ESDU 84009
Nonlinear systems: an introduction to Describing Functions.
Abstract:
ESDU 84009 introduces the use of Describing Functions (DF) to estimate the stability and the steady-state response of autonomous closed-loop non-linear systems. The DF uses a single sinusoidal input to the non-linear element and is therefore classified as a frequency response method. Five DF schemes are given and the characteristics of those DF's when used with eight common non-linear elements (combinations of deadzone, saturation, ideal relay, hysteresis and backlash) defined graphically and by their algebraic expressions. Two practical worked examples of third-order non-linear systems illustrate the use of those DF's in stability investigations and show the accuracy with which they estimate the magnitude of the output. Those DF's are also used to estimate the frequency and magnitude of a self-sustaining, or limit-cycle, oscillation.Indexed under:
Details:
| Data Item ESDU 84009 | |
|---|---|
| Format: |
|
| Status: |
|
| Previous Releases: |
|
| ISBN: |
|
The Data Item document you have requested is available only to subscribers.
- Subscribers login here.
- If you are not an ESDU subscriber find out how to subscribe.
The graphs listed below are available only to subscribers.
- Subscribers login here.
- If you are not an ESDU subscriber find out how to subscribe.
This Data Item contains 16 interactive graph(s) as listed below.
| Graph | Title |
|---|---|
| Figure 1 - Part 1 | Plot of magnitude of linear system defined by Equation (8.2) |
| Figure 1 - Part 2 | Plot of phase of linear system defined by Equation (8.2) |
| Figure 3 | Plots of magnitude versus phase angle for the describing functions for an ideal relay with hysteresis and the system defined by Equation (8.6) |
| Figure A1 | Describing Function characteristics for deadzone |
| Figure A2 | Describing Function characteristics for saturation |
| Figure A3 | Describing Function characteristics for deadzone and saturation (conventional scheme) |
| Figure A4 | Describing Function characteristics for deadzone and saturation |
| Figure A5 | Describing Function characteristics for ideal relay |
| Figure A6 | Describing Function characteristics for deadzone and ideal relay |
| Figure A7 - Part 1 | Describing function characteristics for ideal relay with hysteresis |
| Figure A7 - Part 2 | Describing Function characteristics for ideal relay with hysteresis |
| Figure A8 | Describing Function characteristics for ideal relay, deadzone and hysteresis (conventional scheme) |
| Figure A9 | Describing Function characteristics for ideal relay, deadzone and hysteresis |
| Figure A10 | Describing Function characteristics for ideal relay, deadzone and hysteresis |
| Figure A11 - Part 1 | Describing function characteristics for backlash |
| Figure A11 - Part 2 | Describing Function characteristics for backlash |