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EN
Model predictive control (MPC) algorithms are widely used in practical applications. They are usually formulated as optimization problems. If a model used for prediction is linear (or linearized on-line), then the optimization problem is a standard, i.e., quadratic, one. Otherwise, it is a nonlinear, in general, nonconvex optimization problem. In the latter case, numerical problems may occur during solving this problem, and the time needed to calculate control signals cannot be determined. Therefore, approaches based on linear or linearized models are preferred in practical applications. A novel, fuzzy, numerically efficient MPC algorithm is proposed in the paper. It can offer better performance than the algorithms based on linear models, and very close to that of the algorithms based on nonlinear optimization. Its main advantage is the short time needed to calculate the control value at each sampling instant compared with optimization-based numerical algorithms; it is a combination of analytical and numerical versions of MPC algorithms. The efficiency of the proposed approach is demonstrated using control systems of two nonlinear control plants: the first one is a chemical CSTR reactor with a van de Vusse reaction, and the second one is a pH reactor.
EN
The paper describes a nonlinear controller design technique applied to a servo drive in the presence of hard state constraints. The approach presented is based on nonlinear state-space transformation and adaptive backstepping. It allows us to impose hard constraints on the state variables directly and to achieve asymptotic tracking of any reference trajectory inside the constraints, despite unknown plant parameters. Two control schemes (with and without integral action) are derived, investigated and then compared. Several examples demonstrate the main features of the design procedure and prove that it may be applied in case of motion control problems in electric drive automation.
EN
Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non-minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.
PL
Zastosowanie algorytmów regulacji predykcyjnej MPC do regulacji wielu procesów nieliniowych, o różnym stopniu trudności, często umożliwia osiągniecie bardzo dobrej jakości regulacji. Jest to możliwe ze względu na odpowiednie uwzględnienie w strukturze algorytmu informacji uzyskanych z modelu procesu. Do formułowania zadania optymalizacji dla algorytmów regulacji predykcyjnej najczęściej zakładana jest stała trajektoria referencyjna dla całego horyzontu predykcji. W artykule przedstawiono możliwości poprawy jakości regulacji przez zastosowanie trajektorii referencyjnej zmiennej na horyzoncie predykcji. Podczas porównywania jakości regulacji z wykorzystaniem trajektorii referencyjnych o różnej postaci, wzięto pod uwagę dwie wielkości. Pierwszą z nich jest czas narastania wyjścia obiektu regulacji, a drugą - przeregulowanie. Badania prowadzono w układach regulacji dwóch obiektów: nieminimalnofazowego obiektu liniowego oraz nieliniowego reaktora polimeryzacji. Do regulacji w przypadku pierwszego obiektu, zastosowano algorytm DMC, a w przypadku drugiego - algorytm bazujący na modelu nieliniowym, z nieliniową predykcją i linearyzacją (NDMC-NPL). Przedstawione wyniki dobrze ilustrują możliwości wpływania, za pomocą trajektorii referencyjnych o różnych kształtach, na poprawę jakości regulacji oferowanej przez algorytmy predykcyjne.
EN
Applying model predictive control (MPC) algorithms to control many processes, of different difficulty level, often allows improving control quality. It is possible by including information received from a process model in the algorithm structure. When defining the optimization problem for the predictive control algorithms most often a time-constant reference trajectory is assumed. Possibilities of improving the control quality by applying a time reference trajectory variable on the prediction horizon are presented in the paper. Two quantities are considered when comparing control quality: the rise time of the control plant output, and the overshoot. The experiments were conducted in the control systems of two control plants: a linear nonminimumphase plant and a nonlinear polymerization reactor. In the control system of the first control plant the DMC predictive control algorithm was used. For the nonlinear reactor the NDMC-NPL algorithm based on a nonlinear model was applied. It is demonstrated that by using the reference trajectories of different shapes it is possible to improve control quality offered by the MPC control algorithms.
5
Content available Geometry and flatness of m-crane systems
EN
We propose a class of m-crane control systems that generalizes two- and three-dimensional crane systems. We prove that each representant of the described class is feedback equivalent to the second order chained form with drift. In consequence, we prove that it is differentially flat. Then we investigate its control properties and derive a control law for tracking control problem.
EN
In this paper, we apply the heuristic method for determination of control functions for controllability analysis of nonlinear power systems. The problem of control of quasi-linear systems under proper assumptions on the nonlinear term is considered in the general statement. Making use of the Green’s function solution of nonlinear systems, the exact and approximate controllability conditions are expressed in terms of unknown controls in an explicit form. The way of resolving controls determination is discussed. As a particular application, a one-machine infinite-bus system is considered described by a coupled system of three first order ordinary differential equations. Two heuristic forms of admissible controls are considered providing approximate controllability within the same amount of time having different intensities. Results of numerical simulations are presented and discussed.
EN
In this work, it has been investigated the combination of nonlinear controllers applied to PFC (Power Factor Corrector) boost converter. Advantages of each included technique are discussed and considered: SFL (State Feedback Linearization), PBC (Passivity based control), IDAPBC (InterconnectionandDampingAssignmentPassivityBasedControl)andthePLL(PhaseLockedLoop). Wealsoaddtheanalysesoftuninggainsofthe nonlinear control methods. In addition, we propose practical hybrid solutions to the PFC boost (αβ-IDAPBC), which carry out robustness advantages. To evaluate the feasibility of the proposed methods, a Hardware in The Loop (HIL) tests are developed.
PL
W pracy zbadano możliwość zastosowania nieliniowego sterownika do przekształtnika typu boost stosowanego do poprawy współczynnika mocy. Wzięto pod uwagę: SFL – State Feedback Linearizaton, PBC - Passivity Based Control, IDAPBC – Interconection and Damping Assignement PBC oraz PLL - Phase Locked Loop. Przeanalizowano też strojenie wzmocnienia. Zaproponowano praktyczne hybrydowe rozwiązanie.
8
Content available remote Adaptive control of two-mass drive system with nonlinear stiffness
EN
The paper describes a nonlinear controller design technique for a servo drive in the presence of nonlinear friction together with a flexible shaft connecting the motor and the load. The shaft is characterized by the nonlinear stiffness curve. Two different type of the nonlinear stiffness curve are considered. The proposed controller is based on adaptive backstepping, modified by the use of command filtering. The proposed approach allows to accomplish the rigorous proof of the closed-loop system stability. Several experiments prove the control effectiveness.
PL
Opisano problem sterowania prędkością układu napędowego z nieliniowym tarciem, połączeniem sprężystym i nieznanymi parametrami. Elastyczne połączenie jest opisane przy pomocy nieliniowej funkcji sztywności. Rozważane są dwa typy nieliniowej funkcji sztywności: wypukła i wklęsła. Układy regulacji są projektowane przy pomocy metod „adaptive backstepping” z filtracją wartości zadanych. Opisano szereg eksperymentów, które ilustrują charakterystyczne właściwości układu regulacji.
EN
The main objective of this paper is to present the performance analysis of the oriented flux control of an induction motor associated with a matrix converter. A polynomial technique of RST type is used for speed control. As for the control of internal current loops, the technique used is based on the nonlinear approach. Overall, the proposed feedback law is asymptotically stable, which is shown in the context of the Lyapunov theory. The design of the control laws by the backstepping technique has been detailed while taking account of the non-linearities in the design phase of the control system. The objective is to obtain a good transient response and a good capacity of rejection of charge disturbance. The induction motor incorporating the proposed control techniques (RST-Backstepping) has been successfully implemented in numerical simulation using Matlab/Simulink under different operating conditions where the static and dynamic responses of the system are evaluated. It can be seen that the proposed control technique provides good speed monitoring performance. For internal loops, overall stability is ensured and the proposed approach presents good robustness to the uncertainties of the system parameters.
PL
W artykule zaprezentowano analizę właściwości sterowania silnikiem indukcyjnym za pośrednictwem przetwornika macierzowego. Zastosowano wielomianową technikę RST do sterowania prędkością. Do sterowania pętlą prądową zastosowano metodę nieliniową. Zaproponowane sprzężenie zwrotne jest asymtotycznie stabilne w konteksście teorii Lapunova. Numeryczne symulacje wykazały skuteczność zaproponowanej metody.
EN
Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.
11
Content available remote Velocity controller for a class of vehicles
EN
This paper addresses the problem of velocity tracking control for various fully-actuated robotic vehicles. The presented method, which is based on transformation of equations of motion allows one to use, in the control gain matrix, the dynamical couplings existing in the system. Consequently, the dynamics of the vehicle is incorporated into the control process what leads to fast velocity error convergence. The stability of the system under the controller is derived based on Lyapunov argument. Moreover, the robustness of the proposed controller is shown too. The general approach is valid for 6 DOF models as well as other reduced models of vehicles. Simulation results on a 6 DOF indoor airship validate the described velocity tracking methodology.
EN
Offset-free model predictive control (MPC) algorithms for nonlinear state-space process models, with modeling errors and under asymptotically constant external disturbances, is the subject of the paper. The main result of the paper is the presentation of a novel technique based on constant state disturbance prediction. It was introduced originally by the author for linear state-space models and is generalized to the nonlinear case in the paper. First the case with measured state is considered, in this case the technique allows to avoid disturbance estimation at all. For the cases with process outputs measured only and thus the necessity of state estimation, the technique allows the process state estimation only - as opposed to conventional approach of extended process-and-disturbance state estimation. This leads to simpler design with state observer/filter of lower order and, moreover, without the need of a decision of disturbance placement in the model (under certain restrictions), as in the conventional approach. A theoretical analysis of the proposed algorithm is provided, under applicability conditions which are weaker than in the conventional approach. The presented theory is illustrated by simulation results of nonlinear processes, showing competitiveness of the proposed algorithms.
EN
A control system supporting motion of an underwater robotic vehicle along a reference trajectory in the horizontal plane is presented in the paper. A waypoint line-of-sight scheme and nonlinear PD control law are applied to calculate command signals. Parameters of the proposed control law are tuned using genetic algorithms. The validity and advantages of the approach are illustrated through numerical simulation results.
PL
W artykule przedstawiono koncepcję system automatycznego sterowania ruchem płaskim robota podwodnego wzdłuż trajektorii odniesienia. Układem odpowiedzialnym za wyznaczanie sygnałów sterujących jest autopilot, w którym zaimplementowano nieliniowy regulator PD. Parametry regulatora dostrojono z wykorzystaniem algorytmów genetycznych. Zamieszczono wyniki badań symulacyjnych ruchu robota w płaszczyźnie poziomej z wykorzystaniem zaproponowanego algorytmu sterowania.
14
Content available remote Adaptive motion control with state constraints using barrier Lyapunov functions
EN
A servo control with unknown system parameters and the constraints imposed on the maximal position and velocity is considered. The barrier Lyapunov functions approach is applied to assure the preservation of bounds in any conditions. The system performance is compared for three cases of the controller design: based on quadratic Lyapunov functions, based on barrier Lyapunov functions if only position constraints are imposed and based on barrier Lyapunov functions if both position and velocity bounds are present. The tuning rules are discussed and several numerical experiments demonstrating features of the proposed control and the influence of the parameters are presented.
PL
Opisano problem sterowania napędowym układem nadążnym z nieznanymi parametrami i ograniczeniami nałożonymi na maksymalne wartości położenia i prędkości. Porównano właściwości trzech układów regulacji: ze sterowaniem zaprojektowanym na podstawie kwadratowych funkcji Lapunowa, ze sterowaniem zaprojektowanym na podstawie barierowych funkcji Lapunowa i ograniczeniem na położenie, oraz ze sterowaniem zaprojektowanym na podstawie barierowych funkcji Lapunowa przy ograniczeniach na położenie i prędkość. Opisano szereg eksperymentów, które ilustrują charakterystyczne właściwości układu regulacji i dostarczają wniosków co do wyboru parametrów algorytmu sterowania.
PL
W praktyce, dynamika statku jak również zakłóceń środowiskowych oddziałujących na kadłub nie jest dokładnie znana, co wynika ze zmieniających się warunków eksploatacyjnych jednostki i stanów morza. W artykule przedstawiono zagadnienie projektowania regulatora pozycji i kursu statku z zastosowaniem algorytmu całkowania wstecz (ang. backstepping). W pracy rozważono układ dynamicznego pozycjonowania statku z niepewnościami parametrycznymi modelu oraz pomiarowymi. Niepewności parametryczne związane są z hydrodynamicznymi siłami tłumiącymi, natomiast pomiarowe z niemierzalną predkością statku. Porównano działanie układu adaptacyjnego zakładając występowanie niepewności oraz nieadaptacyjnego przy założeniu dokładnej znajomości modelu statku. Wyniki badań symulacyjnych wskazują zbliżone wyniki w obu rozpatrywanych przypadkach.
EN
In commercial Dynamic Positioning systems is still used PID control, despite a significant increase in the level of automation. To improve the quality of the positioning of the vessel may allow the use of more effective methods and algorithms, providing advanced nonlinear control techniques. The problem of synthesis a dynamic positioning system for surface vessel with uncertainties was considered in this paper. In practice, both the dynamics of a dynamically positioned vessel as well as environmental disturbances affecting on a hull are not precisely known, as a result of the changing operating conditions and the sea states. The article presents the problem of position and heading controller design by vectorial adaptive backstepping methods. The dynamic positioning vessel with parametric model uncertainties associated with hydrodynamic forces damping, low-speed ship and in the presence of waves disturbances was used. Comparison of the system with uncertainties and assuming precise knowledge of ship model was carried out. Finally simulations results demonstrate similar results in both cases. Adaptive controller follows desired trajectory with small neighborhood. All signals in the closed-loop DP control system are bounded.
EN
This work aims to improve and simplify the procedure used in the Control Adjoining Cell Mapping with Reinforcement Learning (CACM-RL) technique, for the tuning process of an optimal contro ller during the pre-learning stage (controller design), making easier the transition from a simulation environment to the real world. Common problems, encountered when working with CACM-RL, are the adjustment of the cell size and the long-term evolution error. In this sense, the main goal of the new approach, developed for CACM-RL that is proposed in this work (CACMRL*), is to give a response to both problems for helping engineers in defining of the control solution with accuracy and stability criteria instead of cell sizes. The new approach improves the mathematical analysis techniques and reduces the engineering effort during the design phase. In order to demonstrate the behaviour of CACM-RL*, three examples are described to show its application to real problems. In All the examples, CACM-RL* improves with respect to the considered alternatives. In some cases, CACM- RL* improves the average controllability by up to 100%.
PL
W pracy przedstawiono koncepcję układu sterowania obiektem nieliniowym, jakim jest system wentylacji klatki schodowej, stanowiącej drogę ewakuacji na wypadek pożaru budynku wielopiętrowego. Opiera się ona na zastosowaniu modelu nieliniowego oraz jego inwersji przy wykorzystaniu techniki sprzężenia zwrotnego. Dzięki wprowadzeniu do struktury regulatora modelu obiektu układ adoptuje się do zmiennych warunków pracy.
EN
The paper presents the concept of a nonlinear control system, which is the stairwell ventilation system, which is a means of escape in case of fire multi-storey building. It is based on the use of non-linear model and its inversion using feedback techniques. With the introduction the model to the structure of the controller system adapts to changing conditions.
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.
EN
This paper presents a control concept for a single-axle mobile robot moving on the horizontal plane. A mathematical model of the nonholonomic mechanical system is derived using Hamel's equations of motion. Subsequently, a concept for a tracking controller is described in detail. This controller keeps the mobile robot on a given reference trajectory while maintaining it in an upright position. The control objective is reached by a cascade control structure. By an appropriate input transformation, we are able to utilize an input-output linearization of a subsystem. For the remaining dynamics a linear set-point control law is presented. Finally, the performance of the implemented control law is illustrated by simulation results.
PL
W artykule przedstawiono koncepcję sterowania ruchem jednoosiowego robota poruszającego się po płaszczyźnie poziomej. Model matematyczny nieholonomicznego systemu mechanicznego wyprowadzono korzystając z równań ruchu Hamela. Opisano następnie szczegółowo koncepcję sterownika śledzącego. Sterownik prowadzi poruszający się robot po zadanej trajektorii utrzymując go jednocześnie w pozycji pionowej. Cel sterowania jest osiągnięty przy zastosowaniu kaskadowej struktury sterowania. Dzięki odpowiedniej transformacji danych wejściowych, w podsystemie istnieje możliwość linearyzacji wejście-wyjście. Dla dynamiki pozostałej części zaprezentowano prawo liniowego sterowania stałowartościowego. Ostatecznie, jakość działania zastosowanych praw sterowania zilustrowano wynikami symulacji.
EN
In this article the knowledge-based control approach will be proposed for nonlinear systems. Firstly some basic concepts from the artificial intelligence will be defined, then the expert system design process will be introduced and finally a practical example will be discussed. The principle of this method is to support the controller with the human-like reasoning to determine the appropriate control mode and to estimate unknown parameters. Note that this is the heuristic approach, hence neither optimal steering, nor stability is guaranteed.
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