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EN
The main objective of the present work is designing a pole placement controller for pitch angle control of an aircraft system based on several bio-inspired optimization methods. Initially, a mathematical model of an aircraft pitch system has been derived and formed in state space representation. Then, pole placement approach is designed with the aid of different optimization techniques, including Genetic Algorithms (GA) and Artificial Bee Colony (ABC), to find an optimal value for the feedback gain matrix. The goal is to choose an optimal target values for the closed loop poles of the system by state feedback method and place them at every targeted location anywhere in the left-half of the complex plane ensuring that the closed-loop poles are stable and controllable. This work also compares the performance of GA with that of ABC algorithm based on different time response characteristics. The efficiency of the control systems responses has been analyzed for the sake of deciding which optimization approach will produce better results concerning the controlled pitch angle. Based on the obtained simulation results, it has been noted that ABC based pole placement controller exhibited more efficient results and overweigh the performance of pole placement controllers based on GA
PL
Głównym celem niniejszej pracy jest zaprojektowanie kontrolera rozmieszczenia biegunów do sterowania kątem pochylenia systemu samolotu w oparciu o kilka metod optymalizacji inspirowanych biologią. Początkowo opracowano model matematyczny układu nachylenia samolotu i utworzono go w reprezentacji w przestrzeni stanów. Następnie projektuje się podejście do umieszczania tyczek za pomocą różnych technik optymalizacji, w tym algorytmów genetycznych (GA) i sztucznej kolonii pszczół (ABC), aby znaleźć optymalną wartość macierzy wzmocnienia sprzężenia zwrotnego. Celem jest wybór optymalnych wartości docelowych dla biegunów pętli zamkniętej systemu metodą sprzężenia zwrotnego stanu i umieszczenie ich w każdym docelowym miejscu w dowolnym miejscu w lewej połowie złożonej płaszczyzny, zapewniając stabilność i kontrolę biegunów pętli zamkniętej. Ta praca porównuje również wydajność GA z wydajnością algorytmu ABC w oparciu o różne charakterystyki czasowe odpowiedzi. Skuteczność odpowiedzi układów sterowania została przeanalizowana w celu określenia, które podejście optymalizacyjne przyniesie lepsze wyniki w zakresie kontrolowanego kąta pochylenia. Na podstawie uzyskanych wyników symulacji zauważono, że sterownik układania słupów oparty na ABC wykazał bardziej wydajne wyniki i przewyższał wydajność sterowników układania słupów opartych na GA.
EN
Tuning rules for PID and PI-PI servo controllers are developed using a pole placement approach with a multiple pole, i.e. a triple one in the case of PID and a quadruple for PI-PI. The controllers involve complex roots in the numerators of the transfer functions. This is not possible in the classical P-PI structure which admits real roots only. The settling time of the servos determined by the multiple time constant is the only design parameter. Nomograms to read out discrete controller settings in terms of the time constant and control cycle are given. As compared to the classical structures, the upper limit on the control cycle is now twice longer in the case of PID, and four times in the case of PI-PI. This implies that the settling times can be shortened by the same ratios. Responses of a PLC-controlled servo confirm the validity of the design.
EN
This paper presents a state feedback controller (SFC) for position control of PMSM servo-drive. Firstly, a short review of the commonly used swarm-based optimization algorithms for tuning of SFC is presented. Then designing process of current control loop as well as of SFC with feedforward path is depicted. Next, coefficients of controller are tuned by using an artificial bee colony (ABC) optimization algorithm. Three of the most commonly applied tuning methods (i.e. linear-quadratic optimization, pole placement technique and direct selection of coefficients) are used and investigated in terms of positioning performance, disturbance compensation and robustness against plant parameter changes. Simulation analysis is supported by experimental tests conducted on laboratory stand with modern PMSM servo-drive.
EN
Electromagnetic mill installation for dry grinding represents a complex dynamical system that requires specially designed control system. The paper presents model-based predictive control which locates closed loop poles in arbitrary places. The controller performs as gains cheduling prototype where nonlinear model – artificial recurrent neural network, is parameterized with additional measurements and serves as a basis for local linear approximation. Application of such a concept to control electromagnetic mill load allows for stable performance of the installation and assures fulfilment of the product quality as well as the optimization of the energy consumption.
EN
The paper recapitulates recently conducted investigations of non-proportional Luenberger observers, applied to reconstruction of state variables of induction motors. Three structures of non-proportional observers are analyzed, a proportional-integral observer, modified integral observer and observer with integrators. Criteria for gain selection of the observer are described, classical ones based on poles, as well as additional, increasing observer’s robustness. Fulfilment of the presented criteria can be ensured with the three proposed methods for gain selection, two analytical, based on dyadic transformation and one based on optimization.
PL
W pracy opisano analityczną metodę syntezy obserwatora proporcjonalnego, pozwalającą na ulokowanie biegunów obserwatora w dowolnym położeniu na płaszczyźnie zespolonej, zależnym lub niezależnym od prędkości silnika. Podano ogólne zależności na bieguny silnika i obserwatora oraz na macierz sprzężenia zwrotnego dla wybranych przypadków lokowania biegunów. Przedstawiono wyniki badań symulacyjnych, wykonanych w multiskalamym układzie sterowania silnika indukcyjnego, pracującym z pomiarem lub z odtwarzaniem prędkości silnika.
EN
This paper describes the analytical method for proportional observer design. The method enables unimpeded observer poles placement in the complex plane. Locus of observer poles can be independent of or dependent on motor speed. General formulas for induction motor poles and proportional observer poles are presented, as well as specific formulas for the elements of the gain matrix for selected cases of pole placement. Results of computer simulations performed for a case of sensored and sensorless multiscalar control system of an induction motor are presented.
PL
W pracy opisano metodę syntezy obserwatora proporcjonalnego, pozwalającą na ulokowanie biegunów obserwatora na płaszczyźnie zespolonej w taki sposób, że wskaźnik wzmocnienia macierzy sprzężenia zwrotnego jest równy lub nie większy od wartości zadanej. Podano zależności na macierz sprzężenia zwrotnego dla dwóch przypadków lokowania biegunów oraz sposób doboru tej macierzy, z uwzględnieniem zadanej wartości wskaźnika wzmocnienia. Przedstawiono wyniki badań symulacyjnych, wykonanych w bezczujnikowym, multiskalamym układzie sterowania silnika indukcyjnego.
EN
This paper describes the analytical method for proportional observer design. The method enables observer poles placement in the complex plane in such a way that the gain matrix amplification index is equal or not greater than the reference value. Specific formulas for the elements of the gain matrix for two cases of pole placement are presented as well as the method of observer design taking into consideration the reference value of gain matrix amplification index. Results of computer simulations performed for sensorless multiscalar control system of an induction motor are presented.
PL
W artykule skrótowo przedstawiono wybrane efekty kilkuletnich badań nad układami odtwarzania zmiennych stanu silnika indukcyjnego na przykładzie adaptacyjnego obserwatora proporcjonalnego. Analiza wybranych właściwości dynamicznych obejmuje analizę stabilności pierwszą metodą Lapunowa, wykonaną dla liniowej aproksymacji równań obserwatora, zapisanych w układzie współrzędnych wirującym z prędkością synchroniczną oraz analizę charakterystyk częstotliwościowych, wyznaczonych na podstawie transmitancji operatorowej obserwatora. Elementy macierzy sprzężenia zwrotnego są funkcjami parametrów modelu silnika, parametrów przyjętej zasady lokowania biegunów i prędkości silnika, co uwzględniono w analizie obserwatora.
EN
This paper summarizes selected results of several years of research on estimators of induction motor state variables, the example of adaptive proportional observer is discussed in detail. The analysis of selected dynamic properties includes stability analysis carried out using Lyapunov's first method for linear approximation of observer equations, transformed to the coordinate system rotating at synchronous speed and analysis of the frequency characteristics, obtained on the basis of the transfer function of the observer. The elements of observer gain matrix are given as analytical functions of parameters of the induction motor model, parameters of assumed pole placement rules and the motor speed.
EN
The main aim of the paper is to present the analysis of anti-windup compensation impact on tracking performance for a second-order plant and continuous-time PID controller and five different simple anti-windup compensators. The performance of the system is compared on the basis of computing differences between the integrals of absolute and squared tracking errors for the system with and without compensation, as well as observing the excess of windup phenomena taking place. Parameters of the controller are computed according to pole-placement scheme. The control system quality is described on the basis of two quality indices for a stable oscillatory second-order plant and a square reference signal.
EN
In many manufacturing segments, container terminals and shipping yards the automation of material handling systems is an important element of enhancing productivity, safety and efficiency. The fast, precise and safe transfer of goods in crane operations requires a control application solving the problems, including non-collision trajectory planning and limitation of payload oscillations. The paper presents the interval arithmetic-based method of designing a discrete-time closed-loop anti-sway crane control system based on the fuzzy interpolation of linear controller parameters. The interval analysis of a closed-loop control system characteristic polynomial coefficients deviation from their nominal values is proposed to define a minimum number of fuzzy sets on the scheduling variables universe of discourse and to determine the distribution of triangular-shaped membership functions parameters, which satisfy the acceptable range of performances deterioration in the presence of the system’s parameters variation. The effectiveness of this method was proved in experiments conducted using the PAC system on the laboratory scaled overhead crane.
11
Content available Algorytm odpornego sterowania adaptacyjnego - DACDM
PL
W artykule przedstawiono studium przypadku nad nową, autorską metodą odpornego sterowania adaptacyjnego - DACDM. Celem proponowanego algorytmu jest wyznaczenie regulatora odpornego na niepewność parametryczną, pracującego w układzie adaptacyjnym. Novum w syntezie regulatora stanowi wykorzystanie trójstopniowej kontroli odporności układu. Przeprowadzone badania numeryczne potwierdzają skuteczność proponowanego rozwiązania.
EN
The paper presents a case study on a new, original, robust adaptive control method - DACDM [1]. The design of a controller robust to parametric uncertainty and working in the adaptive system is an aim of proposed algorithm. The DACDM procedure combines advantages of both control techniques - robust and adaptive. A novelty in the controller synthesis is the use of three stage system robustness control (by the use of coefficient diagram [2], optional step of the robustness index optimization [3], the use of adaptation mechanisms [4]). The case study is performed for the linear model SMFNO (stable, minimum-phase, non-oscillatory) described by equation 1 in the structure of the control system of Figure 1. The proposed algorithm from Figure 2 uses table 2 [5] for the selection of controller structure and design specifications [2] specified by equations 4 and 6. The use of the equation 16 enables to introduce the averaged model to the adaptive control system and the change of parametric uncertainty vector. The case study highlights the clarity of the design procedure. The coefficient diagram analysis (Fig.3) and results of conducted numerical studies (Fig. 4, Fig. 5, Fig. 8) confirm the effectiveness of the proposed solution in relation to the selected SMFNO model.
12
EN
In automated manufacturing processes the safety, precise and fast transfer of goods realized by automated material handling devices is required to raise efficiency and productivity of manufacturing process. Hence, in those industrial branches where cranes are extensively used the problem of an anti-sway crane control is especially important to speed-up the time of transportation operations and ensures the safe and effective transportation operations. The precise positioning of a cargo requires controlling the speed of crane motion mechanisms to reduce the sway of a payload. Moreover, the anti-sway crane control scheme involves applying the adaptive techniques owing to the nonlinearities of a system that comes especially from stochastic variation of rope length on which a payload is suspended and mass of this payload. The paper provides the design method of an adaptive control system for a planar model of crane. The control system is based on the gain scheduling control scheme created using fuzzy logic controller with Takagi-Sugeno-Kang-type fuzzy implications. The design process of a gain scheduling control system consists in selecting such a suitable set of operating points at which the linear controllers are determined that interpolation control scheme ensures the expected control quality within the known range of nonlinear system parameters changes, when those parameters vary in relation to the exogenous variables: rope length and mass of a payload. The method that is proposed in this paper to solve the problem of designing the fuzzy gain scheduling crane control system for minimum set of operating points is based on the pole placement method and genetic algorithm.
EN
The concept of combining robust fault estimation within a controller system to achieve active Fault Tolerant Control (FTC) has been the subject of considerable interest in the recent literature. The current study is motivated by the need to develop model-based FTC schemes for systems that have no unique equilibria and are therefore difficult to linearise. Linear Parameter Varying (LPV) strategies are well suited to model-based control and fault estimation for such systems. This contribution involves pole-placement within suitable LMI regions, guaranteeing both stability and performance of a multi-fault LPV estimator employed within an FTC structure. The proposed design strategy is illustrated using a nonlinear two-link manipulator system with friction forces acting simultaneously at each joint. The friction forces, regarded as a special case of actuator faults, are estimated and their effect is compensated within a polytope controller system, yielding a robust form of active FTC that is easy to apply to real robot systems.
EN
The problem under consideration in the paper of automation transportation operation realized by material handling devices is focused on time and accuracy of an overhead travelling crane's shifting process. The presented anti-sway crane control system was solved in the paper using combination of an indirect adaptive pole placement (IAPP) control method, fuzzy logic and artificial neural network. The presented approach to crane control is based on assuming structure of crane dynamic linear model with varying parameters, and linear closed-loop discrete control system consisting of proportional-derivative controllers with gains adjusted to changes of model's parameters using pole placement method (PPM). The parameters of crane dynamic model are estimated on-line using recursive least squares (RLS) algorithm. The estimation process is speeded up by neuro-fuzzy estimator, created using Takagi-Sugeno-Kang (TSK) fuzzy inference system, which determines the initial parameters of crane model based on scheduling variables, rope length and mass of a load changing in stochastic way. The neuro-fuzzy estimator is created in off-line process of neural network learning using least mean squares (LMS) method, based on a set of parametric output error models of crane dynamic identified for fixed values of rope length and mass of a load. The TSK estimator is next on-line improved by RLS algorithm.
15
Content available remote Pole placement approach to crane control problem
EN
The time and positioning accuracy of transportation operations realized by material handling systems are more and more significant problem in automated manufacturing processes, as well as the exploitation quality, safety and reliability, which can be met by implementing automation systems and improving control quality of material handling devices. The presented problem of anti-sway control system was solved using pole placement method employed to the time-discrete closed loop crane control system, which can be used in adaptive solutions. The proposed solution is based on the assumption, that crane nonlinear system is considered as a linear model with varying parameters.
PL
W zautomatyzowanych procesach produkcyjnych coraz istotniejszą rolę odgrywa zarówno czas i dokładność zadań realizowanych przez urządzenia transportowe, jak również ich niezawodność i jakość eksploatacji. Coraz wyższe wymagania stawiane systemom i urządzeniom transportu technologicznego, w tym również suwnicom, spełnione być mogą poprzez wdrażanie zautomatyzowanych rozwiązań i poprawę jakości sterowania. W artykule przedstawiono metodę projektowania systemu regulacji pozycji i prędkości suwnicy pomostowej oraz kąta wychylenia przemieszczanego przez urządzenie ładunku, opartą na metodzie lokowania biegunów oraz przyjętej do celów identyfikacji strukturze modelu dynamiki obiektu regulacji.
EN
Pole placement feedback controller for linear continuous-time system with dead-time is presented. Properties of the closed loop systems with the controller are discussed. Necessary and sufficient conditions for the controller existence are given. Numerical example illustrates behavior of the control system with proposed controller.
PL
Przedstawiono syntezę regulatora przesuwającego bieguny wielowymiarowego ciągłego układu z opóźnieniem transportowym. Przedyskutowano własności układu zamkniętego z proponowanym regulatorem. Podano warunki konieczne i dostateczne dla istnienia regulatora. Przedstawiono przykład liczbowy ilustrujący działanie układu regulacji z proponowanym regulatorem.
EN
The paper presents methods and tools based on pole placement, fuzzy logic and artificial neural network that were used to determine adaptive anti-sway crane control systems. Proposed crane control systems take into consideration changes of controlled object parameters like the rope length and mass of a payload. The two examples of crane control system were presented, based on adaptive pole placement algorithm (APP) and adaptive neuron-fuzzy controller which was based on Takagi- Sugeno-Kang (TSK) fuzzy inference method. The results of experiments that were carried out using the laboratory overhead traveling crane are shown as well.
PL
Przedmiotem artykułu jest zastosowanie logiki rozmytej, sztucznych sieci neuronowych i metody lokowania biegunów w procesie identyfikacji obiektu sterowania oraz budowy adaptacyjnych systemów sterowania suwnicami. Przedstawione zostały dwa rozwiązania adaptacyjnego sterowania mechanizmami ruchu suwnicy, oparte na metodzie lokowania biegunów oraz neuro-rozmytym regulatorze z wnioskowaniem Takagi-Sugeno-Kang (TSK). Zaprezentowane w artykule wyniki zostały uzyskane w rezultacie eksperymentów przeprowadzonych na laboratoryjnej suwnicy pomostowej z zastosowaniem neuro-rozmytego regulatora adaptacyjnego.
18
Content available remote Pole placement method for DC motor torque controller
EN
The work describes the use of pole placement state-space method for parametric optimization of motor torque controller. Presented method is universal for any type of mathematical model in contrast to standard optimization (optimal shape or optimal modulus criterion). The general oscillatory element is analyzed. Mathematical models of separately excited and brushless DC motors are compared. Ready to use relationship for parametric optimization of motor torque controller is presented. The results of the simulation, in the environment Matlab-Simulink, of the closed-loop control system are shown.
EN
This paper presents the application of active control system to reduce the vibration and the sound radiation of a circular plate which is fluid-loaded and clamped at a finite baffle. The plate is driven by a uniform harmonic primary force and controlled by a distributed secondary force generated by the piezodisks. The aim of the paper is to design a controller to modify the response of the plant in some desired fashion. The mathematical model of the system includes the influence the acoustic wave radiated by the plate, Kelvin-Voigt damping in the plate material and viscous fluid damping. For the considered system the transfer function of controller of 4th order, satisfying the polynomial Diofantine equation, is derived. The influence of the fluid-loading and damping effects on the system response are presented graphically and discussed. The results show that plate modes have been reduced very well by obtained controller for a few assumed values of damping coefficients.
PL
W pracy przedstawiono zastosowanie aktywnego sterowania do redukcji drgań i fal akustycznych promieniowanych przez płytę kołową utwierdzoną na obwodzie. Płyta pobudzana jest do drgań siłą harmoniczną o rozkładzie równomiernym, a sterowana za pomocą pary piezodysków PZT. Celem pracy jest zaprojektowanie układu sterowania, który modyfikuje odpowiedź obiektu w pożądany sposób. Model matematyczny rozważanego obiektu uwzględnia oddziaływanie zwrotne fali akustycznej, tłumienie wewnętrzne materiału oraz tłumienie wiskotyczne. Dla zastosowanego modelu wyznaczono transmitancję regulatora czwartego rzędu, rozwiązując równanie diofantyczne. Wpływ tłumienia wewnętrznego, wiskotycznego oraz sprzężenia pomiędzy drgającą strukturą i ośrodkiem na odpowiedź układu przedstawiono w sposób graficzny i przeanalizowano. Otrzymane wyniki pokazują, że zaprojektowany regulator bardzo dobrze tłumi drgania płyty dla kilku założonych wartości współczynników tłumienia.
20
Content available remote Single stage algorithms for pole placement using static output feedback
EN
Paper presents effective formulae, enabling transfer matrix pole assignment. This is accomplished by the use of generalized matrix inverses and the Kronecker product. All the desired pole distributions are covered - namely simple and multiple, real and complex. On this basis one-stage algorithms were developed, avoiding commonly used reduced orthogonality condition. Computational example of the presented algorithms is given.
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