Unscented Kalman Filter for a coal run-of-mine bin IFAC MMM 2015 Workshop Unscented Kalman Filter for a coal run-of-mine bin Jonathan Meyer, VICENTE ALVARADO – EXXARO PROF. IAN CRAIG – UNIVERSITY OF PRETORIA

Bin Dynamic Model and INDUSTRIAL DATA identification Agenda Introduction Bin Dynamic Model and INDUSTRIAL DATA identification Unscented kalman filter UKF Simulation Results Summary

Introduction General control loop Coal run-of-mine bin operation State observers and LITERATURE ON DYNAMIC MODELS

Introduction GENERAL CONTROL LOOP: In scope Out of scope

COAL RUN-OF-MINE BIN OPERATION Introduction Manual density control COAL RUN-OF-MINE BIN OPERATION Classify run-of-mine (ROM) coal for bin storage Module one DMC Manual feeder control Duff product Manual level control Manual density control Stockpile Bin Crush and screen Module two DMC Duff product Manual density control Plant two DMS Manual feeder control Metallurgical coal Thickeners Bin scope

ESTIMATE VALUES OF STATE VARIABLES: Introduction ESTIMATE VALUES OF STATE VARIABLES: Estimation of the bin model state variables Various observers include: Particle filters Batch filters Exact recursive filters Extended Kalman filter Unscented Kalman filter Unscented Kalman filter chosen as it uses nonlinear state-space model with no approximations

Dynamic models only available for simple fixed area vessels Introduction DYNAMIC MODELS: Dynamic models only available for simple fixed area vessels No dynamic models for stockpile bin geometry or variable area vessels Bin models available normally use discrete element methods Limited minerals processing dynamic models Screens Ball mills Double-roll crushers

Bin dynamic model and Industrial data identification DEVELOPMENT OF DYNAMIC BIN MODEL SYSTEM IDENTIFIICATION RESULTS ADVANCED BIN MODEL DEVELOPMENT

Bin dynamic model and Industrial data identification Inputs: 𝑾 𝒃,𝒊 = Feed mass flow rate 𝑾 𝒃,𝒐,𝟑 = Bin 3 mass flow rate 𝒇 𝒃𝒇,𝟏 = Bin 1 feeder frequency 𝒇 𝒃𝒇,𝟐 = Bin 2 feeder frequency Outputs: 𝑾 𝒃𝒇,𝒐,𝟏 = Bin 1 mass flow rate 𝑾 𝒃𝒇,𝒐,𝟐 = Bin 2 mass flow rate 𝒉 𝒃 = Bin level Parameters: 𝜷 𝒃 = Bin height ratio 𝝆 𝒃 = Bin bulk density 𝑨 𝒃 = Bin base area 𝝉 𝒃𝒇,𝟏 = Bin 1 feeder time constant 𝑲 𝒃𝒇,𝟏 = Bin 1 feeder constant 𝝉 𝒃 f,2 = Bin 2 feeder time constant 𝑲 𝒃 f,2 = Bin 2 feeder constant States: 𝒎 𝒃 = Bin mass 𝒎 𝒃𝒇,𝟏 = Bin 1 feeder mass 𝒎 𝒃𝒇,𝟐 = Bin 2 feeder mass

Bin dynamic model and Industrial data identification CONSERVATION OF MASS (SIMPLIFIED): Found nonlinear relationship in bin level 𝑨𝒄𝒄𝒖𝒎𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝒎𝒂𝒔𝒔 = 𝑴𝒂𝒔𝒔 𝒊𝒏 − 𝑴𝒂𝒔𝒔 𝒐𝒖𝒕

Bin dynamic model and Industrial data identification SIMPLIFIED BIN MODEL FIT AND CORRELATION: FURTHER ANALYTICAL ANALYSIS: Found nonlinear relationship in feeder operation and mass flow proportionality constants Output Fit (%) Correlation Bin 1 mass flow 75.0 0.97 Bin 2 mass flow 73.7 Bin level 40.7 0.83 Linear Inverse exponential Sigmoid

Bin dynamic model and Industrial data identification ADVANCED BIN MODEL SYSTEM IDENTIFICATION: Three experimental sets of data used for each phase Experiment one – Primarily phase I and II

Bin dynamic model and Industrial data identification ADVANCED BIN MODEL SYSTEM IDENTIFICATION: Three experimental sets of data used for each phase Experiment two– Primarily phase II and III

Bin dynamic model and Industrial data identification ADVANCED BIN MODEL SYSTEM IDENTIFICATION: Three experimental sets of data used for each phase Experiment three– Phase III

Bin dynamic model and Industrial data identification ADVANCED BIN MODEL FIT AND CORRELATION: Experiment Output Fit (%) Correlation One Bin 1 mass flow 79.7 0.99 Bin 2 mass flow 64.3 Bin level 71.8 1.00 Two 45.4 0.85 53.8 0.90 49.0 Three 76.2 0.98 66.9 0.95 54.3

Bin dynamic model and Industrial data identification ADVANCED BIN MODEL: Nonlinear relationship in: Bin level Bin feeders Simulated over same industrial production data as in simplified model

Bin dynamic model and Industrial data identification ADVANCED BIN MODEL FIT AND CORRELATION: Output Fit (%) Correlation Bin 1 mass flow 88.9 0.99 Bin 2 mass flow 87.1 Bin level 54.2 0.95

Unscented Kalman Filter UNSCENTED KALMAN FILTER ALGORITHM

Unscented Kalman Filter UNSCENTED KALMAN FILTER (UKF) ALGORITHM: Nonlinear state-space representation of dynamic model Recursive estimation of 𝒙 𝒌 by, Unscented transform (UT) is used to calculate the statistics of random variables [sigma vectors 𝜒 𝑖 through nonlinear function 𝛾 𝑖 =g 𝜒 𝑖 ] Initialise the algorithm with original state ( P 𝟎 𝒂 ), process noise ( P 𝒗 ) and measurement noise ( P 𝒏 ) 𝒚=𝒇 𝒙,𝒖,𝜽 𝒅𝒙 𝒅𝒕 =𝒈(𝒙,𝒖,𝜽) 𝒙 𝒌 = (prediction of 𝒙 𝒌 ) + 𝜿 𝒌 [ 𝒚 𝒌 −( prediction of 𝒚 𝒌 )]

Unscented Kalman Filter UNSCENTED KALMAN FILTER (UKF) ALGORITHM: Original state ( P 𝟎 𝒂 ) Process noise ( P 𝒗 ) Measurement noise ( P 𝒏 ) Initialise P 𝟎 𝒂 = I 𝟒 Standard deviation of measurements P 𝒗 = Q 𝟐 Simulate Scaling factor Fit acceptable? No Yes P 𝒏 = 𝑟 2 I 𝟑 𝑟=0.01 Complete

UKF Simulation results SIMPLIFIED BIN UKF RESULTS ADVANCED BIN UKF RESULTS

UKF Simulation Results SIMPLIFIED BIN MODEL:

UKF Simulation Results SIMPLIFIED BIN UKF FIT AND CORRELATION: Output Fit (%) Correlation Bin 1 mass flow 99.5 1.00 Bin 2 mass flow 99.3 Bin level 99.8

UKF Simulation Results ADVANCED BIN MODEL:

UKF Simulation Results ADVANCED BIN UKF FIT AND CORRELATION: Output Fit (%) Correlation Bin 1 mass flow 99.5 1.00 Bin 2 mass flow 99.3 Bin level 99.7

Summary SUMMARY OF ALL RESULTS FUTURE WORK

MODEL AND UKF FIT RESULTS COMPARISON SUMMARY: Simplified bin model: Advanced bin model Output Model Fit (%) UKF Fit (%) Bin 1 mass flow 75.0 99.5 Bin 2 mass flow 73.7 99.3 Bin level 40.7 99.8 Output Model Fit (%) UKF Fit (%) Bin 1 mass flow 88.9 99.5 Bin 2 mass flow 87.1 99.3 Bin level 54.2 99.7

Summary PROPOSED FUTURE WORK: Implement UKF online over longer time period to validate Develop model-based controller for bin system Implement model-based controller with UKF state estimator Explore the use of the UKF for online parameter identification

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