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Name of the College : Valliammai Engineering College
University : Anna University
Department : Electrical and Electronics Engineering
Subject Code/Name : CL7103-System Theory
Degree : M.E Power Systems
Year : I
Semester : I
Document Type : Question Bank
Website : valliammai.co.in

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Valliammai System Theory Question Bank

Unit I

2 Marks :
1. What is state and state variable?

Related : Valliammai Engineering College PS7101 Advanced Power System Analysis M.E Question Bank : www.pdfquestion.in/2796.html

2. What are the advantages of state space analysis?
3. What are the drawbacks in transfer function analysis?
4. What is state diagram?
5. Draw the block diagram representation of state model.
6. Draw the signal flow representation of state model
7. Write the state model of nth
8. Write the solution of homogeneous state equations order system?
9. What are phase variables?
10. Write the canonical form of state model of nth

11. Explain the concept of state and state variables. order system.
12. Write the state model of linear time invariant systems.
13. Given the system =u ,obtain a state space model.
14. Distinguish between the following :
(a) Linear & nonlinear systems
(b) Time –invariant and time varying system
15. How will you choose the state variables for an electrical network consisting of R,L and C?

16 Marks :
1. Derive the state model of an Armature controlled DC motor. (16)
2. Derive the state model of an field controlled DC motor. (16)
3. Construct the state model of the following electrical system. (16)
4. Develop a state model for the system given by
5. A sytem has the transfer the function :FInd four different state variable models and hence demonstrate the state models are non-unique.

Unit II

2 Marks :
1. List the properties of state transition matrix.
2. State Cayley Hamilton theorem
3. Define the characteristic equation of a matrix
4. What are eigen values and eigen vectors?
5. Write properties of eigen values
6. What is similarity transformation?
7. What is modal matrix?
8. What is canonical form of state model?
9. What is Jordan matrix?
10. How the eigen vectors are calculated when the eigen values are distinct?
11. What is resolvant matrix?
12. Consider the system defined by =Ax where A=.Determine the Eigen values of the system matrix.
13. Determine an expression for the solution of a homogeneous stste equation using laplace transformation.
14.If A= what is .
15. Given .What is the corresponding system matrix A?

16 Marks :
1. For a system represented by state equation X(t)=AX(t).The response is X(t)= where X(0)= and X(t)= when X(0)= Determine the system matrix A and the state transition matrix.
2. Find the time response of the system described by the equation (t)= ,
3. For the system described by the transfer function Y(s)/U(s)=1/(s2
(i) Find the state space representation of the system +5s+6)
(ii) Find the state transition matrix ø(t)
(iii) Find the free response of the system when the initial condition is x1(0)=0 and x2(0)=1..
4. The system matrix A of a discrete time system is given by A= Compute the state transiton matrix Ak Theorem using the Caayley Hamilton
5.. For A= ,Compute Compute the state transiton matrix eAt Cayley Hamilton theorem using the
6. A linear time invariant system is described by the following state model. = + [u] and y= Transform this sate model into a canonical state model.Also compute the state transition matrix e At .
7.Convert the following system matrix to canonical form and hence calculate the state transition matrix eAt/ A=

Unit III

2 Marks :
1. Define controllability
2. Define observability
3. What is the need for observabitlity test?
4. Give two equivalent mathematical expressions which state that a given pair of matrices (A,B) is controllable
5. State the condition for controllability and observability of a system by Gilbert’s test.
6. How will you find the transformation matrix pc
7. State the condition for controllability and observability of a system by Kalman’s test. using the characteristics equation?
8. How to define stability in the sense of Lyapunov?
9. What are Lyapunov’s functions? State their significance.
10. What is minimum energy control?

16 Marks :
1. A system is described by
[x]= [x] + [u]
[y]= [x]. Test its controllability and observability
2. A control system is described by the differential equation d3y(t) /dt3
(i) Describe the system in the state variable form. X=Ax+Bu , Y=Cx+Du = u(t),where y(t) is the observed output and u(t) is the input.
(ii)Calculate the state transition matrix of the system.
(iii) Is the system controllable?
3 Consider the following system x= x + u and C= [1 1 2] check the observability.
ii)For the system [x] = [x] + [u] Check the controllability condition.
4. The state model of a system is given by = + [u] ; Y=[1 0 0] Convert the state model to controllable phase variable form.
5. Consider a linear system described by the transfer function Y(s)/U(s) = 10/s(s+1)(s+2) Design a feedback controller with a state feedback so that the closed loop poles are placed at -2,-1 ± j1
6.The state model of a system is given by = + [u] ; Y= [1 0 0] Convert the state model to observable phase variable form.
7. Convert the following state model into Jordan canonical form and therefore from comment on controllability and observability.
X(t) = x(t) + u(t) ;
Y(t) = x(t)
8. Consider the system = + [u]
Y= [1 1 1]
i) Show that the system is not completely observable.
(ii)Show that the system is completely observable, if the output is given by =
9 .Show that the following system (with a fine varying B(t) matrix ) is not completely controllable. A= 1/12 ; B=