EMCH_407_Topic_2_Part_1

EMCH_407_Topic_2_Part_1 - CHAPTER TWO Modeling Dynamic...

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Unformatted text preview: CHAPTER TWO Modeling Dynamic Systems . In Section 1.2, wesaw that a mathematical model is like a map; it is useful only if it concisely describes that system aSpect of interest to us. The system aspects of interest to control system engineers can be classified as electrical, mechanical, hydraulic, pneumatic, and thermal. Chapter 2 develops the ability to model these aspects for the purpose of control system design. We adopt an approach that emphasizes the similarity of modeling principles and techniques for various system types. We will see, for example, that the steps required to derive a thermal system model are very similar to those required for an electrical, system model. Familiarity with modeling different system types will improve the engineer’s ability to handle a variety of applications. I The control system engineer must employ a model that captures the essential dynamic behavior of the system, no more and no less. If the model is too simplistic, the control system will not function as desired. If the model is too detailed, its complexity will hinder the application of design methods and prevent the designer from understanding the essential behavior of the system. Developing such an appropriate model is made easier because the feedback loop of the control system improves the system’s linearity, parameter sensitivity, and disturbance rejection, as discussed in Section 1.5. This means that a relatively simple model that describes the dominant time-dependent behavior is usually suflicient for control system design. Time-dependent behavior involves both the rate of response and the pattern of the response. For example, a car’s cruise control system should quickly return the car’s _ speed to its desired value when the car begins to ascend a hill. But it should not overrespond and cause the speed to exhibit an oscillatory pattern about the desired value. The models and modeling techniques developed in Chapter 2 are usually sufficient to describe the dominant rate of response and response patterns of typical control system applications. In Chapter 3, we will develop methods for using these models to compute the dominant response rate andpatterns. .. Because we will be using models of realistic systems with typical parameter values as examples, we begin with a review of typical physical units. Then electrical and mechanical system models are introduced first, because their principles are perhaps the most familiar from statics, dynamics, and basic physics courses. These are followed by treatments of two types of fluid systems, hydraulic and pneumatic, and finally an introduction to thermal systems. Coverage of electrical and mechanical systems in Sections 2.2—2.5 is essential for understanding later. chapters. The treatment of hydraulic, pneumatic, and thermal systems in Sections 2.6—2.9 has been greatly simplified thrbugh the generous use of empirical formulas and the easily understood _ principles of conservation of mass and energy. Although the material in these sections is not so vital as the material on electrical and. mechanical systems, its coverage is nevertheless strongly recommended. 33 .3 2.0.3520 U<Z>EB $353.4. ML mfiwflmgm Om. CZHHw 225 on :5 Bomaznm nan—53:2 :6 2E anion @323 o: m $85.” $9.83 on. :33. E 2%.. 5, 5&8 85:23.28 wfimfinanaa 95am 0: :5 Ems—Ea Ego—m. m mg on :55 SE" to 0320on. “Son” asmianlum 55% m: 3.5 Gian @352 :3 fig: .3me a: :5 win? mammaaolzm. mamas... Eggs? :6 5030 33.55 3832558 35 mm mugged a SUE? c0833..“ 90 5.019250 2253? Ca: :5 armsmagg a 83208. 3mm..."on w: :5 Gina mason (a: :35 8 g ESE”... 2:: was” $583? 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EMCH_407_Topic_2_Part_1 - CHAPTER TWO Modeling Dynamic...

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