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The questions will be categorized according to the key concepts in the Chapter.

Stability Robustness

Stability Tests

Controller Tuning
















Check Your Reading

Solidify the Concepts

Which of the following best describes the importance of stability in process control?




All stable control systems perform well.

Stability is not absolutely required for good control performance.


A stable control system returns the controlled variable to its set point.

Stability is required for , but it does not guarantee, good performance.













Why do we use linear models to investigate the stability of (non-linear) systems?




If the linear model is stable, the non-linear system will be stable for a wide range of conditions.

Linearity is necessary for stability.


Rigorous and easily calculated tests are available for linear systems.

If the linear system is stable, the non-linear system is stable at the conditions used in the test..





One test for stability: We evaluate the poles (roots of the denominator), and if a real part is negative, the system is unstable.















Which elements in the loop affect stability?


Only the process.

The controller and the process.


All elements in the drawing.

All elements except one in the drawing..











In an unstable chemical process, 


Some variables will go to + or - infinity.

All variables will go to + or - infinity.


The plant will blow up!

None of the above.













The Bode method is emphasized (over direct evaluation of the poles) because, 


The results of the Bode stability analysis can be plotted.

The Bode method is the most general available.


The Bode method can be applied to systems with dead times!

Actually, direct evaluation of poles (root locus) is used more often in process control.









For the process shown below, identify some variables that are stable and some that are unstable. 


Explain your selections!