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The following differential equations describe the outlet concentrations of A, B, and C from a CSTR: dCa dt dCb = F (Ca₁ - Ca) - k₁ Ca² - k₂Cab A) (ca, V F =(#) (Cb,- Cb) + 2k, Ca² -0.5k, CaCb V dt dCc F dt (#) Cc +0.5 Cc+0.5k,CaCb A linear model can be developed with the form: x'= Ax' + Bu' y' = Cx' + Du' The state vector is [Ca, Cb, Cc], the input vector is [Fi, Cai, Cb;], and the output vector is [Ca]. Define all terms in the B matrix with respect to the given variables.

The following differential equations describe the outlet concentrations of A, B, and C from a CSTR: dCa dt dCb = F (Ca₁ - Ca) - k₁ Ca² - k₂Cab A) (ca, V F =(#) (Cb,- Cb) + 2k, Ca² -0.5k, CaCb V dt dCc F dt (#) Cc +0.5 Cc+0.5k,CaCb A linear model can be developed with the form: x'= Ax' + Bu' y' = Cx' + Du' The state vector is [Ca, Cb, Cc], the input vector is [Fi, Cai, Cb;], and the output vector is [Ca]. Define all terms in the B matrix with respect to the given variables.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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The following differential equations describe the outlet concentrations of A, B, and C from a CSTR: dCa dt dCb = F (Ca₁ - Ca) - k₁ Ca² - k₂Cab A) (ca, V F =(#) (Cb,- Cb) + 2k, Ca² -0.5k, CaCb V dt dCc F dt (#) Cc +0.5 Cc+0.5k,CaCb A linear model can be developed with the form: x'= Ax' + Bu' y' = Cx' + Du' The state vector is [Ca, Cb, Cc], the input vector is [Fi, Cai, Cb;], and the output vector is [Ca]. Define all terms in the B matrix with respect to the given variables.
Transcribed Image Text:The following differential equations describe the outlet concentrations of A, B, and C from a CSTR: dCa dt dCb = F (Ca₁ - Ca) - k₁ Ca² - k₂Cab A) (ca, V F =(#) (Cb,- Cb) + 2k, Ca² -0.5k, CaCb V dt dCc F dt (#) Cc +0.5 Cc+0.5k,CaCb A linear model can be developed with the form: x'= Ax' + Bu' y' = Cx' + Du' The state vector is [Ca, Cb, Cc], the input vector is [Fi, Cai, Cb;], and the output vector is [Ca]. Define all terms in the B matrix with respect to the given variables.
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