Higher Study | Control Systems | State Space Analysis

Which mechanism in control engineering implies an ability to measure the state by taking measurements at output?

ক

Controllability

খ

Observability

গ

Differentiability

ঘ

Adaptability

Consider the following properties attributed to state model of a system: 1. State model is unique. 2. Transfer function for the system is unique. 3. State model can be derived from transfer function of the system. Which of the above statements are correct?

ক

1, 2 and 3

খ

1 and 2 only

গ

2 and 3 only

ঘ

1 and 3 only

For the given circuit, which one of the following is the correct state equation?

ক

\(\frac{d}{{dt}}\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 4}&4\\ { - 2}&{ - 4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&4\\ 4&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{i_1}}\\ {{i_2}} \end{array}} \right]\)

খ

\(\frac{d}{{dt}}\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 4}&{ - 4}\\ { - 2}&4 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 4&4\\ 4&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{i_1}}\\ {{i_2}} \end{array}} \right]\)

গ

\(\frac{d}{{dt}}\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 4&{ - 4}\\ { - 2}&{ - 4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 0&4\\ 4&4 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{i_1}}\\ {{i_2}} \end{array}} \right]\)

ঘ

\(\frac{d}{{dt}}\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} { - 4}&{ - 4}\\ { - 2}&{ - 4} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} v\\ i \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 4&0\\ 0&4 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{i_1}}\\ {{i_2}} \end{array}} \right]\)

For a feedback control system all the roots of the characteristic equation can be placed at the desired location in the s-plane if and only if the system is 1. Observable 2. Controllable Which of the above statements are correct?

ক

1 only

খ

2 only

গ

Both 1 and 2

ঘ

Neither 1 nor 2

Consider the following standard state-space description of a linear time-invariant single input single output system: \(\dot x = Ax + Bu,y = Cx + Du\) Which one of the following statements about the transfer function should be true if D ≠ 0?

ক

The system is stable

খ

The system is strictly proper

গ

The system is low pass

ঘ

The system is of type zero

Which of the following statements are correct? 1. The pair (AB) is controllable implies that the pair (ATBT) is observable. 2. The pair (AB) is controllable implies that the pair (ATBT) is unobservable. 3. The pair (AC) is observable implies that the pair (ATCT) is controllable. 4. The pair (AC) is observable implies that the pair (ATCT) is uncontrollable. where: A, B and C are having their standard meanings

ক

1 and 3 only

খ

1 and 4 only

গ

2 and 3 only

ঘ

2 and 4 only

Which one of the following is the zero-input response of the system y[n] = 3y[n - 1] = 4y[n - 2] = 0 described by the homogeneous second-order difference equation if y[-2] = 0 and y[-1] = 5 ?

ক

yzi(n) = (-1)n+1 + (-4)n+2, n ≥ 0

খ

yzi(n) = (1)n+1 + (4)n+2, n ≥ 0

গ

yzi(n) = (-1)n+1 + (4)n+2, n ≥ 0

ঘ

yzi(n) = (1)n+1 + (-4)n+2, n ≥ 0

Bounded-input bounded-output stability implies asymptotic stability for 1. Completely controllable system 2. Completely observable system 3. Uncontrollable system 4. Unobservable system Which of the above statements are correct?

ক

1 and 4 only

খ

1 and 2 only

গ

2 and 3 only

ঘ

3 and 4 only