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Description
This thesis is concerned with a study of several methods of simulating digital control systems. Two general areas of this problem are considered: the development of schemes to model the digital controller, and the simulation or the model using an analog computer or a digital computer. The indirect and the direct method are the two basic schemes used to model the digital controller. The indirect method, proposed by Sklansky, involves transforming the equation of the digital controller from the z-plane into the Laplace domain in order to build circuits composed only of resistors and capacitors. This method and certain variations are discussed. The direct method avoids this transformation procedure by the awareness that terms involving z⁻¹ can be realized by a weighting factor and a delay of one sample time. This method and two variations are presented. The first scheme for modeling was conceived primarily with the thought that RC networks were to be built. But once the Laplace domain equivalent of the digital controller equation has been found, it lends itself readily to simulation by an analog computer. Both this model and the direct model are used to obtain an iterative analog computer simulation of a digital control system. The entire system--the digital controller, the zero-order hold circuit, and the plant itself--are simulated. A discussion of the analog equipment is also given. Two types of digital computer programs are used in simulating the digital control system. One is a general-purpose integration routine written principally for the solution of differential equations. Once the particular modeling technique has been chosen, the necessary equations describing the model and plant are written and solved using this program. The decision statements necessary to simulate a sampler and zero-order are also written and inserted in the appropriate place. The second type of program is one that simulates the iterative analog computer. After the analog computer simulation has been designed, appropriate changes are made to meet the restrictions imposed by the digital computer program simulating the iterative analog computer; the necessary program written and the solution produced. Specific examples are presented to illustrate application of the modeling procedures and the simulation techniques. Solution graphs produced by each method are included.
