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1

LQG/LTR control of input-delayed discrete-time systems

Horla D., Krolikowski A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 6

1049--1058

EN

A simple robust cheap LQG control is considered for discrete-time systems with constant input delay. It is well known that the full loop transfer recovery (LTR) effect measured by error function ∆(z) can only be obtained for minimum-phase (MPH) systems without time-de-lay. Explicit analytical expressions for ∆(z) versus delay d are derived for both MPH and NMPH (nonminimum-phase) systems. Obviously, introducing delay deteriorates the LTR effect. In this context the ARMAX system as a simple example of noise-correlated system is examined. The robustness of LQG/LTR control is analyzed and compared with state prediction control whose robust stability is formulated via LMI. Also, the robustness with respect to uncertain time-delay is considered including the control systems which are unstable in open-loop. An analysis of LQG/LTR problem for noise-correlated systems, particularly for ARMAX system, is included and the case of proper systems is analyzed. Computer simulations of second-order systems with constant time-delay are given to illustrate the performance and recovery error for considered systems and controllers.

2

Sterowanie modelem fizycznym zbiornikowca wzdłuż zadanej trasy przejścia

Tomera M.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2016

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Nr 51

201--208

PL

W pracy przebadane zostały dwa regulatory zastosowane do sterowania ruchem statku wzdłuż zadanej trasy przejścia. Obiektem sterowania jest model fizyczny statku o nazwie Blue Lady wykorzystywany do szkolenia kapitanów w Ośrodku Manewrowania Statkami na jeziorze Silm w Iławie/Kamionce. Trasa ruchu statku określana jest zazwyczaj przy użyciu tzw. punktów drogi. Poprzez łączenie odcinkami kolejnych punktów drogi tworzona jest trajektoria zadana ruchu statku. Wokół każdego punktu drogi definiowany jest okrąg akceptacji, który statek musi osiągnąć. Kiedy statek wpływa w obszar objęty okręgiem akceptacji to wówczas trajektoria zadana przełączana jest na odcinek łączący dwa kolejne punkty drogi. Z każdym odcinkiem drogi jest powiązania prędkość poruszania się statku. Zadanie sterowania polega na jak najdokładniejszym prowadzeniu statku wzdłuż zadanej trajektorii. W tym celu przebadane zostały dwa regulatory. Pierwszy z nich jest regulatorem stanu (LQG), wykorzystującym dyskretny filtr Kalmana do wyznaczania niemierzonych zmiennych stanu statku, drugi natomiast opiera się na klasycznym regulatorze typu PID.

EN

The study tested two controllers, which were used to control the movement of a ship along a specified route. The control plant is a physical model of a ship called the Blue Lady used for training captains in the Ship Handling Research and Training Center on the lake Silm in Iława/Kamionka, in Poland. The route of the vessel is usually determined using so-called waypoints. The reference trajectory of ship movement is created by combining sections of the successive waypoints. A circle of acceptance, that the ship must achieve is defined around each waypoint. When the ship enters the area of a circle of acceptance then the reference trajectory is switched on the segment connecting two consecutive waypoints. A specified speed of the ship is linked with each section of the road. The task of controlling consists on the most accurate sailing along the ship's trajectory. The first one is a state controller (LQG), which uses discrete-time Kalman filter to determine the unmeasured variables of the ship’s state and the other is based on a classical PID controller.

3

The T-polynomial approach for LQG control applied to a Switched Reluctance Motor (SRM)

Correla W. B., Carvalho Almeida R. N., Silva W. A., Torrico B. C., Pinto V. P., Reis L. L. N. dos

Przegląd Elektrotechniczny

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2016

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R. 92, nr 2

161--167

EN

This paper proposes a tuning procedure that combines the well known T-polynomial, from predictive control, with the LQG algorithm. The proposed scheme was successfully applied to a speed loop of a switched reluctance motor (SRM), which is known by its specific issues related to driving and control. Such characteristics make the SRM a strong set up to exploit the proposed solution. Results are compared with both the predictive controller approach GPCBC and the classical LQG/LTR, analysed regarding the transient and disturbance rejection. Power analysis of the control signal shows a power efficiency improvement favourable for the proposed approach.

PL

Opisano sposób sterowania silnikiem reluktancyjnym wykorzystująca metodę T-wielomianu z algorytmem LQG – linear quadratic Gaussian. Metodę porównano z innymi metodami jak GPCBC I LQG/LTR pod kątem tłumienia zakłóceń i stanów chwilowych.

4

Implementation of the LQG controller for a wind turbine tower-nacelle model with an mr tuned vibration absorber

Rosół M., Martynowicz P.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1109--1123

EN

Vibration of a wind turbine tower is related to fatigue wear, influencing reliability of the whole structure. The current paper deals with the problem of Linear-Quadratic-Gaussian (LQG) tower vibration control using specially designed and built simulation and laboratory tower-nacelle models with a horizontally aligned, magnetorheological (MR) damper based tuned vibration absorber located at the nacelle. Force excitation applied horizontally to the tower itself, or to the nacelle, is considered. The MR damper LQG control algorithm, including the Kalman state observer and LQR (Linear-Quadratic-Regulator) controller is analysed numerically and implemented on the laboratory ground, in comparison with the system with a deactivated absorber. Simulation and experimental results are presented.

5

Solution of the Kalman filtering problem in control and modeling of a double inverted pendulum with rolling friction

Olejnik P., Awrejcewicz J., Niełaczny M.

Pomiary Automatyka Robotyka

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2013

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R. 17, nr 1

63-70

EN

The problem of control and dynamical modeling of a unicycle-cyclist system treated as a double inverted pendulum with rolling friction and vibrating in the plane that is perpendicular to the direction of movement is studied. The object of analysis consists of two basic parts: the wheel and the double pendulum. The equations of motion have been derived using the Lagrange equation of the second kind. The kinematic excitation has been applied to the cyclist. The aim of control is to maintain the unicyclecyclist system in an unstable equilibrium around given angular position. Control moment of force has been applied to the wheel in a numerical procedure performed in Simulink. Kalman filtering problem has been solved basing on the feedback control system and functions included in Control System Toolbox of MATLAB. The proposed approach could be extended in future to solve some dynamical problem of transverse vibrations.

PL

Praca podejmuje rozwiązanie zagadnienia kontroli i modelowania dynamicznego układu monocykl-rowerzysta rozpatrzonego jako podwójne wahadło odwrócone z tarciem tocznym drgające w płaszczyźnie prostopadłej do kierunku ruchu. Analizowany obiekt składa się z dwóch podstawowych części, tzn. koła i podwójnego wahadła. Równania ruchu układu mechanicznego, w którym wymuszenie kinematyczne przyłożono do masy reprezentującej ciało rowerzysty wyprowadzono stosując równania Lagrange’a drugiego rodzaju. Zadaniem kontroli było utrzymanie modelu układu monocykl-rowerzysta w niestabilnym położeniu równowagi w pobliżu zadanej wartości kąta obrotu. W procedurze numerycznej zrealizowanej w Simulinku moment siły kontroli przyłożono do koła napędzającego układ modelowy. Zagadnienie doboru filtru Kalmana rozwiązano w układzie sterowania ze sprzężeniem zwrotnym przy użyciu wbudowanych funkcji numerycznych wchodzących w skład biblioteki Control System Toolbox pakietu MATLAB. Zaproponowane podejście można rozszerzyć w przyszłości w celu rozwiązania podobnego problemu dynamicznego uwzględniającego drgania poprzeczne.

6

Conditioning and error estimates in LQG design

Petkov P. Hr., Konstantinov M. M., Christov N. D.

Control and Cybernetics

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2008

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Vol. 37, no 1

85-87

EN

Efficient conditioning and error estimates are presented for the numerical solution of matrix Riccati equations in the continuous-time and discrete-time LQG design. The estimates implemented involve the solution of triangular Lyapunov equations along with usage of the LAPACK norm estimator.

7

Minimax LQG control

Petersen I. R.

International Journal of Applied Mathematics and Computer Science

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2006

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Vol. 16, no 3

309-323

EN

This paper presents an overview of some recent results concerning the emerging theory of minimax LQG control for uncertain systems with a relative entropy constraint uncertainty description. This is an important new robust control system design methodology providing minimax optimal performance in terms of a quadratic cost functional. The paper first considers some standard uncertainty descriptions to motivate the relative entropy constraint uncertainty description. The minimax LQG problem under consideration is further motivated by analysing the basic properties of relative entropy. The paper then presents a solution to a worst case control system performance problem which can be generalized to the minimax LQG problem. The solution to this minimax LQG control problem is found to be closely connected to the problem of risk-sensitive optimal control.

8

On Fast State-Space Algorithms for Predictive Control

Błachuta M. J.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 1

149-160

EN

A Riccati-equation-based solution to a class of receding-horizon predictive control problems for an explicit-delay state-space model of an ARMAX system is found and the corresponding vector Chandrasekhar-type equations are derived for both filter and controller gains to improve the computational efficiency.