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1
Content available Sterowanie położeniem odwróconego wahadła w pętli zamkniętej
100%
Ciężkowski M. , Siemieniako F.
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tom T. 17, nr 1
57-62
PL
Praca zawiera opis stanowiska pomiarowego do badania odwróconego wahadła oraz wyniki doświadczeń, które zostały uzyskane na tym stanowisku. Ze względu na zastosowanie regulatora liniowo-kwadratowego do sterowania układem, artykuł zawiera opis modelu matematycznego wahadła, który jest niezbędny do wyznaczenia parametrów regulacji.
EN
The paper contains a description of the measurement system for studying the inverted pendulum and the experimental results obtained in this system. Due to applied the linear-quadratic regulator, the article describes a mathematical model of the pendulum, which is necessary to determine the control parameters.
2
Content available Sterowanie nieliniowe backstepping wahadła odwróconego z napędem inercyjnym
100%
Owczarkowski A. , Bachman P. , Gośliński J. , Owczarek P. , Regulski R.
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tom Z. 264
51-63
PL
W artykule przedstawiono działanie nieliniowego algorytmu sterowania backstepping użytego do stabilizacji wahadła odwróconego IWP (Inertia Wheel Pendulum). Analizowanym obiektem jest konstrukcja umocowana na dwóch kołach i posiadająca silnik napędzający koło zamachowe. To czyni z niej nieliniowy układ o dwóch stopniach swobody (kąt odchylenia od pionu i kąt obrotu koła) i jednym wymuszeniu (moment siły na wale silnika). Jako punkt pracy obrano niestabilną pozycję pionową. W oparciu o teorię stabilności Lapunowa, analitycznie wyznaczono prawo sterowania. Dla porównania wyznaczono również sterowanie liniowo-kwadratowe LQR (Linear Quadratic Regulator). Wykonano testy symulacyjne obu algorytmów wykazując, że w wielu sytuacjach sterowanie backstepping pozwala uzyskać lepsze rezultaty niż sterowanie LQR.
EN
This article describes the non-linear backstepping control algorithm used to stabilize the inverted pendulum IWP (Inertia Wheel Pendulum). The analysed object is a construction mounted on two wheels with an electric motor accelerating the flywheel. This is the non-linear system with two degrees of freedom (the angle of inclination and rotation of the wheel) and one actuator (torque on the motor shaft). The vertical position is the unstable operating point. The Lyapunov stability theory allowed to formulate the control law analyticity. The result is compared with the linear-quadratic control LQR (Linear Quadratic Regulator). The simulation tests showed differences of both algorithms and benefits of using backstepping.
3
Content available remote Effect of the thickness of the piezoelectric patches on the active control of a thin plate
100%
Latrache M. , Amrane M. N.
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2018
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tom Vol. 22, nr 4
1345--1354
EN
This paper presents a numerical study pertaining to on the active vibration control (AVC) of the 3-D rectangle simply supported plate bonded of the piezoelectric sensor/actuator pairs. A LQR controller is designed based on the independent mode space control techniques to stifle the vibration of the system. The change in the thickness of the patches was a clear impact on the control results, and also in the values of the voltage in actuator. The results were established by simulating in ANSYS and MATLAB.
4
Content available Identifying the optimal controller strategy for DC motors
99%
Qader M. R.
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tom Vol. 68, nr 1
101--114
EN
The aim of this study is to design a control strategy for the angular rate (speed) of a DC motor by varying the terminal voltage. This paper describes various designs for the control of direct current (DC) motors. We derive a transfer function for the system and connect it to a controller as feedback, taking the applied voltage as the system input and the angular velocity as the output. Different strategies combining proportional, integral, and derivative controllers along with phase lag compensators and lead integral compensators are investigated alongside the linear quadratic regulator. For each controller transfer function, the step response, root locus, and Bode plot are analysed to ascertain the behaviour of the system, and the results are compared to identify the optimal strategy. It is found that the linear quadratic controller provides the best overall performance in terms of steady-state error, response time, and system stability. The purpose of the study that took place was to design the most appropriate controller for the steadiness of DC motors. Throughout this study, analytical means like tuning methods, loop control, and stability criteria were adopted. The reason for this was to suffice the preconditions and obligations. Furthermore, for the sake of verifying the legitimacy of the controller results, modelling by MATLAB and Simulink was practiced on every controller.
5
Content available A new algebraic LQR weight selection algorithm for tracking control of 2 DoF torsion system
85%
Elumalai V. K. , Subramanian R. G.
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tom Vol. 66, nr 1
55--75
EN
This paper proposes a novel linear quadratic regulator (LQR) weight selection algorithm by synthesizing the algebraic Riccati equation (ARE) with the Lagrange multiplier method for command following applications of a 2 degree of freedom (DoF) torsion system. The optimal performance of LQR greatly depends on the elements of weighting matrices Q and R. However, normally these weighting matrices are chosen by a trial and error approach which is not only time consuming but cumbersome. Hence, to address this issue, blending the design criteria in time domain with the ARE, we put forward an algebraic weight selection algorithm, which makes the LQR design both simple and modular. Moreover, to estimate the velocity of a servo angle, a high gain observer (HGO) is designed and integrated with the LQR control scheme. The efficacy of the proposed control scheme is tested on a benchmark 2 DoF torsion system for a trajectory tracking application. Both the steady state and dynamic characteristics of the proposed controller are assessed. The experimental results accentuate that the proposed HGO based LQR scheme can guarantee the system to attain the design requirements with minimal vibrations and tracking errors.
6
Content available remote Lqr-Based Nonlinear Tuning Relay Control Design With Fast Convergence
85%
Yu X. , Xia Y. , Ledwich G. , Oghanna W.
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tom Vol. 9, no 2
313-326
EN
In this article, we present a relay control scheme based on LQR design with fast convergence. This scheme provides a practical and simple way to achieve fast convergence based on the well-known LQR design principle. The controller is a global stabiliser in the sense that for any given initial condition, we can always initialize the controller to drive the system to reach the origin. This controller is tunable in accordance with the position of the system state: the closer to the origin, the larger the control gains, which results in a fast control that maintains bounded control magnitude. It has also been shown that setting matrix Q can significantly influence the tendency of eigenvalues to switch the hyperplane. The relation between matrix Q and the tendency of those eigenvalues has been identified. Simulation results are presented to demonstrate the effectiveness of the scheme.
7
Content available Design of three control algorithms for an averaging tank with variable filling
71%
Kolankowski M. , Piotrowski R.
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tom Vol. 16, no. 2
136--150
EN
An averaging tank with variable filling is a nonlinear multidimensional system and can thus be considered a complex control system. General control objectives of such object include ensuring stability, zero steady-state error, and achieving simultaneously shortest possible settling time and minimal overshoot. The main purpose of this research work was the modeling and synthesis of three control systems for an averaging tank. In order to achieve the intended purpose, in the first step, a mathematical model of the control system was derived. The model was adapted to the form required to design two out of three planned control systems by linearization and reduction of its dimensions, resulting in two system variants. A multivariable proportional-integral-derivative (PID) control system for the averaging tank was developed using optimization for tuning PID controllers. State feedback and output feedback with an integral action control system for the considered control system was designed using a linear-quadratic regulator (LQR) and optimization of weights. A fuzzy control system was designed using the Mamdani inference system. The developed control systems were tested using theMATLAB environment. Finally, the simulation results for each control algorithm (and their variants) were compared and their performance was assessed, as well as the effects of optimization in the case of PID and integral control (IC) systems.
8
Content available remote Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems
71%
Muhafzan
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2010
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tom Vol. 20, no 4
655-664
EN
This paper deals with the Linear Quadratic Regulator (LQR) problem subject to descriptor systems for which the semidefinite programming approach is used as a solution. We propose a new sufficient condition in terms of primal dual semidefinite programming for the existence of the optimal state-control pair of the problem considered. The results show that semidefinite programming is an elegant method to solve the problem under consideration. Numerical examples are given to illustrate the results.
9
Content available Identifying the optimal controller strategy for DC motors
36%
Qader M. R. , Qader M. R.
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nr 1
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