Homework 05 - Linearity Rule of Thumb

# Homework 05 - Linearity Rule of Thumb - y = 9 + y(t) + u(t)...

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Chemical Engineering Department University of Florida ECH 4323 Process Control Theory HOMEWORK No. 5 — LINEARITY OF DYNAMIC SYSTEMS 1.0 Use the rule of thumb discussed in class to determine whether the following dynamic systems are linear or nonlinear with respect to the input and disturbance functions u(t) and d(t). a. ! "# \$ # % y (t) = –3 y(t) + 17 u(t) y(0) = 0 b. ! " # \$ # % y (t) = –3 y(t) + 17 u(t) + 4 y(0) = 0 c. ! "# \$ # % y (t) = –3 y(t) + 17 u(t) y(0) = 2 d. ! " # \$ # % y (t) = 3 y(t)u(t) + 17 u(t) y(0) = 0 e. ! "# \$ # % y (t) = –17 u(t) 2 y(0) = 0 f. ! " # \$ # % y (t) = –3t y(t) + 17 u(t) + 9 d(t) y(0) = 0 g. ! " # \$ # % y •• (t)+9y = –3 y(t) + 17 u(t) y(0) = 0, y (0) = 0 h. ! " # \$ # % y (t) = –3 y(t) + 17 u(t) + 9 d(t) y(0) = 0 2.0 Linearize the following models with respect to a steady state. a.
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Unformatted text preview: y = 9 + y(t) + u(t) d(t) + 4 u(t) b. &amp; VC p T (t) = q F &amp; C p (T F (t)T(t)) K q J (t) 0.8 A (T(t) T J ) where T(t) is the output of a system, T F (t) a temperature disturbance, and q J (t) is the input (volumetric flow rate into a cooling jacket). All variables that do not include the argument &quot;t&quot; may be assumed constant. All variables are defined in problem 2.8 of the textbook. c. &amp; VC p T (t) = q F (t) &amp; C p (T F (t)T(t)) + UA ((f s (P s ) T(t)) where P s is a constant. All variables are defined in problem 2.9 of the textbook. d. dh dt = q i (t) C v m g R MA(Hh(t)) T(t) + &amp; gh(t) P a where P s is assumed constant. All variables that do not include the argument &quot;t&quot; may be assumed constant. All variables are defined in problem 2.4 of the textbook....
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