hw9solution

# hw9solution - Problem1 Find all the steady states for the...

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Problem1. Find all the steady states for the reactor at the specified operating conditions assuming CAf and Tj are the two manipulated inputs and CA and T are the two controlled outputs. function f=hw9prob1(x) k0=3e7; dH=5000; E=12000; rhoCp=400; UA=150; R=1.987; V=0.9; Caf=10; Tf=298; Tj=298; q=1; Ca=x(1); T=x(2); f(1)=(q/V)*(Caf-Ca)-k0*exp(-E/R/T)*Ca; f(2)=(q/V)*(Tf-T)+dH/rhoCp*k0*exp(-E/R/T)*Ca-UA/V/rhoCp*(T-Tj); M-file : x01=[15 300]; x1=fsolve( 'hw9prob1' ,x01) x02=[0 400]; x2=fsolve( 'hw9prob1' ,x02) Optimization terminated: first-order optimality is less than options.TolFun. x1 = 9.4318 303.1659 Optimizer appears to be converging to a minimum that is not a root: Sum of squares of the function values is > sqrt(options.TolFun). Try again with a new starting point. x2 = 3.6399 369.5571 (MATCAD can be used as well OR simple while loop in MATLAB can be used to get the lowest convergence steady state values)

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Linear state space model :
Problem2. Prove that steady state gain can be calculated by K = -C A -1 B At steady state MATLAB code A=[-1.178 0.0415; 0.837 -1.0091]; B=[1.1111 0;0 0.417]; C=[1 0;0 1]; D=[0;0]; K=-C*inv(A)*B K = 0.9716 0.0150 0.8059 0.4257 The preferred control loop pairing is output T controlled by input Tj and output Ca controlled by Caf.

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