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reducespec

Create model order reduction specifications

Since R2023b

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    Syntax

    R = reducespec(sys,method)

    Description

    The reducespec function is the entry point for model order reduction workflows in Control System Toolbox™ and Robust Control Toolbox™ software. Use this function to create a model order reduction (MOR) task based on the model type and selected method.

    For information on configuring model order reduction tasks, see the object corresponding to your model type and selected algorithm. For details on how to select orders and obtain reduced-order models, see the corresponding view and getrom functions.

    Model TypeAlgorithmObjectObject Functions
    Linear time-invariant (LTI)Balanced truncationBalancedTruncation

    Balanced truncation of normalized coprime factors (NCF)

    		NCFBalancedTruncation
    Modal truncationModalTruncation
    Sparse LTIBalanced truncationSparseBalancedTruncation
    Modal truncationSparseModalTruncation

    This function creates only the MOR specification object and does not perform any computation. This allows you to properly configure options before you run the MOR algorithm, which can be computationally expensive in the case of sparse models.

    Tip

    For the full workflow, see Task-Based Model Order Reduction Workflow.

    example

    R = reducespec(sys,method) creates a model order reduction (MOR) specification object for a dense or sparse linear time-invariant (LTI) model sys. method is the model order reduction algorithm, specified as one of the following:

    • "balanced"

    • "ncf" (Requires Robust Control Toolbox software)

    • "modal"

    Examples

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    Open Live Script

    This example shows the basic workflow for obtaining reduced-order models using the task-based model order reduction workflow.

    Generate a random discrete-time state-space model with 40 states.

    rng(0)
sys = drss(40);

    Create a balanced truncation model-order reduction task using reducespec.

    R = reducespec(sys,"balanced");

    The function returns a BalancedTruncation object.

    View the graphical information to help decide the reduced order using the view function.

    view(R)

    Figure contains an axes object. The axes object with title Hankel Singular Values and Approximation Error, xlabel Order (Number of States), ylabel State Contribution contains 3 objects of type bar, line. These objects represent Unstable modes, Stable modes, Absolute error bound.

    For balanced truncation, view plots the state contributions in terms of the Hankel singular values.

    Obtain the reduced order model using getrom. For this example, select an order 15.

    rsys = getrom(R,Order=15);

    Compare the Bode response of both models.

    bode(sys,rsys,'r--')
legend("Original","Order 15")

    Figure contains 2 axes objects. Axes object 1 with ylabel Magnitude (dB) contains 2 objects of type line. These objects represent Original, Order 15. Axes object 2 with ylabel Phase (deg) contains 2 objects of type line. These objects represent Original, Order 15.

    Input Arguments

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    Dynamic system model, specified as an ordinary or sparse LTI model.

    This model must have a valid state-space representation, such as a tf, ss, sparss, or mechss model. For generalized or uncertain state-space models (genss, uss), the function uses the current value of the model. For identified models (idss), the function uses the identified value.

    Model order reduction algorithm, specified as one of these strings:

    • "balanced" — Use the balanced truncation algorithm. This method quantifies the state contributions to the I/O transfer and lets you discard states with weak contribution.

    • "ncf" — Use the balanced truncation algorithm applied to the normalized coprime factors (NCF) of sys. This method requires Robust Control Toolbox software and is available only for ordinary LTI models.

    • "modal" — Use the modal truncation algorithm. This method computes the system modes (poles) and lets you discard modes based on their location or DC contribution.

    Output Arguments

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    Model order reduction specification object, returned as one of the objects in this table. The type of object depends on the model type and algorithm.

    Model Type (sys)Algorithm (method)Object (R)
    LTI"balanced"BalancedTruncation
    "ncf"NCFBalancedTruncation
    "modal"ModalTruncation
    Sparse LTI"balanced"SparseBalancedTruncation
    "modal"SparseModalTruncation

    Limitations

    • Sparse modal truncation is currently limited to first-order models with A = AT and E = ET definite, or second-order models with K = KT, M = MT definite, and Rayleigh-type damping.

    • Sparse balanced truncation is currently limited to continuous-time models.

    References

    [1] Benner, Peter, Jing-Rebecca Li, and Thilo Penzl. “Numerical Solution of Large-Scale Lyapunov Equations, Riccati Equations, and Linear-Quadratic Optimal Control Problems.” Numerical Linear Algebra with Applications 15, no. 9 (November 2008): 755–77. https://doi.org/10.1002/nla.622.

    [2] Benner, Peter, Martin Köhler, and Jens Saak. “Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1—Philosophy, Features, and Application for (Parametric) Model Order Reduction.” In Model Reduction of Complex Dynamical Systems, edited by Peter Benner, Tobias Breiten, Heike Faßbender, Michael Hinze, Tatjana Stykel, and Ralf Zimmermann, 171:369–92. Cham: Springer International Publishing, 2021. https://doi.org/10.1007/978-3-030-72983-7_18.

    [3] Varga, A. “Balancing Free Square-Root Algorithm for Computing Singular Perturbation Approximations.” In [1991] Proceedings of the 30th IEEE Conference on Decision and Control, 1062–65. Brighton, UK: IEEE, 1991. https://doi.org/10.1109/CDC.1991.261486.

    [4] Green, M. “A Relative Error Bound for Balanced Stochastic Truncation.” IEEE Transactions on Automatic Control 33, no. 10 (October 1988): 961–65. https://doi.org/10.1109/9.7255.

    Version History

    Introduced in R2023b

    See Also

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