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1 MODEL IDENTIFICATION AND DATA ANALYSIS (MIDA) – 2nd Module Academic Year 2017/2018 – 20/6/2018 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 I/O system described by the following transfer function: ( ) = ( ) a. Write the system in a state-space representation; draw the corresponding block-scheme. b. From the State-Space representation, check the Reachability and Observability of the system c. Compute the impulse response up to w(3); write the 2nd-order (size 2x2) Hankel matrix H2. Accuracy, clarity and organization of the answers will be evaluated DRAFT solution (only final results an a few steps of the solution procedure) 2 2. Consider the following system (where is a parameter): ( + 1) = ( ) + ( ) ( ) = ( ) + ( ) ( ) ~ (0,1) a. Compute the DRE and its convergence; compute the filter gain K(t). b. Compute the asymptotic predictor ( / 1) c. Compute the asymptotic filter ( / ) and the corresponding variance of the filter error [ ( ) ( / )] 3 3. Consider the system (with inputs ( ), ( ), ( )): ( + 1)= 0.5( )+ ( )+ ( ) ( )= 2( )+ ( ) a. Draw the block-scheme of the system. b. Design the Minimum-Variance controller for the system, when ( )= 1and ( )~ (1,1). c. Draw the block scheme of the control system (system and controller). d. Compute the transfer function of the closed-loop system from the reference ( )to the output ( ) 4 4. Briefly present and discuss the main methods to…