Search results for "Applied Mathematic"
showing 10 items of 4398 documents
Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting
2013
We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameterσassociated with the intensity of harvesting i…
Landing gear suspension control through adaptive backstepping techniques with H∞ performance
2011
Author's version of a chapter published in the book: Proceedings of the 18th IFAC World Congress 2011. Also available from the publisher at: http://dx.doi.org/10.3182/20110828-6-IT-1002.00589 Landing gear suspension systems fulfill the tasks of absorbing the vertical energy of the touch-down as well as providing passenger and crew comfort with a smooth ground ride before take-off and after landing. They are also designed to have optimal performance in the case of a hard landing. In general, the tasks of aircraft landing gears are complex and sometimes lead to a number of contradictory requirements. Although there are existing modifications of aircraft shock absorbers to reduce the problem, …
Influence of unloading modes of spring-mass-damper models on vehicle to pole collision simulation results
2011
Author's verion of a chapter in the book: Proceedings of the 30th Chinese Control Conference. Also available from the publisher at: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=06001448 Our intention, in this brief note, is to investigate what influence the viscoelastic models' unloading properties have on models' accuracy of representing vehicle crash event. Two types of simple spring-mass-damper systems (Kelvin models) such underdamped and critically damped conditions are analyzed. Subsequently, two different unloading scenarios are specified: elastic rebound in which only the damper is an energy dissipating element and plastic collision in which the model's maximum achievable disp…
Robust tool point control for offshore knuckle boom crane
2011
Author's version of a chapter in the book: Proceedings of the 18th IFAC World Congress 2011. Also available from the publisher at: http://dx.doi.org/10.3182/20110828-6-IT-1002.03004 This paper considers the design of an H∞ controller for tool point control of a hydraulically actuated knuckle boom crane. The paper describes the modelling of the crane's mechanical and hydraulic systems and a disturbance model. These are linearised and combined in a state-space model used for the controller design. The controller synthesis problem is to design (if possible) an admissible controller that solves the problem of robust regulation against step inputs with an H∞ constraint based on the internal mode…
Semi-decentralized strategies in structural vibration control
2011
Published version of an article published in the journal: Modeling, Identification and Control. Also available from the publisher at: http://dx.doi.org/10.4173/mic.2011.2.2 In this work, the main ideas involved in the design of overlapping and multi-overlapping controllers via the Inclusion Principle are discussed and illustrated in the context of the Structural Vibration Control of tall buildings under seismic excitation. A detailed theoretical background on the Inclusion Principle and the design of overlapping controllers is provided. Overlapping and multi-overlapping LQR controllers are designed for a simplied five-story building model. Numerical simulations are conducted to asses the pe…
Motion control with optimal nonlinear damping: from theory to experiment
2022
Optimal nonlinear damping control was recently introduced for the second-order SISO systems, showing some advantages over a classical PD feedback controller. This paper summarizes the main theoretical developments and properties of the optimal nonlinear damping controller and demonstrates, for the first time, its practical experimental evaluation. An extended analysis and application to more realistic (than solely the double-integrator) motion systems are also given in the theoretical part of the paper. As comparative linear feedback controller, a PD one is taken, with the single tunable gain and direct compensation of the plant time constant. The second, namely experimental, part of the pa…
Robust adaptive backstepping DP control of ROVs
2022
Dynamic positioning is an important control feature for an underwater remotely operated vehicle. This paper presents a nonlinear dynamic positioning controller suited for application to vehicles with model uncertainties, operating in environments with unpredictable disturbances, such as an aquaculture net cage. The proposed controller combines the backstepping approach with an adaptation term to ensure robustness. Using Lyapunov theory and Matrosov’s theorem the origin of the closed-loop system is proven to be: (i) globally asymptotically stable when assuming persistency of excitation, and (ii) stable and bounded, with the true position converging to the desired position if there is no pers…
Robust Switching Rule Design for Boost Converters with Uncertain Parameters and Disturbances
2013
Pubished version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/120543 Open access This paper is concerned with the design problem of robust H∞ switching rule for Boost converters with uncertain parameters and disturbances. Firstly, the Boost converter is modeled as a switched affine linear system with uncertain parameters and disturbances. Then, using common Lyapunov function approach and linear matrix inequality (LMI) technique, a novel switching rule is proposed such that the H∞ model reference tracking performance is satisfied. Finally, a simulation result is provided to show the validity of the proposed …
Nonstandard Uniserial Modules Over Valuation Domains
1987
Nonstationary response envelope probability densities of nonlinear oscillators
2006
The nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic averaging, the procedure relies on the Markovian modeling of the response envelope process through the definition of an equivalent linear system with response-dependent parameters. An approximate solution of the associated Fokker-Planck equation is derived by resorting to a Galerkin scheme. Specifically, the nonstationary probability density function of the response envelope is expressed as the sum of a time-dependent Rayleigh dis…