This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of them is coded in a Maple 18 environment and their behaviors are compared. For each approximation method, an application example is explained in detail. The advantages and disadvantages of each approximation method are discussed. Afterwards, two model order reduction methods are applied to each rational approximation and assist a posteriori during the synthesis process using analog electronic design or reconfigurable hardware. Examples for each reduction method are discussed, showing the drawbacks and benefits. To wrap up, this survey is very useful for beginners to get started quickly and learn arbitrary-order calculus and then to select and tune the best approximation method for a specific application in the frequency domain. Once the approximation method is selected and the rational transfer function is generated, the order can be reduced by applying a model order reduction method, with the target of facilitating the electronic synthesis.
Autonomous Vehicles (AVs) have caught people’s attention in recent years, not only from an academic or developmental viewpoint but also because of the wide range of applications that these vehicles may entail, such as intelligent mobility and logistics, as well as for industrial purposes, among others. The open literature contains a variety of works related to the subject. They employ a diversity of techniques ranging from probabilistic to ones based on Artificial Intelligence. The increase in computing capacity, well known to many, has opened plentiful opportunities for the algorithmic processing needed by these applications, making way for the development of autonomous navigation, in many cases with astounding results. The following paper presents a low-cost but high-performance minimal sensor open architecture implemented in a modular vehicle. It was developed in a short period of time, surpassing many of the currently available solutions found in the literature. Diverse experiments were carried out in the controlled and circumscribed environment of an autonomous circuit that demonstrates the efficiency of the applicability of the developed solution.
Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable periodic orbits embedded in the chaotic attractor. In this paper, we also propose a parameter-perturbation-like control algorithm to stabilize the behavior of the Pendubot to force its dynamics to be periodic. We control this device using only the measurement of one of its angular position coordinates and consider that the system may be seen as five-dimensional (a non-autonomous, four-dimensional system), taking the amplitude of a sinusoidal external torque as the perturbation parameter. We change this parameter to stabilize one of the equilibrium points in the so-called Lorenz map. The main advantage of the method proposed here is that it can be implemented directly from time series data, irrespective of the overall dimension of the phase space. Also, reconstructions of the attractor based on the measurements are shown, as well as some experimental results of the controlled system.
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