10_Blck_Diag_SS

10_Blck_Diag_SS - Chapter 10 Transfer Functions and State...

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291 Chapter 10 Transfer Functions and State Space Representations Chapter Outline 10.1 THE TRANSFER FUNCTION. ............................................................. 293 10.1.1 Introduction. ............................................................................................................................... 293 10.1.2 Differential Equations. .......................................................................................................... 294 10.1.3 Definition of the Transfer Function. ............................................................................... 297 10.1.4 Examples . ................................................................................................................................... 300 10.1.5 MATLAB Experiments. ....................................................................................................... 302 10.2 BLOCK DIAGRAMS. .......................................................................... 306 10.2.1 Definition of a Block Diagram. ........................................................................................ 306 10.2.2 Simple Interconnections of Systems. ............................................................................ 307 10.3 EXAMPLES OF BLOCK DIAGRAMS. ................................................ 311 10.3.1 Introduction. 311 10.3.2 LRC Network. ........................................................................................................................... 312 10.3.3 Proof-Mass Actuator/Mass-Spring-Damper System . .............................................. 314 10.4 BLOCK DIAGRAM REDUCTION. ....................................................... 317 10.4.1 Introduction. 317 10.4.2 Examples of Block Diagram Reduction . ..................................................................... 319 10.4.3 MATLAB Experiments. 323 10.5 ALL-INTEGRATOR BLOCK DIAGRAMS AND STATE SPACE REPRESENTATIONS. ........................................................................ 324 10.5.1 Introduction. 324 10.5.2 All-Integrator Block Diagrams. 325 10.5.3 State Space Equations. ........................................................................................................ 327 10.5.4 All-Integrator Block Diagrams from State Equations. ........................................... 333 10.5.5 MATLAB Experiments. 335 10.6 CHAPTER SUMMARY. ....................................................................... 336 10.6.1 System Representations. ..................................................................................................... 336 10.6.2 Relationship Between System Representations . ..................................................... 337 10.7 HOMEWORK FOR CHAPTER 10. ...................................................... 339 When we introduced the definition of a system in Chapter 6, we also introduced the concept of a system representation. A system representation is an explicit mathematical expression of a system. In Chapter 6 we identified four system representations which we will investigate extensively: differential equations, Laplace transfer functions, Fourier transfer functions, and the convolution integral. It
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292 Chapter 10 Transfer Functions and State Space Representations is the system representation that we use to analyze a system. The kind of analysis tools that we can bring to bear on the system depend heavily on the particular system representation. The study of system representations is a major component of system analysis. We shall devote a good deal of this text to the study of system representations, their properties, and their interrelationships. A given system can have several, basically equivalent, system representations. A major goal of this text is to introduce four major system representations, and explain how they are interrelated. In addition, we will introduce several minor variations of each system representation. We will also show how to transform one system representation into another representation. The need for different but equivalent system representations is derived from the way these system representations are used. As discussed in Chapter 1, a system representation must yield an acceptable approximation to the experimentally observed physical process. The derivation of the system representation from experimental data may lead quite naturally to a particular system representation. Second, a system representation must lend itself to analysis and design. The analysis could be based on theoretical results or the analysis could be carried out using a computer simulation tool. Almost all theoretical results apply to a particular type of system representation. If the system representation derived from the experimental data is not of the appropriate form, then the system representation must be changed to analyze the system.
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10_Blck_Diag_SS - Chapter 10 Transfer Functions and State...

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