Linerarisation in control system
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All physical components and systems have some degree of nonlinearity in their behavior, contrary to the idealized linear models commonly used. Nonlinear factors like varying spring rigidity, temperature-dependent resistances, and friction introduce complexity. As a result, the true mathematical models of real systems are always nonlinear differential equations. However, there is no universal solution for such equations, so nonlinear systems are typically linearized by representing them as linear differential equations within a small range of variable values, allowing analysis with linear system theories. This approximate approach is convenient for practical analysis and calculation.
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Linerarisation in control system
- 1. 2.2.2 Linearization of Nonlinear Differential Equations The above components and systems are supposed to be linear, so the mathematical models of them are linear differential equations. Actually, all components or systems are nonlinear to some extent. For example, rigidity of a spring is related to its formation. It is not always a constant. Some parameters such as resistant R, inductance L and capacitance C are related to the environment (temperature, humidity, pressure, etc) and the current going through. Thus, they are not always constants. Friction, dead-zone or some other nonlinear factors will make the differential equation complex and nonlinear. Strictly speaking, mathematical models for real systems are always nonlinear. Unfortunately, so far there is no universal solution for nonlinear differential equations. Thus, nonlinear systems are usually linearized based on reasonable rules. Nonlinear systems usually can be represented by linear differential equations in a small value range of variables so that they can be analysis and design by linear system theories. Although it is an approximate solution, it is convenient for analysis and calculation in practice.