System Stability at University Of Durham | Flashcards & Summaries

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# Lernmaterialien für System stability an der University of Durham

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How would you define peak overshoot?

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The maximum overshoot above steady state, this occurs on the first oscillation

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Define peak time

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Time for the first and highest peak

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define rise time

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The time to rise from (for example) 10% to 90% of its steady state value

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Define time constant

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The time interval needed for a system to change from one state to another by a specified percentage. For first order systems this is the time for the output to manifest a 1/e or 63.2% change due to step input

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Define delay time

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The delay time is the time for response to step input to reach 50% of final value

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What is the envelope of a response?

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The envelope of response is given by the term e ^−σt, it determines how long the system takes to settle to the final value

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What is the peak overshoot?

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The peak overshoot is the ratio of the first (and highest) peak to the steady state

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What does a change of sign in the first column of the Routh hertwiz array tell us?

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That the system is unstable

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What are the two cases of having a zero in the first column of the Routh Herwitz array and what does each mean in terms of stability?

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If there is a 0 by other values in the row are non 0, then we use epsilon and see if there is a sign change. They system can be stable or unstable

If there is a 0 and no other non 0 values in the row then the system could be unstable or marginally stable. We use the auxiliary polynomial (polynomial of the row above the row with all 0s) to find this out. Repeated roots mean unstable, complex conjugates means marginally stable

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If a transfer function has poles with a real positive part then is the system stable or unstable?
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Real positive is right of the axis and so unstable

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If a transfer function has poles with no real part and only complex conjugates (therefore on the Y axis), what does this tell us about the stability of the system?

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The system is marginally stable

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If a system has repeated complex roots then what does this tell us about stability?
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The system is unstable

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## Beispielhafte Karteikarten für deinen System stability Kurs an der University of Durham - von Kommilitonen auf StudySmarter erstellt!

Q:

How would you define peak overshoot?

A:

The maximum overshoot above steady state, this occurs on the first oscillation

Q:

Define peak time

A:

Time for the first and highest peak

Q:

define rise time

A:

The time to rise from (for example) 10% to 90% of its steady state value

Q:

Define time constant

A:

The time interval needed for a system to change from one state to another by a specified percentage. For first order systems this is the time for the output to manifest a 1/e or 63.2% change due to step input

Q:

Define delay time

A:

The delay time is the time for response to step input to reach 50% of final value

Q:

What is the envelope of a response?

A:

The envelope of response is given by the term e ^−σt, it determines how long the system takes to settle to the final value

Q:

What is the peak overshoot?

A:

The peak overshoot is the ratio of the first (and highest) peak to the steady state

Q:

What does a change of sign in the first column of the Routh hertwiz array tell us?

A:

That the system is unstable

Q:

What are the two cases of having a zero in the first column of the Routh Herwitz array and what does each mean in terms of stability?

A:

If there is a 0 by other values in the row are non 0, then we use epsilon and see if there is a sign change. They system can be stable or unstable

If there is a 0 and no other non 0 values in the row then the system could be unstable or marginally stable. We use the auxiliary polynomial (polynomial of the row above the row with all 0s) to find this out. Repeated roots mean unstable, complex conjugates means marginally stable

Q:

If a transfer function has poles with a real positive part then is the system stable or unstable?
A:

Real positive is right of the axis and so unstable

Q:

If a transfer function has poles with no real part and only complex conjugates (therefore on the Y axis), what does this tell us about the stability of the system?

A:

The system is marginally stable

Q:

If a system has repeated complex roots then what does this tell us about stability?
A:

The system is unstable

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