Armature Voltage Control of Motor System

Standard Information

• Vairables:
  • x[k] the input at time k (control voltage)
  • y[k] the output at time k (speed of motor)
• Transfer Function (make-up parameter):
  y(s)/x(s) = 1/(s^2 + 2.5*s + 1)
• Difference Equation (sampling time 0.01 s):
  y[k] - 1.9752*y[k-1] + 0.9753*y[k-2] = 4.9585e-5*x[k-1] + 4.9174e-5*x[k-2]

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] - 1.9752*y[k-1] + 0.9753*y[k-2] = 4.9585e-5*x[k-1] + 4.9174e-5*x[k-2]
  • Ideal input + Noise:
    y[k] - 0.4335*y[k-1] - 0.5076*y[k-2] = 0.1821*x[k-1] - 0.1400*x[k-2]
• RARX Method Result
  • Ideal input:
    y[k] - 1.9752*y[k-1] + 0.9753*y[k-2] = 4.9585e-5*x[k-1] + 4.9171e-5*x[k-2]
  • Ideal input + Noise:
    y[k] + 0.6554*y[k-1] + 0.5217*y[k-2] = -1.8035*x[k-1] + 3.7472*x[k-2]
• 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)