Abstract: Both the minimum energy consumption and
smoothness, which is quantified as a function of jerk, are generally
needed in many dynamic systems such as the automobile and the
pick-and-place robot manipulator that handles fragile equipments.
Nevertheless, many researchers come up with either solely
concerning on the minimum energy consumption or minimum jerk
trajectory. This research paper considers the indirect minimum Jerk
method for higher order differential equation in dynamics
optimization proposes a simple yet very interesting indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of indirect jerks are found using the dynamic optimization methods
together with the numerical approximation. This case considers the
linear equation of a simple system, for instance, mass, spring and
damping. The simple system uses two mass connected together by
springs. The boundary initial is defined the fix end time and end
point. The higher differential order is solved by Galerkin-s methods
weight residual. As the result, the 6th higher differential order shows
the faster solving time.
Abstract: This paper deals with under actuator dynamic systems such as spring-mass-damper system when the number of control variable is less than the number of state variable. In order to apply optimal control, the controllability must be checked. There are many objective functions to be selected as the goal of the optimal control such as minimum energy, maximum energy and minimum jerk. As the objective function is the first priority, if one like to have the second goal to be applied; however, it could not fit in the objective function format and also avoiding the vector cost for the objective, this paper will illustrate the problem of under actuator dynamic systems with the easiest to deal with comparing between minimum energy and minimum jerk.