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TUTSIM BLOCKS. The TUTSIM software can solve far more complicated systems than the one shown in Fig. 34.14. Many of the computer blocks were developed specifically for process control calculations, such as blocks that simulate a first-order lag, a second-order lag, a transport lag, a lead-lag transfer function, and a PID controller. There are also blocks (referred
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0.4 FIGURE 34-16 Plot of response from TUTSIM model for Example
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to as Z blocks) that are used to simulate sampled-data systems. There are also thermodynamic property blocks that provide the thermodynamic properties (enthalpy, te mperature, heat capacity, etc.) of air, steam, and other substances. To comprehend the full range of the TUTSIM software, one should have access to the TUTSIM user s manual. SUMMARY Obtaining the response of a control system analytically can be very difficult, if not impossible, for high-order systems or for systems containing nonlinearities and transport lags. To study the effect of control strategies and controller parameters on the response of a complex control system, one must often use a computer simulation. Fortunately, we have today a number of simulation software packages for obtaining the response of control systems. The Appendix lists some of these software packages, along with their features and sources. If one does not have such simulation software, it is necessary to write one s own computer program. Even if one has such simulation software, it is still instructive to learn how to write some computer programs for the purpose of understanding the problems and limitations associated with commercially available simulation software. Examples of such problems are selecting the step size of the independent variable (At), establishing initial conditions, and providing sufficient storage for the simulation of transport lag. In the first part of this chapter, the methods for writing computer programs were presented by means of four examples of control system. A computer routine for integration is at the center of any computer program for dynamic simulation. The fourth-order Runge-Kutta method was selected because of its accuracy and wide use. The literature on numerical analysis, of course, covers many other methods of integration, some of which are needed for difficult cases. The first step in obtaining a computer simulation based on numerical methods is to reduce the block diagram containing the transfer functions of the components to a set of first-order differential equations. This step is equivalent to obtaining a state-space model of the control system (see Chap. 28). Since the Runge-Kutta method is a marching solution, which starts at time zero and moves one time step with each cycle of computation, the selection of initial conditions must be considered. In some cases, the initial conditions are obvious, in other cases (e.g., the presence of derivative action in a controller), selection of the initial conditions are more subtle. The simulation of a transport lag is of great importance in the simulation of control systems. In the example involving a transport lag, a simple method using a stack (an array of computer storage locations) was used and it was shown that the size of the stack depends on the ratio of the transport lag to the step size (r,lAt). In the second part of this chapter, the use of commercially available software for solving control problems was discussed. The program TUTSIM was presented and applied to some simple control problems. The use of TUTSIM is closely related to the block diagram of a control system in that a specific computer cal-
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DIGITAL COMPUTER SIMULATION OF CONTROL SYSTEMS
culation block is used for each transfer function in the block diagram. Much of the other simulation software requires that the model be represented as a state-space model (i.e., a set of first-order differential equations.) Since so many commercial simulation software packages for solving control problems are now being developed and distributed it is impossible to cover all of them in a book of this type. A listing is given in the appendix; however, the list is by no means complete and an entry in the list should not be considered as a recommended product. The field of computer applications changes so rapidly that the reader must keep abreast of developments in this area through technical journals and contacts with professional colleagues.
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