BEE Bachelor of Electrical Engineering Control System Principles Questions and Answers — Questions and Answers
Question 1: A control system has a characteristic equation given by s³ + 6s² + 11s + 6 = 0. According to the Routh-Hurwitz stability criterion, what can be concluded about the stability of this system?
- The system has roots in the right-half plane and is unstable.
- The system is stable. (Correct answer)
- The system is marginally stable.
- The system's stability cannot be determined without a root locus plot.
Correct answer: The system is stable.
To determine stability using the Routh-Hurwitz criterion, we first check the necessary condition: all coefficients must be present and have the same sign. In this case (1, 6, 11, 6), all are positive. Next, we form the Routh array. The first column elements are 1, 6, 10, and 6. Since there are no sign changes in the first column of the Routh array, the system is stable.
Question 2: An engineer is designing a closed-loop control system for a DC motor's position. After implementing a proportional (P) controller, they observe a persistent difference between the desired final position and the actual final position. Which type of control action should be added to eliminate this steady-state error?
- Additional proportional gain
- Derivative (D) control
- Integral (I) control (Correct answer)
- A feedforward controller
Correct answer: Integral (I) control
The integral (I) component of a PID controller sums the error over time. This accumulated sum causes the controller output to increase until the steady-state error is driven to zero. Proportional control alone often results in a non-zero steady-state error, and derivative control primarily affects the transient response (like overshoot) rather than the final error.
Question 3: For a unity feedback control system, what is the steady-state error for a Type 1 system subjected to a unit step input?
- Infinite
- A non-zero constant
- Zero (Correct answer)
- Dependent on the system's zeros
Correct answer: Zero
The 'type' of a system is determined by the number of pure integrators (poles at the origin) in its open-loop transfer function. A Type 1 system has one integrator. The position error constant (Kp) for a Type 1 system is infinite. The steady-state error for a step input is calculated as 1 / (1 + Kp). Since Kp is infinite, the steady-state error is 1 / (1 + ∞), which equals zero.
Question 4: Which of the following correctly defines the phase margin in the context of a Bode plot analysis?
- The amount of additional gain required to make the system marginally stable at the phase crossover frequency.
- The phase angle at the frequency where the magnitude plot crosses 0 dB.
- The difference between the system's phase angle and -180 degrees at the gain crossover frequency. (Correct answer)
- The frequency at which the phase angle is -180 degrees.
Correct answer: The difference between the system's phase angle and -180 degrees at the gain crossover frequency.
The phase margin is a measure of relative stability. It is found at the gain crossover frequency (where the magnitude plot is 0 dB). The phase margin is the amount of additional phase lag required to make the system unstable, calculated as the difference between the system's phase at that frequency and -180 degrees.
Question 5: According to the fundamental rules for constructing a root locus plot for a system with an open-loop transfer function G(s)H(s), where do the branches of the root locus begin (for K=0)?
- At the origin of the s-plane
- At the open-loop zeros of G(s)H(s)
- At the closed-loop poles of the system
- At the open-loop poles of G(s)H(s) (Correct answer)
Correct answer: At the open-loop poles of G(s)H(s)
The root locus plot shows the paths of the closed-loop poles as a system parameter (typically gain K) varies from 0 to infinity. The branches of the root locus always start (when K=0) at the poles of the open-loop transfer function G(s)H(s) and terminate (as K approaches infinity) at the zeros of the open-loop transfer function or at infinity.
Question 6: In comparing open-loop and closed-loop control systems, which statement is most accurate regarding their sensitivity to external disturbances and parameter variations?
- Open-loop systems are more complex and expensive but offer better disturbance rejection.
- Closed-loop systems use feedback to correct for disturbances, making them less sensitive than open-loop systems. (Correct answer)
- Both systems are equally sensitive to disturbances, but closed-loop systems are faster.
- Open-loop systems are less sensitive to parameter variations because they do not have a feedback path.
Correct answer: Closed-loop systems use feedback to correct for disturbances, making them less sensitive than open-loop systems.
A key advantage of a closed-loop (feedback) control system is its ability to reduce the system's sensitivity to external disturbances and variations in system parameters. The feedback mechanism measures the output, compares it to the desired input, and makes corrections, thereby counteracting the effects of such unwanted variations. Open-loop systems lack this corrective action and are therefore more sensitive.
BEE Bachelor of Electrical Engineering Control System Principles Questions and Answers
A control system has a characteristic equation given by s³ + 6s² + 11s + 6 = 0.
According to the Routh-Hurwitz stability criterion, what can be concluded about the stability of this system?