03 Automatic Control Control System Representation

# 03 Automatic Control Control System Representation -...

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Control System Representation 1-Nov-16 Automatic Control

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Aims for this chapter Convert block diagrams to signal-flow diagrams. Reduce a block diagram of multiple subsystems to a single block representing the transfer function from input to output. Find the transfer function of multiple subsystems using Mason’s rule. Represent state equations as signal-flow graphs Represent multiple subsystems in state space in cascade, parallel, controller canonical, and observer canonical forms. Perform transformations between similar systems using transformation matrices; and diagonalize a system matrix
System Block Diagram Representation So far, we have been working with individual subsystems represented by a block with its input and output via considering Modeling & Linearization Laplace Transform & Input/output TF representation For more complicated systems, they are going to be represented by the interconnection of many subsystems u x x x x + + = sin 2 u x x + = ( ) ( ) ( ) 1 1 : + = = s s G s U s X TF ( ) s X ( ) s U ( ) s G modeling linearization Laplace Transform System Block Representation

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System Block Diagram Representation As you already know, a subsystem is represented as a block with an input, an output, and a transfer function. Many systems are composed of multiple subsystems based on the following fundamental signal flow Summation junction point Pickoff point
System Block Diagram Representation We will now examine some common topologies for interconnecting subsystems and derive the single transfer function representation for each of them. These common topologies will form the basis for reducing more complicated systems to a single block (or the so-called equivalent representation ). The topologies include: A. Cascade Form B. Parallel Form C. Feedback Form

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System Block Diagram Representation A. Cascade Form For the cascade form, it can be found that each signal is derived from the product of the input times the transfer function Equivalent Representation
System Block Diagram Representation B. Parallel Form Parallel subsystems have a common input and an output formed by the algebraic sum of the outputs from all of the subsystems. Equivalent Representation

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System Block Diagram Representation C. Feedback Form Note that the feedback system is the basis for our study of control systems engineering. Equivalent Representation