Name: phase shift control in feedback systems
Uploaded: 2024-11-21T14:54:16.000Z
Duration: 1 min 22 s
Channel: JoVE

스테레오에서 볼륨 이퀄라이저를 조정한다고 상상해 보십시오. 저음이 크랭크업되면 위상 리드 컨트롤러가 작동합니다. 고음이 증가하면 위상 지연 컨트롤러가 작동합니다.
PD 컨트롤러는 고역 통과 필터로, PI는 저역 통과 필터로, PID는 대역 통과 또는 대역 정지 필터로 작동합니다.
위상 리드 컨트롤러 또는 고역 통과 필터는 특정 주파수 범위에서 시스템에 양의 위상을 도입합니다. 반대로, 위상 지연 컨트롤러 또는 저역 통과 필터는 음의 위상을 도입합니다.
단일 전달 함수는 두 컨트롤러를 모두 나타낼 수 있으며, 첫 번째 매개변수가 두 번째 매개변수보다 크면 고역 통과이고, 더 작으면 저역 통과입니다.
이 기능은 연산 증폭기 회로를 사용하여 구현할 수 있습니다. 전달 함수는 두 커패시터의 비율과 각 경로에 대한 저항 및 커패시턴스 곱의 합을 통해 출력 및 입력 전압을 관련시킵니다.
커패시터를 동일시하면 설계 매개변수가 4개에서 3개로 줄어들어 회로 방정식이 단순화됩니다.
상수는 저항의 비율과 저항과 커패시턴스의 곱을 대체할 수 있습니다.

위상 리드 및 위상 래그 컨트롤러

다양한 유형의 컨트롤러의 작동 기능을 이해하는 것은 스테레오의 볼륨 이퀄라이저를 조정하는 것과 같은 실제적인 비유로 설명할 수 있습니다. 저음을 크랭킹하려면 하이패스 필터로 작동하는 위상 리드 컨트롤러가 필요하고, 트레블을 높이려면 로우패스 필터로 작동하는 위상 지연 컨트롤러가 사용됩니다. 하이패스 필터와 유사한 PD 컨트롤러는 고주파 성분에 대한 시스템의 응답을 향상시킵니다. 로우패스 필터와 유사한 PI 컨트롤러는 저주파 성분을 관리하여 정상 상태 오류를 줄입니다. PID 컨트롤러는 대역 통과 또는 대역 감쇠 필터로 작동하여 고주파 및 저주파 조정을 모두 균형 있게 조정할 수 있습니다.

위상 리드 컨트롤러는 특정 주파수 범위에서 시스템에 양의 위상 이동을 도입하여 시스템의 응답성을 향상시킵니다. 반면 위상 지연 컨트롤러는 음의 위상 이동을 도입하여 고주파 성분을 감쇠시켜 시스템을 안정화합니다. 두 유형의 컨트롤러 모두 단일 전달 함수로 표현할 수 있습니다. 첫 번째 매개변수가 두 번째 매개변수보다 크면 함수는 고역 통과 필터로 동작하고, 두 번째 매개변수가 작으면 저역 통과 필터로 동작합니다.

이러한 컨트롤러의 구현은 연산 증폭기 회로를 사용하여 달성할 수 있습니다. 이러한 회로의 전달 함수는 두 커패시터의 비율의 곱과 각 경로에 대한 저항과 커패시턴스의 곱의 합을 통해 출력 및 입력 전압을 연관시킵니다. 커패시터를 동일시하여 설계를 단순화하면 설계 매개변수의 수가 4개에서 3개로 줄어들어 회로 방정식이 간소화됩니다.

또한 상수는 저항의 비율과 저항과 커패시턴스의 곱을 대체할 수 있어 회로 설계를 더 간단하게 만들 수 있습니다. 이 접근 방식은 애플리케이션의 요구 사항에 따라 위상 리드 또는 위상 지연 특성을 정밀하게 조정할 수 있습니다. 이러한 매개변수를 조정함으로써 엔지니어는 고역 통과 및 저역 통과 필터의 기본 원리를 활용하여 원하는 결과를 달성하여 시스템 안정성과 성능을 효과적으로 제어할 수 있습니다.

스테레오에서 볼륨 이퀄라이저를 조정한다고 상상해 보십시오. 저음이 크랭크업되면 위상 리드 컨트롤러가 작동합니다. 고음이 증가하면 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Design of Control Systems

제어 시스템 설계

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Phase-lead and Phase-lag Controllers

phase shift control in feedback systems

Phase-lead and phase-lag controllers change how a feedback system responds to different frequencies. A simple stereo equalizer can help explain the idea. Turning up the bass is like using a phase-lead controller, which works like a high-pass filter. Turning up the treble is like using a phase-lag controller, which works like a low-pass filter.

PD controllers respond more to high-frequency parts of a signal, so they act like high-pass filters. PI controllers focus more on low-frequency parts and help reduce steady-state error. PID controllers can work as band-pass or band-attenuate filters, which means they balance both high and low frequencies in different ways.

A phase-lead controller adds a positive phase shift over a certain frequency range. This can make a system respond faster. A phase-lag controller adds a negative phase shift. This helps stabilize the system by reducing high-frequency components.

Both controllers can be written with one transfer function. In that function, if the first parameter is larger than the second, the result behaves like a high-pass filter. If the first parameter is smaller, it behaves like a low-pass filter. Engineers can build these controllers with an op-amp circuit.

The circuit transfer function links output voltage and input voltage through capacitor ratios and resistance-capacitance terms. If the two capacitors are set equal, the design uses fewer parameters. That reduces the design from four values to three. The resistance ratio and the RC product can also be replaced by constants, which makes the circuit easier to tune for phase-lead or phase-lag control.

Phase Shift Control in Feedback Systems

controller configurations

Cruise Control Controller Designs

Cruise control controller designs help a car keep a steady speed over time. They do this by adjusting the system to meet design goals, even when road conditions change. In traditional control systems, a fixed configuration uses a set controller placement. Control-system compensation means changing the system’s performance. A common form is series, or cascade, compensation. In this setup, the controller is placed in series with the plant, which is the part of the system being controlled. This...

pd controller: design

PD Controller Circuits for Car Suspension

PD controllers are used in car suspension systems to adjust damping force as road conditions change. A proportional derivative, or PD, controller combines proportional control and derivative control. In proportional control, the output follows the input with a constant gain. This kind of control is common in continuous-data systems that use parts such as adders and integrators, which also appear in proportional, integral, and derivative, or PID, controllers. A feedback control system often...

time-domain interpretation of pd control

PD Control Reduces Overshoot in Motor Torque

PD control helps reduce overshoot and oscillation in motor torque systems. Proportional control uses the size of the error signal to set the correction. When the response is too large or too small, the output can move away from the target and then swing back. With proportional control alone, the system often goes through three stages. First, a positive error signal creates a rapidly rising positive motor torque. That strong push can cause a large overshoot because the system has high force but...

frequency-domain interpretation of pd control

frequency-domain-interpretation-of-pd-control

PD Control Effects on Fan Stability

PD control changes how a fan responds to speed errors. A fan control system can be modeled with a Bode plot, which shows the transfer function across different frequencies. This makes it easier to see how the proportional-derivative controller acts in the frequency domain. The proportional gain, together with the system’s series gain, normalizes the controller gain at zero frequency. The Bode plot also shows that a PD controller works like a high-pass filter. It boosts the high-frequency parts...

pi controller: design

PI Controller Gains and Error Correction

A PI controller uses proportional and integral action to correct error in a control system. PI stands for proportional integral. It is used in modern control systems to improve performance and reduce steady-state error, which is the small error that remains after a system settles. PI controllers are useful in step-input situations such as automatic brightness adjustment on smartphones. They can handle residual steady-state error that the proportional part alone does not remove. Unlike PD...

time and frequency -domain interpretation of pi control

time-and-frequency-domain-interpretation-of-pi-control

PI Control: Zero Placement and Stability

PI control uses proportional and integral action to improve stability and reduce steady-state error in control systems. It is used in everyday devices such as thermostats, where better damping can improve performance. A well-placed zero in the controller transfer function can make the system more accurate and stable. A PI controller also behaves like a low-pass filter. That means it slows the response and can increase settling time. For that reason, the zero should be placed near the beginning...

pid controller

How PID Control Balances System Response

PID controllers are used to balance system response in control systems. They improve stability and performance by adjusting output as the measured value moves away from the desired value. In a thermostat, for example, the controller changes heating or cooling based on the temperature difference between the actual temperature and the set point. In automotive speed systems, it also helps manage sudden speed changes while keeping speed steady under changing conditions. PID control combines the...

phase-lead and phase-lag controllers

Phase-lead and phase-lag controllers change how a feedback system responds to different frequencies. A simple stereo equalizer can help explain the idea. Turning up the bass is like using a phase-lead controller, which works like a high-pass filter. Turning up the treble is like using a phase-lag controller, which works like a low-pass filter. PD controllers respond more to high-frequency parts of a signal, so they act like high-pass filters. PI controllers focus more on low-frequency parts...

time and frequency -domain interpretation of phase-lead control

time-and-frequency-domain-interpretation-of-phase-lead-control

Phase-Lead Control for Faster System Response

Phase-lead control improves response speed and stability in control systems. It is often used when a system needs to react faster without losing control. A common example is television screen brightness adjustment. When contrast is enhanced, a phase-lead controller is being used. In a phase-lead system, the first parameter is smaller than the second. The design depends on placing poles and zeros in the right positions. The zero is often moved closer to the origin to speed up the response and...

time and frequency -domain interpretation of phase-lag control

time-and-frequency-domain-interpretation-of-phase-lag-control

Phase-Lag Control for Smoother System Response

Phase-lag control helps a system respond more smoothly and stay stable. It is also used to reduce steady-state error, which is the small difference that can remain after a system settles. A dimmer switch for a light bulb is a simple real-world example. It changes brightness gradually instead of all at once. In control systems, phase-lag control is often described with low-pass filtering. This form is represented when the factor a is less than 1. The controller does not place a pole at zero.

key terms and concepts

Learn how phase-lead and phase-lag controllers shape feedback systems, from stereo equalizer analogies to op-amp circuits and transfer functions.

Phase Shift Control in Feedback 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

Phase Shift Control in Feedback Systems

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