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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.
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
In control theory, backstepping is a technique developed circa 1990 by Petar V. Kokotovic, and others [1] [2] for designing stabilizing controls for a special class of nonlinear dynamical systems. These systems are built from subsystems that radiate out from an irreducible subsystem that can be stabilized using some other method.
Nonlinear systems are often analyzed using numerical methods on computers, for example by simulating their operation using a simulation language. If only solutions near a stable point are of interest, nonlinear systems can often be linearized by approximating them by a linear system using perturbation theory, and linear techniques can be used. [16]
For example, in case of aircraft control, a set of controllers are designed at different gridded locations of corresponding parameters such as AoA, Mach, dynamic pressure, CG etc. In brief, gain scheduling is a control design approach that constructs a nonlinear controller for a nonlinear plant by patching together a collection of linear ...
Block diagram illustrating the feedback linearization of a nonlinear system. Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form
It cannot account for the feedback loops, tipping points, and nonlinear dynamics that define complex systems. As a result, it often misleads, offering a false sense of control over phenomena that ...
For example, in an aircraft flight control system, the altitude and Mach number might be the scheduling variables, with different linear controller parameters available (and automatically plugged into the controller) for various combinations of these two variables. In brief, gain scheduling is a control design approach that constructs a ...