Auto-tuning of multivariable PID controllers from decentralized relay feedback

doi:10.1016/S0005-1098(96)00177-X

Automatica

Volume 33, Issue 3, March 1997, Pages 319-330

https://doi.org/10.1016/S0005-1098(96)00177-X Get rights and content

Abstract

A method for auto-tuning fully cross-coupled multivariable PID controllers from decentralized relay feedback is proposed for multivariable processes with significant interactions. Multivariable oscillations under decentralized relay feedback are first investigated, and, in particular, it is shown that for a stable m × m process the oscillation frequency will remain almost unchanged under relatively large relay amplitude variations. Therefore m decentralized relay feedback tests are performed on the process, with their oscillation frequencies close to each other so that the process frequency-response matrix can be estimated at that frequency. A bias is further introduced into the relay to additionally obtain the process steady-state matrix. For multivariable controller tuning, a new set of design equations are derived under the decoupling condition where the equivalent diagonal plants are independent of off-diagonal elements of the controller, and are used to design the controller diagonal elements first. The PID parameters of the controllers are determined individually by solving these equations at the oscillation and zero frequencies. The proposed method is applied to various typical processes, where significant performance improvement over the existing tuning methods is demonstrated.

References (26)

K.J. Åström et al.
Automatic tuning of simple regulators with specifications on phase and amplitude margins
Automatica
(1984)
K.J. Åström et al.
K.J. Åström et al.
Towards intelligent PID control
Automatica
(1991)
D.P. Atherton
P.B. Deshpande
W.K. Ho et al.
Performance and gain and phase margins of well-known PI tuning formulas
IEEE Trans. Control Syst. Technol.
(1995)
W.K. Ho et al.
Tuning of PID controllers based on gain and phase margin specifications
Automatica
(1995)
L. Johansson et al.
Inverse Nyquist array technique in the design of a multivariable controller for a solid-fuel boiler
Int. J. Control
(1984)
H.N. Koivo et al.
Tuning of PID controllers: survey of SISO and MIMO techniques
K.Y. Kong

J. Lieslehto et al.

An expert system for multivariable controller design

Automatica

(1993)

A.P. Loh et al.

Describing function matrix for multivariable systems and its use in multiloop PI design

J. Process Control

(1994)

A.P. Loh et al.

Autotuning of multiloop proportional-integral controllers using relay feedback

Ind. Engng Chem. Res.

(1993)

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^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Guy Dumont under the direction of Editor C. C. Hang.

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PaperAuto-tuning of multivariable PID controllers from decentralized relay feedback☆

Abstract

Automatic tuning of simple regulators with specifications on phase and amplitude margins

Automatica

Towards intelligent PID control

Automatica

Performance and gain and phase margins of well-known PI tuning formulas

IEEE Trans. Control Syst. Technol.

Tuning of PID controllers based on gain and phase margin specifications

Automatica

Inverse Nyquist array technique in the design of a multivariable controller for a solid-fuel boiler

Int. J. Control

Tuning of PID controllers: survey of SISO and MIMO techniques

An expert system for multivariable controller design

Automatica

Describing function matrix for multivariable systems and its use in multiloop PI design

J. Process Control

Autotuning of multiloop proportional-integral controllers using relay feedback

Ind. Engng Chem. Res.

Paper
Auto-tuning of multivariable PID controllers from decentralized relay feedback☆