Name of the College : Kings College Of Engineering
Department : Electrical & Electronics Engineering
Subject : Modern Control Systems
Website : kings.ac.in
Document Type : Question Bank
Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/ki…S%20-final.pdf
Kings Modern Control Systems Question Paper
Unit – I
State Space Analysis Of Continuous Time Systems :
Part – A : (2 Marks)
1. What are the drawbacks in transfer function model analysis? :
(i)Transfer function is defined under zero initial conditions.
(ii)Transfer function is applicable to linear time invariant systems.
(iii)Transfer function analysis is restricted to SISO systems.
(IV)It does not provides information regarding the internal state of the system.
Related : Kings College Of Engineering EE2255 Digital Logic Circuits Question Bank : www.pdfquestion.in/1336.html
2. What is State and state variable? :
The state is the condition of a system at any time instant, t. A set of variable which describes the state of the system at any time instant are called state variables.
3. What is a state vector ? :
The state vector is a (nx1)column matrix (or vector)whose elements are state variables of the system,(where n is the order of the system).It is denoted by X(t).
4. What are the advantages of state space analysis? :
(i)The state space analysis is applicable to any type of systems. They can be used for Modeling and analysis of linear and nonlinear systems, time invariant &time variant systems and Multiple input &Multiple output systems..
(ii)The state space analysis can be performed with initial conditions.
(iii)The variables used to represent the system can be any variables in the system.
(iv)Using this analysis the internal states of the system at any time instant can be predicted.
5. Write the state model of nth order system? :
The state model of a system consists of state equation and output equation. The state model of a nth order system with m-inputs and p-outputs are
X(t) = AX(t) + BU(t) ————— State equation
Y(t) =CX(t) + DU(t) —————- Output equation
Where X(t) = state vector of order (nx1)
U(t) = Input vector of order (mx1)
A = system matrix of order (nxn)
B = Input matrix of order (nxm)
Y(t) = Output vector of order (px1)
C = Output matrix of order (pxn)
D =transmission matrix of order (pxm)
6. The state model of a linear time invariant system is given by
X(t) = AX(t) + BU(t)
Y(t) =CX(t) + DU(t) . Write the expression for transfer function of the system.
Y(s)/ U(s)=C (sI – A) -1 BU(s) +D
7. What is State diagram? :
The Pictorial representation of the state model of the system is called state diagram. The state diagram of the system can be either in block diagram or signal flow graph form.
8. What are the advantages of state space modeling using physical variable? :
(i)The state variable can be utilized for the purpose of feedback.
(ii)The solution of state equation gives time variation of variables which have direct
relevance to the Physical system.
9. What are phase variables? :
The phase variables are defined as those particular state variables which are
obtained from one of the system variable and its derivatives. Usually the variable
used is the system output and the remaining state variables and then derivatives.
Unit – II
11. Write the solution of homogeneous state equations.? :
The solution of homogeneous state equation is, X(t) = eA t x0
Where , X(t) = state vector at time , t
eA t =State transition matrix.
And X0 =Initial condition vector at t=0
13.Write any two properties of eigenvalues.
(i)A matrix and its transpose have the same eigen values.
(ii)The product of the eigen values (counting multiplicities)of the matrix equals the determinant of the matrix.
14.What is similarity transformation? :
The Process of transforming a square matrix A to another similar matrix B by a transformation P-1 AP = B is called similarity transformation. The matrix P is called transformation matrix.
15.Define controllability and observability :
A system is said to be completely state controllable if it is possible to transfer the system state from any initial state X( t0 )at any other desired state X(t),in specified finite time by a control vector U( t ).
A system is said to be completely state observable if every state X(t) can be completely identified by measurements of the output Y(t)over a finite time interval.
16.What is pole placement by state feed back? :
The pole placement by state feedback is a control system design technique ,in which the state variables are used for feedback to achieve the desired closed loop poles.
17. What is state observer? :
A device (or a computer program) that estimates or observes the state variables is called state observer
18.What is the need for state observer? :
In certain systems the state variables may not be available for measurement and feedback. In such situations we need to estimate the un measurable state variables from the knowledge of input and output. Hence a state observer is employed which estimates the state variables from the input and output of the system. The estimated state variable can be used for feedback to design the system by pole placement.
19.What is canonical form of state model? :
If the system matrix, A is in the form of diagonal matrix then the state model is called canonical form.
20.What is meant by diagonalization? :
The process of converting the system matrix A in to a diagonal matrix by a similarity transformation using the modal matrix M is called diagonalization.