Fix the linear model that was derived with the use of linearization and then afterwards simulate the non-linear process with the use of simulink around this nominal operating point of 0.099mol/L, where T is equal to 438.76K and qc(t) is equal to 1.72L/sec. the simulation is for changes in the coolant flowrate qc(t) % CSTR_SteadyState.m % This script computes the steady-state temperature and coolant flow rate % for a Continuous Stirred-Tank Reactor (CSTR) with an exothermic reaction. % Given parameters Q = 100/60; % Feed flow rate (L/sec) V = 100; % Reactor volume (L) k0 = 7.2e10/60; % Pre-exponential factor (sec^-1) E_R = 1e4; % Activation energy ratio (K) T0 = 350; % Feed temperature (K) Tc = 350; % Coolant temperature (K) dH = -2e5; % Heat of reaction (cal/mol) Cp = 1; % Specific heat (cal/g*K) rho = 1e3; % Density (g/L) Ca0 = 1; % Feed concentration (mol/L) ha = 7e5/60; % Heat transfer coefficient (cal/(min*K)) Ca_ss = 0.099; % Target product concentration (mol/L) % Derived constants k1 = (dH * k0) / (rho * Cp); % Reaction term constant k2 = 1 / V; % Cooling term constant (1/L) k3 = ha / (rho * Cp); % Heat transfer term (L/sec) % Solve material balance for steady-state temperature (T) without initial guess T_ss = fminbnd(@(T) abs((Q/V)*(Ca0 - Ca_ss) - k0*Ca_ss*exp(-E_R/T)), 300, 500); % Solve energy balance for coolant flow rate (qc) without initial guess qc_ss = fminbnd(@(qc) abs((Q/V)*(T0 - T_ss) - k1*Ca_ss*exp(-E_R/T_ss) + ... k2 * qc * (1 - exp(-k3/qc)) * (Tc - T_ss)), 1, 100); % Display results fprintf('\nSteady-State Conditions:\n'); fprintf('Product Concentration, Ca = %.4f mol/L\n', Ca_ss); fprintf('Steady-State Temperature, T = %.2f K\n', T_ss); fprintf('Coolant Flowrate, qc = %.2f L/sec\n\n', qc_ss); % Compute Jacobian elements for linearization A11 = -Q/V - k0 * exp(-E_R/T_ss); A12 = k0 * Ca_ss * exp(-E_R/T_ss) * (E_R / T_ss^2); A21 = -(dH / (rho * Cp)) * k0 * exp(-E_R/T_ss); A22 = -Q/V + (dH / (rho * Cp)) * k0 * Ca_ss * exp(-E_R/T_ss) * (E_R / T_ss^2) - ha/(rho*Cp*V); B2 = ha/(rho*Cp*V) * (1 - exp(-ha / (rho * Cp * qc_ss))); % State-space representation A = [A11, A12; A21, A22]; B = [0; B2]; C = eye(2); % Output all states D = [0]; % Create state-space model sys = ss(A, B, C, D); % Display results fprintf('\nLinearized State-Space Model:\n'); disp('A ='); disp(A); disp('B ='); disp(B); disp('C ='); disp(C); disp('D ='); disp(D); eigA = eig(A); fprintf('Eigenvalues of A (system stability check):\n'); disp(eigA); % Plot step response figure; step(sys); title('Step Response of the Linearized CSTR Model');