What does BIBO stability mean in control systems?

Bounded Input Bounded Output - bounded inputs produce bounded outputs

Where must all poles be located for a stable linear system?

Left-half of the s-plane with negative real parts

True or False: A system with poles on the imaginary axis is unstable.

False. Poles on imaginary axis indicate marginal stability, not instability.

The characteristic equation for closed-loop system is: A) 1 + G(s) = 0
B) 1 + G(s)H(s) = 0
C) G(s)H(s) = 0
D) T(s) = 0

B) 1 + G(s)H(s) = 0

Fill in the blank: All coefficients in characteristic equation must have the _____ sign for stability.

Same

What does the number of sign changes in Routh array's first column indicate?

Number of roots with positive real parts (unstable poles)

In root locus, where do the branches start and end?

Start at open-loop poles (K=0), end at open-loop zeros (K=∞)

How many asymptotes exist in root locus construction?

Number of poles minus number of zeros: |n-m|

True or False: Root locus is always symmetric about the real axis.

True. Root locus exhibits symmetry about the real axis.

What is the Nyquist stability criterion formula?

Z = N + P = 0, where Z=closed-loop RHP poles, N=encirclements, P=open-loop RHP poles

For open-loop stable systems, when is closed-loop system stable using Nyquist?

When Nyquist plot does not encircle the -1+j0 point

Fill in the blank: Gain margin is measured at _____ crossover frequency.

Phase

What phase angle defines the phase crossover frequency?

-180 degrees

A system has gain margin of 12 dB and phase margin of 45°. Is it: A) Stable
B) Unstable
C) Marginally stable
D) Cannot determine

A) Stable

What is the typical minimum design value for phase margin?

30 to 60 degrees

In Bode plots, what does -20 dB/decade slope indicate?

Single pole or integrator (1/s factor)

For state-space system ẋ = Ax + Bu, what determines stability?

All eigenvalues of matrix A must have negative real parts

Fill in the blank: Power system steady-state stability limit occurs at δ = _____.

90°

What is the power transfer equation for generator connected to infinite bus?

P = (EgVb/X) sin δ

True or False: The swing equation relates mechanical and electrical power imbalance to rotor acceleration.

True. Swing equation: M(d²δ/dt²) = Pm - Pe

What does the equal-area criterion determine in power systems?

Transient stability by comparing accelerating and decelerating energy areas

For transient stability, what must be true about areas A₁ and A₂?

Decelerating area A₂ must be greater than or equal to accelerating area A₁

A second-order system has ζ = 0.3 and ωn = 10 rad/s. Calculate settling time: A) 0.4 s
B) 1.33 s
C) 2.67 s
D) 4.0 s

B) 1.33 s

What damping ratio value indicates critically damped response?

Ζ = 1

Fill in the blank: Percent overshoot formula is %OS = e^(-πζ/√(1-ζ²)) × _____.

100%

What happens to system response when damping ratio ζ > 1?

System becomes overdamped with no oscillation in response