The constrained averaged controllability of linear one-dimensional heat equation defined on R and R+ is studied. The control is carried out by means of the time-dependent intensity of a heat source located at an uncertain interval of the corresponding domain, the end-points of which are considered as uniformly distributed random variables. Employing the Green’s function approach, it is shown that the heat equation is not constrained averaged controllable neither in R nor in R+. Sufficient conditions on initial and terminal data for the averaged exact and approximate controllabilities are obtained. However, constrained averaged controllability of the heat equation is established in the case of point heat source, the location of which is considered as a uniformly distributed random variable. Moreover, it is obtained that the lack of averaged controllability occurs for random variables with arbitrary symmetric density function.

In the paper finite-dimensional time-variable dynamical control systems described by linear stochastic ordinary differential state equations with single time-variable point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems necessary and sufficient conditions for different kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems are also presented.

The main aim of this article is to survey and discuss the existing state of art concerning the assignability by a feedback of numerical characteristics of linear continuous and discrete time-varying systems. Most of the results present necessary or sufficient conditions for different formulation of the Lyapunov spectrum assignability problem. These conditions are expressed in terms of various controllability types and optimalizability of the controlled systems and certain properties of the free system such as: regularity, diagonalizability, boundness away, integral separation and reducibility.

A novel circuit topology of modified switched boost high frequency hybrid resonant inverter fitted induction heating equipment is presented in this paper for efficient induction heating. Recently, induction heating technique is becoming very popular for both domestic and industrial purposes because of its high energy efficiency and controllability. Generally in induction heating, a high frequency alternating magnetic field is required to induce the eddy currents in the work piece. High frequency resonant inverters are incorporated in induction heating equipment which produce a high frequency alternating magnetic field surrounding the coil. Previously this high frequency alternating magnetic field was produced by voltage source inverters. But VSIs have several demerits. So, in this paper, a new scheme of modified switched boost high frequency hybrid resonant inverter fitted induction heating equipment has been depicted which enhances the energy efficiency and controllability and the same is validated by PSIM.

In the present paper .nite-dimensional, stationary dynamical control systems described by semilinear ordinary di.erential state equations with multiple point delays in control are considered. In.nite-dimensional semilinear stationary dynamical control systems with single point delay in the control are also discussed. Using a generalized open mapping theorem, su.cient 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.

In the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with single point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems, necessary and sufficient conditions for different kinds of stochastic relative controllability are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems with delays are also presented. Finally, minimum energy control problem for stochastic dynamical system is formulated and solved.

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.

A need to control our environment is apparent from an early age. Where does it stem from?

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.

Passive noise reduction methods require thick and heavy barriers to be effective for low frequencies and those clasical ones are thus not suitable for reduction of low frequency noise generated by devices. Active noise-cancelling casings, where casing walls vibrations are actively controlled, are an interesting alternative that can provide much higher low-frequency noise reduction. Such systems, compared to classical ANC systems, can provide not only local, but also global noise reduction, which is highly expected for most applications. For effective control of casing vibrations a large number of actuators is required. Additionally, a high number of error sensors, usually microphones that measure noise emission from the device, is also required. All actuators have an effect on all error sensors, and the control system must take into account all paths, from each actuator to each error sensor. The Multiple Error FXLMS has very high computational requirements. To reduce it a Switched-Error FXLMS, where only one error signal is used at the given time, have been proposed. This, however, significantly reduces convergence rate. In this paper an algorithm that uses multiple errors at once, but not all, is proposed. The performance of various algorithm variants is compared using simulations with the models obtained from real active-noise cancelling casing.

In order to control joints of manipulators with high precision, a position tracking control strategy combining fractional calculus with iterative learning control and sliding mode control is proposed for the control of a single joint of manipulators. Considering the coupling between joints of manipulators, a fractional-order iterative sliding mode cross-coupling control strategy is proposed and the theoretical proof of its progressive stability is given. The paper takes a two-joint manipulator as the research object to verify the control strategy of a single-joint manipulator. The results show that the control strategy proposed in this paper makes the two-joint mechanical arm chatter less and the tracking more accurate. The synchronous control of the manipulator is verified by a three-joint manipulator. The results show that the angular displacement adjustment times of the three-joint manipulator are 0.11 s, 0.31 s and 0.24 s, respectively. 3.25 s > 5 s, 3.15 s of a PD cross-coupling control strategy; 2.85 s, 2.32 s, 4.22 s of a PD iterative cross-coupling control strategy; 0.14 s, 0.33 s, 0.28 s of a fractional-order sliding mode cross-coupling control strategy. The root mean square error of the position error of the designed control strategy is 6.47 × 10-6 rad, 3.69 × 10-4 rad, 6.91 × 10-3 rad, respectively. The root mean square error of the synchronization error is 3.96 × 10-4 rad, 1.36 × 10-3 rad, 7.81 × 10-3 rad, superior to the other three control strategies. The results illustrate the effectiveness of the proposed control method.

The paper presents a simulation analysis of four control systems of the raw coal feed to a jig: stabilization of the volumetric flow of the feed, stabilization of the feed tonnage, stabilization of the feed flow with the additional measurement of the feed bulk density or the additional measurement of ash content in the feed. Analysis has been performed for the first and second compartments of a jig. The aim of the feed control was to stabilize the mass of the bed in the zone where the material stratifies; the mass may change due to changes in the washability characteristics of the feed. Such control should result in stable conditions in which material loosens during subsequent media pulsation cycles; stabilizing conditions minimizes the dispersion of coal particles in the bed. The best results have been achieved for the system of feed control where the ash content was measured in the first compartment, and for feed tonnage control in the second compartment.

This paper presents the design of digital controller for longitudinal aircraft model based on the Dynamic Contraction Method. The control task is formulated as a tracking problem of velocity and flight path angle, where decoupled output transients are accomplished in spite of incomplete information about varying parameters of the system and external disturbances. The design of digital controller based on the pseudo-continuous approach is presented, where the digital controller is the result of continuous-time controller discretization. A resulting output feedback controller has a simple form of a combination of low-order linear dynamical systems and a matrix whose entries depend nonlinearly on certain known process variables. Simulation results for an aircraft model confirm theoretical expectations.

Sterowanie procesów technologicznych wzbogacania węgla odbywa się w obecności licznych zakłóceń. Zatem jednym z podstawowych zadań układów regulacji procesów wzbogacania węgla jest stabilizacja parametrów jakościowych na zadanym poziomie. Istotnym problemem jest wybór regulatora odpornego na różnorodne zakłócenia. Niemniej ważnym zagadnieniem w regulacji procesu jest dobór nastaw regulatora. W wielu metodach doboru nastaw regulatora wykorzystuje się charakterystyki dynamiczne sterowanego procesu (model dynamiczny obiektu sterowania). Na podstawie badań stwierdzono, że dynamika wielu procesów wzbogacania węgla może być przedstawiona za pomocą modelu o właściwościach elementu inercyjnego z opóźnieniem czasowym. Identyfikacja parametrów obiektu (w tym stałej czasowej) w warunkach przemysłowych realizowana jest zwykle w trakcie normalnej eksploatacji (z oddziaływaniem zakłóceń), tym samym wyznaczone parametry modelu dynamicznego mogą się różnić od wartości rzeczywistych procesu. Układ regulacji z nastawami regulatora dobranymi na podstawie takiego modelu może nie spełniać założonych wymagań jakości regulacji.

W artykule przeprowadzono analizę wpływu zmian parametrów modelu obiektu na przebieg wielkości regulowanej. Dla nastaw regulatora wyznaczonych według parametrów T i τ przeprowadzono badania na obiekcie o parametrach różniących się w pewnym zakresie. W badaniach zastosowano analizę wrażliwości. Przedstawiono analizę wrażliwości dla trzech metod doboru nastaw regulatora PI układów regulacji procesów wzbogacania węgla charakteryzujących się właściwościami dynamicznymi obiektu inercyjnego z opóźnieniem. Rozważania przeprowadzono dla różnych parametrów obiektu, na podstawie odpowiedzi układu regulacji dla stałej wartości wielkości zadanej. W podsumowaniu dokonano oceny rozpatrywanych metod doboru w odniesieniu do wybranych wskaźników jakości regulacji.