A methodology for designing critical systems subject to magnitude- and rate-limited reference inputs is proposed. The worst-case tracking error is minimized under the constraint on the control effort. The LMI-based technique developed by Chilali and Gahinet is utilized to assign the resulting closed-loop poles into the intersection of vertical strips and a conic sector. The optimal pole region is searched by means of the simple genetic algorithm. An illustrative design example of the position control system for a two-inertia system is provided to demonstrate the proposed design methodology.
This paper proposes a robust controller design method for an norm-bounded uncertain linear system with disturbance. At First, we derive the necessary and sufficient condition for regional pole assignment for uncertain linear system, then derive the criteria of H 2 /H ∞ performance of uncertain linear system with disturbance. Hence combining them, we get the mixed H 2 /H ∞ controller control with regional assignment for norm-bounded uncertain linear system with disturbance. The problem of the robust controller designed is changed into an optimization problem, and the robust controller is parameterized by the solution of the optimization. Since the optimization problem conditions are expressed in term of linear matrix inequalities, so it makes the proposed method practical utility. Finally the numerical example illustrates the effectiveness of the proposed approach.
Smartphones may be seen as miniature toolboxes to perform Physics experiments. In this paper, we present three different “optics workbenches" mainly based on the light meter of a smartphone. One is aimed at the precise study of Malus law and other effects associated to linearly polarized light, the second allows quantifying the light intensity distribution of diffraction or interference patterns projected on a screen, and the third demonstrates the so-called inverse square law obeyed by the light from a point-like source. These experiments allow to quantitatively demonstrate three fundamental laws of optics using quite inexpensive equipment.