A Nonlinear PID Autotuning Algorithm
(1986) American Control Conference, 1986 p.2118-2123- Abstract
- A nonlinear autotuning regulator algorithm is obtained via a direct combination of the Åström-Hägglund algorithm for the linear case [1] with the sinusoidal-input describing function (SIDEF) approach to nonlinear compensator synthesis of Taylor and Strobel [2]. The basic approach for linear autotuning proceeds as follows: a. install a relay with hysteresis in series with the unknown plant to be controlled; close a unitygain feedback loop around this combination; b. choose several values of hysteresis so that this system exhibits limit cycles; the frequencies and amplitudes of the oscillation at the output of the plant determine points on the plant Nyquist plot; and c. given points on the plant Nyquist plot, set the PID controller gains... (More)
- A nonlinear autotuning regulator algorithm is obtained via a direct combination of the Åström-Hägglund algorithm for the linear case [1] with the sinusoidal-input describing function (SIDEF) approach to nonlinear compensator synthesis of Taylor and Strobel [2]. The basic approach for linear autotuning proceeds as follows: a. install a relay with hysteresis in series with the unknown plant to be controlled; close a unitygain feedback loop around this combination; b. choose several values of hysteresis so that this system exhibits limit cycles; the frequencies and amplitudes of the oscillation at the output of the plant determine points on the plant Nyquist plot; and c. given points on the plant Nyquist plot, set the PID controller gains using an appropriate tuning algorithm (e.g., Ziegler-Nichols). This approach produces good results if the plant is liner or nearly so; however, if the plant behavior is strongly amplitude-dependent, there are likely to be problems with implementing this algorithm. The nonlinear autotuning regulator algorithm which extends the above approach to handle situations where the plant behavior is strongly amplitude-dependent is based on the SIDF approach. In essence, SIDF input/output (I/O) models of the compensated nonlinear system are exploited to directly synthesize a compensator nonlinearity that eliminates or reduces the amplitude dependence of the open-loop I/O relation. The nonlinear synthesis portion of this algorithm is reasonably simple to implement, has been shown to be effective [2], and should be of practical utility. An example application to a precision position control system is provided as an illustration. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8517851
- author
- Taylor, James H. and Åström, Karl Johan LU
- organization
- publishing date
- 1986
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Proceedings of the 1986 American Control Conference : Seattle Sheraton Hotel and Towers, Seattle, WA, June 18-20, 1986 - Seattle Sheraton Hotel and Towers, Seattle, WA, June 18-20, 1986
- pages
- 2118 - 2123
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- American Control Conference, 1986
- conference location
- Seattle, Washington, United States
- conference dates
- 1986-06-18 - 1986-06-20
- external identifiers
-
- scopus:0022593576
- DOI
- 10.23919/ACC.1986.4789280
- language
- English
- LU publication?
- yes
- id
- 5e43a5b3-8ea8-41f6-9111-cc8c9663bf18 (old id 8517851)
- date added to LUP
- 2016-04-04 12:55:18
- date last changed
- 2021-01-03 06:09:17
@inproceedings{5e43a5b3-8ea8-41f6-9111-cc8c9663bf18,
abstract = {{A nonlinear autotuning regulator algorithm is obtained via a direct combination of the Åström-Hägglund algorithm for the linear case [1] with the sinusoidal-input describing function (SIDEF) approach to nonlinear compensator synthesis of Taylor and Strobel [2]. The basic approach for linear autotuning proceeds as follows: a. install a relay with hysteresis in series with the unknown plant to be controlled; close a unitygain feedback loop around this combination; b. choose several values of hysteresis so that this system exhibits limit cycles; the frequencies and amplitudes of the oscillation at the output of the plant determine points on the plant Nyquist plot; and c. given points on the plant Nyquist plot, set the PID controller gains using an appropriate tuning algorithm (e.g., Ziegler-Nichols). This approach produces good results if the plant is liner or nearly so; however, if the plant behavior is strongly amplitude-dependent, there are likely to be problems with implementing this algorithm. The nonlinear autotuning regulator algorithm which extends the above approach to handle situations where the plant behavior is strongly amplitude-dependent is based on the SIDF approach. In essence, SIDF input/output (I/O) models of the compensated nonlinear system are exploited to directly synthesize a compensator nonlinearity that eliminates or reduces the amplitude dependence of the open-loop I/O relation. The nonlinear synthesis portion of this algorithm is reasonably simple to implement, has been shown to be effective [2], and should be of practical utility. An example application to a precision position control system is provided as an illustration.}},
author = {{Taylor, James H. and Åström, Karl Johan}},
booktitle = {{Proceedings of the 1986 American Control Conference : Seattle Sheraton Hotel and Towers, Seattle, WA, June 18-20, 1986}},
language = {{eng}},
pages = {{2118--2123}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{A Nonlinear PID Autotuning Algorithm}},
url = {{http://dx.doi.org/10.23919/ACC.1986.4789280}},
doi = {{10.23919/ACC.1986.4789280}},
year = {{1986}},
}