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1

Robust LFT-LPV H∞ control of an underactuated inverted pendulum on a cart with optimal weighting functions selection by ga and es

Hasseni Seif-El-Islam, Abdoul Latifa

Acta Mechanica et Automatica

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2020

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Vol. 14, no. 4

186--197

EN

This article investigates the robust stabilization and control of the inverted pendulum on a cart against disturbances, measure-ment noises, and parametric uncertainties by the LFT-based LPV technique (Linear-Fractional-Transformation based Linear-Parameter-Varying). To make the applying of the LPV technique possible, the LPV representation of the inverted pendulum on a cart model is devel-oped. Besides, the underactuated constraint of this vehicle is overcome by considering both degrees of freedom (the rotational one and the translational one) in the structure. Moreover, the selection of the weighting functions that represent the desired performance is solved by two approaches of evolutionary algorithms; Genetic Algorithms (GA) and Evolutionary Strategies (ES) to find the weighting functions’ optimal parameters. To validate the proposed approach, simulations are performed and they show the effectiveness of the proposed approach to obtain robust controllers against external signals, as well as the parametric uncertainties.

2

Payload oscillations minimization via open loop control

Kosucki A.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 2

309--327

EN

The results of tests of payload oscillations, forced by linear control function which allows to minimize payload sway after acceleration phase and after overhead crane stopping are presented in this paper. The analysis of solution of this problem has been carried out. The algorithm of operation for real drive system which takes into account the possibilities of driving of an overhead crane is also presented. The impact of inaccuracies of measurement of the ropes length on minimizing a displacements of payload during the duty cycle is shown as well. The correctness of the method is confirmed by results both simulation and experimental tests.

3

Zadanie śledzenia ścieżki dla pojazdu niedosterowanego

Korczak S.

Symulacja w Badaniach i Rozwoju

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2013

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Vol. 4, nr 4

193--201

PL

Niniejszy artykuł przedstawia problem sterowania układami niedosterowanymi na przykładzie prostego modelu bryły sztywnej pod działaniem siły przyłożonej niecentralnie. Zaprezentowano metodę określania sterowalności układów niedosterowanych, a następnie zaproponowano zadanie śledzenia trajektorii kołowej i ósemkowej za pomocą algorytmu obliczanego momentu. Siła sterująca powodująca sprzężenie równań wymusza modyfikację algorytmu sterowania. Proces obliczeniowy uzupełniono o środowisko wizualizacji trójwymiarowych.

EN

This paper shows a problem of control an underactuated dynamic system. The exemplary model of a rigid body controlled by an eccentric force is presented. Method for controlability check is shown, then the usage of a computed torque algorithm for the tracking problem of circular and eight-curve trajectories is proposed. The coupling force causes the need to modify the algorithm. The calculation process has been extended by a virtual environment for three-dimensional visualizations.

4

From orthogonal to tangential control of underactuated mechanical systems in partly specified motion - a case study illustration

Blajer W., Seifried R.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 3

689-706

EN

Underactuated mechanical systems have fewer control inputs than degrees of freedom. Their performance goal may be realization of specified in time outputs, treated as servo-constraints on the system, whose number is equal to the number of inputs. The solution to the inverse simulation problem (servo-constraint problem), that is the determination of an input control strategy that forces an underactuated system to complete the partly specified motion, is a challenging task. This is because mechanical systems may be "underactuated" in several ways and, as opposed to the passive constraint reactions which are orthogonal to the constraint manifold, the control forces may be arbitrary oriented with respect to the servo-constraint manifold. The diversity of servo-constraint problems is discussed using a simple spring-mass system mounted on a carriage, and is related to multiple issues: formulations in generalized coordinates and output-involved coordinates, orthogonal or tangential realization of servo-constraints, the arising ODE/DAE forms of the governing equations, and existence of the uncontrolled internal dynamics. Some computational issues are finally reported, with relevant simulation results for the sample case example.

5

Modeling of underactuated mechanical systems in partly specified motion

Blajer W., Kołodziejczyk K.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 2

383-394

EN

This paper deals with the inverse dynamics problem of underactuated mechanical systems subjected to execute partly specified motions. The modeling methodology focuses on a special class of differentially flat systems, represented by a group of relevant technical examples. The governing equations are obtained as index three differential-algebraic equations, and a simple numerical code for their solution is reported. The solution comprises both the dynamic analysis of the underactuated systems in partly specified motion and the synthesis of control that assures realization of such motion.

PL

Praca dotyczy zagadnienia symulacji dynamicznej odwrotnej klasy układów mechanicznych, w których liczba sygnałów sterowania, równa liczbie zadanych charakterystyk ruchu (sygnałów wyjściowych), jest mniejsza od liczby stopni swobody, reprezentowanej przez liczne przykłady techniczne. Równania tak zdefiniowanego ruchu programowego niezupełnego otrzymywane są w postaci równań różniczkowo-algebraicznych o indeksie równym trzy. Omawiany jest prosty, efektywny i stabilny algorytm całkowania tych równań. Rozwiązaniem są przebiegi w czasie zmiennych stanu układu w zadanym ruchu programowym oraz sterowania wymaganego dla realizacji tego ruchu.

6

Hierarchical sliding mode control for a class of SIMO under-actuated systems

Qian D., Yi J., Zhao D.

Control and Cybernetics

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2008

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Vol. 37, no 1

159-175

EN

A hierarchical sliding mode control approach is proposed for a class of SIMO under-actuated systems. This class of under-actuated systems is made up of several subsystems. Based on this physical structure, the hierarchical structure of the sliding surfaces is designed as follows. At first, the sliding surface of every subsystem is defined. Then the sliding surface of one subsystem is defined as the first layer sliding surface. The first layer sliding surface is used to construct the second layer sliding surface with the sliding surface of another subsystem. This process continues till the sliding surfaces of the entire subsystems are included. According to the hierarchical structure, the total control law is deduced by the Lyapunov theorem. In theory, the asymptotic stability of the entire system of sliding surfaces is proven and the parameter boundaries of the subsystem sliding surfaces are given. Simulation results show the feasibility of this control method through two typical SIMO under-actuated systems.

7

Some insights in path planning of small autonomous blimps

Bestaoui Y., Hima S.

Archives of Control Sciences

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2001

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Vol. 11, no. 3/4

139-166

EN

A blimp is a small airship that has no metal framework and collapses when deflated. In the first part of this paper, kinematics and dynamics modelling of small autonomous non rigid airships is presented. Euler angles and parameters are used in the formulation of this model. In the second part of the paper, path planning is introduced using helices with vertical axes. Motion generation for trim trajectories (helices with constant curvature and torsion) is presented. Then path planning using helices with quadratic curvature and torsion is described, and motion generation on these helices expressed. This motion generation takes into account the dynamics model presented.