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1

Root surface temperature measurement during root canal obturation

Hotra Les, Boyko Oksana, Helzhynskyy Ihor, Barylo Hryhorii, Skoropad Pylyp, Ivanyshyn Alla, Basalkevych Olena

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2024

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T. 14, nr 1

95--98

EN

Prolonged exposure to elevated temperatures exceeding 47°C, which can occur during root canal obturation, can cause damage of both dental and bone tissues. In order to study the temperature distribution on the surface of the tooth root a temperature measuring device with cold-junction compensation is proposed. For in vitro measurement of the temperature distribution on the surface of the tooth, 8 thermocouples placed in direct contact with the cementum of the tooth were used. In order to eliminate the cold-junction temperature variations, the temperature equilibration device and RTD were used. The suggested linear approximation for the thermocouples' conversion function provides a nonlinearity relative error of less than 0.05% for K-type thermocouples and 0.07% for J-type thermocouples over the temperature range from 20 to 60°C.

PL

Długotrwała ekspozycja na podwyższone temperatury przekraczające 47°C, które mogą wystąpić podczas wypełniania kanałów korzeniowych, może spowodować uszkodzenie zarówno tkanek zęba, jak i kości. W celu zbadania rozkładu temperatury na powierzchni korzenia zęba zaproponowano urządzenie do pomiaru temperatury z kompensacją zimnego złącza. Do pomiaru in vitro rozkładu temperatury na powierzchni zęba wykorzystano 8 termopar umieszczonych w bezpośrednim kontakcie z cementem zęba. W celu wyeliminowania wahania temperatury zimnego złącza zastosowano urządzenie do wyrównania temperatur oraz czujnik rezystancyjny RTD. Proponowana aproksymacja liniowa funkcji przetwarzania termopary zapewnia względny błąd nieliniowości mniejszy niż 0,05% dla termopar typu K i 0,07% dla termopar typu J w zakresie temperatur od 20 do 60°C.

2

Nonlinear model predictive control for processes with complex dynamics: A parameterisation approach using Laguerre functions

Ławryńczuk Maciej

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 1

35--46

EN

Classical model predictive control (MPC) algorithms need very long horizons when the controlled process has complex dynamics. In particular, the control horizon, which determines the number of decision variables optimised on-line at each sampling instant, is crucial since it significantly affects computational complexity. This work discusses a nonlinear MPC algorithm with on-line trajectory linearisation, which makes it possible to formulate a quadratic optimisation problem, as well as parameterisation using Laguerre functions, which reduces the number of decision variables. Simulation results of classical (not parameterised) MPC algorithms and some strategies with parameterisation are thoroughly compared. It is shown that for a benchmark system the MPC algorithm with on-line linearisation and parameterisation gives very good quality of control, comparable with that possible in classical MPC with long horizons and nonlinear optimisation.

3

Contact with friction between 3D beams with deformable circular cross-sections

Kawa O., Listewka P.

Engineering Transactions

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2015

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Vol. 63, iss. 4

439--462

EN

In this paper, contact with friction between three-dimensional elastic beams with deformations at the contact zone is analysed. It is assumed that the analysed beams undergo large displacements, although the strains remain small and the cross-sections of the beams are deformed. To include the deformation effect the classical analytical result from Hertzian contact between two elastic cylinders is used [3]. The penalty method is applied to enforce normal contact and friction constraints and the appropriate kinematic variables are defined, linearised and discretised for the finite element method implementation.

4

Visualisation of concurrent processes

Mikulski Ł, Piątkowski M.

Control and Cybernetics

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2013

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Vol. 42, no. 3

699-725

EN

Mazurkiewicz traces are a widely used model for describing the languages of concurrent systems computations. The causal structure of atomic actions occurring in a process modeled as a trace generates a partial order. Hasse diagrams of such order are very common structures used for presentation and investigation in the concurrency theory, especially from the behavioural perspective. We present effective algorithms for Hasse diagrams construction and transformation. Later on, we use them for enumeration of all linearisations of the partial order that represents a concurrent process. Additionally, we attach the flexible visual implementation of all considered Algorithms.

5

Supervisory predictive control and on-line set-point optimization

Tatjewski P.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 3

483-495

EN

The subject of this paper is to discuss selected effective known and novel structures for advanced process control and optimization. The role and techniques of model-based predictive control (MPC) in a supervisory (advanced) control layer are first shortly discussed. The emphasis is put on algorithm efficiency for nonlinear processes and on treating uncertainty in process models, with two solutions presented: the structure of nonlinear prediction and successive linearizations for nonlinear control, and a novel algorithm based on fast model selection to cope with process uncertainty. Issues of cooperation between MPC algorithms and on-line steady-state set-point optimization are next discussed, including integrated approaches. Finally, a recently developed two-purpose supervisory predictive set-point optimizer is discussed, designed to perform simultaneously two goals: economic optimization and constraints handling for the underlying unconstrained direct controllers.

6

Nonlinear predictive control based on neural multi-models

Ławryńczuk M., Tatjewski P.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 1

7-21

EN

This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to avoid nonlinear optimisation, in the discussed suboptimal MPC algorithm the neural multi-model is linearised on-line and, as a result, the future control policy is found by solving of a quadratic programming problem.

7

Efficient nonlinear predictive control based on structured neural models

Ławryńczuk M.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 2

233-246

EN

This paper describes structured neural models and a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm based on such models. The structured neural model has the ability to make future predictions of the process without being used recursively. Thanks to the nature of the model, the prediction error is not propagated. This is particularly important in the case of noise and underparameterisation. Structured models have much better long-range prediction accuracy than the corresponding classical Nonlinear Auto Regressive with eXternal input (NARX) models. The described suboptimal MPC algorithm needs solving on-line only a quadratic programming problem. Nevertheless, it gives closed-loop control performance similar to that obtained in fully-fledged nonlinear MPC, which hinges on online nonconvex optimisation. In order to demonstrate the advantages of structured models as well as the accuracy of the suboptimal MPC algorithm, a polymerisation reactor is studied.

8

Suboptimal Non-linear Predictive Control Based on MLP and RBF Neural Models with Measured Disturbance Compensation

Ławryńczuk M.

Journal of Automation Mobile Robotics and Intelligent Systems

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2008

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Vol. 2, No. 2

54-64

EN

This paper is concerned with a computationally efficient (suboptimal) non-linear Model Predictive Control (MPC) algorithm based on two types of neural models: Multilayer Perceptron (MLP) and Radial Basis Function (RBF) structures. The model takes into account not only controlled but also the uncontrolled input of the process, i.e. the measured disturbance. The algorithm is computationally efficient, because it results in a quadratic programming problem, which can be effectively solved on-line by means of a numerically reliable software subroutine. Moreover, the algorithm gives good closed-loop control performance, comparable to that obtained in the fully-fledged non-linear MPC technique, which hinges on non-linear, usually non-convex optimisation.

9

A computationally efficient stable dual-mode type nonlinear predictive control algorithm

Ławryńczuk M., Tadej W.

Control and Cybernetics

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2008

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Vol. 37, no 1

99-132

EN

This paper describes a computationally efficient (sub-optimal) nonlinear predictive control algorithm. The algorithm uses a modified dual-mode approach which guarantees closed-loop stability. In order to reduce the computational burden, instead of online nonlinear optimisation used in the classical dual-mode control scheme, a nonlinear model of the plant is linearised on-line and a quadratic programming problem is solved. Calculation of the terminal set and implementation steps of the algorithm are detailed, especially for input-output models, which are widely used in practice.

10

Struktury i algorytmy współdziałania regulacji predykcyjnej i bieżącej optymalizacji ekonomicznej

Ławryńczuk M., Marusak P., Tatjewski P.

Pomiary Automatyka Kontrola

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2007

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R. 53, nr 10

55-61

PL

Celem pracy jest omówienie zagadnienia współpracy algorytmów regulacji predykcyjnej z nieliniową optymalizacją ekonomiczną. Problem ten jest szczególnie istotny wówczas, gdy dynamika zmian zakłóceń jest porównywalna z dynamiką procesu, ponieważ zastosowanie klasycznej warstwowej (hierarchicznej) struktury sterowania z rzadko powtarzaną optymalizacją ekonomiczną może nie być efektywne. Omawiane są dwie klasy struktur. W pierwszym przypadku stosuje się pomocniczą optymalizację ekonomiczną, której zadaniem jest aktualizacja punktu pracy poprzedzająca każdą interwencję algorytmu regulacji predykcyjnej. W dodatkowym liniowym lub kwadratowym zadaniu optymalizacji ekonomicznej stosuje się aktualizowaną na bieżąco liniową, liniowo-kwadratową lub odcinkowo-liniową aproksymację modelu. W drugim przypadku zadanie optymalizacji ekonomicznej i algorytm regulacji predykcyjnej są zintegrowane w pojedynczym problemie optymalizacji. Aby ograniczyć nakład obliczeń stosuje się aktualizowaną na bieżąco liniową lub liniowo-kwadratową aproksymację modelu, dzięki czemu otrzymuje się zadanie optymalizacji ekonomicznej w postaci problemu programowania kwadratowego.

EN

The paper is concerned with co-operation of model predictive control (MPC) algorithms with nonlinear economic optimisation. The problem is particularly important when dynamics of disturbances is comparable with dynamics of the process itself, since in such cases application of the classical multilayer (hierarchical) structure with infrequent economic optimisation may be not efficient. Two classes of control structures are investigated. In the first class an additional simplified optimisation is used which recalculates the operating point as frequently as the MPC controller executes. In the supplementary linear or quadratic programming optimisation problem approximate linear, linear-quadratic (updated on-line) or piecewise-linear models of the process are used. In the second class the economic optimisation and MPC manipulated variables computational load, approximate linear or linear-quadratic (updated on-line) models are used, then the resulting optimisation problem is of quadratic programming type.

11

A family of model predictive control algorithms with artificial neural networks

Ławryńczuk M.

International Journal of Applied Mathematics and Computer Science

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2007

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Vol. 17, no 2

217-232

EN

This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used on-line to determine local linearisation and a nonlinear free trajectory. Single-point and multi-point linearisation methods are discussed. The MPC-NPL structure is far more reliable and less computationally demanding in comparison with the MPC-NO one because it solves a quadratic programming problem, which can be done efficiently within a foreseeable time frame. At the same time, closed-loop performance of both algorithm classes is similar. Finally, a hybrid MPC algorithm with Nonlinear Prediction, Linearisation and Nonlinear optimisation (MPC-NPL-NO) is discussed.