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Generalized Models

Generalized and Uncertain LTI Models

Generalized LTI Models represent systems having a mixture of fixed coefficients and tunable or uncertain coefficients. Generalized LTI models arise from combining numeric LTI models with Control Design Blocks. For more information about tunable Generalized LTI models and their applications, see Models with Tunable Coefficients.

Uncertain LTI Models are a special type of Generalized LTI model that include uncertain coefficients but not tunable coefficients. For more information about using uncertain models, see Uncertain State-Space Models (uss) and Create Uncertain Frequency Response Data Models in the Robust Control Toolbox™ documentation.

FamilyModel TypeDescription
Generalized LTI ModelsgenssGeneralized LTI model arising from combination of Numeric LTI models (except frd models) with Control Design Blocks
genfrdGeneralized LTI model arising from combination frd models with Control Design Blocks
Uncertain LTI Models (requires Robust Control Toolbox software)ussGeneralized LTI model arising from combination of Numeric LTI models (except frd models) with uncertain Control Design Blocks
ufrdGeneralized LTI model arising from combination frd models with uncertain Control Design Blocks

Control Design Blocks

Control Design Blocks are building blocks for constructing tunable or uncertain models of control systems. Combine tunable Control Design Blocks with numeric arrays or Numeric LTI models to create Generalized Matrices or Generalized LTI models that include both fixed and tunable components.

Tunable Control Design Blocks include tunable parameter objects as well as tunable linear models with predefined structure. For more information about using tunable Control Design Blocks, see Models with Tunable Coefficients.

If you have Robust Control Toolbox software, you can use uncertain Control Design Blocks to model uncertain parameters or uncertain system dynamics. For more information about using uncertain blocks, see Uncertain LTI Dynamics Elements, Uncertain Real Parameters, and Uncertain Complex Parameters and Matrices in the Robust Control Toolbox documentation.

The following tables summarize the available types of Control Design Blocks.

Dynamic System Model Control Design Blocks

FamilyModel TypeDescription
Tunable Linear Componentsltiblock.gainTunable gain block
ltiblock.tfSISO fixed-order transfer function with tunable coefficients
ltiblock.ssFixed-order state-space model with tunable coefficients
ltiblock.pidOne-degree-of-freedom PID controller with tunable coefficients
ltiblock.pid2Two-degree-of-freedom PID controller with tunable coefficients
Uncertain Dynamics (requires Robust Control Toolbox software)ultidynUncertain linear time-invariant dynamics
udynUnstructured uncertain dynamics
Switch BlockloopswitchSwitch for marking potential loop-opening location in model

Static Model Control Design Blocks

FamilyModel TypeDescription
Tunable ParameterrealpTunable scalar parameter or matrix
Uncertain Parameters (requires Robust Control Toolbox software)urealUncertain real scalar
ucomplexUncertain complex scalar
ucomplexmUncertain complex matrix

Generalized Matrices

Generalized Matrices extend the notion of numeric matrices to matrices that include tunable or uncertain values.

Create tunable generalized matrices by building rational expressions involving realp parameters. You can use generalized matrices as inputs to tf or ss to create tunable linear models with structures other than the predefined structures of the Control Design Blocks. Use such models for parameter studies or some compensator tuning tasks.

If you have Robust Control Toolbox software, you can create uncertain matrices by building rational expressions involving uncertain parameters such as ureal or ucomplex.

Model TypeDescription
genmatGeneralized matrix that includes parametric or tunable entries
umat (requires Robust Control Toolbox software)Generalized matrix that includes uncertain entries

For more information about generalized matrices and their applications, see Models with Tunable Coefficients.

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