scholarly journals PID Controller Singularly Perturbing Impulsive Differential Equations and Optimal Control Problem

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Wichai Witayakiattilerd
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Pid Controller ◽  
Impulsive Differential Equations ◽  
Integral Form ◽  
Impulsive System ◽  
Slow Variable ◽  
Fast Variable

We study singular perturbation of impulsive system with a proportional-integral-derivative controller (PID controller) and solve an optimal control problem. The perturbation system comprises two important variables, a fast variable and a slow variable. Because of the complexity of the system, it is difficult to find its exact solution. This paper presents an approximation method for solving it. The aim of the approximation method is to reduce the complexity of the system by eliminating the fast variable. The solution of the method is expressed in an integral form, and it is called an approximated mild solution of the perturbed system. An example is provided to illustrate our result.

scholarly journals Energy-Optimal Trajectory Planning for Planar UnderactuatedRRRobot Manipulators in the Absence of Gravity

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
John Gregory ◽  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Calculus Of Variations ◽  
Trajectory Planning ◽  
Integral Form ◽  
Necessary Condition ◽  
Planning Problem ◽  
Control Input ◽  
Revolute Joints

In this paper, we study the trajectory planning problem for planar underactuated robot manipulators with two revolute joints in the absence of gravity. This problem is studied as an optimal control problem in which, given the dynamic model of a planar horizontal robot manipulator with two revolute joints one of which is not actuated, the initial state, and some specifications about the final state of the system, we find the available control input and the resulting trajectory that minimize the energy consumption during the motion. Our method consists in a numerical resolution of a reformulation of the optimal control problem as an unconstrained calculus of variations problem in which the dynamic equations of the mechanical system are regarded as constraints and treated using special derivative multipliers. We solve the resulting calculus of variations problem using a numerical approach based on the Euler-Lagrange necessary condition in integral form in which time is discretized and admissible variations for each variable are approximated using a linear combination of piecewise continuous basis functions of time. The use of the Euler-Lagrange necessary condition in integral form avoids the need for numerical corner conditions and the necessity of patching together solutions between corners.

scholarly journals Numerical Methods for Solving Optimal Control Problem Using Scaling Boubaker Function

2020 ◽  
Vol 25 (2) ◽  
pp. 78-89 ◽  
Author(s):  
Eman Hassan Ouda Alfrdji ◽  
Imad Noah Ahmed
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Approximation Method ◽  
Numerical Examples ◽  
Control Parameterization ◽  
Matlab Program ◽  
And Control

      In this paper, the approximation method was used for solving optimal control problem (OCP), two techniques for state parameterization and control parameterization have been considered with the aid of Scaling Polynomials (SBP) represent a new important technique for solving (OCP’s). The algorithms were illustrated by several numerical examples using Matlab program. The results were evaluated and graphed to show the accuracy  of the methods.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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