Non-linear Optimal Filter and Control with Tracking vs Pid Applied to an Electric Resistance System

Author(s):  
Maria Aracelia Alcorta-Garcia ◽  
Mirna Maricela Martinez-Flores ◽  
Santos Mendez-Diaz ◽  
Efrain Alcorta-Garcia ◽  
Luis Arturo Valdez Hinojosa
Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2092
Author(s):  
Simone Fiori

The aim of the present tutorial paper is to recall notions from manifold calculus and to illustrate how these tools prove useful in describing system-theoretic properties. Special emphasis is put on embedded manifold calculus (which is coordinate-free and relies on the embedding of a manifold into a larger ambient space). In addition, we also consider the control of non-linear systems whose states belong to curved manifolds. As a case study, synchronization of non-linear systems by feedback control on smooth manifolds (including Lie groups) is surveyed. Special emphasis is also put on numerical methods to simulate non-linear control systems on curved manifolds. The present tutorial is meant to cover a portion of the mentioned topics, such as first-order systems, but it does not cover topics such as covariant derivation and second-order dynamical systems, which will be covered in a subsequent tutorial paper.


2016 ◽  
Vol 40 (3) ◽  
pp. 918-929 ◽  
Author(s):  
A Manonmani ◽  
T Thyagarajan ◽  
M Elango ◽  
S Sutha

A greenhouse system (GHS) is a closed structure that facilitates modified growth conditions to crops and provides protection from pests, diseases and adverse weather. However, a GHS exhibits non-linearity due to the interaction between the biological subsystem and the physical subsystem. Non-linear systems are difficult to control, particularly when their characteristics change with time. These systems are best handled with methods of computation intelligence, such as artificial neural networks (ANNs) and fuzzy systems. In the present work, the approximation capability of a neural network is used to model and control sufficient growth conditions of a GHS. An optimal neural network-based non-linear auto regressive with exogenous input (NARX) time series model is developed for a GHS. Based on the NARX model, two intelligent control schemes, namely a neural predictive controller (NPC) and non-linear auto regressive moving average (NARMA-L2) controller are proposed to achieve the desired growth conditions such as humidity and temperature for a better yield. Finally, closed-loop performances of the above two control schemes for servo and regulatory operations are analysed for various operating conditions using performance indices.


Author(s):  
A. S. White

This chapter examines the established Systems Dynamics (SD) methods applied to software projects in order to simplify them. These methods are highly non-linear and contain large numbers of variables and built-in decisions. A SIMULINK version of an SD model is used here and conclusions are made with respect to the initial main controlling factors, compared to a NASA project. Control System methods are used to evaluate the critical features of the SD models. The eigenvalues of the linearised system indicate that the important factors are the hiring delay time, the assimilation time, and the employment time. This illustrates how the initial state of the system is at best neutrally stable with control only being achieved with complex non-linear decisions. The purpose is to compare the simplest SD and control models available required for “good” simulation of project behaviour with the Abdel-Hamid software project model. These models give clues to the decision structures that are necessary for good agreement with reality. The final simplified model, with five states, is a good match for the prime states of the Abdel-Hamid model, the NASA data, and compares favourably to the Ruiz model. The linear control system model has a much simpler structure, with the same limitations. Both the simple SD and control models are more suited to preliminary estimates of project performance.


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