2_general_properties - 2 General Properties of Linear and Nonlinear Systems Key points Linear systems satisfy the properties of superposition and

2_general_properties - 2 General Properties of Linear and...

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2 General Properties of Linear and Nonlinear Systems Here we consider general properties of linear and nonlinear systems. We consider the existence and uniqueness of equilibrium points, stability considerations, and the properties of the forced response. We also present a broad classification of nonlinearities. Where Do Nonlinearities Come From? Before we start a discussion of general properties of linear and nonlinear systems, let’s briefly consider standard sources of nonlinearities. Key points Linear systems satisfy the properties of superposition and homogeneity. Any system that does not satisfy these properties is nonlinear. Linear systems have one equilibrium point at the origin. Nonlinear systems may have many equilibrium points. Stability needs to be precisely defined for nonlinear systems. The principle of superposition does not necessarily hold for forced response for nonlinear systems. Nonlinearities can be broadly classified.
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Many physical quantities, such as a vehicle’s velocity, or electrical signals, have an upper bound. When that upper bound is reached, linearity is lost. The differential equations governing some systems, such as some thermal, fluidic, or biological systems, are nonlinear in nature. It is therefore advantageous to consider the nonlinearities directly while analyzing and designing controllers for such systems. Mechanical systems may be designed with backlash – this is so a very small signal will produce no output (for example, in gearboxes). In addition, many mechanical systems are subject to nonlinear friction. Relays, which a re part of many practical control systems, are inherently nonlinear. Finally, ferromagnetic cores in electrical machines and transformers are often described with nonlinear magnetization curves and equations.
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  • Spring '08
  • HEDRICK
  • LTI system theory, Linear system, Equilibrium point, Nonlinear system, Linear and Nonlinear Systems Linear systems, Linear and Nonlinear Systems

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