# EE102: Introduction to Signals & Systems, Lecture 23 | Summary and Q&A

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April 2, 2018
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Stanford
EE102: Introduction to Signals & Systems, Lecture 23

## TL;DR

Feedback control systems use integral action to achieve insensitivity to variations and disturbances, while oscillators rely on delay and feedback to generate periodic signals.

## Key Insights

• 🥺 Integral action in feedback control systems provides insensitivity to variations and disturbances, leading to improved stability and reduced error.
• 📡 Oscillators rely on delay and feedback to generate periodic signals, with the frequency determined by the product of resistance and capacitance values.
• ⌛ The design of feedback control systems and oscillators involves selecting appropriate parameters, such as gain, time constants, and frequency, to achieve the desired performance.
• 🉐 Understanding the bode plot of a system can provide insights into the frequency and gain at which oscillation occurs in an oscillator circuit.

## Transcript

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### Q: How does integral action in feedback control systems help reduce error and improve stability?

Integral action allows for insensitivity to variations and disturbances by continuously adjusting the control signal based on the accumulated error over time. This helps to eliminate steady-state error and enhance stability by maintaining the system at the desired setpoint.

### Q: What is the role of delay in oscillators?

Delay in oscillators plays a crucial role in generating the oscillatory response. The delay allows for the system to build up sufficient voltage or energy before feedback occurs, leading to positive feedback and the regeneration of the input signal.

### Q: How is the frequency of oscillation determined in an oscillator circuit?

The frequency of oscillation in an oscillator circuit is determined by the product of the resistance and capacitance values in the feedback section. The higher the product of RC, the lower the frequency of oscillation.

### Q: Why is it important to have the loop gain equal to -1 at the desired frequency in an oscillator circuit?

The loop gain being -1 at the desired frequency ensures that the phase shift introduced by the feedback section is exactly 180 degrees. This enables the positive feedback to sustain the oscillation by regenerating the input signal without it decaying or amplifying uncontrollably.

## Summary & Key Takeaways

• Integral action in feedback control systems allows for insensitivity to variations and disturbances, leading to reduced error and increased stability.

• Oscillators use delay and feedback to generate periodic signals, relying on the phase shift and gain to achieve oscillation.

• The design of feedback control systems and oscillators involves selecting appropriate parameters, such as gain, time constants, and frequency, to achieve the desired performance.