The characteristic equation for the system is
\[
s^3 + 9s^2 + 26s + 12(2 + K_c) = 0
\]
Using Routh test, the value of Kc that will keep the system stable is:
Show Hint
- 17.5
- 4
- 13.5
- 3.5
The Correct Option is C
Solution and Explanation
Step 1: Apply the Routh-Hurwitz criterion.
The Routh-Hurwitz criterion is applied to determine the stability of the system. We form the Routh array using the coefficients of the characteristic equation. For stability, the number of sign changes in the first column determines the value of \(K_c\) that will keep the system stable.
Step 2: Conclusion.
Using the Routh test, we find that the correct value of \(K_c\) that keeps the system stable is (C) 13.5.
Top Questions on Control Systems
The Block diagram for a control system is shown below:
- Bode diagram is a plot of (AR is amplitude ratio; $\omega$ is frequency factor and $\phi$ is phase angle):
- The transfer function of a PID controller is:
- The Bode diagram stability criterion is applicable when:
- A first-order system with unity gain and time constant \( \tau \) is subjected to sinusoidal input having a frequency \( \omega \) of \( \frac{1}{\tau} \). The amplitude ratio for such system is:
Questions Asked in CUET PG exam
Consider the following four words, out of which three are alike in some manner and one is different.
(A) Arrow
(B) Missile
(C) Sword
(D) Bullet
Choose the combination that has alike words.- CUET (PG) - 2025
- Analogies
Match List-I with List-II:
\[ \begin{array}{|l|l|} \hline \textbf{List-I (Name of Drug)} & \textbf{List-II (Indication)} \\ \hline A. \ \text{Baclofen} & I. \ \text{Spasticity} \\ B. \ \text{Diclofenac} & II. \ \text{Inflammatory pain} \\ C. \ \text{Gabapentin} & III. \ \text{Central or peripheral neurogenic pain} \\ D. \ \text{Amitryptiline} & IV. \ \text{Depression} \\ \hline \end{array} \]- CUET (PG) - 2025
- Pharmacology
Match List-I with List-II:
\[ \begin{array}{|l|l|} \hline \textbf{List-I (Ascending tract of the spinal cord)} & \textbf{List-II (Function)} \\ \hline A. \ \text{Lateral spinothalamic tract} & I. \ \text{Pain and temperature from opposite half of the body} \\ B. \ \text{Anterior spinothalamic tract} & II. \ \text{Vibratory sense} \\ C. \ \text{Fasciculus Cuneatus} & III. \ \text{Crude touch and pressure from opposite half of the body} \\ D. \ \text{Posterior spinocerebellar tract} & IV. \ \text{Unconscious proprioception to cerebellum} \\ \hline \end{array} \]- CUET (PG) - 2025
- Neurophysiology
Match List-I with List-II:
\[ \begin{array}{|l|l|} \hline \textbf{List-I (Muscle)} & \textbf{List-II (Nerve supply)} \\ \hline A. \ \text{Gluteus maximus} & I. \ \text{Ventral rami of S1, S2} \\ B. \ \text{Piriformis} & II. \ \text{Nerve to quadratus femoris} \\ C. \ \text{Gemellus inferior} & III. \ \text{Superior Gluteal nerve} \\ D. \ \text{Gluteus minimus} & IV. \ \text{Inferior gluteal nerve} \\ \hline \end{array} \]Match List-I with List-II:
\[ \begin{array}{|l|l|} \hline \textbf{List-I (Vaccines)} & \textbf{List-II (Their respective contents)} \\ \hline A. \ \text{Typhoid vaccine} & I. \ \text{Killed rickettsia} \\ B. \ \text{Typhus vaccine} & II. \ \text{Killed bacteria} \\ C. \ \text{Measles vaccine} & III. \ \text{Attenuated viruses} \\ D. \ \text{Smallpox vaccine} & IV. \ \text{Killed viruses} \\ \hline \end{array} \]- CUET (PG) - 2025
- Immunology