Online exact differentiation and notion of asymptotic algebraic observers

In recent years, the availability of computer-based methods has created a revival of interests in exploring algebraic methods in nonlinear context. This paper proposes a new approach to algebraic nonlinear observer design. After giving the notion of algebraic observability, and based on a novel algorithm of exact differentiation, the formulation of the nonlinear observer is realized via the construction of a set of linear time-varying differentiators. An example of a chemical reaction is given to show the effectiveness of our approach.     

Observer design for discrete-time systems subject to time-delay nonlinearities

In this paper, we address the problem of designing nonlinear observers for dynamical discrete-time systems with both constant and time-varying delay nonlinearities. The nonlinear system is assumed to verify the usual Lipschitz condition that permits us to transform the nonlinear system into a linear time-delay system with structured uncertainties. The existence of the observer-gain is ensured by the solution of a one linear matrix inequality. An illustrative example is included to demonstrate the advantage of the proposed observation technique.     

Circle-criterion approach to discrete-time nonlinear observer design

This paper addresses the design of discrete-time nonlinear observers through the circle criterion. The new design method is mainly devoted to either globally Lipschitz systems or bounded-state systems whose nonlinearities can be decomposed into a linear combination of positive-slope nonlinearities. The observer design is not restricted to systems with positive-slope nonlinearities, but it encompasses systems with non-positive-slope nonlinearities too. Stability conditions of the observation error are given in terms of numerically tractable linear matrix inequalities. Illustrative examples are presented in order to highlight the main features and advantages of the new proposed technique over some classical designs.     

Linear time-derivative trackers

The design of an ideal differentiator is a difficult and a challenging task. In this paper we discuss the properties and the limitations of two different structures of linear differentiation systems. The first time-derivative observer is formulated as a high-gain observer where the observer gain is calculated through a Lyapunov-like dynamical equation. The second one is given in Brunovski form in which the output to be differentiated appears as a control input and the differentiation gain is calculated from the dual Lyapunov equation of the first differentiation observer. A discrete-time version of the second form is given. Finally, illustrative examples are presented to show their strengths and weaknesses.     

On observer design for nonlinear systems

The main weakness of all control methodologies is the dependency of feedbacks to full state measurements. In practical situations, measuring the states of a given system may fail because sometimes the measurements are impossible and sometimes, possible, but too expensive. Observer design for highly nonlinear dynamics is an important issue, particularly when the locally observable dynamics are not linearly observable. In such circumstances the ability to reduce the system to observable or observer form is key to observer design. This paper provides two observers for nonlinear systems given in Brunovski form. The first observer is a high-gain observer with a classical output injection form, while the second is a high-gain observer with a q-integral path. Finally, the discrete-time implementation of the high-gain observer is discussed in linear matrix inequality framework. A motivating example is shown to highlight the efficacy of the developed observers.     

Observer-based control of discrete-time Lipschitzian non-linear systems: application to one-link flexible joint robot

The problem of designing asymptotic observers along with observer-based feedbacks for a class of discrete-time non-linear systems is considered. We assume that the system non-linearity is globally Lipschitz and the system is supposed to be stabilizable by a linear controller. Sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states. A numerical example of a single-link flexible joint robot is presented to illustrate the efficacy of the theoretical developments.     

Observer-based control of a class of time-delay nonlinear systems having triangular structure

Time-delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering. It has been shown in the literature that the existence of a stabilizing observer-based controller is related to delay-dependent conditions that are generally satisfied for a small time delay. Motivating works towards reducing the conservatism of the results are among the on-going research topics especially when partial-state measurements are imposed. This paper investigates the problem of observer-based stabilization of a class of time-delay nonlinear systems written in triangular form. First, we show that a delay nonlinear observer is globally convergent under the global Lipschitz condition of the system nonlinearity. Then, it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay. An illustrative example is provided to approve the theoretical results.     

Adaptive and Robust Stabilization of Feedforward Nonlinear Systems Driven by Symmetric and Non‐symmetric Dead‐zone Inputs

The stabilization of feedforward nonlinear systems subject to hard‐input nonlinearities is a challenging problem due to the presence of input uncertainties. This paper deals with adaptive control of a class of feedforward nonlinear systems driven by unknown dead‐zone inputs. The unknown dead‐zone input nonlinearity is assumed to be either symmetric or non‐symmetric. The control design is based on the combination of the invariant‐manifold stabilization technique with the classical adaptive and robust compensation methods. Simulation results showed that the presence of the dead‐zone inputs in the system dynamics can be handled even for arbitrary large dead‐zone parameters.     

Microstructure and magnetic properties of HVOF thermally sprayed Fe75Si15B10 coatings

Partially amorphous Fe₇₅Si₁₅B₁₀ coatings were prepared from nanostructured feedstock powders by using high velocity oxy-fuel spraying. Scanning electron microscopy, X-ray diffraction, Vickers indenter and magnetic measurements were used to investigate microstructural, structural, microhardness and magnetic properties of the coatings. The Rietveld refinement of the X-ray diffraction patterns reveals the presence of an amorphous phase, nanocrystalline α-Fe(Si,B) structure having a lattice parameter close to 0.2841 nm and an average crystallite size of about 78-83 nm in addition to small amounts of Fe₃O₄ oxide (104 nm) and Fe₂B boride (151 nm), which disappear completely with increasing coating thickness. Coercivity and microhardness values are 15.5 Oe and 478 Hv, respectively, for 84 μm thickness.