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Unformatted text preview: 1 ` Introduction We consider systems that can be written in the following general form, where x is the state of the system, u is the control input, w is a disturbance, and f is a nonlinear function. ) , , , ( w u x t f x = & p m n w u x ℜ ∈ ℜ ∈ ℜ ∈ , , We are considering dynamical systems that are modeled by a finite number of coupled, first-order ordinary differential equations. The notation above is a vector notation, which allows us to represent the system in a compact form. Key points • Few physical systems are truly linear. • The most common method to analyze and design controllers for system is to start with linearizing the system about some point, which yields a linear model, and then to use linear control techniques. • There are systems for which the nonlinearities are important and cannot be ignored. For these systems, nonlinear analysis and design techniques exist and can be used. These techniques are the focus of this textbook. In many cases, the disturbance is not considered explicitly in the system analysis, that is, we consider the system described by the equation ) , , ( u x t f x = & . In some cases we will look at the properties of the system when f does not depend explicitly on u, that is, ) , ( x t f x = & . This is called the unforced response of the system. This does not necessarily mean that the input to the system is zero. It could be that the input has been necessarily mean that the input to the system is zero....
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This note was uploaded on 08/01/2008 for the course ME 237 taught by Professor Hedrick during the Spring '08 term at Berkeley.
- Spring '08