28 Questions
In representing multiple subsystems as a single transfer function, which graphical representation is usually used for frequency-domain analysis and design?
Block diagrams
How are transfer functions represented in signal-flow graphs?
As lines
What is implicit in signal-flow graphs?
Summing
Why are signal-flow graphs considered convenient for state-space analysis and design?
They represent state variables explicitly
What is the reason for a particular choice of state variables?
To decouple the system of simultaneous differential equations
What is the objective of representing multiple subsystems via block diagrams or signal-flow graphs?
To reduce the representation to a single transfer function
What are the elements of a block diagram of a linear, time-invariant system?
Signals, systems, summing junctions, and pickoff points
What is implicit in signal-flow graphs?
Summing junctions and pickoff points
What is used to derive the system’s transfer function from the signal-flow graph?
Mason’s rule
What do systems in state space use to be represented using different sets of variables?
Different sets of variables
What is the next topic of discussion after the representation of systems using different sets of variables?
System stability
What effect does system stability have on designing a system?
It is crucial for designing a system for the desired transient response
What is the purpose of Mason’s rule in signal-flow graphs?
To derive the system’s transfer function
What do signal-flow graphs consist of?
Nodes representing signals and lines with arrows representing subsystems
What is the objective of reducing a complicated block diagram to a single transfer function?
Relating input to output
What is the primary reason for choosing a particular representation of systems in state space?
Different physical meanings of state variables
What techniques are used to reduce block diagrams and signal-flow graphs to a single transfer function?
Block diagram algebra and Mason’s rule
In what ways can the methods for reducing block diagrams and signal-flow graphs be used?
For frequency-domain or state-space analysis
How are subsystems typically represented in block diagrams?
As blocks with inputs, outputs, and transfer functions
What happens when multiple interconnected subsystems are present in block diagrams?
Additional schematic elements are required
What are the common topologies for interconnecting subsystems that are examined?
Cascaded subsystems, parallel subsystems, and feedback form
What is discussed to establish familiar forms in block diagrams?
Basic block moves
When are equivalent block diagrams formed?
When transfer functions are moved
How can equivalences in block diagrams be verified?
By tracing input signals through to the output
What are the methods used for reducing block diagrams and signal-flow graphs to a single transfer function?
Block diagram algebra and Mason’s rule
Which topologies are examined for interconnecting subsystems?
Cascaded subsystems, parallel subsystems, and feedback form
What is used to find equivalent transfer functions for different topologies?
Equations derived from block diagram algebra
What can be done when familiar forms (cascade, parallel, feedback) are not apparent in block diagrams?
Basic block moves can be used to establish familiar forms
Study Notes
Techniques for Reducing Block Diagrams and Signal-Flow Graphs
- Techniques aim to reduce representations to a single transfer function
- Block diagram algebra and Mason’s rule are used for reduction
- Methods can be used for frequency-domain or state-space analysis
- Subsystems are represented as blocks with inputs, outputs, and transfer functions
- Multiple interconnected subsystems require additional schematic elements
- Common topologies for interconnecting subsystems are examined
- Cascaded subsystems, parallel subsystems, and feedback form are explored
- Equations derived to find equivalent transfer functions for different topologies
- Familiar forms (cascade, parallel, feedback) not always apparent in block diagrams
- Basic block moves discussed to establish familiar forms
- Equivalent block diagrams formed when transfer functions are moved
- Equivalences can be verified by tracing input signals through to the output
Test your knowledge of techniques for reducing block diagrams and signal-flow graphs with this quiz. Explore methods for simplifying representations to a single transfer function, including block diagram algebra and Mason’s rule. Learn how to analyze frequency-domain or state-space systems and understand common topologies for interconnecting subsystems.
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