X 2 3. Derive state transition matrix and its properties [10M] 4. (a) Derive a state space representation of the following system [5M] 1

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QUESTION BANK 6 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code :SYSTEM THEORY(6EE75) Year &Sem: I-M.

(b) What are the advantages of state space approach compare with the all other control system representations.. (a) What are the different properties of state transition matri?

1 QUESTION BANK 6 SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 5758 QUESTION BANK (DESCRIPTIVE) Subject with Code :SYSTEM THEORY(6EE75) Year &Sem: I-M.Tech& I-Sem UNIT-I Course & Branch: M.Tech - EEE Regulation: R6. (a) Consider the mechanical system shown in figure. Obtain state model for shown displacement and velocities. (b) What are the advantages of state space approach compare with the all other control system representations.. (a) What are the different properties of state transition matri? Eplain (b) Compute state transition matri e At for the state model U 6 6. Derive state transition matri and its properties [M] 4. (a) Derive a state space representation of the following system Y S U S S 6S 4S 6 (b) What are the properties of state transition matri? 5. Find the solution of the following state equation [M] The initial conditions are given as ()= and ()=- 6. Consider the system defined by A Bu y C where Analysis of power electronic converters Page

2 QUESTION BANK 6 A B C y obtain the transfer function u 7. (a) For the system described by the differential equation y 6 y y 6y 6u where u is s s [M] the input and y is the output. Obtain state model and also draw its state diagram. (b) State and prove non-uniqueness of state model. 8. Obtain the epression for the solution of linear time-invariant continuous time state equation [M] o t At But t o 9. Obtain the state model of the system whose transfer function is given as [M] ys u s S 4S S. (a) Eplain in details about the conversion of state space model to transfer function model using Fadeeva algorithm. (b) State the similarity transform and invariance of the system. UNIT-II. Determine the canonical state model of the system, whose transfer function is given by s S 5 S S 4S T also give the diagrammatic representation. [M]. Find the transformation matri P that transforms the matri A into diagonal or Jordon canonical form, where 4 A 4 4 [M]. State and prove the necessary and sufficient condition for arbitrary pole placement. [M] y 4. Given the transfer function s us SS S design a feedback controller with a state feedback so that the closed loop poles are placed at-, -±j(using Ackerman s formula). [M] 5. What is similarity transformation? And also discuss in detail various properties that are invariant under similarity transformation. [M] 6. What is the procedure for the designing of controller using output feedback? Eplain. [M] Analysis of power electronic converters Page

3 QUESTION BANK 6 Analysis of power electronic converters Page 7. Consider the following system 6 5 B and where BU A By using state feedback control u=-k, it is desired to have the closed loop poles at S=-+j4 --j4 and -. Determine the state feedback gain matri K. [M] 8. For the system, U design a linear state variable feedback such that the closed loop poles are located at -, - and -. [M] 9. A single input system is described by the following state equation u Design a state feedback controller which will give closed loop poles at -±j,-6.by using state feedback control u=-k, it is designed to have the closed loop poles at s=-+j4 --j4. [M]. Eplain in details the concepts of controllability and observability. [M] UNIT-III. (a) Eplain the linear quadratic regulator problem. (b) Describe the solution of algebraic Riccati equation using alternative method.. Derive the solution or Riccati equation using eigen values and eigen vector method.. (a) State and eplain the continuous linear quadratic regulator problem: (b) For the system Y U consider u dt J T Find Riccatti matri K(t) and state feedback matri. 4. (a) Define eigen value and eigen vector. (b) Eplain canonical form of representation of linear system. 5. What are linear quadratic regulator (LQR) problems? Eplain in detail the method to solve the LQR problems through solutions of algebraic riccati equation. [M] 6. Eplain in detail the concept of linear quadratic regulator. [M]

4 QUESTION BANK 6 7. (a) State and Eplain fundamental theorem of calculus of variation. (b) State and eplain the solution of algebraic riccati equation. 8. Eplain in details about the Iterative method. [M] 9. Write in details the controller design using output feedback method. [M]. Write the procedure of solution of algebraic riccati equation using eigenvalue and eigenvector methods. [M] UNIT-IV. (a) Eplain the controller design using output feedback method. (b) Design the full order observer using Ackermann s formula.. Consider the system A Bu Y C 6 6 where A B C Design a reduced ordered observer. Assume the desired eigen values for minimum order observer are j. [M] j. Obtain observability and observable canonical form for the following state model: [M] B U Y Using the pole placement with observer approach, design full order observer controller for the system shown in figure. The desired closed loop poles for the pole placement part are: S = -+j, S = --j, S = -5. The desired observer poles are: S = -, -, -. [M].6 ordered observer. Assume the desired eigen values for observer matri and μ=.8+j.4, μ=.8+j Consider the system Ẋ=A+BU Y=Cwhere A B C Design a full [M] 6. Consider the system U Y. Design a reduced ordered observer that makes the estimation error to decay atleast as fast as e -t. [M] Analysis of power electronic converters Page 4

5 QUESTION BANK 6 7. Consider the system described by the state model = A, Y=C. where A =, C = [ ] Design a full order state observer. The desired Eigen values for the observer matri are μ= 5, μ= 5. [M] 8. The state model of a system is given by U Y Convert the state model into observable phase variable form. [M] 9. The coefficient matrices of a state model are B C and D Find the transformation (t)=q(t) so that the state canonical form. [M]. Write short notes on full order and reduced order state observers with a suitable eamples. [M] UNIT-V. (a) Eplain the asymptotic stability of linear time invariant continuous. (b) Eplain the asymptotic stability of time invariant discrete system.. (a) Eplain about sensitivity and complementary sensitivity functions. (b) Describe the method of decoupling by state feedback giving an eample.. State and prove Lyapunov stability theorem of linear time invariant continuous time systems[m] 4. (a) Eplain the stability in the sense of Lyapunov. (b) Describe with a neat sketch the internal stability of the system. 5. Eplain in details about asymptotic stability of linear time invariant continuous and discrete time system. [M] 6. A second order system is represented by = A, A = use Lyapunov theorem and 4 determine the stability of the origin of the system. Write the Lyapunov function V(). [M] 7. (a) State and Eplain lyapunov stability theorem. (b) Determine the stability of the origin of the following Analysis of power electronic converters Page 5

6 consider the following quadratic function as a QUESTION BANK 6 possible lyapunov function v()= Draw the phase trajectory of the system described by the equation comment on the stability of the system. [M] 9. (a) Determine asymptotic stability condition of a system using lyapunov approach. (b) Determine the stability of the system dynamics 4. (a) State and prove lyapunov stability theorem. (b) Find the stability of the system described by the equation Prepared by:dr.a.srinivasan Analysis of power electronic converters Page 6

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