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EN
The paper presents the issue position/force control of a manipulator in contact with the flexible environment. It consists of the realisation of manipulator end-effector motion on the environment surface with the simultaneous appliance of desired pressure on the surface. The paper considers the case of a flexible environment when its deformation occurs under the pressure, which has a significant influence on the control purpose realisation. The article presents the model of the controlled system and the problem of tracking control with the use of neural networks. The control algorithm includes contact surface flexibility in order to improve control quality. The article presents the results of numerical simulations, which indicate the correctness of the applied control law.
PL
W pracy przedstawiono projekt układu regulacji poziomu wody w zespole zbiorników o swobodnym wypływie, który w swej strukturze wykorzystuje nieliniowe modele obiektu: neuronowy i model niskiego rzędu uwzględniający zależność stałych czasowych od wartości wielkości regulowanej. Tak przyjęta struktura pozwala realizować sterowanie w układzie otwartym z możliwością korekty wartości zadanej przy wystąpieniu zakłóceń na wejściu lub wyjściu obiektu.
EN
The paper presents the concept of a nonlinear control system, which is the liquid level control system of two tanks It is based on the use in controller structure a non-linear models of the plant: neural and low-order model takes into account the dependence of the time constants and steady state gain of the controlled variable. So adopted structure allows to perform the control in an open-loop system with the possibility of setpoint correction under the influence of disturbances on the input or output of the plant.
EN
In the paper a path following problem for a wheeled mobile robot of (2,0) type has been considered. The kinematic model of the robot was derived with respect to the Serret-Frenet frame. Two kinematic control algorithms - Samson and Morin-Samson - have been tested taking into account their sensitivity to a white noise with a zero mean appearing in the one of state variables. The properties of path following errors have been analysed using statistical techniques. The conclusions related to an acceptable level of noise and a range of applicability of the presented algorithms have been reached.
4
Content available remote Cooperation of model predictive control with steady-state economic optimisation
EN
The problem of cooperation of Model Predictive Control (MPC) algorithms with steady-state economic optimisation is investigated in this paper. It is particularly important when the dynamics of disturbances is comparable with the dynamics of the process, since in such a case the classical hierarchical multilayer structure is likely to be not efficient and give the economic yield smaller than expected. This is because the economic nonlinear optimisation problem cannot be then solved on-line to update the optimal operating point as frequently as needed. On the other hand, simple target set-point optimisation based on linear models can be also insufficiently accurate. This paper introduces approximate formulations of the target set-point optimisation problem which tightly cooperates with the MPC and is solved as frequently as the MPC controller executes. Linear, linear-quadratic and piecewise-linear formulations are discussed, tuning guidelines are also given.
5
Content available remote Direct and indirect control of cancer populations
EN
This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.
6
Content available remote Constrained controllability of semilinear systems with delayed controls
EN
In the present paper finite-dimensional dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Using so-called generalized open mapping theorem, sufficient conditions for constrained local relative controllability near the origin are formulated and proved. Roughly speaking, it will be proved that under suitable assumptions constrained global relative controllability of a linear associated approximated dynamical system implies constrained local relative controllability near the origin of the original semilinear dynamical system. This is generalization to the constrained controllability case some previous results concerning controllability of linear dynamical systems with multiple point delays in the control and with unconstrained controls. Moreover, necessary and sufficient conditions for constrained global relative controllability of an associated linear dynamical system with multiple point delays in control are discussed. Simple numerical example, which illustrates theoretical considerations is also given. Finally, some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
PL
Celem pracy jest omówienie zagadnienia współpracy algorytmów regulacji predykcyjnej z nieliniową optymalizacją ekonomiczną. Problem ten jest szczególnie istotny wówczas, gdy dynamika zmian zakłóceń jest porównywalna z dynamiką procesu, ponieważ zastosowanie klasycznej warstwowej (hierarchicznej) struktury sterowania z rzadko powtarzaną optymalizacją ekonomiczną może nie być efektywne. Omawiane są dwie klasy struktur. W pierwszym przypadku stosuje się pomocniczą optymalizację ekonomiczną, której zadaniem jest aktualizacja punktu pracy poprzedzająca każdą interwencję algorytmu regulacji predykcyjnej. W dodatkowym liniowym lub kwadratowym zadaniu optymalizacji ekonomicznej stosuje się aktualizowaną na bieżąco liniową, liniowo-kwadratową lub odcinkowo-liniową aproksymację modelu. W drugim przypadku zadanie optymalizacji ekonomicznej i algorytm regulacji predykcyjnej są zintegrowane w pojedynczym problemie optymalizacji. Aby ograniczyć nakład obliczeń stosuje się aktualizowaną na bieżąco liniową lub liniowo-kwadratową aproksymację modelu, dzięki czemu otrzymuje się zadanie optymalizacji ekonomicznej w postaci problemu programowania kwadratowego.
EN
The paper is concerned with co-operation of model predictive control (MPC) algorithms with nonlinear economic optimisation. The problem is particularly important when dynamics of disturbances is comparable with dynamics of the process itself, since in such cases application of the classical multilayer (hierarchical) structure with infrequent economic optimisation may be not efficient. Two classes of control structures are investigated. In the first class an additional simplified optimisation is used which recalculates the operating point as frequently as the MPC controller executes. In the supplementary linear or quadratic programming optimisation problem approximate linear, linear-quadratic (updated on-line) or piecewise-linear models of the process are used. In the second class the economic optimisation and MPC manipulated variables computational load, approximate linear or linear-quadratic (updated on-line) models are used, then the resulting optimisation problem is of quadratic programming type.
8
Content available remote Realization of nonlinear composite systems
EN
The paper studies the realization problem for series and parallel connections of nonlinear single-input single-output systems, described by higher order differential equations. Necessary and sufficient conditions are given for the existence of the classical state space realization in both cases. It is proved that post- and parallel compensators are of no help in overcoming non-realizability. Results are illustrated by an example.
EN
This paper deals with the problem of robustness of P-type iterative learning control for uncertain nonlinear system. Besides the vector field, the control matrix and output matrix of the control system considered in this paper all have uncertainties. Iterative learning laws for initial states and for inputs are presented. A new technique has been developed to estimate the tracking errors of iterative control systems, which have an initial state error. Based on the estimation, upper bounds of the norms of the uncertainties of the control matrix and the output matrix are obtained, which guarantee that the iterative learning laws for initial states and for inputs are convergent. The results in this paper show that the P-type iterative learning control has robustness with respect to the uncertainties of the control matrix and the output matrix.
10
Content available remote Constrained controllability of semilinear systems with multiple delays in control
EN
In the present paper finite-dimensional, stationary dynamical control systems described by semi linear ordinary differential state equations with multiple point delays in control are considered. Infinite-dimensional semi linear stationary dynamical control systems with single point delay in the control are also discussed. Using a generalized open mapping theorem, sufficient conditions for constrained local relative controllability are formulated and proved. It is generally assumed, that the values of admissible controls are in a convex and closed cone with vertex at zero. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.
EN
The paper proposed a control design method for servo-controlled pneumatic systems, which is based on the feedback linearization theory. The pneumatic actuator system model is transformed into a linear system description first by regular static state feedback and state coordinate transformation. A servo/tracking controller is then developed for the linear model. Since there exists an inverse transformation for the new co-ordinate system, the designed servo control is finally transformed back to the original state co-ordinates and input. Two different cases are discussed in the paper - the pneumatic cylinder is driven by a single five-port proportional valve and driven by two three-port proportional valves. At the initial stage, for the convenience of finding a suitable set of new co-ordinates, the static friction forces are ignored. The static friction forces can be treated as uncertainties to the system for robust controller design.
EN
The notion of small-time local attainability (STLA) of a closed set with respect to a nonlinear control system is discussed and a new sufficient STLA condition is proved.
EN
A new approach to robust control systems synthesis, both linear and nonlinear, and non-stationary is offered. The control is carried out, providing the given phase constrains varied in acceptable limits, in view of constraints on its value and incompleteness of the information about functioning disturbances. The approach is based on introduction of auxiliary integral surfaces, on which the initial moving is projected. As a result the reduced equivalent moving is formed, being described by the scalar equation which in many important cases can be integrated directly. On the basis of the equation obtained solving a synthesis task is carried out and can be reduced to algebraic or integral inequalities. The final relations defined for linear equivalent moving are presented.
EN
For nonlinear time-invariant input-output dynamical systems the passivity conditions are obtained under some restrictions. The conditions imply storage functions satisfying dissipation inequality. A class of storage functions allowing unique reconstruction of a passive dynamical system is defined. These results are illustrated by an example of a linear system with fading memory. An important, for practical application, class of the linear relaxation systems without direct input-output interaction is considered. A new necessary condition for dynamical systems to be of the relaxation type is obtained for this class. The condition is connected with the existence of a unique quadratic Lyapunov function satisfying the complete monotonicity condition. This unique Lyapunov function corresponds to a "standard" thermodynamic potential in a compact family of potentials in the non-equilibrium thermodynamics. The results obtained can be useful in automatic control, mechanics of viscoelastic materials, and various applications in physics and the system theory.
EN
The nonlinear and time-varying uncertain system with a constant unknown vector of parameters is considered. The unknown parameter is assumed to be a value of an uncertain variable described by a certainty distribution given by an expert. The estimation of the certainty index that the system is globally asymptotically stable based on the necessary and sufficient stability conditions is proposed and considered. A simple example illustrates the approach presented.
EN
The paper discusses a generic two-degree of freedom controller scheme for linear plants and then extends the results to block-oriented factorable nonlinear processes. This generalization is quite straightforward for both IS and IU Hammerstein models, however, it can be performed only for IS Wiener models. An iterative controller refinement scheme is also presented.
EN
In this paper a new robust adaptive control scheme for robotic manipulators is presented. The design consists of: 1) a composite adaptive controller, driven by both the tracking and the prediction errors, for learning the modelled dynamics; and 2) a nonlinear sliding mode control law that overcomes the unmodelled dynamics and noise. As a whole, the closed-loop system is proved to be stable and it is shown that the tracking error converges to zero in finite time.
EN
This paper refers to application of the Schauder's fixed point theorem together with linear controllability results in getting the sufficient controllability conditions for various kinds of controllability and for different types of nonlinear control systems. The following nonlinear control systems are considered : finite-dimensional systems, systems with delays in control or in the state variables, and infinite-dimensional systems. The paper presents the review of results existing in the literature which show how Schauder's fixed-point theorem can be practically used to solve several controllability problems for different types of nonlinear control systems.
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