13_Exam1_ReviewW12

13_Exam1_ReviewW12 - Page 1 of 2 EXAM 1 preview/review CHE...

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Unformatted text preview: Page 1 of 2 EXAM 1 preview/review CHE 361 WINTER 2012 Remember...... Midterm #1 is 10 - 11:50 am Thur. Feb. 2, 2012 = Week 4. Bring your own SEMD3 textbook+, paper, pencils, calculator with charged batteries, etc. “ Open Textbook + ” = SEMD3, KLL handouts, and your notes. You must show your work and put FINAL answers in the boxes provided !! TOPICS: review Course Learning Outcomes 1-4 (1) Laplace transforms: "pairs" and theorems, including Table 3.1. ∞ Definition : F ( s ) = L [ f ( t ) ] = ∫ f ( t ) e - s t dt 0 (2) Transforms of common functions: constant, unit step, ramp, and combinations. (3) Time delay in time and Laplace domains: use of the "switch" or delay unit step = S ( t - θ ). (4) Transform of time derivatives or an integral. (5) Partial fraction expansion: single real roots (complex conjugate pairs, repeated real roots only by using Table 3.1). (6) Final value theorem and initial value theorem = method and when you can use them. (7) Differential equations from MTH 256: initial value problems = ODE + initial conditions. (8) "Story" problem descriptions of dynamics / rate of accumulation: steady-state relationship and description of dynamic changes and functions of time. (9) It is useful to review methods for solutions of dynamic problems - see handout containing "sequences of steps" to use, in particular the "all-at-once" linearization and deviation variable introduction used in the derivation of transfer functions. Chap. 3: Chap. 4: Laplace transforms for initial value problems Transfer function approach and derivation of G(s) including derivation of linear ODEs from nonlinear ODEs when necessary. Chap. 5: Familiarity with "simple" (no zeros) first-order and second-order dynamics, "cook book" 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). Page 2 of 2 POTENTIAL TYPES OF PROBLEMS 1) Mathematical initial value problem (IVP): linear ODE type, solve for y(t) and evaluate y at specified times by solving the ODE in "full" variable form. 2) Mathematical initial value problem (IVP): linear or nonlinear ODE type, solve for y(t) and evaluate the deviation variable y'(t) or the full variable y(t) at specified times using the transfer function approach, i.e. using deviation variables in the ODE. 3) Given a written description and/or sketch of a simple process and its operating procedures, calculate process variables as functions of time after setting up and solving the appropriate dynamic material and/or energy balances - which may be linear or nonlinear. For example: Be able to solve a "tank problem" using the transfer function approach. Describe any differences between linear and nonlinear model predictions of responses to step changes in input. 4) Given a transfer function model, reverse the normal procedure to obtain an ODE for the deviation output and input variables or for the full version of the variables. 5) 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. 6) 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 Gain = 2, 2(0.2s + 1) 4(0.2s + 1) 0.8( s + 5) =2 = Factored form 2 0.5s + 1.5s + 1 s + 3s + 2 ( s + 2)( s + 1) 2 Poles: at s = -1, s = -2, and 1 Zero at s = -5. 7) Be able to derive the overall transfer function between an output and input from a component block diagram arrangement: series, parallel, feedback arrangements. These relationships can be derived from the algebraic properties of G(s) = ratio of Y(s) / U(s) and linearity of the Laplace Transform. 8) Given a single or set of nonlinear ODEs, be able to linearize (when necessary) each ODE to derive a specified transfer function model between one output and one input. Describe any differences between linear and nonlinear model predictions of responses to step changes in input. ...
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