Create option set for model order reduction
opts = balredOptions
opts = balredOptions('OptionName', OptionValue)
opts = balredOptions returns the default option set for the balred command.
opts = balredOptions('OptionName', OptionValue) accepts one or more comma-separated name/value pairs. Specify OptionName inside single quotes.
State elimination method. Specifies how to eliminate the weakly coupled states (states with smallest Hankel singular values). Specified as one of the following values:
Absolute and relative error tolerance for stable/unstable decomposition. Positive scalar values. For an input model G with unstable poles, balred first extracts the stable dynamics by computing the stable/unstable decomposition G → GS + GU. The AbsTol and RelTol tolerances control the accuracy of this decomposition by ensuring that the frequency responses of G and GS + GU differ by no more than AbsTol + RelTol*abs(G). Increasing these tolerances helps separate nearby stable and unstable modes at the expense of accuracy. See stabsep for more information.
Default: AbsTol = 0; RelTol = 1e-8
Offset for the stable/unstable boundary. Positive scalar value. In the stable/unstable decomposition, the stable term includes only poles satisfying
Increase the value of Offset to treat poles close to the stability boundary as unstable.
For additional information on the options and how to use them, see the balred reference page.
Compute a reduced-order approximation of the system given by:
Use the Offset option to exclude the pole at s = 10–6 from the stable term of the stable/unstable decomposition.
sys = zpk([-.5 -1.1 -2.9],[-1e-6 -2 -1 -3],1); % Create balredOptions opt = balredOptions('Offset',.001,'StateElimMethod','Truncate'); % Compute second-order approximation rsys = balred(sys,2,opt)
Compare the original and reduced-order models with bode: