Control of Dynamic Systems Using Time Scaling

Abstract

Human brain capabilities to control are undeniable, but embedding that capacity in an algorithm for the control of a dynamic system has proven limited by natural human bounds such as the reaction time, which restricts the number of industrial applications using a human in the loop. Thus, the authors of this paper propose a new procedure to scale linear systems in time, which makes human control of dynamic systems not only feasible but also comfortable. The scaling method comprises moving poles and zeros of a transfer function proportionally to a scaling factor. Thus, a person controls the scaled version of the system, while the computer acquires his/her reactions, then a neural network learns those reactions. This network controls both scaled and original systems. The new control strategy controls slow and fast systems, as well as stable and unstable systems, achieving high performance for all conditions. Appropriate time scaling, and practice, facilitate the control of any dynamic system.

Performance evaluation of a Time Scale Controller

“…Thus, this section starts by scaling the linear components of the motor, as defined in eq. ( 1), according to the presentation in [18]. The scaling requires the definition of the scaling factor, 𝑘 .…”

Control of a Direct Current Motor Using Time Scaling

“…The model in Figure 3 uses the traditional definition of time, but that dynamic is too fast for a human to control. Thus, this section starts by scaling the linear components of the motor, as defined in Equation ( 1), according to the presentation in Rairán (2017). It can be seen that the nonlinear components are not time-dependent, but constant, so the nonlinear part remains equal regardless of the time scale.…”