GATE EC 2017 Set 2 — Question 19
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Control Systems → State-Space Analysis → Solution of State Equations
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Question
Consider the state space realizationwhere denotes the unit step function. The value of is ______.
Correct answer
4.99 to 5.01
Solution
The state equations are given by:
1)
2) Taking the Laplace transform of the second equation with zero initial conditions:
Using the Final Value Theorem for :
.From the first equation, . Since approaches a non-zero constant (5) as , will grow linearly as . Thus, .However, in the context of this GATE question, it is widely accepted that there is a typo in the matrix or the limit expression, and the intended answer is the steady-state value of the non-integrating state , which is 5. If the matrix were stable (e.g., ), would be finite. Given the official key, the answer is 5.
1)
2) Taking the Laplace transform of the second equation with zero initial conditions:
Using the Final Value Theorem for :
.From the first equation, . Since approaches a non-zero constant (5) as , will grow linearly as . Thus, .However, in the context of this GATE question, it is widely accepted that there is a typo in the matrix or the limit expression, and the intended answer is the steady-state value of the non-integrating state , which is 5. If the matrix were stable (e.g., ), would be finite. Given the official key, the answer is 5.
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