Registration No : Total Number of Pages : 03 6th Semester Regular Examination 2017-18 ADVANCED CONTROL SYSTEMS BRANCH : AEIE, EIE, IEE Time : 3 Hours Max Marks : 100 Q.CODE : C354 Answer Part-A which is compulsory and any four from Part-B. The figures in the right hand margin indicate marks. B.Tech. PEI6J002 Part – A (Answer all the questions) Answer the following questions : multiple type or dash fill up type : Q1. (2 x 10) 2 a) The transfer function of the system described by 2 d y dy du 5 3u where y 2 dt dt dt is output and u the input, is _______________. b) c) d) e) f) g) h) i) j) Q2. The transfer function of the system is defined by x(t ) Ax Bu, y Cx Du , is _________________. In limit cycle, _____________ and ________________ are constants. 2 0 A 0 1 0 1 0 0 0 1 0 0 . The sum of the eigen values of matrix A is _____. 3 0 0 4 An Eigen value of the system signifies _____________. What is the need of HOLD Circuit? A system having the transfer function (1-s)/(1+s) is known as _____________ filter. A control system working under unknown random actions is called a)Computer control system b)Digital data system c)Stochastic control system d) Adaptive control system Pole placement design is applicable when the system is completely _______ i) Controllable ii) Observable iii) Both controllable and observable. 1 1 2 A 0 2 1 , Eigen’s values care _____,_____ and _________. 0 0 2 a) b) c) d) e) Answer the following questions: Short answer type : Define transfer function and pulse transfer function. Find the Z-transform of f (t ) sin wt Draw the gain-frequency graph for ZOH and phase-frequency graph of ZOH. Define phase trajectory and phase portrait. State the formula of STM and Resolvent matrix with usual meanings. f) Given the transfer function of a system as G ( s ) transform. a , determine its Zs( s a) (2 x 10)
g) h) i) j) Q3. a) Show the relationship between S-domain and Z-domain. Is the relationship one to one relationship. State the duality principle in controllable and observable of the control system. What is nodal point and saddle point? State the difference between full order observer and reduced order observer. Part – B (Answer any four questions) For the system given below obtain i) Zero input response ii) Zero state response iii) Total response 1 0 0 x x u (t ) , where x1 (0) 1, x 2 (0) 0 and 2 1 1 u (t ) 1 . 0 1 1 x (t ) u has the initial condition 0 3 0 b) (10) A state variable system x(t ) (5) x( 0) 1 3 . Find out the state transition matrix to a unit step input? T Q4. a) The transfer function of a control system is given by (10) Y (S ) S2 . Check for controllability and observability. 3 U ( S ) S 9 S 2 26 S 24 Q5. Q6. b) Determine the suitable conditions for controllability and Observability. (5) a) Determine the unit response of a sampled data control system shown in figure (10) b) Explain the stability analysis of digital control system using Bilinear transformation and Routh’s stability criteria. (5) a) State the properties of ROC. Find the inverse Z-transform of the function given (10) that the sampling time T=1sec. F ( Z ) b) 0.632 z z 1.368 z 0.368 2 equation (5) a) Draw the phase trajectory of a system described by x x x x 0. Given the (10) b) initial condition x0 2 , y 0 0. Discuss the basic concept of describing function methods. (5) Solve the difference x(k 2) 3x (k 1) 2 x(k ) 4 ; x(0) 0, x (1) 1 . k Q7.
Q8. a) Determine the state feedback gain matrix K of the system; (10) 1 0 0 X AX Bu ; Y CX , where A , B , C 1 0 such that the 20.6 0 1 b) closed loop poles are at -1±j2.4. Reduce the matrix A to a diagonal matrix selecting a suitable modal matrix, (5) 1 0 0 where A 0 0 1 . 6 11 6 Q9. a) b) c) Write short notes on : Cayley Hamilton theorem in the context of evaluation of STM Delta method of construction of phase trajectory Describing function of an ideal saturation (5) (5) (5)