ps1 - EE 429 Reading assignment Ch 1 and Ch 2 PROBLEM SET 1...

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EE 429 PROBLEM SET 1 DUE: 5 Feb 2008 Reading assignment: Ch 1 and Ch 2 The goal of the Frst problem set is to develop your ability to: 1. Convert from one method of representing a dynamic system to another method of representation. ±or example, given an ODE (DE) representation, Fnd a corresponding state-space representation. 2. Determine the ZOH discrete-time equivalent model of a continuous-time process using state-space techniques. Problem 1: (20 points) A single-input single-output (SISO) system is represented by the second-order ordinary differential equation d 3 y dt 3 +4 d 2 y dt 2 +8 dy dt +2 y ( t )=2 u ( t ) , where y ( t ) is the system output and u ( t ) is the system input. At time t = 0 the initial conditions for the system are y (0) = 3, ˙ y (0) = 8, and ¨ y (0) = 0. 1. (2 points) Determine the system transfer function Y ( s ) /U ( s ). 2. (9 points) Represent the system by an all-integrator block diagram. State the initial condition for each inte- grator. 3. (9 points) ±ind a state-space representation for the system using the state-variables x 1 = y and x 2 y , and x 3 y . Specify the initial state vector x (0). Problem 2: (20 points) A single-input single-output (SISO) system is represented by the ordinary differential equation ¨ y - y u u, where y ( t ) is the system output and u ( t ) is the system input. 1. (2 points) Determine the system transfer function Y ( s ) /U ( s ). Are there any pole-zero cancelations? 2. (2 points) What are the poles of the transfer function ( do not include poles canceled by zeros !)?
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ps1 - EE 429 Reading assignment Ch 1 and Ch 2 PROBLEM SET 1...

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