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1

On the robustness of the integrable trajectories of the control systems with limited control resources

Huseyin Nesir, Huseyin Anar, Guseinov Khalik G.

Archives of Control Sciences

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2023

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Vol. 33, No. 3

527--537

EN

The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space Lq(Ω; ℝm), q > 1, with radius r and centered at the origin. The trajectory of the system is defined as p-integrable multivariable function from the space Lp(Ω; ℝn), (1/q) + (1/p) = 1, satisfying the system’s equation almost everywhere. It is shown that the system’s trajectories are robust with respect to the fast consumption of the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.

2

Fundamental limitations of the decay of generalized energy in controlled (discrete-time) nonlinear systems subject to state and input constraints

Selek István, Ikonen Enso

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 4

629--639

EN

This paper is devoted to the analysis of fundamental limitations regarding closed-loop control performance of discrete-time nonlinear systems subject to hard constraints (which are nonlinear in state and manipulated input variables). The control performance for the problem of interest is quantified by the decline (decay) of the generalized energy of the controlled system. The paper develops (upper and lower) barriers bounding the decay of the system’s generalized energy, which can be achieved over a set of asymptotically stabilizing feedback laws. The corresponding problem is treated without the loss of generality, resulting in a theoretical framework that provides a solid basis for practical implementations. To enhance understanding, the main results are illustrated in a simple example.

3

Nieliniowe sterowanie predykcyjne kaskadowym układem zbiorników

Bieniek B., Piotrowski R.

Pomiary Automatyka Robotyka

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2017

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R. 21, nr 1

25--30

PL

Obiektem regulacji jest kaskadowy układ trzech zbiorników firmy INTECO. Do sterowania wykorzystywane są dwa z nich. Zaprojektowano dwa układy regulacji poziomu wody: jednowymiarowe algorytmy MPC – po jednym dla każdego ze zbiorników oraz wielowymiarowy algorytm MPC sterujący całym układem. Przeprowadzono analizę porównawczą opracowanych algorytmów sterowania dla zmiennej trajektorii zadanej.

EN

The control system is a cascade of three tanks of INTECO. They are used to control two of them. Two algorithms of water level control are used: two single dimensional model predictive control (MPC) algorithms, one for each tank, and a multi-dimensional MPC controlling both tanks simultaneously. A comparative analysis of developed control algorithms for variable set-point trajectory.

4

Wieloobszarowy układ regulacji PI do sterowania prędkością obrotową samochodu z silnikiem spalinowym

Strojny R., Piotrowski R.

Pomiary Automatyka Robotyka

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2013

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R. 17, nr 6

90--95

PL

Sterowanie pojazdami stanowi istotny obszar działalności koncernów samochodowych. W pracy przedstawiono nieliniowy model matematyczny układu napędowego samochodu osobowego z silnikiem spalinowym. Następnie zaproponowano strukturę systemu sterowania i zaprojektowano nieliniowy wieloobszarowy układ regulacji PI. Przeprowadzono testy symulacyjne zaproponowanego rozwiązania i dokonano krytycznej analizy uzyskanych wyników.

EN

Control of vehicles has a key role in the activities of car companies. The paper presents a nonlinear mathematical model of the propulsion system of a passenger car with a petrol engine. Next, new control structure and the nonlinear multiregional PI control system of the rotational speed are designed. Finally, the results of simulation and a critical analysis are presented.

5

Precompensator of nonlinear multivariable systems for a diagonal interactor

Mutoh Y.

Systems Science

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2005

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Vol. 31, no 2

45-55

EN

An interactor is another expression of the structure at infinity of linear multivariable systems, which can be extended to nonlinear multivariable systems. Hence, as for linear systems, the interactor plays an important role also in the nonlinear control problems, e.g., decoupling control, model matching control, disturbance decoupling control, etc. But, in general, the interactor is a lower triangular polynomial matrix, which makes the control design problem complicated. This paper considers the precompensator for the affine nonlinear multivariable system such that the total system has a diagonal interactor. Our main purpose is to present the design algorithm of such a compensator and prove the convergence property of the algorithm for nonlinear systems.

6

Nonlinear model predictive control method for control nonaffine systems

Domek S., Tarasiejski L.

Systems Science

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2005

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Vol. 31, no 3

13-20

EN

In the paper, it is proposed to modify the known nonlinear predictive control method with a dynamic linearization around the prediction error or current process variable measurements. The approach is intended for strongly nonlinear control nonaffine processes, particularly for those that can be modeled by generalized MIMO Hammerstein models. Such models are often used, for example, for modeling various processes in chemistry. The proposed nonlinear control method allows for control constraints through including appropriate approximating functions into the model input matrix. To minimize the plant-model mismatch, an auxiliary control loop is proposed, which creates an additional control signal from the difference between the model and the plant states.

7

Sliding mode control of the third order system with state constraints

Bartoszewicz A., Nowacka A.

Systems Science

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2004

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Vol. 30, no 2

35-44

EN

In this paper, a new sliding mode control algorithm for the third order, nonlinear system subject to velocity and acceleration constraints is considered. The algorithm guarantees fast transient behaviour, zero steady state error and insensitivity of the system with respect to matched model uncertainty and external disturbance from the very beginning of the control process. For that purpose, the algorithm employs a time varying switching plane selected in such a way that at the initial time the representative point of the system belongs to the plane. Afterwards, the plane moves in a finite time towards the origin of the coordinate frame and then remains fixed. A proper choice of the plane parameters ensures non-oscillatory system response and the minimisation of the integral of the absolute value of the system position error.

8

A new approach to stability analysis of nonlinear control systems

Švarc I.

Elektronika : konstrukcje, technologie, zastosowania

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2004

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Vol. 45, nr 8-9

18-21

EN

Three methods for stability analysis of nonlinear control systems are introduced in this contribution: method of linearization, Lyapunov direct method and Popov criterion. Since stability analysis of nonlinear control systems is difficult task in engineering practice, these methods are made easier and tabulated. Method of linearization: The table includes the nonlinear equations and their linear approximation. Lyapunov direct method: The table contains Lyapunov functions for usually used equations second order. Popov criterion: The table will allow us to directly determine the stability of the nonlinear circuit with the transfer function G(s) and the nonlinearity that satisfies the slope k.

PL

W artykule przedstawiono trzy metody analizy stabilności nieliniowych systemów sterowania: metodę linearyzacji, bezpośrednią metodę Ljapunowa oraz kryterium Popowa. Ponieważ w praktyce inżynierskiej analiza stabilności nieliniowych systemów sterowania jest trudnym zadaniem, wspomniane metody zostały uproszczone i stablicowane. W przypadku metody linearyzacji tabela zawiera równania nieliniowe oraz ich liniowe aproksymacje. W przypadku bezpośredniej metody Ljapunowa tabela zawiera funkcje Ljapunowa dla wykorzystywanych zazwyczaj równań drugiego rzędu. W przypadku kryterium Popowa tabela pozwala na bezpośrednie wyznaczenie stabilności układu nieliniowego o transmitancji G(s) oraz nieliniowości, która cechuje się nachyleniem k.

9

Chattering attenuation in sliding mode control systems

Bartoszewicz A.

Control and Cybernetics

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2000

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Vol. 29, no 2

585-584

EN

In this paper sliding mode control systems are considered and a new technique to attenuate chattering is proposed. The technique employs simple, first-order dynamical devices, i.e. an integrator or a low-pass filter, to compensate in part for unknown and changing disturbance. As a result of this compensation, the magnitude of the discontinuous control term is essentially reduced. The term does not depend on the admissible disturbance or its change rate, but only on the uncertainty of the disturbance at the initial time t = t[sub o]. The technique proposed in this paper attenuates the undesirable chattering without any deterioration of the system performance.

10

Lokalna obserwowalność układów z czasem ciągłym i z czasem dyskretnym

Bartosiewicz Z.

Zeszyty Naukowe Politechniki Białostockiej. Matematyka, Fizyka, Chemia

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1999

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Z. 19

7-19

PL

Praca zawiera charakteryzacje lokalnej obserwowalności i stabilnej lokalnej obserwowalności dla analitycznych układów sterowania. Podano wyniki zarówno dla układów z czasem ciągłym , jak i dla układów z czasem dyskretnym. Wyniki mają charakter algebraiczny. Wyrażone sa w języku rzeczywistej geometrii analitycznej.

EN

Necessary and sufficient conditions of local observability for analytic systems are given. The results hold for both continuous-time and discrete-time systems. They have algebraic from and are expressed with the language of real analytic geometry.

11

A comparison of center-manifold reduction of nonlinear integro-differential flutter equation and approximate set of ordinary differential equations

Grzędziński J.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

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1999

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nr 9

7-14

EN

A nonlinear integro-differential flutter equation of a thin airfoil placed in an incompressible flow is solved by two different methods. The first method involves the center-manifold reduction and gives the asymptotic limit cycle amplitude and frequency in terms of power series expansions. The second method replaces the integro-differential equation by an approximate set of first-order ordinary differential equations which are solved by using bifurcation and continuation software package. A comparison of these two methods shows that the domain of a good agreement between them varies significantly depending on the parameters of the problem.