H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Copyright @ 2012 John Wiley & SonsIn this paper, the H ∞  sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞  performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov–Krasovskii functional based on the idea of ‘delay fractioning’ and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme

Sliding mode adaptive state observation for time-delay uncertain nonlinear systems

In this paper a method to design robust adaptive sliding mode observers (ASMO) for a class of nonlinear time- delay systems with uncertainties, is proposed. The objective is to achieve insensitivity and robustness of the proposed sliding mode observer to matched disturbances. A novel systematic design method is synthesized to solve matching conditions and compute observer stabilizing gains. The Lyapunov-Krasovskii theorem is employed to prove the ultimate stability with arbitrary boundedness radius of the estimation error of the proposed filter. Finally, the ability of ASMO for fault reconstruction is studied

Sampled-data sliding mode observer for robust fault reconstruction: A time-delay approach

A sliding mode observer in the presence of sampled output information and its application to robust fault reconstruction is studied. The observer is designed by using the delayed continuous-time representation of the sampled-data system, for which sufficient conditions are given in the form of linear matrix inequalities (LMIs) to guarantee the ultimate boundedness of the error dynamics. Though an ideal sliding motion cannot be achieved in the observer when the outputs are sampled, ultimately bounded solutions can be obtained provided the sampling frequency is fast enough. The bound on the solution is proportional to the sampling interval and the magnitude of the switching gain. The proposed observer design is applied to the problem of fault reconstruction under sampled outputs and system uncertainties. It is shown that actuator or sensor faults can be reconstructed reliably from the output error dynamics. An example of observer design for an inverted pendulum system is used to demonstrate the merit of the proposed methodology compared to existing sliding mode observer design approaches

Delay compensation for nonlinear teleoperators using predictor observers

This paper presents a delay compensation technique for nonlinear teleoperators by developing a predictor type sliding mode observer (SMO) that estimates future states of the slave operator. Predicted states are then used in control formulation. In the proposed scheme, disturbance observers (DOB) are also utilized to linearize nonlinear dynamics of the master and slave operators. It is shown that utilization of disturbance observers and predictor observer allow simple PD controllers to be used to provide stable position tracking for bilateral teleoperation. Proposed approach is verified with simulations where it is compared with two state-of-the-art methods. Successful experimental results with a bilateral teleoperation system consisting of a pair of pantograph robots also validates the proposed method

A Sliding Mode Control for a Sensorless Tracker: Application on a Photovoltaic System

The photovoltaic sun tracker allows us to increase the energy production. The sun tracker considered in this study has two degrees of freedom (2-DOF) and especially specified by the lack of sensors. In this way, the tracker will have as a set point the sun position at every second during the day for a period of five years. After sunset, the tracker goes back to the initial position (which of sunrise). The sliding mode control (SMC) will be applied to ensure at best the tracking mechanism and, in another hand, the sliding mode observer will replace the velocity sensor which suffers from a lot of measurement disturbances. Experimental measurements show that this autonomic dual axis Sun Tracker increases the power production by over 40%

Interpreting Quantum Mechanics in Terms of Random Discontinuous Motion of Particles

This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity

Interval observers for continuous-time linear systems

International audienceWe consider continuous-time linear systems with additive disturbances and discrete-time measurements. First, we construct an observer, which converges to the state trajectory of the linear system when the maximum time interval between two consecutive measurements is sufficiently small and there are no disturbances. Second, we construct interval observers allowing to determine, for any solution, a set that is guaranteed to contain the actual state of the system when bounded disturbances are present