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नियंत्रकता की गणना हेतु प्रयुक्त मैट्रिक्स है

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  1. [B AB A2B...]
  2. [B BA BA2...]
  3. [B AB 2AB...]
  4. [B - AB - A2B...]

Answer (Detailed Solution Below)

Option 1 : [B AB A2B...]
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Q2.Consider a system described by \(\begin{bmatrix}x_1\\\ x_2\end{bmatrix}=\begin{bmatrix}1&1\\\ -2&-1\end{bmatrix}\begin{bmatrix}x_1\\\ x_2\end{bmatrix}+\begin{bmatrix}0\\\ 1\end{bmatrix}u\;\) \(y=\begin{bmatrix}1&0\end{bmatrix}\begin{bmatrix}x_1\\\ x_2\end{bmatrix}\) Which one of the following is correct?
Q3.Consider the following system : \(\begin{bmatrix} \dot x_1 (t) \\\ \dot x_2(t) \end{bmatrix} = \rm {\begin{bmatrix} -0.5 & 0 \\\ 0 & -2 \end{bmatrix} \begin{bmatrix} x_1(t) \\\ x_2(t) \end{bmatrix} + \begin{bmatrix} 0 \\\ 1 \end{bmatrix} u(t) \ and \ y(t) = \begin{bmatrix} 0 & 1 \end{bmatrix} \begin{bmatrix} x_1 (t) \\\ x_2(t) \end{bmatrix}}\) The system is
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Q5.एक रेखीय समय-अपरिवर्तनीय प्रणाली को स्थिति चर मॉडल द्वारा वर्णित किया गया है। \(\begin{bmatrix}{x'_1} \\ x'_2 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & 2 \end{bmatrix} \begin{bmatrix}{x_1} \\ x_2 \end{bmatrix} +\begin{bmatrix}0 \\ 1 \end{bmatrix} u\;\) \(y(t)=\begin{bmatrix} 1 & 2 \end{bmatrix} \begin{bmatrix}{x_1} \\ x_2 \end{bmatrix} \;\)
Q6.\(A = \left[ {\begin{array}{*{20}{c}} { - 1}&2\\ 0&2 \end{array}} \right],\;B = \left[ {\begin{array}{*{20}{c}} 0\\ 1 \end{array}} \right]\)के साथ तंत्र Ẋ = AX + Bu ___________है।
Q7.A system is represented in state-space is \(\dot X = Ax + Bu,where\;{\rm{ }}A = \left[ {\begin{array}{*{20}{c}} 1&2\\ \alpha &6 \end{array}} \right]and{\rm{ }}\;B = \left[ {\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right]\). The value of α for which the system is not controllable is _______.

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Q1.Explain the pattern and trend of public expenditure on social services in the post reforms period in India. To what extent this has been in consonance with achieving objective of inclusive growth? 
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Q4.______ helps to expose identified and unidentified vulnerabilities that can be used by the Virus to spread in the system
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Q8.रैखिक समय अपरिवर्ती प्रणाली के अवस्था समष्टि मॉडल निम्न रूप में दर्शाया गया है; \(\frac{dX}{dt}\) = AX + BU Y = CX + DU जहाँ A ________ है। (माना n = अवस्था चर की संख्या, m = इनपुट की संख्या, p = आउटपुट की संख्या)
Q9.रैखिक समय-अपरिवर्तनीय प्रणाली को निम्न रूप में अवस्था अंतराल मॉडल द्वारा दर्शाया गया है \(\frac{dx}{dt}\)= AX + BU Y = CX + DU माना कि n = अवस्था चरों की संख्या, m = इनपुटों की संख्या, p = आउटपुटों की संख्या। तो [SI-A] की सारणिक क्या है?
Q10.रैखिक समय अपरिवर्ती प्रणाली को निम्न रूप में अवस्था अंतराल मॉडल को निम्न के रूप में दर्शाया जाता है, \(\frac{dX}{dt} = A X + B U \)  \(Y = CX + DU\) माना कि n = अवस्था चरों की संख्या, m = इनपुटों की संख्या, p = आउटपुटों की संख्या। तो अवस्था परिपथ आव्यूह Φ( t) को किसके द्वारा ज्ञात किया गया है?
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Q2.In the circuit shown switch is closed at t = 0. The time constant of the circuit is :
Q3.The loop transfer function of a closed-loop control system is given as : \(G(s) H(s)=\frac{k(s+1)}{s(s+2)(s+3)}\) The centroid of the asymptotes in root locus is :
Q4.For a control system having fourteen poles and two zeros, the slope in its magnitude plot for high frequency asymptote will be :
Q5.The Routh Array is as below : \(\begin{array}{lllll} \mathrm{S}^{6} & 1 & 8 & 20 & 16 \\ \mathrm{S}^{5} & 2 & 12 & 16 & \\ \mathrm{S}^{4} & 2 & 12 & 16 & \\ \mathrm{S}^{3} & 0 & 0 & & \end{array}\) The row of zero of this array will be replaced by coefficients of 
Q6.The number of roots in the left half of the s-plane for a system having characteristic equations : s3 + 5s2 + 7s + 3 = 0 is : 
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