Name: spring-mass-damper laplace block diagram
Uploaded: 2024-11-21T14:54:07.000Z
Duration: 1 min 20 s
Channel: JoVE

스프링-질량-댐퍼 시스템의 2차 미분 방정식을 생각해 보십시오. 이 시스템은 초기 조건이 0인 상태에서 라플라스 도메인으로 변환됩니다.
그런 다음 방정식을 재배열하여 출력을 분리하며, 이는 특정 전달 함수가 있는 블록에 들어가는 신호로 해석될 수 있습니다.
출력은 두 번 적분하거나 그에 따라 사후 곱하여 얻습니다.
단순화하기 위해 오른쪽의 신호가 연결되어 시스템의 최종 블록 다이어그램 표현으로 이어집니다.
내부 피드백 루프에서 항을 인수분해하여 추가 단순화를 달성할 수 있으며, 그 결과 대체 블록 다이어그램이 생성됩니다.
블록 다이어그램 모델은 가속도와 속도를 나타내는 내부 변수를 통합할 수도 있습니다.
1/s는 라플라스 영역의 적분에 해당하므로 가속도는 처음에 속도를 얻기 위해 적분되고 이후에 속도를 적분하여 변위 신호를 생성합니다.
시스템의 전달 함수는 입력 및 피드백 신호의 블록을 비교기의 오른쪽으로 이동하고 내부 피드백 루프를 단순화하여 찾을 수 있습니다. 결과 방정식은 시스템의 전달 함수입니다.

수학 방정식과 블록 다이어그램 간의 관계

Relation between Mathematical Equations and Block Diagrams

스프링-질량-댐퍼 시스템에서 2차 미분 방정식은 시스템의 동적 거동을 설명합니다. 초기 조건이 0인 라플라스 도메인으로 변환하면 이 방정식을 효과적으로 분석하고 조작할 수 있습니다. 라플라스 도메인으로 변환하면 미분 방정식이 대수 방정식으로 변환되어 출력을 분리하는 프로세스가 간소화됩니다.

<img alt="Equation1" src="/files/ftp_upload/16105/16105_PT_Equation_001.svg" style="height: 36px;">

스프링-질량-댐퍼 시스템의 표준 미분 방정식에 라플라스 변환을 적용하면 다음과 같은 출력이 나옵니다.

<img alt="Equation2" src="/files/ftp_upload/16105/16105_PT_Equation_002.svg" style="height: 24px;">

블록 다이어그램을 구성할 때, 오른쪽의 신호를 연결하여 표현을 단순화할 수 있습니다. 블록 다이어그램은 가속도 및 속도와 같은 내부 변수를 통합하기 위해 더욱 세분화할 수 있습니다. 1/s는 라플라스 도메인에서의 적분에 해당하므로 가속도 신호는 속도를 얻기 위해 적분되고, 속도는 변위 신호를 생성하기 위해 적분됩니다.

블록 다이어그램 단순화는 내부 피드백 루프에서 항을 인수분해하는 것을 포함합니다. 이 프로세스는 가속도, 속도 및 변위 간의 관계를 시각적으로 표현하는 대체 블록 다이어그램으로 이어집니다.

시스템의 전달 함수를 도출하기 위해 입력 및 피드백 신호를 나타내는 블록을 비교기의 오른쪽으로 옮기고 내부 피드백 루프를 단순화합니다. 결과 방정식은 전달 함수를 제공합니다.

<img alt="Equation3" src="/files/ftp_upload/16105/16105_PT_Equation_003.svg" style="height: 38px;">
<img alt="Equation4" src="/files/ftp_upload/16105/16105_PT_Equation_004.svg" style="height: 120px;">

이 전달 함수는 시스템 동작을 분석하고, 다양한 입력에 대한 반응을 예측하고, 원하는 성능 특성을 달성하기 위한 제어 전략을 설계하는 데 필수적입니다.

스프링-질량-댐퍼 시스템의 2차 미분 방정식을 생각해 보십시오. 시스템은 초기가 0 미만인 라플라스 도메인으로 변환됩니다 ...

relation-between-mathematical-equations-and-block-diagrams

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Diagrams and Signal Flow Graphs

다이어그램 및 신호 흐름 그래프

KEY TERMS AND CONCEPTS

주요 용어 및 개념

spring-mass-damper laplace block diagram

A spring-mass-damper system can be written as a second-order differential equation. This equation describes how the system changes over time. When the equation is transformed into the Laplace domain with zero initial conditions, it becomes easier to analyze and rearrange.

The Laplace transform changes a differential equation into an algebraic equation. That makes it simpler to isolate the output. For the standard spring-mass-damper model, the transformed equation gives the output in a form that can be used directly for block diagram construction.

The block diagram is built by connecting the signals on the right-hand side of the equation. It can also include internal variables such as acceleration and velocity. In the Laplace domain, 1/s means integration. So acceleration is integrated to get velocity, and velocity is integrated to get displacement.

The diagram can be simplified by factoring terms from the internal feedback loop. This creates another block diagram that shows the links between acceleration, velocity, and displacement more clearly. To find the transfer function, the block for the input and feedback signals is moved to the right side of the comparator, and the internal feedback loop is reduced. The final transfer function helps describe system behavior, predict the response to inputs, and support control design.

Spring-Mass-Damper Laplace Block Diagram

elements of block diagrams

Block Diagrams in Control Systems

Block diagrams show the input-output relationships in a system. They help students see how one signal affects another. A heating system is a simple example. The set temperature turns the furnace on, and the room warms to the desired level. Block diagrams can model both linear and nonlinear systems. Linear systems often use Laplace transform variables. Nonlinear systems are usually described with time domain variables. This makes block diagrams useful for many kinds of control problems. A...

relation between mathematical equations and block diagrams

A spring-mass-damper system can be written as a second-order differential equation. This equation describes how the system changes over time. When the equation is transformed into the Laplace domain with zero initial conditions, it becomes easier to analyze and rearrange. The Laplace transform changes a differential equation into an algebraic equation. That makes it simpler to isolate the output. For the standard spring-mass-damper model, the transformed equation gives the output in a form...

block diagram reduction

Simplifying Control System Block Diagrams

Simplifying control system block diagrams helps make a system easier to analyze. The goal is to reduce several connected blocks to one block so the transfer function can be found more easily. This process keeps the system behavior the same while making the diagram simpler to work with. A branch point is the place where one signal splits into multiple paths. To simplify the diagram, the branch point can be moved to a new location. The new position must preserve the mathematical relationship...

multi-input and multi-variable systems

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Cruise control systems show how a control system can handle more than one input. In a car, the driver sets a desired speed, and the system also responds to outside disturbances such as changes in road slope. The throttle is adjusted so the vehicle speed stays as close as possible to the target value. When the disturbance is ignored, the cruise control block diagram can be reduced to a transfer function. This transfer function describes how the desired speed input, R(s), affects the actual...

mason&#39;s rule

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Mason's rule helps students find transfer functions from signal-flow graphs in control systems and signal processing. It gives a clear path for solving graphs that can look complicated at first. The method uses loop gains, forward-path gains, and non-touching loops to organize the calculation. A loop gain comes from tracing a path from a node back to the same node. The gain is the product of the branch gains along that loop. Each loop gain matters because it feeds into the later...

signal flow graphs

Mason’s Rule in Signal Flow Graphs

Signal-flow graphs are a clear way to represent control systems. They offer an alternative to traditional block diagrams. In these graphs, branches stand for systems and nodes stand for signals. Arrows show the direction of signal flow, and the transfer function is written next to each arrow. Signal-flow graphs also handle subtraction in a different way from block diagrams. In a block diagram, summing junctions often use negative signs. In a signal-flow graph, those negative signs are built...

sfg algebra

Signal Flow Graph Branch Rules

Signal flow graph (SFG) branch rules show how signals move through a control system. Each node in an SFG stands for a variable. The value at a node is the sum of all signals entering it. That summed value then travels through every branch leaving the node. Branches connect the nodes and show the relationship between variables. Each branch has a gain, which tells how strongly the signal is passed along. When several branches enter the same node, their signals are added together. When one node...

key terms and concepts

Learn how a spring-mass-damper equation becomes a Laplace-domain block diagram, with acceleration, velocity, displacement, and transfer function steps.

Spring-Mass-Damper Laplace Block Diagram | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Spring-Mass-Damper Laplace Block Diagram

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