On The Design of a Novel Finite-Time Nonlinear Extended State Observer for Class of Nonlinear Systems with Mismatch Disturbances and Uncertainties

In this paper, a novel finite - time Nonlinear Extended State Observer (NLESO) is proposed and employed in Active Disturbance Rejection Control (ADRC) to stabilize a nonlinear system against system's uncertainties and discontinuous disturbances using output feedback technique. The first task was to aggregate the uncertainties, disturbances, and any other undesired nonlinearities in the system into a single term called the "generalized disturbance". Consequently, the ESO estimates the generalized disturbance and cancel it from the input channel in an online fashion. A peaking phenomenon that existed in Linear ESO (LESO) has been reduced significantly by adopting a saturation - like nonlinear function in the proposed Nonlinear ESO (NLESO). Stability analysis of the NLEO is studied using finite - time Lyapunov theory, and the comparisons are presented over simulations on Permanent Magnet DC (PMDC) motor to confirm the effectiveness of the proposed observer concerning LESO

Nonlinear PID Controller Design for a 6-DOF UAV Quadrotor System

A Nonlinear PID (NLPID) controller is proposed to stabilize the translational and rotational motion of a 6-DOF UAV quadrotor system and enforce it to track a given trajectory with minimum energy and error. The complete nonlinear model of the 6-DOF quadrotor system are obtained using Euler-Newton formalism and used in the design process, taking into account the velocity and acceleration vectors resulting in a more accurate 6-DOF quadrotor model and closer to the actual system. Six NLPID controllers are designed, each for Roll, Pitch, Yaw, Altitude, and the Position subsystems, where their parameters are tuned using GA to minimize a multi-objective Output Performance Index (OPI). The stability of the 6-DOF UAV subsystems has been analyzed in the sense of Hurwitz stability theorem under certain conditions on the gains of the NLPID controllers. The simulations have been accomplished under MATLAB/SIMULINK environment and included three different trajectories, i.e., circular, helical, and square. The proposed NLPID controller for each of the six subsystems of the 6-DOF UAV quadrotor system has been compared with the Linear PID (LPID) one and the simulations showed the effectiveness of the proposed NLPID controller in terms of speed, control energy, and steady-state error

On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design

This paper presents a new improved nonlinear tracking differentiator (INTD) with hyperbolic tangent function in the state space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. the INTD has the required filtering features and can cope with th nonlinearities caused by the niose. Through simulations, the INTD is implemented as signal derivative generator for the closed loop feedback control system with a nolinear PID controller for the nonlinear Mass Spring Damper system and showed that it could achieve the signal tracking and differentiation faster with a minimum mean square error

A Novel Second-Order Nonlinear Differentiator With Application to Active Disturbance Rejection Control

A Second-order Nonlinear Differentiator (SOND) is presented in this paper. By combining both linear and nonlinear terms, this tracking differentiator shows better dynamical performances than other conventional differentiators do. The hyperbolic tangent tanh(.) function is introduced due to two reasons; firstly, the high slope of the continuous tanh(.) function near the origin significantly accelerates the convergence of the proposed tracking differentiator and reduces the chattering phenomenon. Secondly, the saturation feature of the function due to its nonlinearity increases the robustness against the noise components in the signal. The stability of the suggested tracking differentiator is proven based on the Lyapunov analysis. In addition, a frequency-based analysis is applied to investigate the dynamical performances. The performance of the proposed tracking differentiator has been tested in active disturbance rejection control (ADRC) paradigm, which is a recent robust control technique. The numerical simulations emphasize the expected improvements

Model-Free Active Input-Output Feedback Linearization of a Single-Link Flexible Joint Manipulator: An Improved ADRC Approach

Traditional Input-Output Feedback Linearization (IOFL) requires full knowledge of system dynamics and assumes no disturbance at the input channel and no system's uncertainties. In this paper, a model-free Active Input-Output Feedback Linearization (AIOFL) technique based on an Improved Active Disturbance Rejection Control (IADRC) paradigm is proposed to design feedback linearization control law for a generalized nonlinear system with known relative degree. The Linearization Control Law(LCL) is composed of a scaled generalized disturbance estimated by an Improved Nonlinear Extended State Observer (INLESO) with saturation-like behavior and the nominal control law produced by an Improved Nonlinear State Error Feedback (INLSEF). The proposed AIOFL cancels in real-time fashion the generalized disturbances which represent all the unwanted dynamics, exogenous disturbances, and system uncertainties and transforms the system into a chain of integrators up to the relative degree of the system, the only information required about the nonlinear system. Stability analysis has been conducted based on Lyapunov functions and revealed the convergence of the INLESO and the asymptotic stability of the closed-loop system. Verification of the outcomes has been achieved by applying the proposed AIOFL technique on the Flexible Joint Single Link Manipulator (SLFJM). The simulations results validated the effectiveness of the proposed AIOFL tool based on IADRC as compared to the conventional ADRC based AIOFL and the traditional IOFL techniques

Modeling and Correspondence of Topologically Complex 3D Shapes

3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of detailed shapes. This report surveys different approaches of shape modeling and correspondence especially for shapes exhibiting topological complexity. We focus on methods designed to help generate or process shapes with large number of interconnected components often found in man-made shapes. We first discuss a variety of modeling techniques, that leverage existing shapes, in easy to use creative modeling systems. We then discuss possible correspondence strategies for topologically different shapes as it is a requirement for such systems. Finally, we look at different shape representations and tools that facilitate the modification of shape topology and we focus on those particularly useful in free-form 3D modeling

Compact Shape Trees: A Contribution to the Forest of Shape Correspondences and Matching Methods

We propose a novel technique, termed compact shape trees, for computing correspondences of single-boundary 2-D shapes in O(n2) time. Together with zero or more features defined at each of n sample points on the shape's boundary, the compact shape tree of a shape comprises the O(n) collection of vectors emanating from any of the sample points on the shape's boundary to the rest of the sample points on the boundary. As it turns out, compact shape trees have a number of elegant properties both in the spatial and frequency domains. In particular, via a simple vector-algebraic argument, we show that the O(n) collection of vectors in a compact shape tree possesses at least the same discriminatory power as the O(n2) collection of lines emanating from each sample point to every other sample point on a shape's boundary. In addition, we describe neat approaches for achieving scale and rotation invariance with compact shape trees in the spatial domain; by viewing compact shape trees as aperiodic discrete signals, we also prove scale and rotation invariance properties for them in the Fourier domain. Towards these, along the way, using concepts from differential geometry and the Calculus, we propose a novel theory for sampling 2-D shape boundaries in a scale and rotation invariant manner. Finally, we propose a number of shape recognition experiments to test the efficacy of our concept

A Comparative Study of Single-Constraint Routing in Wireless Mesh Networks Using Different Dynamic Programming Algorithms

Finding the shortest route in wireless mesh networks is an important aspect. Many techniques are used to solve this problem like dynamic programming, evolutionary algorithms, weighted-sum techniques, and others. In this paper, we use dynamic programming techniques to find the shortest path in wireless mesh networks due to their generality, reduction of complexity and facilitation of numerical computation, simplicity in incorporating constraints, and their conformity to the stochastic nature of some problems. The routing problem is a multi-objective optimization problem with some constraints such as path capacity and end-to-end delay. Single-constraint routing problems and solutions using Dijkstra, Bellman- Ford, and Floyd-Warshall algorithms are proposed in this work with a discussion on the difference between them. These algorithms find the shortest route through finding the optimal rate between two nodes in the wireless networks but with bounded end-to-end delay. The Dijkstra-based algorithm is especially favorable in terms of processing time. We also present a comparison between our proposed single-constraint Dijkstra-based routing algorithm and the mesh routing algorithm (MRA) existing in the literature to clarify the merits of the former

Teleoperated Robotic Arm Movement Using EMG Signal With Wearable MYO Armband

The main purpose of this research is to move the robotic arm (5DoF) in real-time, based on the surface Electromyography (sEMG) signals, as obtained from the wireless Myo gesture armband to distinguish seven hand movements. The sEMG signals are biomedical signals that estimate and record the electrical signals produced in muscles through their contraction and relaxation, representing neuromuscular activities. Therefore, controlling the robotic arm via the muscles of the human arm using sEMG signals is considered to be one of the most significant methods. The wireless Myo gesture armband is used to record sEMG signals from the forearm. In order to analyze these signals, the pattern recognition system is employed, which consists of three main parts: segmentation, feature extraction, and classification. Overlap technique is chosen for segmenting part of the signal. Six time domain features (MAV, WL, RMS, AR, ZC, and SSC) are extracted from each segment. The classifiers (SVM, LDA, and KNN) are employed to enable comparison between them in order to obtain optimum accuracy of the system. The results show that the SVM achieves higher system accuracy at 96.57 %, compared to LDA reaching 96.01 %, and 92.67 % accuracy achieved by KNN

Correlation of Data Reconstruction Error and Shrinkages in Pair-wise Distances under Principal Component Analysis (PCA)

In this on-going work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding eigenvector rows is injective, but looses this injectivity when eigenvector rows are discarded 2). PCA without discarding eigen- vector rows preserves pair-wise distances, but tends to cause pair-wise distances to shrink when eigenvector rows are discarded. 3). For any pair of points, the shrinkage in pair-wise distance is bounded above by an L1 norm reconstruction error associated with the points. Clearly, 3). suggests that there might exist some correlation between shrinkages in pair-wise distances and mean square reconstruction error which is defined as the sum of those eigenvalues associated with the discarded eigenvectors. I therefore decided to perform numerical experiments to obtain the corre- lation between the sum of those eigenvalues and shrinkages in pair-wise distances. In addition, I have also performed some experiments to check respectively the effect of the sum of those eigenvalues and the effect of the shrinkages on classification accuracies under the PCA map. So far, I have obtained the following results on some publicly available data from the UCI Machine Learning Repository: 1). There seems to be a strong cor- relation between the sum of those eigenvalues associated with discarded eigenvectors and shrinkages in pair-wise distances. 2). Neither the sum of those eigenvalues nor pair-wise distances have any strong correlations with classification accuracies.