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ANALYSIS

Frequency Response Analysis ​

The Frequency Response Analysis computes the frequency response from an input analysis point to one or more output analysis points in a model. This is useful for identifying system dynamics, resonance, and bandwidth, and for validating models against experimental data.

Method Overview ​

Frequency-response analysis excites the system with a wide range of frequencies (chirp or multisine) and estimates the transfer function from a specified input to one or more specified outputs over the selected frequency range. The result is typically visualized as a Bode plot (magnitude and phase).

  • Chirp excitation: A single frequency-swept signal, fast and efficient for most systems.

  • Multisine excitation: Multiple experiments are performed, each one with a different frequency. This alternative is typically slower but more accurate.

Example Definition ​

We set w_motor to zero to analyze the system response around a stationary operating point, avoiding controller saturation. To make MTK's initialization deterministic we wrap the test model in a component that adds guess statements for the algebraic variables that would otherwise have cyclic guesses:

dyad
component DCMotorForFrequencyResponse
  extends DyadExampleComponents.TestDCMotorLoadControlled(w_motor = 0)
relations
  guess controller.u_s = 0
  guess controller.u_m = 0
  guess motor.R1.v = 0
  guess motor.emf.tau = 0
  guess motor.friction.phi_rel = 0
  guess controller.proportional.y = 0
  guess controller.add_pid.y = 0
  guess controller.derivative.y = 0
end

analysis DCMotorFrequencyResponse
  extends DyadControlSystems.FrequencyResponseAnalysis(
    input   = "r",
    outputs = ["y"],
    wl = 0.1,
    wu = 100.0
  )
  model = DCMotorForFrequencyResponse()
end
julia
using DyadInterface: artifacts
asol = DCMotorFrequencyResponse()
artifacts(asol, :BodePlot)

The resulting Bode plot shows the frequency response from the reference input r to the measured output y. The magnitude plot reveals the system bandwidth and resonance characteristics, while the phase plot indicates stability margins and time delays in the control loop.

Analysis Arguments ​

The following arguments define a FrequencyResponseAnalysis:

Required Arguments ​

  • model: The model to be analyzed.

  • input::String: Name of the input analysis point.

  • outputs::Vector{String}: Names of the output analysis points. Can be a single output or multiple outputs for MIMO analysis.

  • wl: Lower frequency bound for the analysis.

  • wu: Upper frequency bound for the analysis.

Optional Arguments ​

  • input_type::String = "chirp": Type of excitation signal, either "chirp" or "multisine".

  • num_frequencies::Int = 50: Number of frequencies (only for "multisine").

  • duration::Float64 = -1.0: Duration of the experiment (for chirp). If -1, use default.

  • Ts::Float64 = -1.0: Sample time for the experiment. If -1, use default based on the frequency range.

Artifacts ​

A FrequencyResponseAnalysis returns the following artifact:

Standard Plot ​

  • BodePlot: Bode plot (magnitude and phase) of the transfer function from input to each output.

Further Reading ​