Specify Options for Proper Orthogonal Decomposition in Model Reducer

Visualization Settings

Frequency vector

For sparse models, the dialog allows you to specify the frequencies at which to compute and plot the frequency response.

State Data Collection

Frequency focus

Frequency range of interest in rad/s, specified as a vector of form [fmix,fmax]. Use this option to specify a range where the POD approximation must be most accurate.

Excitation

Excitation signal for simulation, specified a Impulse, Chirp, or PRBS.

  • Impulse — Use Dirac impulse δ(t) in continuous time and a unit pulse in discrete time. This is the same notion as simulation using impulse.

  • Chirp — Use a chirp pulse covering about one decade.

  • PRBS — Use a pseudorandom binary sequence.

Reduction Settings

Preserve DC gain

Select this option to preserve the DC gain (steady-state value of step response) to match the time response better. Otherwise, the software tends to match the frequency response better.

Remove bias from POD data

Select this option to subtract the mean state value from the POD data. Biases typically only affect the largest hankel singular values (HSV) and have limited impact on the quality of the approximation except for a tendency to emphasize low frequency. The main impact of biases is to skew the error and loss values, making it harder to select the order.

POD algorithm

Proper orthogonal decomposition algorithm, specified as one of the following.

  • Balanced — This algorithm preserves the input-output response and considers both the input-to-state and state-to-output maps.

  • Galerkin — This algorithm focuses on dominant mode shapes and only considers input-to-state map.

  • Compress — This algorithm is a variant of the balanced algorithm and is typically faster when you have tall or wide models (few inputs, many outputs or many inputs, few outputs).

Input weight and Output weight

Static input and output weights, specified as matrices of size compatible with model inputs and outputs. Use these weights for input and output scaling in MIMO models, or to implicitly reduce the input-output size in large MIMO models. The software applies POD to the smaller model Wy(sys)Wu to obtain the model order reduction projectors. Here, Wy is the output weight and Wu is the input weight. The reduced model has the same input-output size as the original model.

Advanced

  • SVD tolerance — Relative rank tolerance, specified as a scalar value between 0 and 1. This tolerance controls how many principal components (state dimensions) to retain in the POD and is used for SVD truncation during the POD process.

  • Compression tolerance — Relative tolerance for input-output compression, specified as a scalar value between 0 and 1. This option controls the amount of output or input compression in the "compress" algorithm.

  • Simulation steps — Number of steps per simulation, specified as a positive scalar value. Use this option to specify how many fixed steps to take in the continuous-time simulations. The default value is usually sufficient for well-damped systems. You may require more steps for undamped or poorly damped systems.

See Also

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