Marat Rafikov

An Intelligent Controller Design for Magnetorheological Damper Based on a Quarter-car Model

This paper presents the control strategies of nonlinear vehicle suspension using a magnetorheological (MR) damper. We used two different approaches for modeling and control of the mechanical and electrical parts of the suspension systems with the MR damper. First, we have formulated and resolved the control problem in order to design the linear feedback dumping force controller for a nonlinear suspension system. Then the values of the control dumping force functions were transformed into electrical control signals by the application of a fuzzy logic control method. The numerical simulations were provided in order to show the effectiveness of this method for the semi-active control of the quarter-car suspension.

Mathematical modeling and control of population systems: Applications in biological pest control

Abstract The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton–Jacobi–Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka–Volterra models are provided to show the effectiveness of this method.

Nonlinear Mathematical Modeling in Pneumatic Servo Position Applications

This paper addresses a new methodology for servo pneumatic actuators mathematical modeling and selection from the dynamic behavior study in engineering applications. The pneumatic actuator is very common in industrial application because it has the following advantages: its maintenance is easy and simple, with relatively low cost, self-cooling properties, good power density (power/dimension rate), fast acting with high accelerations, and installation flexibility. The proposed fifth-order nonlinear mathematical model represents the main characteristics of this nonlinear dynamic system, as servo valve dead zone, air flow-pressure relationship through valve orifice, air compressibility, and friction effects between contact surfaces in actuator seals. Simulation results show the dynamic performance for different pneumatic cylinders in order to see which features contribute to a better behavior of the system. The knowledge of this behavior allows an appropriate choice of pneumatic actuator, mainly contributing to the success of their precise control in several applications.

An optimal linear control design for nonlinear systems

This paper studies the linear feedback control strategies for nonlinear systems. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function, which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations the Duffing oscillator and the nonlinear automotive active suspension system are provided to show the effectiveness of this method.

Optimal pest control problem in population dynamics

One of the main goals of the pest control is to maintain the density of the pest population in the equilibrium level below economic damages. For reaching this goal, the optimal pest control problem was divided in two parts. In the first part, the two optimal control functions were considered. These functions move the ecosystem pest-natural enemy at an equilibrium state below the economic injury level. In the second part, the one optimal control function stabilizes the ecosystem in this level, minimizing the functional that characterizes quadratic deviations of this level. The first problem was resolved through the application of the Maximum Principle of Pontryagin. The Dynamic Programming was used for the resolution of the second optimal pest control problem.

Mathematical modelling of the biological pest control of the sugarcane borer

In this paper, we propose a simple mathematical model of interaction between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid Trichogramma galloi. In this model, the sugarcane borer is represented by the egg and the larval stages, and the parasitoid is considered in terms of the parasitized eggs. Linear feedback control strategy is proposed to indicate how the natural enemies should be introduced into the environment.

Optimal Linear and Nonlinear Control Design for Chaotic Systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rossler system and the Duffing oscillator are provided to show the effectiveness of this method.Copyright

Impulsive Biological Pest Control Strategies of the Sugarcane Borer

We propose an impulsive biological pest control of the sugarcane borer (Diatraea saccharalis) by its egg parasitoid Trichogramma galloi based on a mathematical model in which the sugarcane borer is represented by the egg and larval stages, and the parasitoid is considered in terms of the parasitized eggs. By using the Floquet theory and the small amplitude perturbation method, we show that there exists a globally asymptotically stable pest-eradication periodic solution when some conditions hold. The numerical simulations show that the impulsive release of parasitoids provides reliable strategies of the biological pest control of the sugarcane borer.

Optimal control of indirect matrix converter based microturbine generation system

This paper deals with a microturbine generation scheme based on an indirect matrix converter, to interface a high-speed electric generator and a local load, as an alternative to conventional back-to-back converters. An optimal controller is proposed for performance enhancement and efficiency optimization aiming a unit input power factor. Principles of space vector modulation and switch commutation strategy in indirect matrix converters are reviewed. A numerical evaluation of the optimal control and the matrix converter is developed considering the ideal and non-ideal switch models. The simulation analysis considers the input power factor, filter parameters tuning accuracy and numerical stability issues as performance variables.

Real time simulation of Two-Stage Matrix Converter using ideal and nonideal IGBT models

This work analyzes the case of an AC-AC matrix converter, as an alternative to back-to-back converter, to interface a high-speed micro-turbine generator to a utility load as a distributed generation unit. It is proposed an evaluation procedure of an input-state feedback linearization control of Two-Stage Matrix Converters, in continuous and discrete time, aiming a unit input power factor. Principals of spatial modulation and IGBT bidirectional switch commutation in matrix converters are reviewed. The assessment considers, using ideal and nonideal IGBT models, an indirect evaluation of the inserted error in the output signal expectations due the lack of synchronization between the integration time used in the simulation and the firing times of the power devices.