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

ステレオのボリュームイコライザーを調整することを想像してみてください。ベースがクランクアップすると、フェーズリードコントローラーが作動します。高音を上げると、位相遅れコントローラーが機能します。
PDコントローラはハイパスフィルタ、PIはローパスフィルタ、PIDはバンドパスフィルタまたはバンドストップフィルタとして機能します。
フェーズリードコントローラ(ハイパスフィルタ)は、特定の周波数範囲でシステムに正の位相を導入します。逆に、位相遅れコントローラー (ローパス フィルター) では、負の位相が発生します。
1 つの伝達関数で両方のコントローラーを表すことができ、最初のパラメーターが 2 番目のパラメーターより大きい場合はハイパス、小さい場合はローパスです。
この機能は、オペアンプ回路を使用して実現できます。その伝達関数は、2つのコンデンサの比率と各パスの抵抗と静電容量の積の合計の積を通じて、出力電圧と入力電圧を関連付けます。
コンデンサを同等にすると、設計パラメータが4つから3つに減り、回路方程式が簡素化されます。
定数は、抵抗の比率と、抵抗と静電容量の積を置き換えることができます。

位相進みおよび位相遅れ制御

さまざまなタイプの制御における動作機能の理解は、ステレオのボリュームイコライザの調整などの実際的な例えで説明できます。低音を上げるには、ハイパスフィルタとして機能する位相進み制御を使用し、高音を上げるには、ローパスフィルタとして機能する位相遅れ制御を使用します。ハイパスフィルタに似た PD 制御は、高周波成分に対するシステムの応答を強化します。ローパスフィルタに似た PI 制御は、低周波成分を管理して定常誤差を減らします。PID 制御は、バンドパスフィルタまたはバンド減衰フィルタとして機能し、高周波調整と低周波調整の両方のバランスをとります。 
位相進み制御は、特定の周波数範囲でシステムに正の位相シフトを導入し、システムの応答性を高めます。対照的に、位相遅れ制御は負の位相シフトを導入し、高周波成分を減衰させることでシステムを安定させます。両タイプの制御は、単一の伝達関数で表すことができます。最初のパラメータが 2 番目のパラメータより大きい場合、関数はハイパスフィルタとして動作し、小さい場合はローパスフィルタとして動作します。 
これらの制御の実装は、オペアンプ回路を使用して実現できます。このような回路の伝達関数は、2 つのコンデンサの比の積と、各経路の抵抗と静電容量の積の合計を介して、出力電圧と入力電圧を関連付けます。コンデンサを等しくすることで設計を簡素化すると、設計パラメータの数が 4 から 3 に減り、回路方程式が合理化されます。 
さらに、抵抗の比率や抵抗と静電容量の積を定数に置き換えることで、回路設計がより簡単になります。このアプローチにより、アプリケーションの要件に応じて位相進み特性や位相遅れ特性を正確に調整できます。これらのパラメータを調整することで、エンジニアはハイパスフィルタとローパスフィルタの基本原理を活用してシステムの安定性とパフォーマンスを効果的に制御し、望ましい結果を得ることができます。

ステレオのボリュームイコライザーを調整することを想像してみてください。ベースがクランクアップすると、フェーズリードコントローラーが作動します。高音を上げると、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Design of Control Systems

制御システムの設計

KEY TERMS AND CONCEPTS

主要用語と概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Phase Shift Control in Feedback Systems

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