3. Mathematically Model Dynamic Systems and Derive Transfer Functions
Dynamic systems react over time to inputs and are described through differential equations. Analyzing these systems involves converting time-domain equations into the frequency domain using transfer functions, which represent the input-output relationship of linear time-invariant systems. The chapter provides the basis for modeling different dynamic systems, deriving their transfer functions, and understanding the relationship between system parameters and behavior.
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What we have learnt
- Dynamic systems are modeled using physical principles.
- Transfer functions are essential for analyzing and designing control systems.
- The significance of transfer functions includes stability analysis, frequency response determination, and system behavior prediction.
Key Concepts
- -- Dynamic Systems
- Systems that change over time in response to inputs, described by differential equations.
- -- Transfer Function
- A mathematical representation of the input-output relationship of a linear time-invariant system in the Laplace domain.
- -- Laplace Transform
- A technique used to convert time-domain differential equations into their frequency domain equivalents.
- -- Mechanical System
- Systems that involve physical components like masses, springs, and dampers.
- -- Electrical System
- Systems that involve electrical components such as resistors, inductors, and capacitors.
- -- RLC Circuit
- A type of electrical circuit consisting of a resistor, inductor, and capacitor connected in series.
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