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Model Interconnection

Series, parallel, and feedback connections; block diagram building

Interconnecting models of components allows you to construct models of control systems. You can conceptualize your control system as a block diagram containing multiple interconnected components, such as a plant and a controller connected in a feedback configuration. Using model arithmetic or interconnection commands, you combine models of each of these components into a single model representing the entire block diagram.


feedbackFeedback connection of multiple models
connectBlock diagram interconnections of dynamic systems
sumblkSumming junction for name-based interconnections
seriesSeries connection of two models
parallelParallel connection of two models
appendGroup models by appending their inputs and outputs
blkdiagBlock-diagonal concatenation of models
imp2expConvert implicit linear relationship to explicit input-output relation
invInvert models
ctransposeConjugate dynamic system model
lftGeneralized feedback interconnection of two models (Redheffer star product)
connectOptionsOptions for the connect command


Model Interconnection Basics

Why Interconnect Models?

Interconnecting models of system components allows you to construct models of control systems.

Connecting Models

This example shows how to model interconnections of LTI systems, from simple series and parallel connections to complex block diagrams.

Numeric Model of SISO Feedback Loop

Interconnect numeric LTI models to build a single model of a closed-loop system.

Control System Model With Both Numeric and Tunable Components

Interconnect fixed components and tunable components to build a tunable control system model.

Multi-Loop Control System

Build arbitrary block diagrams with any number of control loops by interconnecting models using the connect command.

MIMO Control System

Build a MIMO control system with both fixed and tunable components.

MIMO Feedback Loop

Obtain the closed-loop response of a MIMO feedback loop three different ways.

Using FEEDBACK to Close Feedback Loops

This example shows why you should always use FEEDBACK to close feedback loops.

Analysis Points

Mark Analysis Points in Closed-Loop Models

Insert analysis points at locations of interest when you build control system models. Use analysis points for extracting system responses from the model.

Control System with Multichannel Analysis Points

Build a control-system model with analysis points for extracting responses at different points in the system.

More About Model Interconnections

Catalog of Model Interconnections

Block diagram connections correspond to model interconnection commands or arithmetic expressions.

How the Software Determines Properties of Connected Models

When you interconnect models, the resulting model’s properties depend on the properties of the models you are connecting.

Rules That Determine Model Type

Precedence rules determine the resulting model type when you interconnect models of different types.

Recommended Model Type for Building Block Diagrams

Choice of model type can affect numerical accuracy when you interconnect models.

Preventing State Duplication in System Interconnections

This example shows guidelines for building minimum-order models of LTI system interconnections.