• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.203-214
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• 2005

In this study the optimal control of fed-batch glycerol fermentation is investigated based on an impulsive dynamical system. Considering the sudden increase of the glycerol and alkali in fed-batch culture of biodissimilation of glycerol to 1,3-propanediol, this paper proposes a non-linear impulsive system of fed-batch culture. The existence, uniqueness and regularity properties of piecewise solution for the system are proved. In view of the controllability of volumes of glycerol added to the reactor instantaneously, the paper constructs an optimal control model based on the nonlinear impulsive system and the existence of the optimal control is obtained. The control variables here are the moments and the sizes of jumps in the states at the discrete instants and the objective is to maximize the productivity of 1,3-propanediol over one cycle.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.879-890
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• 2020

In this paper we study the stability properties of solutions of nonlinear impulsive integro-differential systems by using an integral inequality under the stability of the corresponding variational impulsive integro-differential systems. Also, we give examples to illustrate our results.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.681-696
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• 2011

In this paper, we consider the existence of mild solutions for a certain class of nonlinear impulsive functional evolution integrodifferential equation with nonlocal conditions in Banach spaces. A sufficient condition is established by using Schaefer's fixed point theorem combined with an evolution system. An example is also given to illustrate our result.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.387-397
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• 2007

According to the controllability of pulse times and the amount of jumps in the states at these times in the process of fed-batch culture producing 1,3-propanediol, this paper proposes a terminal optimal control model, whose constraint condition is the nonlinear impulsive delay system. The existence of optimal control is discussed and an optimization algorithm which is applied to each subinternal over one cycle for this optimal control problem is constructed. Finally, the numerical simulations show that the terminal intensity of producing 1,3-propanediol has been increased obviously.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.593-611
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• 2008

Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

• Structural Engineering and Mechanics
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• v.29 no.4
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• pp.433-453
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• 2008

The equation of motion of a one way (vertical) spanning strip wall, as an assembly of two rigid bodies, is presented. Only one degree of freedom is needed to completely describe the wall response as the bodies are assumed to be perfectly rectangular and are allowed to rock but not to slide horizontally. Furthermore, no arching action occurs since vertical motion of the upper body is not restrained. Consequently, the equation of motion is nonlinear, with non constant coefficients and a Coriolis acceleration term. Phenomena associated with overburden to self weight ratio, motion triggering, impulsive energy dissipation, amplitude dependency of damping and period of vibration, and scale effect are discussed, contributing to a more complete understanding of experimental observations and to an estimation of system parameters based on the wall characteristics, such as intermediate hinge height and energy damping, necessary to perform nonlinear time history analyses. A comparison to a simple standing, or parapet, wall is developed in order to better highlight the characteristics of this assembly.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.11
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• pp.1403-1412
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• 1997

When a high-speed railway train enters a tunnel, a compression wave is generated ahead of the train and propagates through the tunnel, compressing and accelerating the rest air in front of the wave. At the exit of the tunnel, an impulsive wave is emitted outward toward the surrounding, which causes a positive impulsive noise like a kind of sonic boom produced by a supersonic aircraft. With the advent of high-speed train, such an impulsive noise can be large enough to cause the noise problem, unless some attempts are made to alleviate its pressure levels. In the purpose of the impulsive noise reduction, the present study calculated the effect of porous walls on the compression wave propagating into a model tunnel. Two-dimensional unsteady compressible equations were differenced by using a Piecewise Linear Method. Calculation results show that the cavity/porous wall system is very effective for a compression wave with a large nonlinear effect. The porosity of 30% is most effective for the reduction of the maximum pressure gradient of the compression wave front. The present calculation results are in a good agreement with experimental ones obtained previously.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.6
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• pp.915-923
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• 2008

This paper focuses on optimal tuning of nonlinear parameters of a dual-input power system stabilizer(dual-input PSS), which can improve the system damping performance immediately following a large disturbance. Until recently, various PSS models have developed to bring stability and reliability to power systems, and some of these models are used in industry applications. However, due to non-smooth nonlinearities from the interaction between linear parameters(gains and time constants of linear controllers) and nonlinear parameters(saturation output limits), the output limit parameters cannot be determined by the conventional tuning methods based on linear analysis. Only ad hoc tuning procedures('trial and error' approach) have been used. Therefore, the steepest descent method is applied to implement the optimal tuning of the nonlinear parameters of the dual-input PSS. The gradient required in this optimization technique can be computed from trajectory sensitivities in hybrid system modeling with the differential-algebraic-impulsive-switched(DAIS) structure. The optimal output limits of the dual-input PSS are evaluated by time-domain simulation in both a single machine infinite bus(SMIB) system and a multi-machine power system in comparison with those of a single-input PSS.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Journal of Electrical Engineering and Technology
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• v.11 no.3
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• pp.707-714
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• 2016

We present a piezoelectric energy harvester with stopper-engaged dynamic magnifier which is capable of significantly increasing the operating bandwidth and the energy (power) harvested from a broad range of low frequency vibrations (<30 Hz). It uses a mass-loaded polymer beam (primary spring-mass system) that works as a dynamic magnifier for another mass-loaded piezoelectric beam (secondary spring-mass system) clamped on primary mass, constituting a two-degree-of-freedom (2-DOF) system. Use of polymer (polycarbonate) as the primary beam allows the harvester not only to respond to low frequency vibrations but also generates high impulsive force while the primary mass engages the base stopper. Upon excitation, the dynamic magnifier causes mechanical impact on the base stopper and transfers a secondary shock (in the form of impulsive force) to the energy harvesting element resulting in an increased strain in it and triggers nonlinear frequency up-conversion mechanism. Therefore, it generates almost four times larger average power and exhibits over 250% wider half-power bandwidth than those of its conventional 2-DOF counterpart (without stopper). Experimental results indicate that the proposed device is highly applicable to vibration energy harvesting in automobiles.