Nonlinear System Techniques and Applications

Nonlinear control

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  • Nonlinear System Techniques and Applications
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    • Mardanov and Telman K. Stouboulos and George S.

    Nonlinear System Techniques and Applications

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    Edited by Jan Awrejcewicz. Edited by Bishnu Pal.

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    Dissipative Systems Analysis and Control 2nd ed. Browse book content About the book Search in this book. These systems are often governed by nonlinear differential equations. Would you like to change to the United States site? Description Nonlinear Systems Techniques and Applications provides the most practical techniques currently available for analyzing and identifying nonlinear systems from random data measured at the input and output points of the nonlinear systems.

    Edited by Alexander Kokorin. Edited by Theophanides Theophile. Edited by Kresimir Delac. Edited by Sergey Mikhailov. Edited by Sylvie Manguin.

    October 19th DOI: Vassileva Open access peer-reviewed 6. Melikov Open access peer-reviewed 9. Tombras Open access peer-reviewed Edited volume and chapters are indexed in.

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    Open access peer-reviewed 1. Open access peer-reviewed 2. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback. The system to be controlled is called the " plant ".

    In order to make the output of a system follow a desired reference signal a controller is designed which compares the output of the plant to the desired output, and provides feedback to the plant to modify the output to bring it closer to the desired output. Control theory is divided into two branches. Linear control theory applies to systems made of devices which obey the superposition principle , which means roughly that the output is proportional to the input.

    Description

    They are governed by linear differential equations. A major subclass is systems which in addition have parameters which do not change with time, called linear time invariant LTI systems.

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    These systems can be solved by powerful frequency domain mathematical techniques of great generality, such as the Laplace transform , Fourier transform , Z transform , Bode plot , root locus , and Nyquist stability criterion. Nonlinear control theory covers a wider class of systems that do not obey the superposition principle. It applies to more real-world systems, because all real control systems are nonlinear. These systems are often governed by nonlinear differential equations. The mathematical techniques which have been developed to handle them are more rigorous and much less general, often applying only to narrow categories of systems.

    If only solutions near a stable point are of interest, nonlinear systems can often be linearized by approximating them by a linear system obtained by expanding the nonlinear solution in a series , and then linear techniques can be used.

    Even if the plant is linear, a nonlinear controller can often have attractive features such as simpler implementation, faster speed, more accuracy, or reduced control energy, which justify the more difficult design procedure. An example of a nonlinear control system is a thermostat -controlled heating system.

    A building heating system such as a furnace has a nonlinear response to changes in temperature; it is either "on" or "off", it does not have the fine control in response to temperature differences that a proportional linear device would have.

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    Therefore, the furnace is off until the temperature falls below the "turn on" setpoint of the thermostat, when it turns on. Due to the heat added by the furnace, the temperature increases until it reaches the "turn off" setpoint of the thermostat, which turns the furnace off, and the cycle repeats. This cycling of the temperature about the desired temperature is called a limit cycle , and is characteristic of nonlinear control systems. Control design techniques for nonlinear systems also exist.

    These can be subdivided into techniques which attempt to treat the system as a linear system in a limited range of operation and use well-known linear design techniques for each region:. Those that attempt to introduce auxiliary nonlinear feedback in such a way that the system can be treated as linear for purposes of control design:.