In instrumentation and control, systems are often represented by mathematical models that describe their behavior. These models can be classified based on their order, which is determined by the highest derivative of the output variable that appears in the system's differential equation. First-order and second-order systems are commonly used in instrumentation and control because they provide a simple and effective way to model and analyze the behavior of complex systems. A first-order system is a system whose behavior can be described by a first-order ordinary differential equation of the form: τ (dy/dt) + y = K*u where y is the output variable, u is the input variable, K is the steady-state gain, and τ is the time constant. The time constant represents the time it takes for the system to reach 63.2% of its steady-state value after a step input is applied. The transfer function of a first-order system is given by: G(s) = K/(τs + 1) where s is the Laplace variable. The transfer f...
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