Discussion Overview
The discussion revolves around the representation of closed loop systems using open loop systems, exploring the implications of such representations in control theory. Participants examine the differences in transfer functions between closed and open loop systems and the potential for analyzing closed loop performance through open loop methods.
Discussion Character
- Debate/contested
- Technical explanation
- Mathematical reasoning
Main Points Raised
- Some participants recall that closed loop systems can be represented by open loop systems, but express confusion about why they would behave differently if their transfer functions were the same.
- Others clarify that the transfer functions of closed loop and open loop systems are not the same due to the feedback network altering the transfer function when the loop is closed.
- One participant suggests that a closed loop system can be represented as a cascade of open loop systems, where each subsection operates as an open loop, but the overall system remains closed loop.
- Another participant proposes that it might be possible to analyze loop performance in an open loop manner by perturbing the input and observing the response.
- Discussion includes a specific closed loop transfer function example and questions whether an open loop system could be constructed to yield the same transfer function without feedback.
- Some participants express uncertainty about how to create an open loop system that matches the closed loop transfer function without embedding the closed loop system itself.
- References to external materials are provided, which discuss block diagram algebra and the representation of feedback systems, but do not definitively resolve the questions posed.
Areas of Agreement / Disagreement
Participants do not reach a consensus on whether a closed loop system can be represented as an open loop system with the same transfer function. Multiple competing views remain regarding the nature of the transfer functions and the feasibility of such representations.
Contextual Notes
There are limitations in the discussion regarding the assumptions made about the transfer functions and the definitions of open and closed loop systems. Some mathematical steps and conditions for the proposed representations remain unresolved.
Who May Find This Useful
This discussion may be useful for students and professionals in control theory, engineering, and related fields who are exploring the relationships between open and closed loop systems and their representations.