Dynamic system design

Control Strategies for Dynamic Systems Design and Implementation, John H. Lumkes, Jr. 

Dynamics of Process Measurements Especially where the measurement device is incorporated into a closed loop control configuration, dynamics are important. The dynamic characteristics depend on the nature of the measurement device, and also on the nature of components associated with the measurement device (for example, thermowells and sample conditioning equipment). The term mea-.sui ement system designates the measurement device and its associated components. 

A deflected shaft is absolutely straight when rotated in a lathe or dynamic balancer. The deflection is the result of a problem induced either by operation or. system design. The deflected shaft also will fail prematurely in the pump, leaving similar, but different evidence on the elo.se tolerance rubbing parts in the pump. The next two pictures show how a bent shaft appears when rotated 180 degrees (Figure 9-9 and Figure 9-10). 

The GHH Borsig Turbolog DSP control system used for controlling the machine train is designed to enable dynamic system simulation using the control system hardware and software. Tliis offers two major benefits ... 

If instead of precise parameter estimation, we are designing experiments for model discrimination, the best grid point of the operability region is chosen by maximizing the overall divergence, defined for dynamic systems as... 

As an example for precise parameter estimation of dynamic systems we consider the simple consecutive chemical reactions in a batch reactor used by Hosten and Emig (1975) and Kalogerakis and Luus (1984) for the evaluation of sequential experimental design procedures of dynamic systems. The reactions are... 

As a second example let us consider the fed-batch bioreactor used by Ka-logerakis and Luus (1984) to illustrate sequential experimental design methods for dynamic systems. The governing differential equations are (Lim et al., 1977) ... 

As a third example let us consider the growth kinetics in a chemostat used by Kalogerakis (1984) to evaluate sequential design procedures for model discrimination in dynamic systems. We consider the following four kinetic models for biomass growth and substrate utilization in the continuous baker s yeast fermentation. 

Kalogerakis, N., "Sequential Experimental Design for Model Discrimination in Dynamic Systems", proc. 34th Can. Chem. Eng. Conference, Quebec City, Oct. 3-6 (1984). 

Kalogerakis, N., and R. Luus, "Sequential Experimental Design of Dynamic Systems Through the Use of Information Index", Can. J. Chem. Eng., 62, 730-737(1984). 

From the solution of the underdamped step response (0 < f < 1), we can derive the following characteristics (Fig. 3.2). They are useful in two respects (1) fitting experimental data in the measurements of natural period and damping factor, and (2) making control system design specifications with respect to the dynamic response. 

When we design a closed-loop system, the specifications may dictate features in dynamic response. However, we cannot do that unless the system is stable. Thus the foremost concern in a control system design is to keep the system stable, which in itself can be used as a design tool. 

For example, it is usually impossible to prove that a given algorithm will find the global minimum of a nonlinear programming problem unless the problem is convex. For nonconvex problems, however, many such algorithms find at least a local minimum. Convexity thus plays a role much like that of linearity in the study of dynamic systems. For example, many results derived from linear theory are used in the design of nonlinear control systems. 

Before focusing in the controller design, it is important to review some basic concepts of the geometric control theory. The control tools based in differential geometry are proposed for those nonlinear dynamical systems called affine systems. So, let s star by its definition. 

A.S. Willsky. A survey of design methods for failure detection in dynamic systems. Automatica, 12(6) 601-611, 1976. 

In applying the resulting state space model for control system design, the order of the state space model is important. This order is directly affected by the number of ordinary differential equations (moment equations) required to describe the population balance. From the structure of the moment equations, it follows that the dynamics of m.(t) is described by the moment equations for m (t) to m. t). Because the concentration balance contains c(t)=l-k m Vt), at I east the first four moments equations are required to close off the overall model. The final number of equations is determined by the moment m (t) in the equation for the nucleation rate (usually m (t)) and the highest moment to be controlled. 

The purpose of the present work is to claim that a third method exists in quantum chemistry for the dynamical conformational analysis of large molecules. We challenged that it would be possible to design such a new route by skilfully using a very simple micro-computing dynamic system in order to reduce the n-dimensional problem to a much smaller one, the size of which would be then compatible with the currently low budget of an academic laboratory. 

This chapter presents an analysis of the development of dynamic models for packed bed reactors, with particular emphasis on models that can be used in control system design. Our method of attack will be first to formulate a comprehensive, relatively detailed packed bed reactor model next to consider the techniques available for numerical solution of the model then, utilizing... 

The real power of the model developed in this work lies in the transient or dynamic simulations such as those necessary for control system design. The model we have developed can be used to simulate the effects on the reactor of various process disturbances and input changes. Under normal reactor operating conditions, step or pulse changes in inlet gas temperatures, concentrations, or velocity or changes in cooling rates can significantly affect... 

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