Question 1

Consider a system if represented by state space equation and x1 (t) =x2 (t), then the system is:&#10;A)controllable&#10;B)uncontrollable&#10;C)observable&#10;D)unstable

Accepted Answer

The condition x1(t) = x2(t) by itself does not directly imply controllability, observability, or stability of the system. However, it suggests a potential redundancy or dependency in the state variables, which might lead to unobservability or uncontrollability if these states cannot be independently controlled or observed. Without additional context or information about the system matrices (A, B, C, D), it's challenging to definitively conclude the system's properties solely based on the relationship between x1(t) and x2(t). However, the closest applicable choice given the options and typical interpretations would be related to controllability or observability issues rather than stability. Since the question specifically asks in the context of this relationship and does not provide enough information to deduce stability, the most appropriate choice under typical assumptions would be to consider potential issues with controllability or observability. Yet, the correct answer strictly based on the provided options and common interpretations in control theory literature is not fully determinable without further context.

Question 2

A transfer function of the system does not have pole-zero cancellation? Which of the following statements is true?&#10;A)system is neither controllable nor observable&#10;B)system is completely controllable and observable&#10;C)system is observable but uncontrollable&#10;D)system is controllable and unobservable

Accepted Answer

A system without pole-zero cancellation is typically considered to be both completely controllable and observable. This is because pole-zero cancellation can obscure parts of the system state from the output (affecting observability) or from the input (affecting controllability), and without such cancellations, the full state of the system is accessible from the input and observable from the output.

Question 3

The impulse response of a linear LTI system is given as g (t) = e(-t)The transfer function of the system is equal to:&#10;A)1/s&#10;B)1/s(s+1)&#10;C)1/(s+1)&#10;D)s/(s+1)

Accepted Answer

The transfer function of a linear time-invariant (LTI) system in the Laplace domain is obtained by taking the Laplace transform of its impulse response. The Laplace transform of $g(t) = e^{-t}$ (for $t > 0$) is $G(s) = \frac{1}{s+1}$, making option C correct.

Question 4

An oberser or program that that estimates less than n state variables, where n is dimension of stage vector is called&#10;A)reduced order state observer&#10;B)simply a reduced order observer&#10;C)full observer&#10;D)state observer

Accepted Answer

A reduced order state observer estimates fewer state variables than the full state vector dimension, which is n.

Question 5

Gilbert's test is used to check&#10;A)controllabilty&#10;B)observability&#10;C)observer&#10;D)controlability & observability

Accepted Answer

Gilbert's test is used to check both controllability and observability of a system.

Question 6

The necessary and sufficient condition for the system to be completely state controllable is that therank of the composite matrix QC is&#10;A)1&#10;B)n&#10;C)2&#10;D)3

Accepted Answer

The necessary and sufficient condition for a system to be completely state controllable is that the rank of the controllability matrix (often denoted as QC) must be equal to the dimension of the state vector, n. This means that all n states of the system can be controlled/influenced by the input.

Question 7

In control system an error detector&#10;A)detects error and signal out an alarm&#10;B)detects error of the system&#10;C)produces an error signal as actual difference of value and desired value of output&#10;D)any of the above

Accepted Answer

An error detector in a control system produces an error signal by calculating the actual difference between the desired value (set point) and the actual value of the output. This error signal is then used to correct the system's performance.

Deck 4: Control System