MATLAB stage

Optional reading In the initial learning stage, it can be a bad habit to rely on MATLAB too much. Hence the following tutorial goes the slow way in making root locus plots, which hopefully may make us more aware of how the loci relate to pole and zero positions. The first thing, of course, is to identify the open-loop poles. 

In this chapter, we present the basic matrix mathematics that is required for understanding the methods introduced later in the book. In line with the philosophy that all concepts are immediately implemented in Matlab and/or Excel, this will be done here as well. This way, Chapter 2 not only revises the basic mathematics, it also serves as a very short introduction to the Matlab and Excel languages. It is not meant to be a manual on Matlab or Excel the reader will need to refer to more specialised texts and proper manuals. Several more advanced features of both languages are not covered at this introductory stage but will be explained as they emerge in later chapters. 

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. 

Various simulation tools were also developed based on software including Simulink and Matlab to predict expected production from the RES technologies and to analyse the performance of the components. The efficiency of the electrolyser stack was estimated at 75% but that was reduced to 49% if the BOP and compression stages were taken into consideration. The round-trip efficiency of the hydrogen system was estimated at 16% (RES electricity to hydrogen and then back to electricity) while that of the complete system was 44% (thanks to the direct use of RES electricity by existing demand). 

This paper presents the application of a model based predictive control strategy for the primary stage of the freeze drying process, which has not been tackled until now. A model predictive control framework is provided to minimize the sublimation time. The problem is directly addressed for the non linear distributed parameters system that describes the dynamic of the process. The mathematical model takes in account the main phenomena, including the heat and mass transfer in both the dried and frozen layers, and the moving sublimation front. The obtained results show the efficiency of the control software developed (MPC CB) under Matlab. The MPC( CB based on a modified levenberg-marquardt algorithm allows to control a continuous process in the open or closed loop and to find the optimal constrained control. 

In the present stage of interfacial science, there exists a number of models which give a more or less rigorous explanation of the phenomena observed at interfaces on a molecular level. These models inevitably involve mathematics which is more complicated than that used earlier and the related calculations, in general, cannot be performed even using quite advanced computational software available now, e.g. MatCad or MatLab packages. 

The equations to calculate the capital cost of all the equipment and the energy cost of the energy are given in the Matlab program shown in Table 4.2. The numerical example is for the 32-stage column studied in Chapter 3. 

Binous, H., Equilibrium-Staged Separations Using MATLAB and Mathmatica, Chem. Engr. Educ., 42 (2), 69 (Spring 2008). 

Binous, H., Equilibrium-Staged Separations Using MATLAB and Mathematica, Chem. Engr. 

The recommended tools for safety assessment during the requirements stage are table based tools like Excel or Doors. Both tools are well known in the engineering domain. In the later stages, Matlab Simulink may be used for the evaluation of system and safety aspects. Depending on applied safety methods, specialized tools, comply the safety analysis in those stages. 

Suppose that we would like to have sin (x) be separately plotted from cos (x). MATLAB allows such a luxury via holding on the plot mode and invoking a subplot function. Since we have two functions, we will have two separate plots at this stage. Now we can either sort the two subplots as 2 rows x 1 column, or 1 row x 2 columns. In the first case, the two subplots will be vertically aligned above one another in the second case, the two subplots will be horizontally aligned beside one another. 

Figure 10.43 shows mywork.m file that defines the two-stage compressor work as a function of the intermediate pressure, Pmiddie> which is denoted here as x. The output of the MATLAB built-in fminbnd gives X that minimizes the work. Note that 1 and 4 represent the lower and upper limit for the variable X, respectively. 

Figure 10.44 shows the mywork3.m file that defines the three-stage compressor work as a function of the intermediate pressures, P2 andpg, which are denoted here asx(l) andx(2). The output of MATLAB built-in fminunc gives x, which minimizes the work. The MATLAB built-in fminunc finds the minimum of a multi-variable, unconstrained function on a fixed interval. 

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