Using Lagged Spectral Data in Feedback Control Using Particle Swarm - - PowerPoint PPT Presentation

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Using Lagged Spectral Data in Feedback Control Using Particle Swarm - - PowerPoint PPT Presentation

Nov 21, 2023 419 likes •558 views

Using Lagged Spectral Data in Feedback Control Using Particle Swarm Optimisation Mr. Caleb Rascon Prof. Barry Lennox Dr. Ognjen Marjanovic Combining the strengths of UMIST and 1 The Victoria University of Manchester Using Spectral Data in

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Combining the strengths of UMIST and The Victoria University of Manchester

Using Lagged Spectral Data in Feedback Control Using Particle Swarm Optimisation

  • Mr. Caleb Rascon
  • Prof. Barry Lennox
  • Dr. Ognjen Marjanovic

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Combining the strengths of UMIST and The Victoria University of Manchester

Using Spectral Data in Monitoring

  • Pharmaceutical Industry

– Crystallisation of active ingredients (Yu et. al., 2003) – Confirm sample temperature – Identify material concentrations

  • Viable as observed variables in feedback control

– Or are they?

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Combining the strengths of UMIST and The Victoria University of Manchester

Difficulties of Using Spectral Measurements

  • Known for inconsistency due to:

– Instrument de-calibration – External and/or sample temperature – Presence of undesired material

  • Results in frequency displacement (aka, shift, lag)
  • Disastrous if using reference spectra for analysis

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Combining the strengths of UMIST and The Victoria University of Manchester

Classical Least Square Regression

  • D: a spectral measurement
  • S: set of reference spectra
  • C: set of concentrations
  • S and C need to be aligned

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C = DS(ST S)−1

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Combining the strengths of UMIST and The Victoria University of Manchester

Example: Components

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50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

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Controller Plant

1 s + 1 1 2s + 1 1 2s + 2 1 s + 2 s + 1 s + 0.001 2s + 1 s + 0.001 s + 2 s + 0.001 2s + 2 s + 0.001

50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Component 1 Spectrum

50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Component 2 Spectrum

50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Component 3 Spectrum

50 100 150 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Component 4 Spectrum White Noise (70 SNR)

Σ Π Π Π Π

Simulated Sampled Spectra Automatic Spectral Analysis (PSO or Least Squares) Benchmark (Components Spectra)

Σ Σ Σ Σ

Component 1 Concentration Component 2 Concentration Component 3 Concentration Component 4 Concentration Desired Component 1 Concentration (0.5) Desired Component 2 Concentration (0.6) Desired Component 3 Concentration (0.7) Desired Component 4 Concentration (0.8) Estimated Component 4 Concentration Estimated Component 3 Concentration Estimated Component 2 Concentration Estimated Component 1 Concentration Random Lag [0,20] Random Lag [0,20] Random Lag [0,20] Random Lag [0,20] Combining the strengths of UMIST and The Victoria University of Manchester

System

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2 4 6 8 10 12 14 16 18 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Combining the strengths of UMIST and The Victoria University of Manchester

Response using CLSR wo. Applying Lag

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2 4 6 8 10 12 14 16 18 20 0.2 0.4 0.6 0.8 1

Combining the strengths of UMIST and The Victoria University of Manchester

Response using CLSR Applying Lag

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Combining the strengths of UMIST and The Victoria University of Manchester

Approach as a Search Problem

  • Find combination of reference spectra that best fits sample
  • For each reference spectrum, look for:

– Magnitudes → concentrations – Shift suffered – [Others can be added…]

  • Use Euclidian distance to grade the combination

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Combining the strengths of UMIST and The Victoria University of Manchester

Particle Swarm Optimisation

  • Created by Kennedy in 1995
  • Simulates a flock of birds ‘flying’ in the solution space
  • Proven to do as well or better than Genetic Algorithms (Kennedy et.

al., 1995)

  • Easier to implement and visualise
  • Can incorporate the concept of inertia to speed up search

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2 4 6 8 10 12 14 16 18 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Combining the strengths of UMIST and The Victoria University of Manchester

Response using PSO Applying Lag

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Combining the strengths of UMIST and The Victoria University of Manchester

Comparison

Mean Square Error of responses using CLSR and PSO Component 1 2 3 4 MSE w. CLSR 0.9639 1.0171 0.6966 1.6604 MSE w. PSO 0.0339 0.0319 0.0375 0.0373

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The baseline of comparison is the response obtained when no lag was applied.

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Combining the strengths of UMIST and The Victoria University of Manchester

Conclusions & Future Work

  • Classical spectral analysis methods are frail towards lag
  • As a search problem, lag can be factored in

– Other disturbances too

  • Useful in monitoring:

– Inform the need for sensor calibration – Alternative temperature measurements

  • Search per sample: ~ 6 min

– Future work: shortening time of completion

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