The robust control of a servomechanism problem for linear time-invariant multivariable systems
Abstract
Necessary and sufficient conditions are found for there to exist a robust controller for a linear, time-invariant, multivariable system (plant) so that asymptotic tracking/regulation occurs independent of input disturbances and arbitrary perturbations in the plant parameters of the system. In this problem, the class of plant parameter perturbations allowed is quite large; in particular, any perturbations in the plant data are allowed as long as the resultant closed-loop system remains stable. A complete characterization of all such robust controllers is made. It is shown that any robust controller must consist of two devices 1) a servocompensator and 2) a stabilizing compensator. The servocompensator is a feedback compensator with error input consisting of a number of unstable subsystems (equal to the number of outputs to be regulated) with identical dynamics which depend on the disturbances and reference inputs to the system. The sorvocompensator is a compensator in its own right, quite distinct from an observer and corresponds to a generalization of the integral controller of classical control theory. The sole purpose of the stabilizing compensator is to stabilize the resultant system obtained by applying the servocompensator to the plant. It is shown that there exists a robust controller for "almost all" systems provided that the number of independent plant inputs is not less than the number of independent plant outputs to be regulated, and that the outputs to be regulated are contained in the measurable outputs of the system; if either of these two conditions is not satisfied, there exists no robust controller for the system.
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Early lumping approximates the infinite-dimensional system with a finite-dimensional model.
“One is early lumping, which approximates the infinitedimensional system with a finite-dimensional model.[2,3]”
From Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport <scp>PDEs</scp> (2025) · cites this paper as [2]
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Moadeli, B., Cassol, G. O., & Dubljevic, S. (2025) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.25629 · Cited by 4 · see citing works
- Authors
- Davison, E.
- Affiliations
- University of Toronto (CA)
- Corresponding author
- Davison, E.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1976-02
- Volume
- 21
- Issue
- 1
- Pages
- 25-34
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2149087996
- Cited by
- 1,271
- References
- 20
- Citations by year
- 2026: 27 · 2025: 54 · 2024: 30 · 2023: 46 · 2022: 34 · 2021: 41 · 2020: 32 · 2019: 63 · 2018: 43 · 2017: 50 · 2016: 40 · 2015: 32 · 2014: 39 · 2013: 36 · 2012: 39
- FWCI
- 16.28
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
- Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
- Keywords
- robust control, output regulation, multivariable systems, linear time-invariant systems, input perturbation, asymptotic tracking, regulation, stabilizing compensators, integral controller, closed-loop stability, necessary and sufficient conditions
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