Example Using MATLAB

You can solve the same problem using MA TLAB. First, you define a function that rep- 

Step 1 Program the function and save it in your working directory as vpequil.m. 

Step 2 Issue the command vpequil(0.2) in the command window the output should be  

Calculation with a calculator gives the same answers, so you have verified that the program is correct. 

Step 3 Add semi-colons at the end of each line of the m-file and save it. Solve the problem by issuing the fzero command in the command 

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Appendix B Numerical Method of Lines Example Using MATLAB ... 

The examples given in this Appendix were generated using MATLAB Version 5.3. Onee the software has been installed, MATLAB is most easily entered by elieking the MATLAB ieon. Alternatively, in a Windows environment, MATLAB ean be entered by elieking the following sequenee... 

This example uses the MATLAB eommand Iqr to provide the eontinuous solution of the redueed matrix Rieeati equation (9.25)... 

When you use MATLAB to solve this problem, be careful when you interpret the results. The computer is useless unless we know what we are doing. We provide only the necessary statements.1 For this example, all we need is ... 

Use MATLAB to observe the effect of higher order multicapacity models as in Example 3.3. 

Example 5.6 Provide illustrative closed-loop time response simulations. Most texts have schematic plots to illustrate the general properties of a feedback system. This is something that we can do ourselves using MATLAB. Simulate the observations that we have made in previous examples. Use a unity feedback system. 

From here on, we will provide only the important analytical equations or plots of asymptotes in the examples. You should generate plots with sample numerical values using MATLAB as you read them. 

In this book we shall use MATLAB codes and explain more involved features of MAT-LAB as we encounter them. MATLAB has a built-in help menu typing help format at the prompt, or help, for example, will show the syntax and variations of these two commands format and backslash . Whenever a student encounters a MATLAB command that is not self explanatory, we suggest using this built-in help function of MATLAB. 

Several important types of reactions are considered in the following sections. The equations describing each of these systems are developed. The steady-state design of CSTRs with these reactions are discussed, using Matlab programs for hypothetical chemical examples and the commercial software Aspen Plus for a real chemical example. 

Figure 7.15 shows the calculated corresponding concentration profiles using the rate constants = 10" s 1 and k2 = 1 M s 1 for initial concentrations [A]0 = 1 M and [B](i = 0M. We used MATLAB s Runge-Kutta-type ODE-solver oae45. In MATLAB Example 7.6b, the function is given that generates the differential equations. It is repeatedly called by the ODE-solver in MATLAB Example 7.6a. 

The major requirement to simulate an ODE-based model using Matlab (or most other packages) is to supply a code that computes the time derivatives of the state variables - the right-hand side of Equations (3.27). An example of a function that computes the time derivatives for this model using Matlab syntax is given below.2... 

Another Example of a Chemical Engineering Problem Solved Using MATLAB... 

In the preceding example we derived the expression for T( ) analytically for a step change in An alternative approach is to use MATLAB to calculate the step response of the closedloop servo transfer function... 

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