Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
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Wojciech Przemysław Hunek
Abstract
A new perfect control algorithm dedicated to fractional-order right-invertible systems, i.e. plants with a greater number of input than output variables, is presented in this paper. It is shown that such a control strategy can be particularly applied with regard to practical tasks. Henceforth, the Grünwald-Letnikov difference operator Δα of an assumed order α can be truncated without loss of generality. For that reason, the so-called pole-free perfect control formula can be used to minimize the essential drawback of the Grünwald-Letnikov approach engaged, so as to define the intriguing issue regarding the robust perfect control for non-integer-order right-invertible LTI discrete-time state-space systems. Simulation examples show that the presented method can compete with a classical stable-pole one, for which the actual systems described by a fractional-order model often correspond with an inconvenient asymptotic perfect control solution given by the unlimited original operator Δα. In the end, the possibility of employing of author’s nonunique right inverses dedicated to nonsquare MIMO system matrices is demonstrated, thus giving rise to the introduction of a new powerful tool for robustification of non-integer-order closed-loop perfect control plants as well.
- Acronyms
- LTI
linear time-invariant
- MIMO
multi-input/multi-output
- MVC
minimum variance control
- SISO
single-input/single-output
8 Appendix
Program allowing to present the signal runs of truncated fractional-order perfect control is presented below.
Acknowledgements
Invaluable comments from the anonymous reviewers are gratefully acknowledged.
References
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© 2019 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–2–2019)
- Discussion Paper
- The flaw in the conformable calculus: It is conformable because it is not fractional
- The failure of certain fractional calculus operators in two physical models
- Research Paper
- Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
- On Riesz derivative
- A note on fractional powers of strongly positive operators and their applications
- Semi-fractional diffusion equations
- Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
- Well-posedness of fractional degenerate differential equations in Banach spaces
- Structure factors for generalized grey Browinian motion
- Linear stationary fractional differential equations
- Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
- On fractional differential inclusions with Nonlocal boundary conditions
- On solutions of linear fractional differential equations and systems thereof
- Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
- A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
- On representation and interpretation of Fractional calculus and fractional order systems
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 22–2–2019)
- Discussion Paper
- The flaw in the conformable calculus: It is conformable because it is not fractional
- The failure of certain fractional calculus operators in two physical models
- Research Paper
- Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
- On Riesz derivative
- A note on fractional powers of strongly positive operators and their applications
- Semi-fractional diffusion equations
- Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
- Well-posedness of fractional degenerate differential equations in Banach spaces
- Structure factors for generalized grey Browinian motion
- Linear stationary fractional differential equations
- Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
- On fractional differential inclusions with Nonlocal boundary conditions
- On solutions of linear fractional differential equations and systems thereof
- Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
- A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
- On representation and interpretation of Fractional calculus and fractional order systems
