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Keywords = LTI MIMO state-space

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13 pages, 935 KiB  
Article
Energy Optimization of the Continuous-Time Perfect Control Algorithm
by Marek Krok, Paweł Majewski, Wojciech P. Hunek and Tomasz Feliks
Energies 2022, 15(4), 1555; https://doi.org/10.3390/en15041555 - 19 Feb 2022
Cited by 3 | Viewed by 1833
Abstract
In this paper, an attempt at the energy optimization of perfect control systems is performed. The perfect control law is the maximum-speed and maximum-accuracy procedure, which allows us to obtain a reference value on the plant’s output just after a time delay. Based [...] Read more.
In this paper, an attempt at the energy optimization of perfect control systems is performed. The perfect control law is the maximum-speed and maximum-accuracy procedure, which allows us to obtain a reference value on the plant’s output just after a time delay. Based on the continuous-time state-space description, the minimum-error strategy is discussed in the context of possible solutions aiming for the minimization of the control energy. The approach presented within this study is focused on the nonunique matrix inverse-originated so-called degrees of freedom being the core of perfect control scenarios. Thus, in order to obtain the desired energy-saving parameters, a genetic algorithm has been employed during the inverse model control synthesis process. Now, the innovative continuous-time procedure can be applied to a wide range of multivariable plants without any stress caused by technological limitations. Simulation examples made in the MATLAB/Simulink environment have proven the usefulness of the new method shown within the paper. In the extreme case, the energy consumption has been reduced by approximately 80% in comparison with the well-known Moore–Penrose inverse. Full article
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21 pages, 2919 KiB  
Article
A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework
by Wojciech Przemysław Hunek and Łukasz Wach
Symmetry 2019, 11(10), 1322; https://doi.org/10.3390/sym11101322 - 22 Oct 2019
Cited by 3 | Viewed by 3046
Abstract
The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due [...] Read more.
The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and σ -inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology. Full article
(This article belongs to the Special Issue Recent Advances in Discrete and Fractional Mathematics)
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