Please help with simulink in matlab. A continuously stirred tank reactor is used
ID: 3855977 • Letter: P
Question
Please help with simulink in matlab.
A continuously stirred tank reactor is used to produce a product P from A and B. The reaction is A + B rightarrow P. A is in excess and the rate of decomposition of B is given by r_b = k_1 x_2/(1 + k_2 x_2)^2 where k_1 and k_2 are constants and x_2 is the product concentration. The equations describing the system are given by: dx_1/dt = u_1 + u_2 - 0.2 squareroot x_1 dx_2/dt = (C_b1 - x_2) u_1/x_1 + (C_b2 - x_2) u_2/x_1 - k_1 x_2/(1 + k_2 x_2)^2 The parameters are C_b1 = 24.9, C_b2 = 0.1, k_1 = k_2 = 1, and u_1 = u_2 = 1. The initial conditions are x_1 (0) = 10 and x_2 (0) = 0. a) Simulate the equation for x_1 only since it does not depend on x2 and note the steady-state. Initialize the integrator for x1 to the steady-state value and determine x_2 and its steady-state by running the simulation with x_2 (0) = 0 b) Repeat and note the new steady state by rerunning the procedure by changing the initial state for x_2 to x_2 (0) = 10 c) Both of the previous cases are stable. There is another steady-state corresponding to everything else being the same and x_2 = 2.793 and x_1 = 100. This is an unstable steady-state. Demonstrate this by setting the initial value of the integrator for x_2 to 2.8 and show that the simulation goes to the upper steady state and repeat for an initial value of 2.79 and show that it goes to the lower steady state. That means that any small fluctuation will cause the system to fall to steady-state of part a or the steady-state of part b. Also, demonstrate that this is an unstable steady-state by linearizing the equation for x_2 about the steady-state values and showing that the linear system that results is unstable. You can do that by either solving the differential equation or by simulating the system with a small initial delta x_2.Explanation / Answer
The parameters of the CSTR model structure are defined and F, V, R and H are specified to be fixed.
Through physical reasoning we also know that all but the heat of reaction parameter (always negative because the reaction is exothermic) are positive. Let us also incorporate this (somewhat crude) knowledge into our CSTR model structure:
A summary of the entered CSTR model structure is next obtained through the PRESENT command:
Input-Output Data