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Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) PDF Download

Q16: A system is described by the following state and output equations
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) when u(t) is the input and y(t) is the output
The system transfer function is (2009)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (c)
Sol: Selecting x1(t) and x2(t) as state variable,
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q17: The state space equation of a system is described by
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)where x is state vector, u is input, y is output and Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)C = [1 0]
A unity feedback is provided to the above system G(s) to make it a closed loop system as shown in figure.
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)For a unit step input r(t), the steady state error in the input will be (2008)
(a) 0
(b) 1
(c) 2
(d) ∞
Ans:
(a)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Steady state error, using final value theorem
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q18: The state space equation of a system is described by
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)where x is state vector, u is input, y is output and Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)C = [1 0]
The transfer function G(s) of this system will be (2008)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
 Ans: (d)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q19: The state equation for the current I1 in the network shown below in terms of the voltage Vx and the independent source V, is given by  (2007)
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Any state equation represents the dynamical behaviour of the given network. State equations usually follow a specific 'format' while beong represented. On the left side of each state equation, the derivative of only one variable is used. On the right hand side a mathematical function is represnted involving any or all the state varibles and the sources.
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Using KVL in Loop-I
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Using KVL in Loop-II,
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Eliminating I2 from equation (i) and (ii), we get,
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q20: For a system with the transfer function Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) the matrix A in the state space form X = AX + Bu is equal to (2006)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Ans: 
(b)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Replacing s by d/dt,
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q21: A state variable system
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) with the initial condition Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) and the unit step input u(t) has the state transition equation  (2005)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (c)
Sol: ZIR (zero Input Response) = ϕ(t) × X(0)
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)ZSR (Zero State Response)
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)∴ State transition equation
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q22: A state variable system
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)with the initial condition Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) and the unit step input u(t) has
The state transition matrix  (2005)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Comparing equation (i) and (ii), we get
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q23: The state variable description of a linear autonomous system is X = AX,
where X is the two dimensional state vector and A is the system matrix given byPrevious Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) The roots of the characteristic equation are  (2004)
(a) -2 and +2
(b) -j2 and +j2
(c) -2 and -2
(d) +2 and -2
Ans:
(a)
Sol: 
System matrix Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) Characteristic equation ⇒ ∣sI −A∣ = 0
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Roots of the characteristic equation are -2 and +2.

Q24: The following equation defines a separately excited dc motor in the form of a differential equation
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) The above equation may be organized in the state-space form as follows
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) where the P matrix is given by  (2003)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q25: A second order system starts with an initial condition of Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) without any external input. The state transition matrix for the system is given by Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)The state of the system at the end of 1 second is given by  (2003)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: State transition matrix,
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Initial conditions,
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Zero input response is given by
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)State of the system at t = 1s
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q26: For the system Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) with u as unit impulse and with zero initial state, the output, y, becomes   (2002)
(a) 2e2t
(b) 4e2t
(c) 2e4t
(d) 4e4t
Ans: 
(b)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Q27: For the system Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) which of the following statements is true?  (2002)
(a) The system is controllable but unstable
(b) The system is uncontrollable but unstable
(c) The system is controllable but stable
(d) The system is uncontrollable but stable
Ans:
(b)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)⇒ Uncontrollable.
Characteristic equation:
Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)⇒ eigen values, s = 3.5 ± j0.866
i.e. roots lies on right side of s-plane .
⇒ unstable.

Q28: The state transition matrix for the system Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) with initial state X(0) is  (2002)
(a) (sIA)1(sI − A)−1
(b) eAt X(0)
(c) Laplace inverse of [(sI − A)−1]
(d) Laplace inverse of [(sI − A)−1 X(0)]
Ans:
(c)
Sol: eAt = L−1[sI−A]−1 

Q29: Given the homogeneous state-space equaion  Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) the steady state value xss = lim⁡t→∞x(t), given the initial state value of x(t) = [10 − 10]T, is  (2001)
(a) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE)

The document Previous Year Questions- State Variable Analysis - 2 | Control Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Control Systems.
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FAQs on Previous Year Questions- State Variable Analysis - 2 - Control Systems - Electrical Engineering (EE)

1. What is State Variable Analysis in control systems?
Ans.State Variable Analysis is a method used in control systems to model and analyze dynamic systems using state variables. These state variables represent the system's state at any given time and help in understanding how the system evolves over time. This approach allows for a comprehensive analysis of system behavior, including stability, controllability, and observability.
2. How do you define state variables in a system?
Ans.State variables are defined as a set of variables that capture the essential information about the state of a dynamic system. They are typically chosen to represent the minimum number of variables needed to describe the system's behavior completely. In practice, these variables could represent quantities like position, velocity, or current in electrical systems.
3. What is the importance of controllability and observability in state variable analysis?
Ans.Controllability and observability are critical concepts in state variable analysis. Controllability refers to the ability to steer a system's state to a desired value using appropriate inputs. Observability, on the other hand, indicates whether the internal state of a system can be inferred from its output measurements. Both concepts are vital for ensuring that a system can be effectively controlled and monitored.
4. How can state variable models be converted to transfer function models?
Ans.State variable models can be converted to transfer function models using mathematical techniques such as the Laplace transform. This involves expressing the state equations in matrix form, obtaining the system's output in terms of the input, and then deriving the transfer function by manipulating the equations to relate output to input in the s-domain.
5. What are common applications of state variable analysis in engineering?
Ans.Common applications of state variable analysis include control system design, robotics, aerospace engineering, and electrical circuit design. It is particularly useful in systems that require precise control and monitoring, as it provides a clear framework for analyzing dynamic behavior and implementing control strategies.
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