Quiz 1 - Stability Analysis in Control Systems

What is the definition of a stable system?

• A system that produces an unbounded output for a bounded input

• A system that produces a bounded output for a bounded input

• A system that has no output

• A system that is always unstable

Which type of system is stable for all ranges of component values?

• Unstable system

• Conditionally stable system

• Marginally stable system

• Absolutely stable system

What is the necessary condition for Routh-Hurwitz stability?

• The roots of the characteristic equation must be complex

• All coefficients of the characteristic polynomial should be negative

• All coefficients of the characteristic polynomial should be positive

• The characteristic polynomial must have at least one zero coefficient

What does the Routh array method help to determine?

• The stability of the control system

• The input-output relationship of the system

• The frequency response of the system

• The exact roots of the characteristic equation

What indicates that a control system is unstable according to the Routh array?

• All elements of the first column are positive

• At least one root exists in the left half of the s-plane

• At least one root exists in the right half of the s-plane

• All elements of the first column are negative

In the context of root locus, what does the angle condition refer to?

• The angle of the open loop transfer function is an odd multiple of 180 degrees

• The angle of the open loop transfer function is an even multiple of 180 degrees

• The angle of the system response is constant

• The angle of the closed loop transfer function is zero

What happens to the damping ratio when an open loop pole is added?

• It becomes zero

• It increases

• It remains the same

• It decreases

What is the centroid in the context of root locus?

• The point where all root locus branches meet

• The intersection point of asymptotes on the real axis

• The average of all poles in the s-plane

• The point where the system becomes unstable

What is a break-away point in root locus?

• A point where the root locus branches start at open loop zeros

• A point where the root locus branches start at open loop poles

• A point between two open loop poles where a real axis root locus branch exists

• A point where the root locus branches intersect the imaginary axis

What is the effect of adding an open loop zero to the transfer function?

• It decreases system stability

• It increases system stability

• It has no effect on stability

• It makes the system unstable