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gramOptions

Options for the gram command

Syntax

opt = gramOptions
opt = gramOptions(Name,Value)

Description

opt = gramOptions returns an option set with the default options for gram.

example

opt = gramOptions(Name,Value) returns an options set with the options specified by one or more Name,Value pair arguments.

Examples

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Compute the controllability Gramian of the following state-space model. Focus the computation on the frequency interval with the most energy.

sys = ss([-.1 -1;1 0],[1;0],[0 1],0);

The model contains a peak at 1 rad/s. Use gramOptions to specify an interval around that frequency.

opt = gramOptions('FreqIntervals',[0.8 1.2]);
gc = gram(sys,'c',opt)
gc = 2×2

    4.2132   -0.0000
   -0.0000    4.2433

Input Arguments

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Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: 'FreqIntervals',[0.8 1.2]

Frequency intervals for computing frequency-limited controllability and observability Gramians, specified as a matrix with two columns. Each row specifies a frequency interval [fmin fmax], where fmin and fmax are nonnegative frequencies, expressed in the frequency unit of the model. For example:

  • To restrict the computation to the range between 3 rad/s and 15 rad/s, assuming the frequency unit of the model is rad/s, set FreqIntervals to [3 15].

  • To restrict the computation to two frequency intervals, 3-15 rad/s and 40-60 rad/s, use [3 15; 40 60].

  • To specify all frequencies below a cutoff frequency fcut, use [0 fcut].

  • To specify all frequencies above the cutoff, use [fcut Inf] in continuous time, or [fcut pi/Ts] in discrete time, where Ts is the sample time of the model.

The default value, [], imposes no frequency limitation and is equivalent to [0 Inf] in continuous time or [0 pi/Ts] in discrete time. However, if you specify a TimeIntervals value other than [], then this limit overrides FreqIntervals = []. If you specify both a TimeIntervals value and a FreqIntervals value, then the computation uses the union of these intervals.

Time intervals for computing time-limited controllability and observability Gramians, specified as a matrix with two columns. Each row specifies a time interval [tmin tmax], where tmin and tmax are nonnegative times, expressed in the time unit of the model. For example:

  • To restrict the computation to the range between 3 s and 15 s, assuming the time unit of the model is seconds, set TimeIntervals to [3 15].

  • To restrict the computation to two time intervals, 3-15 s and 40-60 s, use [3 15; 40 60].

  • To specify all times from zero up to a cutoff time tcut, use [0 tcut]. To specify all times after the cutoff, use [tcut Inf].

The default value, [], imposes no time limitation and is equivalent to [0 Inf]. However, if you specify a FreqIntervals value other than [], then this limit overrides Timeintervals = []. If you specify both a TimeIntervals value and a FreqIntervals value, then the computation uses the union of these intervals.

Output Arguments

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Options for gram, returned as a gramOptions options set. Use opt as the last argument to gram to compute time-limited or frequency-limited Gramians.

See Also

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Introduced in R2016a