minimum energy of nonlinear dynamic systems with given boundary conditions on control inputs by applying jerk equations

Name: Tawiwat Veeraklaew

Email : tawiwat.v@dti.or.th

Name: Phermsak Siriphala

Email : phermsak.s@dti.or.th

keyword: Jerk equation

; Nonlinear dynamic system

; Constrained inputs on boundaries.

Abstract: The most of the dynamic systems such as robots, automation systems and advanced mobile machines nowadays are designed so that they are either optimized on their energy consumption or on their greatest smoothness of motion, [3]. Consequently, the trajectory planning and designs of these dynamic systems are done exclusively through many approaches such as the minimum energy, minimum time and minimum jerk, [4]. Nevertheless, in some applications, the system is needed to work very smoothly in order to avoid damaging the specimen that the system is handling while consuming least amount of energy at the same time. In other words, we may want to minimize the jerk of the movement of the dynamic system as to give it the smoothest motion as well as optimize that system in the energy consumption issue. The general format of the dynamic problems is consisting of the equation of motions, the initial conditions, and the boundary conditions. The area of interest in this paper will involve the problems with two-point-boundary-value conditions. Each of the problems may contain many possible solutions depending on the objective of application. Obviously, the robot that aims to run at lowest cost of energy will be designed to have the lowest actuator inputs during the motion. This is basically the optimization problem of the dynamic systems. Research shows that many of the researchers pay a lot of their attention on the minimization of energy while many tend to seek for the smoothness of the system. According to the second law of Newton’s laws, there is a relationship between acceleration and summation of all forces including the control inputs of any linear dynamic system. By taking derivative with respect to time, there is a relationship between derivative of the acceleration called Jerk and derivative of all forces including the derivative of the control inputs of the dynamic system. In this paper, the derivative of the control inputs with respect to time are called indirect jerks. The problem of nonlinear dynamic system is quite challenge in the way of applying minimum energy or minimum jerk in order to have the most benefit. Moreover, assigning both end boundaries for the control input is changing the common dynamic optimization problem. Therefore, this research paper aims to compare the solutions of the nonlinear dynamic system that has control input applied on between the minimum energy and minimum indirect jerk by using the direct optimization method so that conclusion can be made.

Defence Technology Institute (Public Organisation)

Address: Nonthaburi

Email: nukulrat.l@dti.or.th

Created: 2011-04-04

Modified: 2011-04-04

Issued: 2554-04-04

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