b ,k = state variable coefficient B ’= reactant C = reaction product
SUBSCRIPTS
C = concentration of a chemical species C = number of controlled state variables E = reaction product f = element of a control matrix G = reaction product I = number of control actuating internal variables j = imaginary unit K = number of known inputs M = number of manipulable inputs A‘ = number of non-control-actuating internal variables P = reaction product q = heat-removal rate s = Laplace variable t = time T = temperature U = number of unknown inputs X = transformed process input JV = flow rate Y = transformed process output x j = input to a process y k = state variable of a process
GREEKSYMBOLS A = characteristic equation defined by Equation 2.18 e = linear valve angle w = continuous frequency variable
A = reactant or reactant stream A B = reactant or reactant stream B E = reaction product E G = reaction product G P = reaction product P R = variable describes a condition in a reactor rF = cooling water literature Cited
Bollinger, R. E., ’.Analysis and Control of hfultivariable Processes,” Ph.D. thesis (chemical engineering), University of Delaware,h-ewark, De!., 1963. Bollinger, R. E., Lamb, D. E., C i i m . Eng. Progr. 61, 55, 66 (1965). Bollinger, R . E., Lamb, D. E., ISD. CNG.C m b i . FUNDAMENTALS 1, 245 (1962).
Greenfield, G. G., \Vard, T . J.: I N D ESG. . CHEM. FUKDhWENl.4Ls 6 , 564 (1967).
Horowitz, I. M , ,I R E Trans. .-lutoinutic Coritroi AC-5, 5 (1959). Kalman, K . E., J . SIA.\iControl, Ser. A 1,152 (1963). Lee, Y. \V., “Statistical Theory of Communication,” \$-iley, New, York, 1960. Luecke, I
