32_Midterm2_ReviewW12 - EXAM 2 preview/review CHE 361...

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Unformatted text preview: EXAM 2 preview/review CHE 361 Winter 2012 Remember...... Midterm # 2 is 10 - 11:50 am Thur. Mar. 1, 2012 in Kearney 212. Bring your own (Textbook+), paper, pencils, calculator with charged batteries, etc. (Textbook+) = SEMD3, KLL handouts, notes and your own HWs. You must show your work and put FINAL answers in the boxes or spaces provided !! Numerical answers must not be “expressions”, e.g. x not = 37 π / 44 but rather x = 1.49 if required “to 3 significant figures”. NEW TOPICS - exam may include previous topics as well as new ones ! Review = Chap. 4: Derivation of G(s) from nonlinear ODEs, example = Bioreactor. Chap. 5: Familiarity with "simple" (no zeros) first-order and second-order dynamics, explicit availability of responses to standard inputs of step, ramp and sinusoidal functions of time. Standard parameters of TF models, i.e. zeta as damping coefficient, tau for first-order and second-order systems (over-, critically- and under-damped systems). Chap. 6: More complex G(s) => TFs with more than two poles, zeros, and time delay. "Story" problem descriptions of dynamics / rate of accumulation: steady-state relationship and description of dynamic changes and functions of time. Solution of nonlinear dynamics using linear approximation (transfer function model) theory. Some familiarity with the use of MATLAB and Simulink software tools for CHE 361 problems, including step2g and numerical methods ode45 to solve ODEs, e.g. be able to solve a nonlinear ODE using Euler method using a calculator for a specified step size and for a specified number of steps. Chap. 7: Identifying transfer function models from step response data, theory and "noncomputer" methods for 1st and 2nd order systems, step2g software for leastsquares fit of G(s) => data file format (3 columns) and use, specifications of parameters, interpretation of program output and results. Chap. 5,14: Frequency Response - Given G(s): physical meaning of AR and phase angle, shortcut method and complex numbers / algebra, "Bode plots" including time delay, the "G-plane plot" of Real and Imag parts of G ( jω ) as frequency changes is called a "Nyquist diagram". Components of overall AR and phase angle due to simple “factors” of G ( s ) poles and zeros - handouts on frequency response. Use of CHE 361 / MATLAB frequency response data file format (5 columns) and programs: freqg, chebodei, chebode2i and plots, and pulsec for pulse experiment analysis. See back side for more !! → “SOME” OF THE TYPES OF PROBLEMS ..... 1) Be able to identity type of transfer function model from a process step response curve or datafile and vice versa: solve for y(t) given G(s) and size of step, solve for G(s) given y(t) and size of step. 2) Be able to switch among any of the possible "forms" of G(s). Some examples are: - standard form (coefficient of lowest order in s = 1) - factored form (equivalent to coefficient of highest order in s = 1) - specification of location of poles and zeros along with gain - given values of standard parameters ( K, θ, τ = 1st or 2nd, ζ and τz ) Standard form 2(0.2 s + 1) 4(0.2 s + 1) 0.8( s + 5) == Factored form 2 2 0.5s + 1.5s + 1 s + 3s + 2 ( s + 2)( s + 1) Gain = 2, Poles at s = -1, s = -2, Zero at s = -5. 3) Be able to derive the overall transfer function between an output and input from a component block diagram arrangement: series, parallel, feedback arrangements as shown in Chap.6 and in-class notes for handout “Interacting Tanks - Block Diagrams” (feedback loop in block diagrams). 4) Given a set or single nonlinear ODE, be able to linearize (when necessary) terms to derive a transfer function model of the process dynamics. Be able to solve a first-order ODE problem using the transfer function approach. Describe differences between linear and nonlinear model predictions of responses to step changes in input. Be familiar with Bioreactor project. 5) Be able to numerically solve ODE(s) using Euler's method and a calculator - understand effects of the choice of step size on the accuracy and stability of numerical solutions of ODE(s). 6) Be able to interpret physical story-type problems which depend on frequency response interpretation, such as EXAMPLE 5.6 ( page 85 SEMD3) and EXERCISE 14.3 (page 268 SEMD3). 7) Given a transfer function, use the short-cut method to calculate the amplitude ratio (AR) and phase angle (PA) for a specific frequency. This requires calculations using complex numbers and their interpretation. Be able to calculate the frequency response of a complex transfer function based on its "parts", as discussed in the "components" handout. 8) Given a BODE plot, determine an appropriate form/type of transfer function and determine numerical values of simple parameter problems, e.g. K value or time constant and damping coefficient for 1st or 2nd order systems from AR/PA plots/data. ...
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