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1. Consider the second order model: 4 +y - 4x(t), with x(t) as a unit step. Using the at2 at solution for a second order lag subject to a step response from the book (see section 2-5), explore the response of the given model. You do not need to derive the solution, but rather identify the various constants (time constant, SS gain and damping ratio) and use these to find the specific time domain solution for this case. Include the following activities a. Determination of time constant, SS gain and damping ratio b. Show the equation for the time response c. Calculate the Rise Time, Overshoot, Decay Ratio and settling time (see page 46) d. Prepare a plot using Excel that shows the time response for a time period of about 20 time constants 2. Problem 2-24 - The differential equation provided describes the temperature vS time for a turkey baking in an over with radiant heat transfer. Do the following: a. Assure yourself that you can obtain this same equation by doing an energy balance on the turkey, using the assumptions stated in the book. b. Obtain the equation for cooking the turkey in a convection oven. c. Linearize both models and put each into standard form for a 1st order lag. d. Compare the two models - specifically the time constants and SS gains. e. Describe an experiment to obtain values for the model constants. 3. Modified problem 3-3. This involves the development of the model for level in a tank with a ramp input disturbance and analysis of the situation from a safety perspective. Use the following: Flow out given by: F - .8 h / Tank diameter - 4 meters, tank height - 4 meters Initial flow in and out is 2.0 m3/min Ar time zero a ramp imput is introduced so that the flow becomes F = 2 + 0.050 * t To complete the problem you will need to derive the Laplace solution for the response of this tank to a ramp imput in flow. You can then obtain the time domain solution by matching with the general solution for a first order lag subject to a ramp input from the book. You can then find the time using solver. For extra insight (not required), create a table of height vS time and plot - compare to the numerical solution of the original (not linearized) differential equation. Compare this with the Laplace model. 4. Problem 3-5 development of a model for a process with energy considerations 5. Problem 3-18 development of the model for a blending process and finding transfer functions

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