MATLAB dynamics

In the model simulations, the settling and decanting phase were characterized by a reactive point-settler model. The simulations were carried out using matlab 6.5 simulation platform. A systematic model calibration methodology as described in Fig. 2 was applied to the SBR. Fig. 3. shows the simulation results from the calibrated model. The model predicted the dynamics of the SBR with good accuracy. 

We could also modify the M-file by changing the PI controller to a PD or PID controller to observe the effects of changing the derivative time constant. (Help is in MATLAB Session 5.) We ll understand the features of these dynamic simulations better when we cover later chapters. For now, the simulations should give us a qualitative feel on the characteristics of a PID controller and (hopefully) also the feeling that we need a better way to select controller settings. 

It can be synthesized with the MATLAB function feedback (). As an illustration, we will use a simple first order function for Gp and Gm, and a PI controller for Gc. When all is done, we test the dynamic response with a unit step change in the reference. To make the reading easier, we break the task up into steps. Generally, we would put the transfer function statements inside an M-file and define the values of the gains and time constants outside in the workspace. 

Figueroa, J. L., and Romagnoli, J. A. (1994). A strategy for dynamic data reconciliation within Matlab environment. Australas. Chem. Eng. Conf. 22nd, Perth, Australia, pp. 819-826. 

Equation (27) expresses an error in the dynamic matrix element Lij obtained from full matrix analysis if the error in peak volumes is Aa [50]. It also assumes that volume errors are equal for all peaks and are uncorrelated Aa is volume error normalized to the volume of a single spin at Tm = 0. Modem computer programs (Matlab, Mathematica, Mapple) can calculate the dynamic matrix from eq. (11) directly. 

The solver is implemented in Fortran, using optimized treatment of diagonal-band matrices and analytical derivatives of reaction rates to minimize computation time. The software structure is modular, so that different reaction-kinetic modules for individual types of catalysts can be easily employed in the monolith channel model. The compiled converter models are then linked in the form of dynamic libraries into the common environment (ExACT) under Matlab/Simulink. Such combination enables fast and effective simulation of combined systems of catalytic monolith converters for automobile exhaust treatment. 

The set of four ordinary differential equations (7.64) to (7.67) for the dynamical system are quite sensitive numerically. Extreme care should be exercised in order to obtain reliable results. We advise our students to experiment with the standard IVP integrators ode... in MATLAB as we have done previously in the book. In particular, the stiff integrator odel5s should be tried if ode45 turns out to converge too slowly and the system is thus found to be stiff by numerical experimentation. 

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... 

The dynamic behavior of the model consisting of the four ODEs in (7.189) to (7.192) can be found using a suitable MATLAB IVP solver ode... as previously outlined. 

Our model consists of the four ordinary differential equations (7.189) to (7.192) in the dynamics case and of the corresponding set of coupled rational equations in the static case. These two sets of equations can be solved and studied via MATLAB in order to find the system s steady states, the fermentor s dynamic behavior and to control it. 

Nonlinear Dynamic Simulation The nonlinear ordinary differential equations are numerically integrated in the Matlab program given in Figure 4.2. A simple Euler integration algorithm is used with a step size of 2 s. The effects of several equipment and operating parameters are explored below. 

The dynamics and control of a number of tubular reactor systems have been studied in this chapter. Both adiabatic and cooled tubular reactors have been explored in both isolation and a plantwide environment. Ideal systems have been studied using Matlab programs. Real chemical systems have been studied using Aspen Dynamics. 

Using the symbolic calculation engine available in Matlab ,2 we obtained the following description of the intermediate dynamics of the reactor-condenser process ... 

Throughout this book, we have seen that when more than one species is involved in a process or when energy balances are required, several balance equations must be derived and solved simultaneously. For steady-state systems the equations are algebraic, but when the systems are transient, simultaneous differential equations must be solved. For the simplest systems, analytical solutions may be obtained by hand, but more commonly numerical solutions are required. Software packages that solve general systems of ordinary differential equations— such as Mathematica , Maple , Matlab , TK-Solver , Polymath , and EZ-Solve —are readily obtained for most computers. Other software packages have been designed specifically to simulate transient chemical processes. Some of these dynamic process simulators run in conjunction with the steady-state flowsheet simulators mentioned in Chapter 10 (e.g.. SPEEDUP, which runs with Aspen Plus, and a dynamic component of HYSYS ) and so have access to physical property databases and thermodynamic correlations. 

We see that for Fq =70°F the reactor has dropped below the extinetion temperature and can no longer operate at the upper steady state. In Problem P9-16, we will see it is not always necessary for the temperature to drop below the extinetion temperature in order to fall to the lower steady state. The equations deseribing the dynamic drop from the upper steady state to the lower steady state are identieal to those given in Example 9-4 only the initial conditions and entering temperature are different. Consequently, the same POLYMATH and MATLAB programs ean be used with these modifications. (See CD-ROM)... 

For consequence analysis, we have developed a dynamic simulation model of the refinery SC, called Integrated Refinery In-Silico (IRIS) (Pitty et al., 2007). It is implemented in Matlab/Simulink (MathWorks, 1996). Four types of entities are incorporated in the model external SC entities (e.g. suppliers), refinery functional departments (e.g. procurement), refinery units (e.g. crude distillation), and refinery economics. Some of these entities, such as the refinery units, operate continuously while others embody discrete events such as arrival of a VLCC, delivery of products, etc. Both are considered here using a unified discrete-time model. The model explicitly considers the various SC activities such as crude oil supply and transportation, along with intra-refinery SC activities such as procurement planning, scheduling, and operations management. Stochastic variations in transportation, yields, prices, and operational problems are considered. The economics of the refinery SC includes consideration of different crude slates, product prices, operation costs, transportation, etc. The impact of any disruptions or risks such as demand uncertainties on the profit and customer satisfaction level of the refinery can be simulated through IRIS. 

All simulations were performed with the dynamic simulator Diva and visualized with Matlab. For simplicity the delay behavior between infection and virus release was reproduced by simply shifting the simulation results by tshifi = 4.5 h [4]. 

For the distillation columns, linear model-order reduction will be used. The linear model is obtained in Aspen Dynamics. Some modifications to the previous study have been done to the linear models, in order to have the reboiler duty and the reflux ratio as input or output variables of the linear models. This is needed to have access to those variables in the reduced model, for the purpose of the dynamic optimization. A balanced realization of the linear models is performed in Matlab. The obtained balanced models are then redueed. The redueed models of the distillation columns are further implemented in gProms. When all the reduced models of the individual units are available, these models are further connected in order to obtain the full reduced model of the alkylation plant. The outeome of the model reduction procedure is presented in Table 1, together with some performances of the reduced model. 

Control results of the PI decentralised approach will be further presented together with the MFC results, for the case of the dry weather input disturbance scenario. The dynamic simulator and the control simulations have been implemented on the Matlab/Simulink platform. 

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. 

Both formulations EKF and CEKF were implemented in MatLab 7.3.0.267 (R2006b) and applied in the process dynamic model, previously presented. The system initial condition is an operating point that presents a minimum-phase behavior (lstep changes in the valve distribution flow factors during the process simulation the system moves to an operating region presenting non-minimum phase behavior (l[Pg.523]

The control strategies are programmed in Matlab-Simulink, compiled in C-H-and then downloaded into the DSP processor of the d-Space board. The controlled management of the fuel cell system during the dynamic tests operates on hydrogen purge, air flow rate regulation (stoichiometric ratio), external humidification, and stack temperature. 

Hydrolysis and fermentation models were developed using two hydrolysis datasets and two SSF datasets and by using modified Michaelis-Menten and Monod-type kinetics. Validation experiments made to represent typical kitchen waste correlated well with both models. The models were generated in Matlab Simulink and represent a simple method for implementing ODE system solvers and parameter estimation tools. These types of visual dynamic models may be useful for applying kinetic or linear-based metabolic engineering of bioconversion processes in the future. 

Nonlinear dynamics is becoming an important topic in design, since implied not only in safety aspects, but also in design for flexibility. Some applications will be presented in Chapter 13. An advanced treatment of nonlinear dynamics can be found in the book of Bequette (1998). More complex dynamic phenomena, as the occurrence of multiple steady states and chaotic behaviour, are presented in accessible but rigorous manner. Numerous examples built in Matlab illustrate the mathematical issues. 

Aspen Dynamics generates automatically a linear model by means of a Control Design Interface (CDI). The state space matrices A, B, C, D are saved as sparse matrices in ASCII files. These can be imported in MATLAB and used for further calculations. 

A scaled linearised state-space description around the nominal operating point of the dynamic model has been generated. The matrices A, B, C, and D have been exported in MATLAB , where a controllability analysis as fimction of fi equency has been performed. Alternatively, transfer fimctions have been generated. The results are similar. 

The mathematics of the subject are minimized, aaJ more emphasis is placed on examples that illustrate principles and concepts of great practical importance. Simulation programs (in FORTRAN) for a number of example processes are used to generate dynamic results. Plotting and analysis are accomplished using computer-aided software (MATLAB). 

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