Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph

Motivated by the need of observers that are both robust to disturbances and guarantee fast convergence to zero of the estimation error, we propose an observer for linear time-invariant systems with noisy output that consists of the combination of N coupled observers over a connectivity graph. At each node of the graph, the output of these interconnected observers is defined as the average of the estimates obtained using local information. The convergence rate and the robustness to measurement noise of the proposed observer's output are characterized in terms of $\mathcal{KL}$ bounds. Several optimization problems are formulated to design the proposed observer so as to satisfy a given rate of convergence specification while minimizing the $H_\infty$ gain from noise to estimates or the size of the connectivity graph. It is shown that that the interconnected observers relax the well-known tradeoff between rate of convergence and noise amplification, which is a property attributed to the proposed innovation term that, over the graph, couples the estimates between the individual observers. Sufficient conditions involving information of the plant only, assuring that the estimate obtained at each node of the graph outperforms the one obtained with a single, standard Luenberger observer are given. The results are illustrated in several examples throughout the paper.Comment: The technical report accompanying "Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph" to be published in IEEE Transactions on Control of Network Systems, 201

GA-tuning of nonlinear observers for sensorless control of automotive power steering IPMSMs

The paper considers two observer-based rotor position estimation schemes for sensorless control of interior permanent magnet synchronous motors (IPMSMs) for use in future automotive power steering systems. Specifically, emphasis is given to techniques based on feedback-linearisation followed by classical Luenberger observer design, and direct design of non-linear observers. Genetic algorithms (GAs), using the principles of evolution, natural selection and genetic mutation, are introduced to address difficulties in selecting correction gains for the observers, since no analytical tuning mechanisms yet exist. Experimental measurements from an automotive power steering test-facility are included, to demonstrate the enhanced performance attributes offered by tuning the proposed observer schemes, online, in this manner

Nonlinear state-observer techniques for sensorless control of automotive PMSM's, including load-torque estimation and saliency

The paper investigates various non-linear observer-based rotor position estimation schemes for sensorless control of permanent magnet synchronous motors (PMSMs). Attributes of particular importance to the application of brushless motors in the automotive sector, are considered e.g. implementation cost, accuracy of predictions during load transients, the impact of motor saliency and algorithm complexity. Emphasis is given to techniques based on model linearisation during each sampling period (EKF); feedback-linearisation followed by Luenberger observer design based on the resulting �linear� motor characteristics; and direct design of non-linear observers. Although the benefits of sensorless commutation of PMSMs have been well expounded in the literature, an integrated approach to their design for application to salient machines subject to load torque transients remains outstanding. Furthermore, this paper shows that the inherent characteristics of some non-linear observer structures are particularly attractive since they provide a phase-locked-loop (PLL)-type of configuration that can encourage stable rotor position estimation, thereby enhancing the overall sensorless scheme. Moreover, experimental results show how operation through, and from, zero speed, is readily obtainable. Experimental results are also employed to demonstrate the attributes of each methodology, and provide dynamic and computational performance comparisons

GA-based tuning of nonlinear observers for sensorless control of IPMSMs

The paper considers two observer-based rotor position estimation schemes for sensorless control of interior permanent magnet synchronous machines (IPMSMs). Emphasis is given to techniques based on feedback linearisation followed by Luenberger observer design, and direct design of nonlinear observers. Genetic algorithms (GAs) based on the principles of evolution, natural selection and genetic mutation are employed to address difficulties in selecting correction gains for the observers, since no analytical tuning mechanisms yet exist, with results included to demonstrate the enhanced performance attributes offered by observers tuned in this way

On the Existence of a Kazantzis-Kravaris/Luenberger Observer

We state sufficient conditions for the existence, on a given open set, of the extension, to nonlinear systems, of the Luenberger observer as it has been proposed by Kazantzis and Kravaris. We prove it is sufficient to choose the dimension of the system, giving the observer, less than or equal to 2 + twice the dimension of the state to be observed. We show that it is sufficient to know only an approximation of the solution of a PDE, needed for the implementation. We establish a link with high gain observers. Finally we extend our results to systems satisfying an unboundedness observability property

A robust asymptotic observer for systems that converge to unobservable states. A batch reactor case study

International audienceIn this paper we propose an observer for a dynam-ical system for which the states on the frontier of its domain are not observable, and all trajectories converge to the frontier. The proposed case study, a bioreactor in batch operating conditions with a single microbial reaction and gas production, is standard and largely encountered in practical situations. We show also how to extend this observer to obtain an observer in higher dimension that is robust with respect to unbiased noise