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 (Robust Control Toolbox) and Create Uncertain Frequency Response Data Models (Robust Control Toolbox).

Family	Model Type	Description
Generalized LTI Models	genss	Generalized LTI model arising from combination of Numeric LTI models (except frd models) with Control Design Blocks
	genfrd	Generalized LTI model arising from combination frd models with Control Design Blocks
Uncertain LTI Models (requires Robust Control Toolbox™ software)	uss (Robust Control Toolbox)	Generalized LTI model arising from combination of Numeric LTI models (except frd models) with uncertain Control Design Blocks
	ufrd (Robust Control Toolbox)	Generalized 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 (Robust Control Toolbox), Uncertain Real Parameters (Robust Control Toolbox), and Uncertain Complex Parameters and Matrices (Robust Control Toolbox).

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

Dynamic System Model Control Design Blocks

Family	Model Type	Description
Tunable Linear Components	tunableGain	Tunable gain block
	tunableTF	SISO fixed-order transfer function with tunable coefficients
	tunableSS	Fixed-order state-space model with tunable coefficients
	tunablePID	One-degree-of-freedom PID controller with tunable coefficients
	tunablePID2	Two-degree-of-freedom PID controller with tunable coefficients
Uncertain Dynamics (requires Robust Control Toolbox software)	ultidyn (Robust Control Toolbox)	Uncertain linear time-invariant dynamics
	umargin (Robust Control Toolbox)	Uncertain gain and phase
	udyn (Robust Control Toolbox)	Unmodeled dynamics
Analysis Point Block	AnalysisPoint	Points of interest for linear analysis or control system tuning

Static Model Control Design Blocks

Family	Model Type	Description
Tunable Parameter	realp	Tunable scalar parameter or matrix
Uncertain Parameters (requires Robust Control Toolbox software)	ureal (Robust Control Toolbox)	Uncertain real scalar
	ucomplex (Robust Control Toolbox)	Uncertain complex scalar
	ucomplexm (Robust Control Toolbox)	Uncertain 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 (Robust Control Toolbox) or ucomplex (Robust Control Toolbox).

Model Type	Description
genmat	Generalized matrix that includes parametric or tunable entries
umat (Robust Control Toolbox) (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.