Abstract: A vibration isolation technology for precise position
control of a rotary system powered by two permanent magnet DC
(PMDC) motors is proposed, where this system is mounted on an
oscillatory frame. To achieve vibration isolation for this system,
active damping and disturbance rejection (ADDR) technology
is presented which introduces a cooperation of a main and
an auxiliary PMDC, controlled by discrete-time sliding mode
control (DTSMC) based schemes. The controller of the main
actuator tracks a desired position and the auxiliary actuator
simultaneously isolates the induced vibration, as its controller
follows a torque trend. To determine this torque trend, a
combination of two algorithms is introduced by the ADDR
technology. The first torque-trend producing algorithm rejects
the disturbance by counteracting the perturbation, estimated
using a model-based observer. The second torque trend applies
active variable damping to minimize the oscillation of the output
shaft. In this practice, the presented technology is implemented
on a rotary system with a pendulum attached, mounted on a
linear actuator simulating an oscillation-transmitting structure.
In addition, the obtained results illustrate the functionality of the
proposed technology.
Abstract: Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.
Abstract: An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.