Showing papers in "International Journal of Dynamics and Control in 2015"

State of the art: hardware in the loop modeling and simulation with its applications in design, development and implementation of system and control software

Abstract: Nowadays due to the technology development and use of digital computers in various systems, need for development of high performance and robust software is attracting great attentions. Because of increasing complexity in algorithms and implementation hardware for embedded systems, proper simulation tools are required. In sophisticated systems design, hardware in the loop (HIL) simulation is known as a prominent simulation tool before realistic tests of the system and a step after software simulation. Simultaneously it can be used for verification and validation of automation and control software. HIL has had an historical background in aerospace industries. Recently, this tool has spread in different steps of system life cycle such as design, development, implementation and test of various applications including automobile industry, shipbuilding, power lines, robotic systems and etc. Utilizing a suitable hardware in the loop laboratory, in system design stages is a practical way to increase the system reliability and efficiency as well as value of product. Also, by proper investigation in this modelling and simulation method, many errors can be avoided in design procedure of software and hardware as well as their interconnections. In this study, structure and components of an hardware in the loop laboratory for different systems are explored, also it is tried to more evaluate the applications of HIL simulations in dynamics and control engineering. At last, general structure of an hardware in the loop lab for diverse industries is proposed and discussed.

Analysis of a drinking epidemic model

Abstract: In this paper, we have developed a mathematical model of alcohol abuse which consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. We have discussed about basic properties of the system. Sensitivity analysis of the system is also discussed. Next, Basic reproduction number ( $$R_0$$ ) is calculated. The stability analysis of the model shows that the system is locally asymptotically stable at disease free equilibrium $$E_0$$ when $$R_0<1.$$ When $$R_0>1$$ , endemic equilibrium $$E^*$$ exists and the system becomes locally asymptotically stable at $$E^*$$ and $$E_0$$ becomes unstable. We have also discussed the global stability of the system at $$E_0.$$ It is also found that a backward bifurcation may occur at $$R_0=1$$ . Next we have discussed the drinking epidemic model with treatment control. An objective functional is considered which is based on a combination of minimizing the number of heavy drinkers and the cost of treatment. Then an optimal control is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB, which show the reliability of our model from the practical point of view. Epidemiological implications of our analytical findings are addressed critically.

Response localization in micro-scale oscillator arrays: influence of cubic coupling nonlinearities

Abstract: In this article, the authors study response localization in coupled arrays of nonlinear oscillators with cubic coupling nonlinearities. For illustration, an array of micro-scale oscillators with intersite or coupling nonlinearities is considered and attention is focused on intrinsic localized modes. Free oscillations and forced oscillations of this system are considered, and the interplay between noise and cubic coupling nonlinearities is studied through numerical studies. These studies help elucidate the role of coupling nonlinearities on energy localization in micro-scale oscillators.

Complex period-1 motions of a periodically forced Duffing oscillator with a time-delay feedback

Abstract: In this paper, complex period-1 motions in a periodically forced Duffing oscillator with a time-delay feedback are investigated, and the symmetric and asymmetric, complex period-1 motions exist in lower excitation frequency. The analytical solutions of complex period-1 motions in such a Duffing oscillator are obtained through the finite Fourier series, and the corresponding stability and bifurcations of complex period-1 motions are discussed by eigenvalue analysis. The frequency–amplitude characteristics of complex period-1 motions in the periodically forced Duffing oscillator with a time-delay feedback are discussed. Complex period-1 motions generated numerically and analytically are illustrated. As excitation frequency is close to zero, the complex period-1 motions need almost infinite harmonic terms in the Fourier series to express the analytical solutions. From this study, the initial time-delay in the time-delayed, nonlinear systems should be uniquely determined to achieve a specific periodic motion.

Bifurcation analysis of predator–prey model with time delay and harvesting efforts using interval parameter

Abstract: This paper presents a prey–predator harvesting model with time delay for bifurcation analysis. We consider the parameters of the proposed model with imprecise data as form of interval in nature, due to the lack of precise numerical information of the biological parameters such as prey population growth rate and predator population decay rate. The proposed prey–predator harvesting model is presented with Holling type of predation and time delay under impreciseness of parameters by introducing parametric functional form of interval number. Our study reveals that along with delay and harvesting efforts role on the stability of the system, interval parameters also play a significant role. Computer simulations of numerical examples are given to explain our proposed imprecise model and for observing of chaotic behaviors.

Analysis of prey-predator three species models with vertebral and invertebral predators

Abstract: In this paper, we consider a mathematical model involving three species namely prey, predator and super predator. Different type functional responses have been considered to formulate the mathematical model for predator and super predator. Main intention of this study is to establish the local and global stabilities for the proposed model around its interior equilibrium points. A numerical example is considered to illustrate the proposed system of our paper. The stability of the system has been analyzed using some graphical representation.

Dynamics of a generalized viral infection model with adaptive immune response

Abstract: A mathematical model for viral infection is formulated by five nonlinear differential equations to describe the interactions between virus, host cells, and the adaptive immune response represented by cytotoxic T lymphocytes (CTL) cells and the antibodies The infection transmission process is modeled by a general incidence function which covers several forms existing in models that studied viral infections such as HIV and HBV infections Based on the direct Lyapunov method, the global stability of the equilibria is investigated Furthermore, under certain hypotheses on the incidence function it is proved that the dynamical behavior of the model is fully characterized by the reproduction numbers for viral infection $$R_{0}$$ , for CTL immune response $$R_{1}^{z}$$ , for antibody immune response $$R_{1}^{w}$$ , for CTL immune competition $$R_{2}^{z}$$ and for antibody immune competition $$R_{3}^{w}$$

Design of unknown input observer for nonlinear systems with time-varying delays

Abstract: A method of designing unknown input observer (UIO) for a class of nonlinear systems with time-varying delays is presented. The observer is designed using linear matrix inequality approach for the nonlinear systems whose nonlinear state update function satisfies Lipschitz condition. It is also assumed that the unknown inputs can be decoupled from nonlinear function when these appear in the function. Two types of time-delay scenarios have been considered for designing the observers. First an UIO is designed considering state time-delays only in the linear part of the system. Then the idea is expanded for designing the observer for more general kind of time-delay setup where the time-delays arise in both linear and nonlinear parts of the system. Sufficient conditions for the existence of these observers are also derived. The effectiveness of the proposed observer is shown with numerical results, which confirm that it estimates the states quite precisely for nonlinear time-delay systems.

An approach to the dynamics and control of a planar tensegrity structure with application in locomotion systems

Abstract: The use of mechanically compliant tensegrity structures in vibration-driven mobile robots is an attractive research topic, due to the principal possibility to adjust their dynamic properties reversibly during locomotion. In this paper vibration driven planar locomotion of mobile robots, based on a simple tensegrity structure, consisting of two rigid disconnected compressed members connected to a continuous net of four prestressed tensional members with pronounced elasticity, is discussed. The dynamic behaviour of the considered system is nonlinear, due to large vibration amplitudes and friction between robot and environment, and is mainly influenced by the magnitude of prestress. Therefore, the movement performance of the robot can be essentially influenced by the actuation parameters, e.g. by modifying the frequency or the magnitude of actuation the locomotion direction of the system varies. To study the system behaviour, the nonlinear equations of motion are derived and transient dynamic analyses are performed, including the consideration of chaotic system behaviour near to the primary and secondary eigenfrequencies. The dependency of the movement behaviour on the actuation parameters and on the prestress are discussed focused on single-actuated systems with minimal control effort.

Analysis of a two prey one predator system with disease in the first prey population

Abstract: In this paper we have developed an eco-epidemic model with two prey one predator population where only first prey population is infected by an infectious disease. The interaction between first prey and predator is assumed to be governed by a Holling type II functional response where the handling time of predator for second prey is also involved. A Lotka–Volterra functional response is taken to represent the interaction between second prey and predator. Next we have studied the positivity of the solutions of the system and analyzed the existence and stability of various equilibrium points. We have introduced a time delay in the model and discussed about the stability of delayed model. It is observed that the existence of stability switches occur around the interior equilibrium. Our important mathematical findings are also numerically verified using MATLAB. Finally eco-epidemiological implications of our analytical findings are addressed critically.

Fuzzy control of passenger ride performance using MR shock absorber suspension in quarter car model

Abstract: This paper presents vibration control performance of quarter car model with three-degrees-of-freedom having Magneto- Rheological (MR) suspension system. Experimental work is performed on an MR shock absorber prototype under various cyclic excitation conditions. A polynomial model is selected to characterize the test results of MR shock absorber. The designed forward fuzzy logic controller (FFLC) and inverse fuzzy logic controller (IFLC) are assembled in the secondary suspension system of quarter car model. The response plots in time domain due to bump road disturbance related to passenger seat are obtained for uncontrolled and controlled quarter car models. Simulation results are compared for selection of best option which can provide maximum ride comfort to travelling passengers. Simulation results demonstrate that semi-active quarter car system provides improved overall performance in terms of passenger ride comfort and safety compared to uncontrolled system.

Vibration frequency analysis of an electrically-actuated microbeam resonator accounting for thermoelastic coupling effects

Abstract: The paper deals with a thermo-mechanical problem for a slender microbeam subjected to an electric actuation; the purpose of the study is to improve the knowledge of loss mechanisms in micro-electro-mechanical devices and to predict accurately the dynamical behaviour. The thermoelastic damping in microbeam resonators is strictly correlated to the mechanical behaviour, and the thermoelastic response of the structure changes significantly near critical frequencies. To fully understand the thermoelastic coupling effects, we add the description of the thermal phenomena to the mechanical problem obtaining a system of two coupled PDEs. The proposed governing equations, by making use of a unified model, are able to describe the response by using the classical thermoelastic formulation and two distinct generalized theories, namely, the Lord–Shulman and the Green–Lindsay models. The study is carried out by means of a spectral approximation method and numerical simulations. The results show the influence of the relaxation times and the presence of dissipation peaks in the different formulations.

Spatial double physical pendulum with axial excitation: computer simulation and experimental set-up

Abstract: Physical and mathematical model of a three- dimensional double physical pendulum being coupled by two universal joints is studied. Upper joint of this pendu- lum is periodically rotated in its axial direction. Damping forces and torques inside joints as well as an influence of the gravitational field and damping forces and torques inside joints are taken into account during derivation of the ODEs of this mechanical system. The work consists of mathemati- cal modelling, computer simulation and parts of the experi- mental analysis to confirm the numerical simulations. The experimental setup realizes kinetic excitation by an non- constant periodic torque of servomotor, controlled by the computer. Four incremental encoders are mounted on pen- dulum joints, so the angles of rotation of the pendulum are measured in real-time and analysed by an originally devel- oped acquisition software. Future plans of the mathematical and experimental model are also discussed. Presented exem- plary results showed a number of non-linear effects, includ- ing chaos, quasi-periodic and periodic dynamics.

Observability for optimal sensor locations in data assimilation

Abstract: In this paper we will discuss the application of observability to the planning of sensor configurations in numerical weather prediction (NWP). The dimensions used in NWP make conventional definitions of observability impractical. For this reason we will rely partial observability which is obtained using dynamic optimization to approximate the observability. Using this metric we will form an optimization problem to select sensor configurations that maximize the partial observability of the dynamical system. This leads to a max–min problem which using an empirical gramian matrix we reduce to an eigenvalue optimization problem. Atmospheric data assimilation is the process of combining prior knowledge with observations to form an estimate of the system state required to produce a forecast of future weather conditions. Optimal sensor configurations leading to improved forecast quality are of interest. Due to the potential size of our intended application we will focus on computational methods that are both efficient and scalable. We will also leverage existing tools used in data assimilation and introduce tools used in nonsmooth optimization.

Frequency locking in a nonlinear MEMS oscillator driven by harmonic force and time delay

Abstract: Vibrations of a nonlinear self- and parametrically excited MEMS device driven by external excitation and time delay inputs are analysed in the paper. The model of MEMS resonator includes a nonlinear van der Pol function producing self-excitation, a periodically varied coefficient which represents Mathieu type of parametric excitation and furthermore, periodic force acting on the resonator. Analysis of frequency locking zones is presented with suggestions for a strategy of a closed loop control. Interactions between self- and parametric excitation lead to quasi-periodic oscillations but under specific conditions the motion becomes harmonic. The so called frequency locking, near the resonance zones is observed. This is caused by the second kind Hopf bifurcation (Neimark–Sacker bifurcation). The amplitudes of periodic oscillations are determined analytically by the multiple time scale method (MS) in the second order perturbation. The effect of external force has been observed by the internal loop occurring inside the frequency locking zone. The localisation of the zones and existence of the internal loop can be controlled by a selection of gains and time delay of displacement or velocity feedbacks.

Hyperchaos and bifurcations in a driven Van der Pol–Duffing oscillator circuit

Abstract: We investigate the dynamics of a driven Van der Pol–Duffing oscillator circuit and show the existence of higher-dimensional chaotic orbits (or hyperchaos), transient chaos, strange-nonchaotic attractors, as well as quasiperiodic orbits born from Hopf bifurcating orbits. By computing all the Lyapunov exponent spectra, scanning a wide range of the driving frequency and driving amplitude parameter space, we explore in two-parameter space the regimes of different dynamical behaviours.

Experimental research of oil-free support systems to predict the high-speed rotor bearing dynamics

Abstract: In modern dissipated power generation systems, microturbines of power output ranging between 1 and 20 kW are applied. The development of a reliable bearing technology for high-speed small turbomachinery could be essential to these power-generating devices. In order to introduce this technology to common use, the optimal design selection from the viewpoint of machine reliability must be conducted. Therefore, one should analyze thoroughly the dynamics of the rotor-bearing-casing system in the whole operating range of the machine. The rotating system presented in the paper is supported in oil-free, airfoil bearings. Compliant surface foil gas bearings are a class of hydrodynamic bearings that use the ambient gas as their working fluid and thus require no dedicated lubrication systems, which makes their design much simpler. The article presents the development and experimental verification of a theoretical numerical model of the foil bearing for analysis of its dynamic characteristics (a sum of properties: two elastic elements connected in a series and their relative motion, friction that is related to this motion with respect to the elastic and cylindrical foils subjected to deformation) that will be an useable part of the study referring to numerical analyses oriented on developing a model of the high-speed rotor supported in bump-foil bearings.

A modified control method for congested traffic in car-following model

Abstract: In order to describe the car-following behavior more actually in real traffic, an extended car-following model incorporating the headway of arbitrary number of vehicles that precede and the relative velocity is proposed from the viewpoint of control. The stability condition of the extended model is obtained by using the linear stability theory. The modified control signal will play an effect only if the traffic is in congested state. The numerical simulations and results are in accordance with our theoretical analysis.

Stability of the vibrations of an inhomogeneous flexible structure with thermal effect

Abstract: We consider the vibrations of a cantilever structure modeled by the standard linear flexible model of viscoelasticity coupled to an expectedly dissipative effect through heat conduction. It is shown that the amplitude of such vibrations is bounded under some restriction of the disturbing force. Using multiplier technique, an uniform exponential stability of the system is obtained directly, when the disturbing force is insignificant.

Central inertia moments and gravity center of large volume and weight bodies

Abstract: The aim of the work is to propose methodology applied for investigation of central inertia moments and gravity center of large volume and weight bodies, e.g. rail vehicles. The methodology is applicable for various large dimensions of bodies and high weight machines. Two mode of the designed methodology is presented one with the direct support of the body frame and second utilizes the additional weight represented by additional frame substituting the wheel set. The result of the experiment processed by proposed methodology is determined inertia effect within arbitrary axes. These results are useful for investigation of the movement dynamic stability and design construction optimization of rail and road vehicles. The proposed methodology is based on the known fact that the inertia moment could be obtained from oscillation period of vibratory movement body which is embedded on the rigid and elastic supports. The position of the gravity center is determined by derived equations based upon the mode of proposed of methodology.

Period-3 motions to chaos in a periodically forced duffing oscillator with a linear time-delay

Abstract: In this paper, bifurcation trees of period-3 motions to chaos in a periodically excited, Duffing oscillator with a linear delay are investigated through the Fourier series. The analytical solutions of period-m motions are presented and the stability and bifurcation of such period-m motions in the bifurcation trees are discussed by eigenvalue analysis. Two independent symmetric period-3 motions were obtained, and the two independent symmetric period-3 motions are not relative to chaos. Two bifurcation trees of period-3 motions to chaos are presented through period-3 to period-6 motion. Numerical illustrations of stable and unstable period-3 and period-6 motions are given by numerical and analytical solutions. The complicated period-3 and period-6 motions exist in the range of low excitation frequency.

Investigation of the dynamics of a clamped–clamped microbeam near symmetric higher order modes using partial electrodes

Abstract: We present an investigation of the dynamics of a clamped–clamped microbeam excited electrostatically near its third and fifth natural frequencies. We study the effect of partial electrodes on the static and dynamic response of the beam. Different lower electrode configurations are utilized. A new concept of the divided lower electrode and its actuation with voltage sources of various phase shifts is introduced. A multi-mode Galerkin method is used to develop a reduced order model of the beam. Shooting and longtime integration methods are used to find the periodic motion and to generate frequency response curves. The curves show hardening behavior and dynamic pull-in. We show that the dynamic amplitude of the divided lower electrode, actuated with two voltage sources with phase shift, is higher than actuating the full electrode with one voltage source. These results are promising for the use of higher-order modes for mass detection and for ultra-sensitive resonant sensors.

Permanence and coexistence in a diffusive complex ratio-dependent food chain

Abstract: In this article, we study a complex ratio-dependent food chain model with diffusion in bounded habitat and various boundary conditions As an extension of simple food chain models studied in earlier literature (Ko and Ahn, Math Biosci Eng 4:1–11, 2007; Kuang and Beretta, J Math Biol 36:389–406, 1998), this model has a more complicated (and general) dynamical structure where the super-predator consumes both the prey and predator For Dirichlet, Robin, and Neumann boundary conditions, we obtain straightforward criterion for the existence of a positive global attractor which ensures the permanence effect in the ecological system and the presence of a positive steady-state solution Sufficient conditions on the interaction rates are further given for the uniqueness and global stability of the coexistence state Several examples give specific parameter sets which satisfy the permanence criteria, or violate the criteria with multiple coexistence states Numerical simulations of the diffusive food-chain models are also provided to demonstrate and compare the asymptotic behavior of the time-dependent density functions

Dynamical simulation of a nonlinear stepper motor system

Abstract: Coupled electromechanical interactions obser- ved in a closed-loop control system actuated by a stepper motor are studied. Analysed system consists of a PID con- troller used to maintain constant vertical inclination of a sin- gle DOF pendulum. This pendulum serves as a tensioner for astringbeingpulledbyarotarymotionoftheelectricstepper motor. The second end of the string is being fed to the motor with a variable speed. The mathematical model governing dynamics of the mentioned system consists of a non-linear system of four ordinary differential equations. In addition to the mathematical model, various ways of control of the elec- tric stepper motor have been applied. In particular, the rotor control using the micro-stepping approach has been used to modeltherealdynamicsofthemotorcontroller.Comparison of the proposed theoretical considerations and modelling of the studied system fits well with the experimental investiga- tions.

Impulsive control dosing BCG immunotherapy for non-muscle invasive bladder cancer

Abstract: This article provides a solution for a control system derived from a mathematical model of four ordinary differential equations that describe the dynamics between the bacillus Calmette-Guerin (BCG) vaccine concentration, immune-system and tumor cells in non-muscle invasive bladder cancer. Generally, in cancer treatments, such as immunotherapies, the problems of administration procedures, do not take place through continuous injections of clinical agents in the diseased organs, but are often referred to therapeutic optimization problems with pulse vaccinations. For our study, we discuss the advantages of BCG immunotherapy when it is administered as a sequence of pulsed instillations in the bladder. We include numerical simulations based on the variational equation method resolved using a fourth-order iterative Runge–Kutta scheme combined with an optimization technique that computes the gradient of the objective function to find the optimal vaccination times and BCG dosage amounts.

Reconstruction of chaotic systems of a certain class

Abstract: We use a scalar time series to find an unknown original system (OS) of ordinary differential equations in a given class. To solve this problem, we first construct a standard system (SS) of a known type having the observable and its derivatives as variables. Then we pass from the SS to the sought OS. To this end, we propose a new method that we call a method of perspective coefficients. It involves an analysis of relations between the coefficients of the OS, the SS, and the numerical values of the SS coefficients obtained for the studied time series. The method permits to obtain a number of OS’s that yield the given scalar time series. Here we recover exactly the observable variable rather than obtain its approximation. In some cases, using the proposed approach one can obtain a unique candidate system even if no additional information is available. The obtained candidate system can be considered as the thought OS. An exact reconstruction of the Rossler system structure was obtained in the paper in such a way. Moreover, in all considered cases, we could not only determine the structure of the OS but also find numerical values for some of the coefficients in the OS.

Post-buckling dynamics of Timoshenko microbeams under axial loads

Abstract: The nonlinear buckling and post-buckling dynamics of a Timoshenko microbeam under an axial load are examined in this paper. The microbeam is assumed to be subject to an axial force along with a distributed harmonically-varying transverse force. As the axial load is increased, in the absence of the transverse load, the stability of the microbeam is lost by a super-critical pitchfork bifurcation at the critical axial load, leading to a static divergence (buckling). The post-buckling state, due to a sufficiently high axial load, is obtained numerically; the resonant response over the buckled state, due to the harmonic transverse loading, is also examined. More specifically, Hamilton’s principle is employed to derive the equations of motion taking into account the effect of the length-scale parameter via the modified couple stress theory. These partial differential equations are then discretized by means of the Galerkin scheme, yielding a set of ordinary differential equations. The resultant equations are then solved via a continuation technique as well as a direct time-integration method. Results are shown through bifurcation diagrams, frequency-responses, and force-response curves. Points of interest in the parameter space in the form of time histories, phase-plane portraitists, and fast Fourier transforms are also highlighted. Finally, the effect of taking into account the length-scale parameter on the buckling and post-buckling behaviour of the system is highlighted by comparing the results obtained through use of the classical and modified couple stress theories.

Investigation of a laboratory mechanical system with fibre and pulley

Abstract: Experimental measurements focused on the investigation of a fibre behaviour are performed on an assembled weigh-fibre-pulley-drive mechanical system. The fibre is driven with one drive and is led over a pulley. On its other end there is a prism-shaped steel weight, which moves in prismatic linkage on an inclined plane. The angle of inclination of the inclined plane could be changed. The position of the weight is asymmetric with respect to the vertical plane of drive-pulley symmetry. Drive exciting signals can be of a rectangular, a trapezoidal and a quasi-sinusoidal shape and there is a possibility of variation of a signal rate. Dynamic responses of the weight and the fibre (time histories of the weight position, of the drive position and of the force acting in the fibre) are measured. The same system is numerically investigated by means of a multibody model. The influence of the model parameters on the coincidence of results of experimental measurements and the simulations results are evaluated. The simulations aim is to create a phenomenological model of a fibre, which will be utilizable in fibre modelling in the case of more complicated mechanical or mechatronic systems.

Work cycle optimization problem of manipulator with revolute joints

Abstract: In this work the problem of motion modeling and work cycle optimization of manipulator with revolute joints has been considered. The motion equations of the manipulator elements under any spatial work cycle conditions have been formulated. The formulation has been completed by using the classic vector mechanics and Lagrange equations of second kind. The equations of motion of the system have been obtained using commercial software. The chosen motion model for each considered actuator is point-to-point motion model with quasi-trapezoid velocity profile. Additionally, the problem of optimization of a particular work cycle has been presented. The optimization objective has been chosen as minimization of loads (torques) in actuators. The objective function has been formulated using performance indexes and the design variables are rated velocity value and initial time value of work cycle in each considered actuator. The formulated optimization problem has been solved using constrained Multi-Objective Particle Swarm Optimization algorithm. A numerical computation has been completed using specially performed software and results of the computation have been attached to the paperwork.

Analysis of a delayed epidemic model of diseases through droplet infection and direct contact with pulse vaccination

Abstract: In this paper, we have considered a dynamical model of diseases that spread by droplet infection and also through direct contact. It is assumed that there is a time lag due to incubation period of pathogens, i.e. the development of an infection from the time the pathogen enters the body until signs or symptoms first appear. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination and saturation incidence rate. We have defined two positive numbers $$R_{1}$$ and $$R_{2}$$ . It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{1}<1$$ and the disease is permanent if $$R_{2}>1.$$ The important mathematical findings for the dynamical behaviour of the model are also numerically verified using MATLAB. Finally epidemiological implications of our analytical findings are addressed critically.