MATLAB processes

T oolbox Lafon [38] MATLAB processing algorithm available upon request... 

The script file kalfild.m solves, in forward-time, the discrete solution of the Kalman filter equations, using equations (9.74), (9.75) and (9.76) in a recursive process. The MATLAB command Iqed gives the same result. 

Chemical Process Control A First Course with MATLAB... 

However, MATLAB allows us to get the answer with very little work—something that is very useful when we deal with more complex systems. Consider a numerical problem with values of the process gain Kp = 1, and process time constants X = 2 and x2 = 4 such that the closed-loop equation is... 

The very first step is to find the ultimate gain. With the given third order process transfer function, we use the following MATLAB commands,... 

The Wegstein method is a secant method applied to g(x) = x - Fix). In Microsoft Excel, roots are found by using Goal Seek or Solver. Assign one cell to be x, put the equation for/(x) in another cell, and let Goal Seek or Solver find the value of x that makes the equation cell zero. In MATLAB, the process is similar except that a function (m-file) is defined and the command fzeroCf .xO) provides the solution x, starting from the initial guess xO. 

To solve the alkylation process problem, the code NPSOL, a successive quadratic programming code in MATLAB, was employed. 

Soumekh, M., Synthetic Aperture Radar Signal Processing with MatLab Algorithms, Artech House, 1999. 

Mathematical software, for process control, 20 694-695. See also Software MATLAB program, 20 695 MatML extensible mark-up language, 75 759... 

Excel does not provide functions for the factor analysis of matrices. Further, Excel does not support iterative processes. Consequently, there are no Excel examples in Chapter 5, Model-Free Analyses. There are vast numbers of free add-ins available on the internet, e.g. for the Singular Value Decomposition. Alternatively, it is possible to write Visual Basic programs for the task and link them to Excel. We strongly believe that such algorithms are much better written in Matlab and decided not to include such options in our Excel collection. 

Initially, we develop Matlab code and Excel spreadsheets for relatively simple systems that have explicit analytical solutions. The main thrust of this chapter is the development of a toolbox of methods for modelling equilibrium and kinetic systems of any complexity. The computations are all iterative processes where, starting from initial guesses, the algorithms converge toward the correct solutions. Computations of this nature are beyond the limits of straightforward Excel calculations. Matlab, on the other hand, is ideally suited for these tasks, as most of them can be formulated as matrix operations. Many readers will be surprised at the simplicity and compactness of well-written Matlab functions that resolve equilibrium systems of any complexity. 

In general, non-linear problems cannot be resolved explicitly, i.e. there is no equation that allows the computation of the result in a direct way. Usually such systems can be resolved numerically in an iterative process. In most instances, this is done via a truncated Taylor series expansion. This downgrades the problem to a linear one that can be resolved with a stroke of the brush or the Matlab / and commands see The Pseudo-Inverse (p.ll 7). 

The calculation process has been implemented by using a Matlab program throughout the following steps. 

Overall, most of the requirements for a process spectrometer/analyzer are straightforward to implement, but they do require attention at the design level. Another important area, which is FTIR specific, is the user interface and the need to provide for industry standard data communications. Standard software packages do exist for process instrumentation. For prototype development, and even for the front-end interface in a stand-alone mode of operation, software products, such as National Instraments Lab View and the Mathworks MatLab, are also important instrumentation development tools. Note that National Instruments also provides important computer-based electronics and hardware that meet most of the computer interfacing, and system control and communications needs for modem instrumentation. For practical installations, a product known... 

A large number of chemical/biological processes will be presented, modeled and efficient numerical techniques will be developed and programmed using MATLAB 2. This is a sophisticated numerical software package. MATLAB is powerful numerically through its built-in functions and it allows us to easily develop and evaluate complicated numerical codes that fulfill very specialized tasks. Our solution techniques will be developed and discussed from both the chemical/biological point of view and the numerical point of view. 

Here is our MATLAB program, specialized for acetone cracking, but easily adaptable for other chemico-physical processes. 

The axial dispersion model has led to the two-point boundary value problem (5.37) for uj from uj = ujstart = 0 to u> = uJend = 1- DEs are standardly solved by numerical integration over subintervals of the desired interval [uj start, we d. For more on the process of solving BVPs, see Section 1.2.4 or click on the Help line under the View icon on the MATLAB desktop, followed by a click on the Search tab in the Help window and searching for BVP . 

In this chapter we have presented multistage systems with special emphasis on absorption processes. We have studied multitray countercurrent absorption towers with equilibrium trays for both cases when the equilibrium relation is linear and when it is nonlinear. This study was accompanied by MATLAB codes that can solve either of the cases numerically. We have also introduced cases where the trays are not efficient enough to be treated as equilibrium stages. Using the rate of mass transfer RMT in this case, we have shown how the equilibrium case is the limit of the nonequilibrium cases when the rate of mass transfer becomes high. Both the linear and the nonlinear equilibrium relation were used to investigate the nonequi-librium case. We have developed MATLAB programs for the nonequilibrium cases as well. 

We have developed a detailed two-phase model for the UNIPOtr process. This model was used to investigate the steady and dynamic characteristics of this important industrial process that creates polymers directly from gaseous components. The reader should develop MATLAB programs to solve for the steady state and the unsteady-state equations of this model. This will enable him or her to investigate... 

Figure 2.61 Matlab program for design of reactor-stripper process.

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