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Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.
- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'C'. Can you explain this answer?
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Assertion (A): For a system to be stable, the roots of the characteris...
Poles of the closed loop transfer function is the characteristic equation of a closed loop control system. For the system to be stable all roots of characteristic equation should lie in LH s-plane. Hence reason is false.
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Assertion (A): For a system to be stable, the roots of the characteris...
Introduction:
In control systems, stability is a crucial aspect to ensure the system operates in a desired manner. Stability refers to the ability of a system to return to its equilibrium state after undergoing disturbances. There are different criteria to determine the stability of a control system. One such criterion is based on the location of the roots of the characteristic equation or the zeros of the closed loop transfer function in the s-plane.
Explanation:
Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.
Understanding Assertion (A):
The roots of the characteristic equation are obtained by setting the denominator of the transfer function equal to zero. These roots represent the poles of the system.
In the s-plane, the right half represents the region where the real part of s is positive. If the roots of the characteristic equation lie in this region, it indicates the presence of exponential growth in the system, leading to instability. Therefore, for stability, the roots should not lie in the right half of the s-plane.
Understanding Reason (R):
The closed loop transfer function relates the output of the system to the input when a feedback loop is employed. The zeros of this transfer function represent the points where the output becomes zero for certain input values.
If all the zeros of the closed loop transfer function lie in the left half of the s-plane, it implies that there are no values of s for which the output becomes zero, except at the origin. This indicates that the system does not exhibit any unstable behavior and remains stable.
Explanation of Correct Answer (C):
The assertion (A) is true because the presence of roots in the right half of the s-plane or on the imaginary axis indicates instability in the system.
However, the reason (R) is false because the stability of a system does not solely depend on the zeros of the closed loop transfer function. It is determined by the locations of the roots of the characteristic equation. Therefore, the reason does not provide a correct explanation for the assertion.
Hence, the correct answer is option (C), where assertion (A) is true but reason (R) is false.
In control systems, stability is a crucial aspect to ensure the system operates in a desired manner. Stability refers to the ability of a system to return to its equilibrium state after undergoing disturbances. There are different criteria to determine the stability of a control system. One such criterion is based on the location of the roots of the characteristic equation or the zeros of the closed loop transfer function in the s-plane.
Explanation:
Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.
Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.
Understanding Assertion (A):
The roots of the characteristic equation are obtained by setting the denominator of the transfer function equal to zero. These roots represent the poles of the system.
In the s-plane, the right half represents the region where the real part of s is positive. If the roots of the characteristic equation lie in this region, it indicates the presence of exponential growth in the system, leading to instability. Therefore, for stability, the roots should not lie in the right half of the s-plane.
Understanding Reason (R):
The closed loop transfer function relates the output of the system to the input when a feedback loop is employed. The zeros of this transfer function represent the points where the output becomes zero for certain input values.
If all the zeros of the closed loop transfer function lie in the left half of the s-plane, it implies that there are no values of s for which the output becomes zero, except at the origin. This indicates that the system does not exhibit any unstable behavior and remains stable.
Explanation of Correct Answer (C):
The assertion (A) is true because the presence of roots in the right half of the s-plane or on the imaginary axis indicates instability in the system.
However, the reason (R) is false because the stability of a system does not solely depend on the zeros of the closed loop transfer function. It is determined by the locations of the roots of the characteristic equation. Therefore, the reason does not provide a correct explanation for the assertion.
Hence, the correct answer is option (C), where assertion (A) is true but reason (R) is false.
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Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer?
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Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer?.
Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer?.
Solutions for Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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ample number of questions to practice Assertion (A): For a system to be stable, the roots of the characteristic equation should not lie in the right half of the s-plane or on the imaginary axis.Reason (R): A system is said to be stable if the zeros of the closed loop transfer function are all in the left half of s-plane.a)Both A and R are true and R is a correct explanation of A.b)Both A and R are true but R is not a correct explanation of A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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