Sharif Digital Repository

The economical operations of power plants and environmental awareness are the major factors affecting the importance of control in boiler-turbine units. In this paper, a multivariable nonlinear model of boiler-turbine unit is considered. Drum pressure, electric output and water level of drum (as output variables) are adjusted at desired values by manipulation of valve positions for fuel, steam and feed-water flow rates (as input variables). Nonlinear dynamics of the unit is investigated through the concepts of bifurcation and limit cycles behaviour. In the presence of harmonic disturbances, some coefficients of the dynamic model, fuel and steam flow rates play as the bifurcation parameters.... 

Nowadays, dynamic analysis of air-conditioner units is essential to achieve satisfactory comfort conditions in buildings with low energy consumption and operation cost. In this paper, a nonlinear multi input-multi output model (MIMO) of an air-handling unit (AHU) is considered. In the presence of realistic harmonic disturbances, nonlinear dynamics of AHU is investigated. The effect of various thermodynamics and geometrical parameters on limit cycles behaviour of the indoor temperature is investigated. It is observed that the indoor space volume plays as the bifurcation parameter of the system. Decreasing the indoor space volume leads to the occurrence of secondary Hopf (Neimark) bifurcation... 

The economical operations of power plants and environmental awareness are the major factors affecting the importance of control in boiler-turbine units. In this paper, a multivariable nonlinear model of boiler-turbine unit is considered. Drum pressure, electric output and water level of drum (as output variables) are adjusted at desired values by manipulation of valve positions for fuel, steam and feed-water flow rates (as input variables). Nonlinear dynamics of the unit is investigated through the concepts of bifurcation and limit cycles behaviour. In the presence of harmonic disturbances, some coefficients of the dynamic model, fuel and steam flow rates play as the bifurcation parameters.... 

Nowadays, dynamic analysis of air-conditioner units is essential to achieve satisfactory comfort conditions in buildings with low energy consumption and operation cost. In this paper, a nonlinear multi input-multi output model (MIMO) of an air-handling unit (AHU) is considered. In the presence of realistic harmonic disturbances, nonlinear dynamics of AHU is investigated. The effect of various thermodynamics and geometrical parameters on limit cycles behaviour of the indoor temperature is investigated. It is observed that the indoor space volume plays as the bifurcation parameter of the system. Decreasing the indoor space volume leads to the occurrence of secondary Hopf (Neimark) bifurcation... 

This paper deals with the existence and the characteristics of the limit cycles in the fractional-order Arneodo system. The analysis is done using the describing function method. Our focus is on a special case where two limit cycles exist. The parametric range for the case of interest is derived, and the frequency and the amplitude of the oscillation are predicted. Numerical simulation results are presented to further demonstrate the reliability of the analysis  

In this paper, the occurrence of various types of bifurcation including symmetry breaking, period-doubling (flip) and secondary Hopf (Neimark) bifurcations in milling process with tool-wear and process damping effects are investigated. An extended dynamic model of the milling process with tool flank wear, process damping and nonlinearities in regenerative chatter terms is presented. Closed form expressions for the nonlinear cutting forces are derived through their Fourier series components. Non-autonomous parametrically excited equations of the system with time delay terms are developed. The multiple-scale approach is used to construct analytical approximate solutions under primary... 

In this paper, a novel nonlinear joint dynamical model is presented, which is based on a set of coupled ordinary differential equations of motion and a Gaussian mixture model representation of pulsatile cardiovascular (CV) signals. In the proposed framework, the joint interdependences of CV signals are incorporated by assuming a unique angular frequency that controls the limit cycle of the heart rate. Moreover, the time consequence of CV signals is controlled by the same phase parameter that results in the space dimensionality reduction. These joint equations together with linear assignments to observation are further used in the Kalman filter structure for estimation and tracking. Moreover,... 

The labels mathematician, engineer, and physicist have all been used in reference to Balthazar van der Pol. The van der Pol oscillator, which we study in this paper, is a model developed by him to describe the behavior of nonlinear vacuum tube circuits in the relatively early days of the development of electronics technology. Our study in this paper will be based entirely on numerical solutions. The rigorous foundations for the analysis (e.g., the proof that the equation has a limit cycle solution which is a global attractor) date back to the work of Lienard in 1928, with later more general analysis by Levinson and others  

In this work, a powerful analytical method, called Liao's homotopy analysis method is used to study the limit cycle of a two-dimensional nonlinear dynamical system, namely the van der Pol oscillator with delayed amplitude limiting. It is shown that the solutions are valid for a wide range of variation of the system parameters. Comparison of the obtained solutions with those achieved by numerical solutions and by other perturbation techniques shows that the utilized method is effective and convenient to solve this type of problems with the desired order of approximation  

Limit cycle walkers are known as a class of walking robots capable of presenting periodic repetitive gaits without having local controllability at all times during motion. A well-known subclass of these robots is McGeer’s passive dynamic walkers solely activated by the gravity field. The mathematics governing this style of walking is hybrid and described by a set of nonlinear differential equations along with impulses. In this paper, by applying perturbation method to a simple model of these machines, we analytically prove that for this type of nonlinear impulsive system, there exist different switching surfaces, leading to the same equilibrium points (periodic solutions) with different... 

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing the pitchfork bifurcation of non-trivial rest point. The asymptotic stability and possible Hopf bifurcations of the trivial rest point are studied by analyzing the corresponding characteristic equation. Homoclinic, fold, and pitchfork bifurcations of limit cycles are found. The delay-dependent stability... 

This paper presents a modified astrocyte model that allows a convenient digital implementation. This model is aimed at reproducing relevant biological astrocyte behaviors, which provide appropriate feedback control in regulating neuronal activities in the central nervous system. Accordingly, we investigate the feasibility of a digital implementation for a single astrocyte and a biological neuronal network model constructed by connecting two limit-cycle Hopf oscillators to an implementation of the proposed astrocyte model using oscillator-astrocyte interactions with weak coupling. Hardware synthesis, physical implementation on field-programmable gate array, and theoretical analysis confirm... 

The problem of nonlinear aeroelasticity of a general laminated composite plate in supersonic air flow is examined. The classical plate theory along with the von-Karman nonlinear strains is used for structural modeling, and linear piston theory is used for aerodynamic modeling. The coupled partial differential equations of motion are derived by use of Hamilton's principle and Galerkin's method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping on the nonlinear aeroelastic... 

Presented is a novel approach for designing continuous-time update laws to update the parameters of stabilising controllers during continuous phases of bipedal walking such that (i) a general cost function, such as the energy of the control input over single support, can be minimised in an online manner, and (ii) the exponential stability of the corresponding limit cycle for the closed-loop impulsive system is not affected. Formally, a class of update laws with a radial basis step length is developed to minimise a cost function in terms of the stabilising controller parameters and initial states of the mechanical system  

Stable and unstable limit cycles are important orbits in chaotic systems. So many works are done to find and to quench chaos by stabilizing them. In this paper a new family of limit cycle orbits around the Moon is introduced as a result of restricted three-body problem. The family is completely spatial and can be used as an out-of-plane velocity magnifier. Lyapunov exponent in the Floquet theory has also been checked and stability of the orbits has been measured  

In this research, nonlinear dynamics of an air-ehandling unit (AHU) is studied for tracking objectives, in the presence of harmonic perturbations. Three arbitrary realistic set-paths are considered for the indoor temperature and relative humidity. Two controllers based on feedback linearization (FBL) and pole placement approaches are designed to preserve the dynamic system around the desired tracking paths. It is shown that FBL controller works efficiently in bifurcation control and transforms the quasi-periodic limit cycles into the periodic ones (and consequently comfortable indoor conditions). In addition, FBL controller guarantees suppression of larger periodic limit cycles into the... 

Challenging problems in the design and analysis of photovoltaic (PV) systems stem from the nonlinear current–voltage (I–V) characteristics of solar cells. This paper presents an analytical analysis based on a describing function method to investigate the transient and steady-state characteristics of a three-phase single-stage grid-connected PV system. In this study, the nonlinear I–V characteristic of the PV array is linearized around the operating point. The nonlinear dynamic of the maximum power point tracking controller is divided into two parts of continuous and discrete. For the continuous part, the common small-signal linearization is applied, while for the discontinuous part, a... 

In this paper, the dynamic instability of a nonlinear system has been studied using the stochastic vibration analysis and employing statistical properties of the system response. In this method neither the time domain analysis nor limit cycle oscillations were used. A two degrees-of-freedom airfoil subjected to an aerodynamic quasi-steady flow with a nonlinear torsional spring was considered as the case study. The spring nonlinearity was examined in hardening and softening states. A random force in the form of the white noise with Gaussian function was added to the aerodynamic lift force. The statistical linearization and random vibration analysis were applied to the nonlinear system to...