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EN
In this research, a model of a robotic manipulator flexible structure and an equation of motion for controller design is planned. The structural material chosen for the robot structure was a hybrid composite. A comparison study was carried out for the aluminium 6082 alloy for the flexible manipulator arm application. Vibration behavior and control implementation was analyzed by adding joint flexibility in the system. Using a simulation algorithm, the system parameter calculation is carried out through MATLAB software for vibration amplitude, transient period, steady-state error, and settling time of flexible robotic arm system. In a systematized motion equation, flexible robotic deflections are organized via the assumed mode (AM) and Lagrange techniques (LT). The graph analysis of hybrid composite and AL6082 materials with high stiffness coefficients is plotted. These obtained values from the plot are utilized for Linear Quadratic Regulator (LQR) controller design. The LQR output facts for both aluminium structural robotic arm and composite material robotic arms are established.
2
Content available remote LQR controller design for mini motion package electro-hydraulic actuator control
EN
Electro-hydraulic actuators have been widely applied in the industry because they have several major advantages. In this paper, we focused on controlling the mini motion package electro-hydraulics actuator. First, a mathematical model of the electro-hydraulic actuator (EHA) was implemented to apply the control process to the proposed system. Second, we applied the linear quadratic regulator (LQR) controller to a linear model that is converted from the nonlinear EHA system. Finally, the numerical simulation results were performed in which the results obtained from the LQR controller were compared with the PID controller to show the superiority of the proposed solution.
3
Content available remote LQR controller with an integral action for Z-source DC-DC converter
EN
This paper presents a robust linear quadratic regulator with an integral action (LQR+i) designed for Z-source DC-DC converter (ZSC) operating in conduction continuous mode (CCM). Depending on converter’s commutation states and using the electrical equivalent circuits, both switched and small-signal models of ZSC are built. The design procedure of LQR + i controller is described. The robustness of the controller is tested, using Matlab/Simulink software, considering circuit parameter (source and load) uncertainties and external signal (reference voltage) disturbance. A comparison study with classical PI controller are performed. It has been shown that the robustness of LQR + i controller is better than classical PI controller.
PL
W artykule zaprezentowano liniowy, kwadraturowy sterownik w włączonym LQR zaprojektowany do przekształtników DC-DC ze źródłem Z. Odporność kontrolera była testowania przy wykorzystaniu programu Matlab/Simulink. Porównano sterownik z klasycznym układem PI.
EN
This paper presents an adaptive particle swarm optimization (APSO) based LQR controller for optimal tuning of state feedback controller gains for a class of under actuated system (Inverted pendulum). Normally, the weights of LQR controller are chosen based on trial and error approach to obtain the optimum controller gains, but it is often cumbersome and tedious to tune the controller gains via trial and error method. To address this problem, an intelligent approach employing adaptive PSO (APSO) for optimum tuning of LQR is proposed. In this approach, an adaptive inertia weight factor (AIWF), which adjusts the inertia weight according to the success rate of the particles, is employed to not only speed up the search process but also to increase the accuracy of the algorithm towards obtaining the optimum controller gain. The performance of the proposed approach is tested on a bench mark inverted pendulum system, and the experimental results of APSO are compared with that of the conventional PSO and GA. Experimental results prove that the proposed algorithm remarkably improves the convergence speed and precision of PSO in obtaining the robust trajectory tracking of inverted pendulum.
5
Content available remote Metody sterowania w obwodzie elektrycznym Chuy
PL
W pracy zaprezentowano sposoby stabilizacji obwodu elektycznego Chuy w niestabilnych punktach równowagi. Do stabilizacji obwodu Chuy wykorzystano klasyczny regulator proporcjonalny do stanu, którego parametry dobierano w różny sposób (lokowanie biegunów, LQR). W pracy zamieszczono krótki opis, w jaki sposób można wykorzystać podejście stosowane przy projektowaniu obserwatorów do wyznaczania regulatora. Zaproponowano pewne przybliżenie nieliniowości występujące w oryginalnym obwodzie Chuy, dzięki któremu obwód Chuy może być rozpatrywany jako obwód liniowy. Rozważania teoretyczne były testowane symulacyjne, a wyniki symulacji zamieszczono w pracy. Rozważono także możliwość stabilizacji obwodu Chuy za pomocą regulatora proporcjonalnego, który może sterować tylko jedną zmienną stanu. Dla każdej ze zmiennych stanu wykreślono linie pierwiastkowego układu z takim regulatorem.
EN
In this paper various control methods of Chua's circuit are proposed. The goal is to stabilise Chua's circuit in unstable equilibria points. The paper contains description of the standard Chua's circuit, see the equation (1) and schema 1, and some modification of this circuit. The nonlinearity (2) was replaced by a piecewise-linear function (11). Figure 4 shows that this simplification is enough if state variables belong to some intervals. By using an idea borrowed from the state observer theory, the proportional full state controller (7) is constructed. The parameters of this controller are obtained by using the pole placement techniques and by solving the linear-quadratic problem. Simulation results show the effectiveness of the proposed controllers, see figures 5, 6, 7 and 8. The second part the paper contains discussion about stabilisation of Chua's circuit in unstable equilibria points by using proportional controller. However, in this case the controller can control only single variable of the state space vector. For these types of controllers, a root locus method is used to analyse the corresponding closed-loop systems (see figures 9, 10 and 11).
6
Content available remote Effect of active vibration control of a circular plate on sound radiation
EN
An active control of the vibration cancellation of a circular fluid-loaded plate is analytically studied. The purpose of this paper is to examine the effect of the active vibration control strategy on the sound radiation generated by a plate. It was assumed that a planar vibrating structure located in a finite baffle and interacting with fluid is driven by a periodic force with constant amplitude. This structure radiates the acoustic waves into a surrounding fluid and a point control force is used to reduce its vibrations. The simulations of the active cancellation of the plate vibrations were made with a Simulink/Matlab computer program. The results demonstrate, that while a control law provided a significant reduction in the plate vibration, it is rather ineffective for noise attenuation.
EN
This work presents the BDU technique (Bounded Data Uncertainties) and the tuning of the linear quadratic regulator (LQR) via this technique, which considers models with bounded uncertainties. The BDU method is based on constrained game-type formulations, and allows the designer to explicitly incorporate a priori information about bounds on the sizes of the uncertainties into the problem statement. Thus, on the one hand, the uncertainty effect is not over-emphasized, avoiding an overly conservative design and, on the other hand, the uncertainty effect is not under-emphasized, avoiding an overly sensitive to errors design. A feature of this technique consists of its geometric interpretation. The structure of the paper is the following, in the first section, some problems about the least-squares method in the presence of uncertainty are introduced. The BDU technique is shown in the second section and the LQR controller in the third. After that a new guided way of tuning the LQR is offered, taking into account the uncertainties bounds via the BDU. The consequence of this method is that both recursive and algebraic Riccati equations are modified. Finally, some examples are shown and the main conclusions and future work are commented.
8
Content available Adaptacyjny układ stabilizacji kursu statku
PL
Zaprojektowano adaptacyjny układ stabilizacji kursu statku, opierając się na mode-lu Nomoto. Jako algorytm sterowania przyjęto regulator optymalny LQR, natomiast identyfikacji modelu dokonano na podstawie "ciągłą wersję" metody najmniejszych kwadratów. Jakość działania systemu sprawdzono symulacyjnie, używając jako modelu rzeczywistego statku nieliniowego modelu de Witt-Oppe'go.
EN
The paper presents a design of an adaptive system of ship course stabilization based on Nomoto's model. As a control algorithm the LQR control was adopted,whereas the model identification is performed on the basis of 'continuous version' of the least-squares algorithm. The performance of the system operation was simulated using a de Witt-Oppe nonlinear model as a real ship model.
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