Robust fractional-order perfect control for non-full rank plants described in the Grünwald-Letnikov IMC framework. (English) Zbl 1498.93439
Summary: The advanced analytical study in the field of fractional-order non-full rank inverse model control design is presented in the paper. Following the recent results in this matter it is certain, that the inverse model control-oriented perfect control law can be established for the non-full rank integer-order systems being under the discrete-time state-space reference with zero value. It is shown here, that the perfect control paradigm can be extended to cover the multivariable non-full rank plants governed by the more general Grünwald-Letnikov discrete-time state-space model. Indeed, the postulated approach significantly reduces both iterative and non-iterative computational effort, mainly derived from the approximation of the Moore-Penrose inverse of the non-full rank matrices to finally be inverted. A prevention provided by the new method excludes the detrimental matrix behavior in the form of singularity, often avoided due to the observed ill-conditioned sensitivity. Thus, the new defined robust fractional-order non-full rank instance of such control strategy, supported by the pole-free mechanism, gives rise to the introduction of the general unified non-full rank perfect control-originated theory. Numerical algorithms with simulation investigation clearly confirm the innovative peculiarities provided by the manuscript.
MSC:
| 93C55 | Discrete-time control/observation systems |
| 93B35 | Sensitivity (robustness) |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 15A09 | Theory of matrix inversion and generalized inverses |
Keywords:
fractional-order systems; perfect control; non-full rank; generalized inverses; LTI discrete-time plants; state-space; MIMO; robustness; numerical solutions - overdetermined systems (pseudoinverses)References:
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