Tham khảo tài liệu 'ogata - modern control engineering part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Linearization of nonlinear systems. In control engineering a normal operation of the system may be around an equilibrium point and the signals may be considered small signals around the equilibrium. It should be pointed out that there are many exceptions to such a case. However if the system operates around an equilibrium point and if the signals involved are small signals then it is possible to approximate the nonlinear system by a linear system. Such a linear system is equivalent to the nonlinear _system considered within a limited operating range. Such a linearized model linear time-invariant model is very important in control engineering. We shall discuss a linearization technique in Section 3-10. Outline of the chapter. Section 3-1 has presented an introduction to the mathe-_matical modeling of dynamic systems including discussions of linear and nonlinear sys-tems. Section 3-2 presents the transfer function and impulse-response function. Section 3-3 introduces block diagrams and Section 3-4 discusses concepts of modeling in state space. Section 3-5 presents state-space representation of dynamic systems. Section 3-6 treats mathematical modeling of mechanical systems. We discuss Newton s approach to _modeling mechanical systems. Section 3-7 deals with mathematical modeling of circuits Section 3-8 treats liquid-level systems and Section 3-9 presents mathematical modeling of thermal systems. Finally Section 3-10 discusses the linearization of nonlinear mathematical models. Mathematical modeling of other types of systems is treated throughout the remaining chapters of the book. 3-2 TRANSFER FUNCTION AND IMPULSE- RESPONSE FUNCTION In control theory functions called transfer functions are commonly used to character-ize the input-output relationships of components or systems that can be described by linear time-invariant differential equations. We begin by defining the transfer function and .
