A geometric-based approach to the maximum-speed state and output variables for some class of IMC structures

2020

IEEE Access

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A new geometric approach providing the minimum-energy issue for inverse model controlrelated perfect regulation of linear time-invariant multi-input/single-output plants described in the discretetime state-space framework is proposed in the paper. Recent results have shown that the minimum-norm T-inverse does not guarantee the minimum-energy perfect control design, which has been confirmed by heuristic studies only. The new proposal, postulated throughout the manuscript, certifies the potential of nonunique σ-inverse regarding the minimum-energy behavior of inverse model control-based structures. After application of the proposed geometric approach dedicated to some class of state-space systems, we can precisely calculate the total energy of the multivariable perfect control runs. Thus, the analytical new methodology allows to obtain the minimum-energy inverse model control schemes, what constitutes the main accomplishment of the paper. Additionally, the aim of future analytical exploration covering the entire class of right-invertible state-space systems is clearly focused. INDEX TERMS Geometric solution, perfect control, minimum-energy problem, inverses of nonsquare matrices, discrete-time state-space domain, LTI MIMO.

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Section: Perfect Control Law In the State-space Domainmentioning

confidence: 99%

A New Geometric-Oriented Minimum-Energy Perfect Control Design in the IMC-Based State-Space Domain

2020

IEEE Access

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“…It should be emphasized, that in order to fulfill the condition (3), the full rank plant has to be square or right invertible (n u n y ), see Refs. [8], [9].…”

Section: Control System Descriptionmentioning

confidence: 99%

“…attaches the infinite number of the DOFs-derived β(q −1 ) forms. Thus, we can obtain the infinite number of inverses and consequently different peculiarities of the controlled plant [1], [9].…”

Section: Control System Descriptionmentioning

confidence: 99%

“…The inverse model control (IMC) has widely been investigated over the past decades due to its application in many scientific and engineering fields [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25]. The unique behaviors of the discussed technique such as robustness, maximumspeed or minimum-energy properties make it attractive in many practical implementations [1], [9], [12], [23], [26], [27], [28]. The widely known IMC-based perfect control law, which constitutes the deterministic instance of the minimum variance control (MVC), has not only been associated with the full-rank square MIMO systems, including SISO ones [1].…”

Section: Introductionmentioning

confidence: 99%

“…systems with greater number of input than output variables, can also be subjected by such noise-free control law [3]. In such a case, through the application of nonunique parameter/polynomial right inverses, we can redefine the special properties of the closed-loop state-feedback plant [1], [9], [26]. The IMC methodology, both in the input-output and the state-space domains, has necessitated the system to be under full-rank regulation, hence the non-full rank instance has not been considered, in general [29], [30].…”

Section: Introductionmentioning

confidence: 99%

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A New Non-Full Rank Algorithm for the IMC-Derived d-Step MIMO Structures in the Pole-Free State Space

2020

IEEE Access

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In this paper, the powerful issue of a non-full rank inverse model control investigation is provided. It is broadly known, that the inverse-based methodology is associated with the full-rank control systems only. However, following the recently obtained authors' results in this matter, it should be concluded, that for single-delayed non-full rank state-space plants, the inverse model control-related perfect control expression can also be established. It is shown here, that for all right-and left-oriented multivariable LTI non-full rank systems, including the square ones, governed by the discrete-time statespace domain arranging the zero-reference value, the maximum-speed pole-free instance of such inverse model control strategy can be achieved. Thus, the new non-full rank algorithm does not coincide with the z-transfer-function scenario, which additionally sounds the intriguing peculiarity. The innovative content of the manuscript, that has never been seen before, is strongly supported by the numerical examples. Henceforth, the presented methodology covers the entire set of LTI MIMO state-space-oriented plants in the discrete-time domain, which is also a consequence of conducted research investigation in the past. INDEX TERMS Non-full rank, perfect control procedure, Moore-Penrose inverse, generalized inverses, skeleton factorization, pole-free delayed plants, discrete-time state-space MIMO structures

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Towards a new general IMC-based high-order minimum-energy perfect control design paradigm

2020 7th International Conference on Control, Decision and Information Technologies (CoDIT)

Krok

2020