SSC · Control Systems practice

Correct answer: C

Feedback lets the system compare the output with the desired value and correct errors.

Correct answer: B

G(s) = C(s)/R(s), valid for linear time-invariant systems.

Correct answer: D

The type is the number of poles at the origin, here one.

Correct answer: C

Poles in the left half give decaying exponentials. A pole in the right half gives a growing response.

Correct answer: D

For 0 < ζ < 1 the response oscillates with a decaying amplitude.

Correct answer: A

The integral term keeps building up the control output as long as an error persists.

Correct answer: C

ωn² = 16, so ωn = 4. 2ζωn = 4, so ζ = 4/(2 × 4) = 0.5.

Correct answer: C

Mp = exp(−πζ / √(1 − ζ²)) = exp(−1.814) = 0.163.

Correct answer: A

A type-1 system has an integrator, so it follows a step input exactly. The error for a ramp is 1/Kv.

Correct answer: D

The Routh array has a zero row at s¹: (2 × 3 − 6)/2 = 0. The roots are −2 and ±j√3, so there are poles on the imaginary axis.

Correct answer: D

Positive gain and phase margins in a minimum phase system mean the closed loop is stable.

Correct answer: D

The criterion relates the encirclements of the critical point to the right half plane poles of the closed loop.

Correct answer: A

For s³ + a s² + b s + c, the Routh test uses ab − c. Here 3 × 10 − 20 = 10, so the system is stable.

Correct answer: C

For s³ + a s² + b s + c, the Routh test uses ab − c. Here 7 × 8 − 25 = 31, so the system is stable.

Correct answer: A

For s³ + a s² + b s + c, the Routh test uses ab − c. Here 5 × 4 − 29 = -9, so the system is unstable.

Correct answer: A

For s³ + a s² + b s + c, the Routh test uses ab − c. Here 6 × 2 − 23 = -11, so the system is unstable.

Correct answer: A

For s³ + a s² + b s + c, the Routh test uses ab − c. Here 9 × 12 − 27 = 81, so the system is stable.

Correct answer: C

For s³ + a s² + b s + c, the Routh test uses ab − c. Here 8 × 11 − 19 = 69, so the system is stable.

Correct answer: C

ts = 4/(ζωn) = 4/(0.4 × 2) = 5 s.

Correct answer: D

ess (ramp) = 1/Kv = 1/189 = 0.00529.