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1 MODEL IDENTIFICATION AND DATA ANALYSIS 2ndmodule (MIDA2) Academic Year 2017/2018–5/7/2018 Surname Name Matr.Number Signature ................................ ............................... .....................………. .....................………. Answer each question in the blank space after the exercise text. Do not include additional papers. It is not allowed to consult books, notes, lecture notes etc. =============================================================================================================== 1.Consider the following impulse response of an LTI system: (0)= 0; (1)= 1; (2)= 0; (3)=1 2; (4)= 0; (5)=1 4; (6)= 0; (7)=1 8a. Compute the order of the system b. Using the 4SID method, estimate a state-space representation of the system {F, G, H] c. Starting from the state-space representation, compute the impulse response (for t=1,2,3,4) for the output and for the states of the systems; plot these impulse responses. d. Starting from the state-space-representation compute the I/O transfer function Accuracy, clarity and organizationof the answers will be evaluated 2 2. Consider the following ARMAX system: ( )= 1 3 ( 1)+ ( 1)+ 3( 2)+ ( ) e ( )~ (0,1) a. Explain why MV-control cannot be used b. Find the controller that fulfils the following objective: ( + 1/)+ 4u(t) =(t) c. Draw the block-scheme of the so-obtained control system d. check the stability of the so-obtained control system 3 3. Consider the following system: )()()( )()(5.0)1( )()(2)(5.0)1( 21 22 211 txtaxty tbutxtx tautaxtxtx whereaand bare parameters (real numbers) Is the system asymptotically stable? Discuss for which values of aand bthe system is observable and/or reachable Rewrite the system in the I/O form: )()()( tuzGty . 4 4.Give the definition of class of universal approximating functions(in…