Name: dc motor modeling in electromechanical systems
Uploaded: 2024-09-26T13:17:19.000Z
Duration: 1 min 19 s
Channel: JoVE

전기 기계 시스템은 매끄럽게 통합되는 전기 및 기계 구성 요소의 고유한 조합을 나타냅니다.
DC 모터는 전압을 각 변위로 변환하여 전기 입력에서 기계적 결과를 생성하는 장치입니다.
자기장 내부에 배치된 전기자 회로에 전류가 흐르면 힘이 발생하여 회전자를 회전시키는 토크로 이어집니다.
전기자는 자기장에서 회전하는 동안 전류를 전달하기 때문에 전압은 속도에 비례합니다.
라플라스 변환된 전기자 회로에 루프 방정식을 적용하면 전기자 전류, 적용된 전기자 전압 및 역기전력 간의 상관 관계가 나타납니다.
모터의 토크는 전기자 전류에 비례하며 비례 성은 모터와 자기장 특성에 따라 일정합니다.
토크는 전기자에서 관성 및 점성 댐핑과 관련이 있습니다.
토크 방정식은 먼저 모터 샤프트의 각도 위치로 표현하기 위해 다시 작성됩니다.
이에 따라 전기자 인덕턴스가 전기자 저항보다 상당히 작다고 가정합니다.
단순화하면 전달 함수가 얻어집니다.

전기_기계 시스템

전기_기계 시스템은 전기 및 기계적 요소를 효과적으로 결합하여 원하는 결과를 얻는 복잡한 구성입니다. 이러한 시스템의 대부분은 전기 에너지를 기계적 운동으로 변환하는 장치인 DC 모터로, 간단한 팬에서 복잡한 로봇 메커니즘에 이르기까지 다양한 응용법을 가능하게 합니다.

DC 모터의 핵심 구성 요소는 자기장 내에 위치한 회전 회로인 전기자입니다. 전류가 전기자를 통과할 때 자기장과의 상호 작용으로 인해 힘을 만나 토크를 생성합니다. 이 토크는 회전자의 회전을 시작하여 전기 에너지를 기계적 운동으로 변환합니다. 전기자에 유도된 전압은 속도에 직접 비례하며, 이 현상을 역기전력(EMF)이라고 합니다.

DC 모터의 동작을 분석하기 위해 전기 원리를 전기자 회로에 적용합니다. 루프 방정식을 사용하고 라플라스 방법을 통해 변환하면 전기자 전류(i_a), 인가된 전기자 전압(V_a), 역기전력(E_b) 간의 관계를 밝힐 수 있습니다. 방정식은 다음과 같습니다.

<img alt="Equation1" src="/files/ftp_upload/16098/16098_PT%20EQUATION_1.svg" style="text-align: center; height: 32px;">

여기서 R_a는 전기자 저항을 나타내고 E_b는 역기전력을 나타냅니다.

s 도메인에서 모터가 생성하는 토크(T)는 전기자 전류에 직접 비례하며 다음과 같이 설명됩니다.

<img alt="Equation2" src="/files/ftp_upload/16098/16098_PT%20EQUATION_2.svg" style="text-align: center; height: 20px;">

​여기서 k_t는 토크 상수입니다. 이 토크는 로터의 관성(J)으로 작성할 수도 있습니다.

<img alt="Equation3" src="/files/ftp_upload/16098/16098_PT%20EQUATION_3.svg" style="text-align: center; height: 20px;">

모터 샤프트의 각 위치(θ)로 토크를 표현하고 단순화하면 전달 함수를 도출할 수 있습니다. 전기자 유도계수를 전기자 저항에 비해 무시할 수 있다고 가정하면 DC 모터의 단순화된 전달 함수는 다음과 같습니다.

<img alt="Equation4" src="/files/ftp_upload/16098/16098_PT%20EQUATION_4.svg" style="text-align: center; height: 64px;">

이 전달 함수는 모터의 동적 응답에 대한 포괄적인 이해를 제공하여 전기 입력을 기계적 출력에 연결하고 전기 기계 시스템의 설계 및 제어를 용이하게 합니다.

전기 기계 시스템은 매끄럽게 통합되는 전기 및 기계 구성 요소의 고유한 조합을 나타냅니다.
DC 모터는 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Modeling in Time and Frequency Domain

시간 및 주파수 영역 모델링

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Electro-mechanical Systems

dc motor modeling in electromechanical systems

DC motor modeling is a key part of electromechanical systems. These systems combine electrical parts and mechanical parts to produce a useful output. A DC motor is one common example because it turns electrical energy into mechanical motion. It is used in many places, from simple fans to complex robotic mechanisms.

Inside the DC motor, the armature is a rotating circuit placed in a magnetic field. When current flows through the armature, it experiences a force from the magnetic field. That force creates torque, which starts the rotor spinning. As the motor turns, it also produces a voltage in the armature that rises with speed. This voltage is called back electromotive force, or back EMF.

To study how the motor behaves, electrical principles are applied to the armature circuit. A loop equation is written for the armature current, the applied armature voltage, and the back EMF. The equation can then be transformed with the Laplace method to help show the motor response in the s domain. This makes it easier to relate the input voltage to the motor’s electrical and mechanical behavior.

The torque produced by the motor is directly proportional to the armature current in the s domain. The torque constant, k_t, sets that relationship. Torque can also be written in terms of the rotor inertia, J, and the motion of the motor shaft. By expressing the torque through the angular position, θ, and simplifying the result, a transfer function can be derived. When armature inductance is assumed to be negligible compared with armature resistance, the DC motor transfer function becomes simpler and shows how electrical input leads to mechanical output.

DC Motor Modeling in Electromechanical Systems

dc-motor-modeling-electromechanical-systems

transfer function in control systems

Transfer Function from Input to Output

The transfer function describes how a linear time-invariant, or LTI, system maps an input to an output in the frequency domain. It gives a compact way to study system behavior without working only in the time domain. It also connects the differential equations of the system to a form that is easier to handle mathematically. For an nth-order LTI system, the behavior is written as a differential equation with constant coefficients. In that equation, r(t) is the input and c(t) is the output. The...

electrical systems

RLC Circuit Transfer Functions

RLC circuits use resistors, capacitors, and inductors to show how electrical signals change over time. In circuit analysis, these passive linear components are arranged so the link between an input and an output can be described with a transfer function. For this topic, the output is the voltage across the capacitor, compared with the input voltage. A series RLC circuit can be analyzed with Kirchhoff's Voltage Law, or KVL. KVL says that the sum of all voltages around a closed loop is zero.

mechanical systems

Transfer Functions in Mechanical Motion

Mechanical motion can be modeled with springs, masses, and viscous dampers. In these models, springs behave like inductors and masses act like capacitors in an electrical network. A viscous damper works like a resistor because it removes energy from the system. A force acts on the mass in the direction of motion. It is balanced by the spring force, the damping force, and the force from the mass’s acceleration. Newton’s second law is used to describe this balance, and the sum of the forces on...

electro-mechanical systems

DC motor modeling is a key part of electromechanical systems. These systems combine electrical parts and mechanical parts to produce a useful output. A DC motor is one common example because it turns electrical energy into mechanical motion. It is used in many places, from simple fans to complex robotic mechanisms. Inside the DC motor, the armature is a rotating circuit placed in a magnetic field. When current flows through the armature, it experiences a force from the magnetic field. That...

linear approximation in frequency domain

Linearizing Nonlinear RL Circuits

Linearizing nonlinear RL circuits helps turn a hard circuit problem into a simpler linear one. Linear systems follow superposition, which means the total response equals the sum of the responses to separate inputs. They also follow homogeneity, which means scaling the input scales the output by the same amount. Nonlinear systems do not automatically have those properties. For small changes around an operating point, though, a nonlinear system can often be treated as linear. This is done with a...

state space representation

RLC Circuit State Equations

RLC circuit state equations show how a circuit changes over time using state variables. This time-domain method is useful for linear, time-invariant systems, but it also helps when frequency-domain analysis is not enough. It is especially useful for nonlinear systems, time-varying systems, and multiple-input multiple-output systems. The state-space approach turns an nth-order system into a set of simultaneous first-order differential equations called state equations. For a common second-order...

transfer function to state space

Phase-Variable State Equations from Transfer Functions

Phase-variable state equations show how a transfer function can be rewritten for computer simulation. In state-space form, the system is described with state variables, which are the output and its first several derivatives. This makes it easier to model a physical system on a digital computer. The starting point is an nth-order linear differential equation with constant coefficients. Systems like an RLC circuit can be written this way. To build the state equations, the transfer function is...

state space to transfer function

Finding a Transfer Function from State Space

Finding a transfer function from state-space form is a key step in system analysis. It changes a time-domain model into a frequency-domain form. That makes it easier to study and design control systems. The process starts with the state-space equations. These include the state equation and the output equation. In these equations, x(t) is the state vector, u(t) is the input vector, y(t) is the output vector, and A, B, C, and D are the matrices that define the system dynamics. Next, the Laplace...

linear approximation in time domain

Linearizing Nonlinear State-Space Models

Linearizing nonlinear state-space models helps describe systems that change with time or operating conditions. State-space representation is often effective for this kind of modeling. It is especially useful for systems such as a simple pendulum or a translational mechanical system with nonlinear springs. A simple pendulum can be modeled by summing torques around the pivot point. In this case, the mass is evenly distributed along the pendulum, and the center of mass is located at half its...

key terms and concepts

Learn how a DC motor turns electrical input into motion, how back EMF affects armature current, and how Laplace methods help derive the transfer function.

DC Motor Modeling in Electromechanical Systems | 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

DC Motor Modeling in Electromechanical Systems

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