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ChE 182 Chemical Process Dynamics and Control

ChE 182 Chemical Process Dynamics and Control. Frequency Response Analysis. Frequency response analysis. -how a process responds to a sinusoidal forcing input -how the response depends on the frequency of the input

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ChE 182 Chemical Process Dynamics and Control

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  1. ChE 182Chemical Process Dynamics and Control Frequency Response Analysis

  2. Frequency response analysis -how a process responds to a sinusoidal forcing input -how the response depends on the frequency of the input -used for stability analysis, control system design, and robustness analysis

  3. Motivation for Frequency Response Analysis Problems with Routh Stability Criterion: • No measure of relative stability; does not indicate how much uncertainty can be tolerated before system becomes unstable • Only approximate results for processes with time-delay -These limitations are addressed by frequency response analysis

  4. Frequency response analysis Two ways to perform frequency response analysis: • Conversion of input signal to Laplace domain and inversion to time domain • Substitution of s = jω in the transfer function Two ways to present frequency response information: • Bode plot • Nyquist plot

  5. Method 1: First-order system Sinusoidal input:

  6. Method 1: First-order system As t →∞: Long-time response or Frequency response

  7. First-Order System Output signal amplitude: Amplitude ratio, AR: Normalized amplitude ratio, ARN:

  8. First-Order System

  9. Method 2: Stable Transfer Function

  10. Method 2: Stable Transfer Function

  11. Bode plot Plot of AR and φ as a function of ω • log-log plot of AR versus ω • semilog plot of φ versus ω

  12. Nyquist plot Polar plot of G(jω) and ∠G(jω) • plot of Im(ω) versus Re(ω)

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