By Harold, Allen, Randal Klee
Read Online or Download Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition PDF
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Extra info for Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
Example text
10. The downstream process requires that the sustained fluctuations in the flow F0(t) be no larger than 10 ft3=min. 25 ft per ft3=min. 10 (a) Find the difference equation for F0, A(n), n ¼ 0, 1, 2, 3, . . Leave the tank cross-sectional area A as a parameter. 5 min for a starting value of A ¼ 100 ft2. Graph both F0, A(n) and HA(n), n ¼ 0, 1, 2, . . for a period of time sufficient to determine if the design criterion is satisfied. Assume that the tank is initially empty. (c) Repeat part (b) with a new value of A until the design criterion is satisfied.
5% interest annually. (a) Track the end of year fund balance for the first several years. (b) Find the account balance at the end of 18th year. (a) The discrete-time model is y(k) ¼ y(k À 1) þ 0:075y(k À 1) þ u(k), k ¼ 1, 2, 3, . . with input u(k) ¼ 1000, k ¼ 1, 2, 3, . . and initial condition y(0) ¼ 5000. 19 Mathematical Modeling The account balance at the end of years 1, 2, and 3 are worked out as follows: k ¼ 1: k ¼ 2: k ¼ 3: y(1) ¼ y(0) þ 0:075y(0) þ u(1) ¼ 5000 þ 0:075(5000) þ 1000 ¼ 6375 y(2) ¼ y(1) þ 0:075y(1) þ u(2) ¼ 6375 þ 0:075(6375) þ 1000 ¼ 7853:13 y(3) ¼ y(2) þ 0:075y(2) þ u(3) ¼ 7853:13 þ 0:075(7853:13) þ 1000 ¼ 9442:11 (b) The recursive solution could be continued for k ¼ 4, 5, 6, .
18 is a continuous-time model and the system is a continuous-time system because it involves only continuous-time variables. In contrast to the continuous-time signals F1(t), F0(t), and H(t), the sequence of sampled input flow values, F1(nDt), n ¼ 0, 1, 2, . . and the sequence of approximate tank levels HA(nDt), n ¼ 0, 1, 2, . . are classified as discrete-time (discrete for short) signals because the independent variable ‘‘n’’ is discrete in nature. 31) is classified as a discrete-time model, and the underlying system with purely discrete-time input and output signals is likewise a discrete-time system.