Gildas Besancon

Technical communique: A note on state and parameter estimation in a van der Pol oscillator

An exact observer approach for simultaneous state and parameter estimation is proposed for the well-known van der Pol oscillator. The approach is based on an appropriate state space representation-using the so-called Lienard transformation-allowing for an exact Kalman-like observer design. The stability is then formally checked relying on the natural oscillatory behaviour of the system, and the corresponding results are illustrated in simulation.

Original article: Exponential nonlinear observer for parametric identification and synchronization of chaotic systems

This work proposes the use of a new exponential nonlinear observer for the purpose of parametric identification and synchronization of chaotic systems. The exponential convergence of the observer is guaranteed by a persistent excitation condition. This approach is shown to be suitable for a wide variety of chaotic systems. In order to illustrate the observer design procedure, several examples with simulation results are presented.

EKF-Like Observer With Stability for a Class of Nonlinear Systems

An Extended-Kalman-Filter (EKF)-like observer is derived from a former observer result for a class of nonlinear systems, which can be written as a linear part in the unmeasured states on the one hand, and some additive nonlinearity with a triangular Jacobian on the other hand. It is shown how the previously presented excitation condition for exponential stability of the observer, extends to this EKF version. The observer is illustrated in simulation with two challenging examples, the first one in leak detection, and the second one in chaos synchronization.

Calibration of Fitting Loss Coefficients for modelling purpose of a plastic pipeline

Motivated by the sensitivity of model-based monitoring algorithms to the so-called Equivalent Straight Length (ESL) of a pipeline, this paper proposes an experiment-based calibration of this parameter and also for the values of the Fitting Loss Coefficients (FLC). This comes as an alternative to achieve a better description of the real flow behavior in a pipeline than the modelling obtained by using the FLC from the manufacturer data-sheet. The proposed calibration method relies on a flow modelling, and Kalman observer-based estimation of the FLC of a pipeline. The friction coefficient in the model is estimated by the explicit so-called Swamee-Jain equation. The approach only assumes sensors of flow and pressure at the ends of the duct. Experimental results are presented.

State and parameter estimation in 1-D hyperbolic PDEs based on an adjoint method

An optimal estimation method for state and distributed parameters in 1-D hyperbolic system based on adjoint method is proposed in this paper. A general form of the partial differential equations governing the dynamics of system is first introduced. In this equation, the initial condition or state variable as well as some empirical parameters are supposed to be unknown and need to be estimated. The Lagrangian multiplier method is used to connect the dynamics of the system and the cost function defined as the least square error between the simulation values and the measurements. The adjoint state method is applied to the objective functional in order to get the adjoint system and the gradients with respect to parameters and initial state. The objective functional is minimized by Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Due to the non-linearity of both direct and adjoint system, the nonlinear explicit Lax-Wendroff scheme is used to solve them numerically. The presented optimal estimation approach is validated by two illustrative examples, the first one about state and parameter estimation in a traffic flow, and the second one in an overland flow system.

An LQG/LTR approach towards piezoactuator vibration reduction with observer-based hysteresis compensation

Abstract This paper presents a SISO robust control of some lightly damped micro/nano-positioning system equipped with a piezoactuator. The adverse phenomenon of nonlinear hysteresis in the actuator is first compensated using an observer-based approach. Then an LQG/LTR method is proposed to additionally reduce vibrations affecting the system in a higher frequency range. Illustrative experimental results show a significant improvement of the closed-loop system behaviour with respect to the open-loop one.

Decentralized-coordinated model predictive control for a hydro-power valley

This paper aims at improving control systems for hydro-power production, by combining model predictive control techniques with decomposition-coordination methods for a global optimization over a whole hydro-power valley. It first recalls the model predictive control formulation for a centralized solution presented as the reference for comparison, and emphasizes the possible use of explicit solutions in the considered problem, making easier its practical use. It then highlights the further interest of such solutions in a decomposition-coordination approach, allowing to reduce the computational cost even more with a purpose of real-time implementation, and at the same time to take advantage of the distributed nature of the considered system. The results are illustrated on the basis of a real-data-based case-study provided by EDF group.

Observer-based parameter estimation in Liénard systems

Abstract A general excitation condition is provided for parameter identification in so-called Lienard second order nonlinear systems. This condition allows a quite simple observer design for asymptotic state and parameter estimation. Such a condition has already been very recently shown to be satisfied for Van der Pol ocillators Besancon et al. (2010), and is further checked here for nonlinear pendulum equations, for which illustrative simulation results are provided.

Control-Based Strategy for Effective Wind Speed Estimation in Wind Turbines

Abstract This paper deals with a control-based observer structure used for effective wind speed estimation in a wind turbine operating in partial load. The central idea is that this input estimation can be achieved based on system output tracking using a high-gain control loop. One of the consequences is that the system entire state estimation can also be performed. The resulted observer is simple and easy to tune. Numerical simulations show that effective wind speed is reconstructed with a good dynamic, thus being able to replace anemometer information for diagnosis and output power assessment purposes. The basic idea of this paper is quite general, as it can be applied to a large class of systems having unknown inputs.

Modeling and Identification of the Restoring Force of a Marine Riser

The purpose of this paper is to provide a novel model to characterize the nonlinear restoring force of a marine vertical riser by using position-and-velocity-dependent polynomials. This model permits the obtaining of a specific state space representation—via the Lienard transformation—for the design of state observers that identify the structural parameters of vertical risers. The main results presented here are: (i) an approximation of the nonlinear restoring force by means of polynomials and its incorporation into a distributed parameter (DP) model, (ii) the transformation of the DP model into a Lienard system and (iii) an analysis of its observability and identifiability properties.