2 FI 4 Scope of Analysis

Data Description Data Set: 2880 samples, 1 min. data, Variables: 45 Tags + 15 Controller Outputs (MV) • 15 SISO control loops • 5 cascade control loops • 2 DMCs

Detection Philosophy • Which variables are oscillating? • Which variables have common oscillations? • Important to find • All variables with common oscillations • Root cause likely to lie within this set

Detection by Visual Inspection • Multiple oscillations destroy Regularity • Noise overshadows Oscillations Fourier Transform Time trends Power Spectrum Presence of Oscillation – Peak in Spectra Period and Regularity – Difficult to Judge

Detection using ACF Time Trend Power Spectrum Auto Correlation Function Effect of Noise Reduced ACF oscillates at same frequency as signal Regularity of oscillations – Zero Crossings of ACF

Detection using ACF ACF Zero Crossings Period of Oscillation Oscillation regular if

Clustering using ACF Two signals – same frequency oscillation if Oscillation considered significant if (Power in selected band)/(Power in entire spectrum) > Ref: Thornhill et al., JPC, 2003

Multiple Oscillations Fourier Transform Two peaks in Spectra Use Band pass filters Calculate ACF for each filtered signal

Detect and cluster oscillations Narrow ranges of band pass filters around detected oscillations Detection Algorithm Remove Non-stationary trends Repeat if more than one oscillations present in every filter range OR stop

Detection: Results Low frequency range • 158 min./cycle – 27 tags • 137 min./cycle – 10 tags Medium frequency range • 62 min./cycle – 11 tags • 75 min./cycle – 23 tags • 86 min./cycle – 5 tags High frequency range • 43 min./cycle – 5 tags • 25 min./cycle – 1 tag • 4 min./cycle – 1 tag Condenser Level

Heat Exchanger Chain Column 2 FC 4 FC 3 LC 10 LC 9 LC 8 LC 7 FC 8 TC 2 FC 7 FC 5 FC 6 LI 5 LI 4 LI 1 LC 3 LC 6 LC 11 PC 1 FI 2 LC 2 AC 2 TI 1 TI 4 TI 5 PC 4 PC 5 PC 2 TC 1 PC 3 LC 1 LC 5 LI 3 LC 4 LI 2 FC 1 FI 1 Compressor SI 1 FC 2 FI 3 AC 1 Column 1 TI 3 TI 6 TI 2 FI 4 Low frequency detections 158 samples/cycle 137 samples/cycle OP PV PV OP

Summary of Detection • Low frequency oscillations • 158 minute/cycle • 26 tags other than condenser level • Plant wide nature of oscillations revealed • Root cause should lie in this set

Diagnosis of Oscillations

Possible Reasons • Poorly tuned Controller • External disturbances • Process induced oscillations • Valve Problems • MPC model mismatch

Definition of Stiction stickband + deadband E F G moving phase D slip jump, j B A C deadband stickband s valve output (mv) valve input (op)

Test of Nonlinearity Central Idea: Nonlinear interactions between different frequencies Bispectrum DFT Normalized Bispectrum – squaredBicoherence

Linear and nonlinear Signal

Test of Non-linearity (cont’d) NGI>0 , NLI=0 NGI>0, NLI>0 NGI <= 0 Non-Gaussianity Index and Nonlinearity Index Critical Values of bic2crit is determined at 95% or 99% confidence interval of the squared bicoherence Gaussian Linear Non-Gaussian Linear Non-Gaussian Nonlinear Frequency independent Frequency dependent

Flow Control Loop in a Refinery Assumptions: • The process is locally linear in the current operating region • Disturbances entering the loop are linear Loop is Nonlinear NGI = 0.02 and NLI = 0.55

Pattern of Stiction in PV-OP Plot apparent stiction = maximum width of the cycles in pv-op plot PV PV OP OP

Quantification of Apparent Stiction 4 x 10 1.145 1.14 1.135 1.13 a b 1.125 PV  P Q 1.12 1.115 1.11 1.105 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.9 OP Apparent Stiction = 0.35 %

Nonlinearity Analysis

Stiction Quantification FC5 PC1 TC2 No Stiction 0.5% 1.25%

Research Directions • ACF based Detection Algorithm • False Detection, Premature Termination • Stiction Quantification • Assumption of linear disturbance • Path Analysis • Oscillation Propagation • Model Predictive Controller • Oscillations due to model mismatch

Acknowledgements • NSERC • Dr. Nina Thornhill, UK • Ebara San, Amano San, Oonodera San • Computer Process Control group

Detection and Diagnosis of Plant-wide Oscillations: An Application Study