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hw1 - ECE 147A FEEDBACK CONTROL SYSTEMS THEORY AND DESIGN...

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ECE 147A FEEDBACK CONTROL SYSTEMS - THEORY AND DESIGN F09 Homework 1 Due Friday, October 2nd, 2009 Explain all answers! Start early if you haven’t used Simulink before. In this assignment you will learn Simulink by using it, and by asking questions when you get stuck. Problem 1 Complete the following tasks: 1. Find the complex number K and the real number a so that 200 ( s 2 + 25)( s + 8) = K s - 5 j + K * s + 5 j + a s + 8 . (Hint: Isolate an unknown and then make a particular choice for s that makes the other unknowns disappear.) 2. Using your answer from part 1, determine the mathematical formula for sin(5 t ) * e - 8 t , where ‘*’ represents the convolution operation, without performing the convolution oper- ation. Instead use Laplace transforms and inverse Laplace transforms. 3. Using the plot commands in MATLAB, plot your answer to part 2. 4. Build a SIMULINK diagram that performs the convolution operation of part 2. (Hint: Use a function generator to generate a sinusoidal input and apply it to an appropriate linear dynamical system.) 5. Save the output of your SIMULINK diagram to the MATLAB workspace and plot the
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