Mechatronics Systems: Linearity and Sensitivity

Questions and Answers

Output is directly proportional to input

Small input changes result in large output changes

Closeness of the system's output to its true value

Produces identical outputs for repeated inputs Signup and view all the answers

System returns to its equilibrium state after a disturbance Signup and view all the answers

It enables the use of linear approximation within a certain range Signup and view all the answers

Large input changes result in small output changes Signup and view all the answers

Critical in applications where precise measurements are required Signup and view all the answers

Study Notes

Definition: The ability of a system to respond proportionally to changes in input
Characteristics:
- Ideal linear system: output directly proportional to input
- Real-world systems: non-ideal, but approximated as linear within a certain range
- Linearity is important for system analysis and design

Definition: The ratio of change in output to change in input
Characteristics:
- Measures how much the output changes in response to a unit change in input
- High sensitivity: small input changes result in large output changes
- Low sensitivity: large input changes result in small output changes
- Importance: crucial in system design for amplification or attenuation of signals

Definition: The closeness of the system's output to its true value
Characteristics:
- Measures how close the system's output is to the actual value
- High accuracy: system output is very close to true value
- Low accuracy: system output is far from true value
- Importance: critical in applications where precise measurements are required

Definition: The ability of a system to produce the same output for repeated inputs
Characteristics:
- Measures how consistent the system's output is for identical inputs
- High repeatability: system produces same output for repeated inputs
- Low repeatability: system produces varying outputs for repeated inputs
- Importance: essential in applications where consistent results are required

Definition: The ability of a system to return to its equilibrium state after a disturbance
Characteristics:
- Measures how well the system resists changes to its output
- Stable system: returns to equilibrium state after a disturbance
- Unstable system: output diverges or oscillates after a disturbance
- Importance: critical in applications where system stability is essential for safety and performance

A system is considered linear if its output responds proportionally to changes in input
Ideal linear systems have outputs directly proportional to inputs
Real-world systems are non-ideal, but can be approximated as linear within a certain range
Linearity is crucial for system analysis and design

Sensitivity is the ratio of change in output to change in input
It measures how much the output changes in response to a unit change in input
High sensitivity means small input changes result in large output changes
Low sensitivity means large input changes result in small output changes
Sensitivity is critical in system design for amplification or attenuation of signals

Repeatability is the ability of a system to produce the same output for repeated inputs
It measures how consistent the system's output is for identical inputs
High repeatability means the system produces the same output for repeated inputs
Low repeatability means the system produces varying outputs for repeated inputs
Repeatability is essential in applications where consistent results are required

Stability is the ability of a system to return to its equilibrium state after a disturbance
It measures how well the system resists changes to its output
A stable system returns to its equilibrium state after a disturbance
An unstable system's output diverges or oscillates after a disturbance
Stability is critical in applications where system stability is essential for safety and performance