y[k] + 0.98*y[k-1] = 5*10e-3*x[k-1]*w[k-1] + 3*x[k-1] + 2*10e-3*x[k]*x[k]

Standard Information

• Vairables:
  • x[k] the first input at time k
  • w[k] the second input at time k
  • xw[k] the modified input to represent 10e-3*x[k]*w[k] at time k
  • xx[k] the modified input to represent 10e-3*x[k]*x[k] at time k
  • y[k] the output at time k
• Difference Equation
  y[k] + 0.98*y[k-1] = 5*10e-3*x[k-1]*w[k-1] + 3*x[k-1] + 2*10e-3*x[k]*x[k]
• Modified Difference Equation
  y[k] + 0.98*y[k-1] = 5*xw[k-1] + 3*x[k-1] + 2*xx[k]

First Homework

• MATLAB file: hw1.m
• example input: graph
• simulated output: graph
• Ouput with Noise
  • Noise Amplitude: 10% of the maximum value of the output
  • Noise Characteristic: uniform random noise
  • simulated output + noise: graph
• ARX Method Result
  • Ideal input:
    y[k] + 0.98*y[k-1] = 5*xw[k-1] + 3*x[k-1] + 2*xx[k]
  • Ideal input + Noise:
    y[k] + 0.7438*y[k-1] = 4.3793*xw[k-1] + 0.7213*x[k-1] + 5.0416*xx[k]
• RARX Method Result
  • Ideal input:
    y[k] + 0.98*y[k-1] = 5*xw[k-1] + 3*x[k-1] + 2*xx[k]
  • Ideal input + Noise:
    y[k] + 0.4212*y[k-1] = 3.5561*xw[k-1] + 0.2339*x[k-1] + 5.0982*xx[k]
• Comparision of the Quality of Parameters (2 Feb 1996)
  • MATLAB file: hw1_e.m
  • Simulated output, graph, from ideal input with
    • the original parameter (yellow)
    • the parameter from ARX method when there is noise (red)
    • the parameter from RARX method when there is noise (green)