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1

Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems

Siwczyński M., Żaba S., Drwal A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 3

613--620

EN

In the complex RLC network, apart from the currents flows arising from the normal laws of Kirchhoff, other distributions of current, resulting from certain optimization criteria, may also be received. This paper is the development of research on distribution that meets the condition of the minimum energy losses within the network called energy-optimal distribution. Optimal distribution is not reachable itself, but in order to trigger it off, it is necessary to introduce the control system in current-dependent voltage sources vector, entered into a mesh set of a complex RLC network. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this the operator R(s) is replaced by the R’ operator which is a?matrix, but non-dispersive one (it does not depend on s). This type of control is called the suboptimal control. Therefore, it is important to make appropriate selection of the R’ operator and hence the suboptimal control. This article shows how to implement such control through the use of matrix operators of multiple differentiation or integration. The key aspect is the distribution of a single rational function H(s) in a series of ‘s’ or ‘s1’. The paper presents a new way of developing a given, stable rational transmittance with real coefficients in power series of ‘s/s1. The formulas to determine values of series coefficients (with ‘s/s1’) have been shown and the conditions for convergence of differential/integral operators given as series of ‘s/s1’ have been defined.

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Energetycznie optymalny rozkład napięć w złożonej liniowej sieci elektrycznej z impulsowymi lub okresowymi przebiegami sygnałów napięciowych i prądowych. Sterowanie suboptymalne

Siwczyński M., Drwal A., Żaba S.

Przegląd Elektrotechniczny

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2016

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R. 92, nr 4

187--190

PL

W obwodach sygnałów elektrycznych należących do tzw. przestrzeni L1-impulsów, bądź przestrzeni sygnałów okresowych występujący tam rzeczywisty rozpływ prądów nie spełnia zasady minimum strat energetycznych [1,2]. Rozwiązaniem tego zagadnienia jest wprowadzenie sterowania wektorem źródeł prądowych napięciowo zależnych wprowadzonego do zbioru węzłów złożonej sieci typu RLC. Sterowanie to jest energetycznie obojętne (sterowanie optymalne). Dla sterowania energetycznie optymalnego do otrzymania operatora sterowania potrzebne jest odwrócenie operatora R(s). Jest to operator macierzowy i dyspersyjny (zależy od częstotliwości). Odwrócenie takich operatorów jest niewygodne gdyż jest algorytmicznie skomplikowane. Aby tego uniknąć zastępuje się operator R(s) operatorem R’, który jest macierzą, ale niedyspersyjną (nie zależy od s). Takie sterowanie zostanie nazwane sterowaniem suboptymalnym.

EN

In the circuits of electrical signals belonging to the L1-impulses space or periodic signals space, occurring over there real distribution of electrical voltage does not meet the principle of minimum energy losses [1,2]. The solution to this problem is to introduce the control system as voltage-dependent current sources vector, entered into a nodes set of a complex RLC network. The paper presents a solution of this problem by introduced the control system in current-dependent voltage source vector, entered into a nodes set of a complex RLC network. It has been shown that the control is energy-neutral (optimal control). For energy-optimal controlling, to obtain control operator it is required inversion R(s) operator. It is the matrix operator and the dispersive operator (depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this, the operator R(s) is replaced by the R’ operator which is a matrix, but nondispersive (does not depends on s). Such control is called the suboptimal control.

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Energy-optimal current distribution in a complex linear electrical network with pulse or periodic voltage and current signals. Suboptimal control

Żaba S., Siwczyński M., Drwal A.

Measurement Automation Monitoring

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2016

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Vol. 62, No. 4

125--128

EN

In the circuits of electrical signals belonging to the L1-impulses space or periodic signals space, occurring there real distribution of electrical currents does not meet the principle of minimum energy losses [1, 2]. The solution to this problem is to introduce the control system as current-dependent voltage sources vector, entered into a meshes set of a complex RLC network. It has been shown that the control is energy-neutral (optimal control) [2]. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this, the operator R(s) is replaced by the R’ operator which is a matrix, but nondispersive one (does not depend on s). Such control is called the suboptimal control.

4

Process-oriented suboptimal controller for SiC bulk crystal growth system

Orzyłowski M.

Elektronika : konstrukcje, technologie, zastosowania

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2012

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Vol. 53, nr 8

11-15

EN

This paper presents a solution of a dedicated suboptimal controller, oriented on the designed thermal system and technological process for SiC bulk crystal growth. The arrangement is innovative and rather unconventional, so the control had to be worked out from the very basis. The goal of this work was to determine The simplest controller that would bring on a significant cost reduction and reliability increase. It was assumed that the controller should meet rigorous quality requirements in all typical states during the significant phases of the process. However, a reasonable deterioration of the quality index is tolerated during the process phases of low influence on the final result and during the failure states. For the controller synthesis a sixth-order model and the quadratic performance index of infinite horizon have been used. The simulation of the state vector and input vector trajectories has been applied for the gain matrix optimization. In the analysis the typical dynamic states of the plant during the process have been taken into account. The choice of the controller structure has been based on the control quality deterioration coefficient, which was defined as a ratio of the quality index of the suboptimal control to the quality index of the optimal control calculated in the same control conditions. Finally the structure of suboptimal controller with two single feedback loops has been chosen. The simulation of typical dynamic states for crystallization process has shown that the performance index doesn't rise more than by 30% in relation to its optimal value. It can be bigger for non-typical states, but it doesn't have any significant consequences. The designed suboptimal controller has been used in the constructed plant for SiC monocrystallization. The tests of this system in the production conditions have proved that it meets all requirements.

PL

Artykuł prezentuje rozwiązanie suboptymalnego regulatora przeznaczonego do opracowywanego elektrotermicznego stanowiska, który jest dostosowany do procesu technologicznego hodowli kryształów SiC. Rozwiązanie urządzenia jest innowacyjne i niekonwencjonalne, zaś projekt sterowania był prowadzony łącznie z konstrukcją urządzenia. Celem pracy było określenie najprostszego regulatora, który przyniesie znaczącą obniżkę kosztów i wzrost niezawodności. Założono, że regulator spełni rygorystyczne wymagania jakości we wszystkich typowych stanach podczas znaczących faz procesu. Jednocześnie dopuszczono istotne pogorszenie wskaźnika jakości sterowania w stanach małoznaczących dla przebiegu procesu oraz w stanach awaryjnych. Dla syntezy suboptymalnego regulatora przyjęto model szóstego rzędu i kwadratowy wskaźnik jakości sterowania o nieskończonym horyzoncie czasowym. Dla syntezy macierzy sterowania optymalnego przyjęto symulację trajektorii wektora sterowania. W analizie wzięto pod uwagę typowe stany dynamiczne obiektu podczas procesu. Wybór struktury regulatora bazował na współczynniku pogorszenia wskaźnika jakości sterowania zdefiniowanego jako stosunek wskaźnika jakości sterowania suboptymalnego do wskaźnika sterowania optymalnego określonego w tych samych warunkach sterowania. Ostatecznie przyjęto strukturę regulatora suboptymalnego w postaci dwóch pętli sprzężenia zwrotnego. Symulacja typowych stanów dynamicznych podczas procesu krystalizacji wykazała, że wskaźnik jakości sterownia nie wzrósł bardziej niz 30% w stosunku do wskaźnika sterowania optymalnego. Wzrost ten może być większy w stanach nietypowych jednak nie wiąże się jednak to z istotnymi konsekwencjami. Zaprojektowany regulator suboptymalny został wykorzystany w skonstruowanym stanowisku do monokrystalizacji SiC zaś testy tego stanowiska wykazały pełną, zgodność z postawionymi wymaganiami.

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Correctness of a constrained control Mayer's problem for a class of singularly perturbed functional-differential systems

Glizer V. Y.

Control and Cybernetics

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2008

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Vol. 37, no 2

329-351

EN

A Mayer's problem for a singularly perturbed controlled system with the general type of a small state delay is considered. The control is subject to geometrical constraints. The cost functional is a function of the terminal value of the slow state variable. A simpler parameter-free optimal control problem (the reduced problem) is associated with the original problem. A convergence of the optimal value of the cost functional in the original problem to the optimal value of the cost functional in the reduced problem, as a parameter of singular perturbation tends to zero, is established. An asymptotic suboptimality of the optimal control of the reduced problem in the original problem is shown. These results are extended to some more general optimal control problems. An illustrative example is presented.

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An approach to decentralized adaptive control

Perutka K., Bobal V.

Archives of Control Sciences

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2003

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Vol. 13, no. 1

33-46

EN

The paper presents a way of control of decentralized two inputs two outputs (TITO) systems. The base of the approach is usage of the set of one-dimensional self-tuning controllers wiyh reduced orders, being tuned simultaneously, in contrast to methods using relays in feedback. A method of the recursive least squares with directional forgetting factor applied to the continuous-time system is used as the identification algorithm for the self-tuning controllers. Itobtains data using the differential filters. verification was done in MATLAB-SIMULINK on the systems with "P" and "V" structures. two methods of tuning the controllers were used: the suboptimal linear quadratic method, and the dynamics inversion method. This approach give good results, and enables to use arbitary method of tuning the controllers, in particular, to apply the approaches of control of SISO systems, which are quite common for the multi-variable systems.