Observer Design Method Research Articles

Observers and Feedback Control for a Rotating Vortex Pair

An observer is developed to estimate and to feedback-regulate the location of the vorticity centroid and the mutual distance of an interacting, same sign vortex pair. The combination of the crude approximation provided by very low-order vortex models, and high nonlinearity, even at that level, seem to make sensitive gain scheduling and high-order vector field derivatives in geometrical observer design methods, ill suited for the system at hand. This paper explores possibilities for dynamic extraction of needed information directly from leading frequencies and phasors of a sensor signal, using an extended Kalman filter. Intended advantages include simplicity, robustness, and the filtering of unmodeled dynamics.

Stress, instability and design of underground excavations

When the stress-induced risks to a projects warrant it, in situ stress must be measured. However, as the stress-induced risks increase, i.e., the stress magnitudes approach the rock mass strength , the confidence in commonly used stress measurement techniques decrease. The design of underground openings at depth requires knowledge of the in situ stress state, yet it is for these design conditions where our confidence in stress measurement techniques is at its lowest. To quantify the stress state for these conditions, elements of the Observational Design Method have to be used. These elements rely on the development of a geological site model, documented observations of over stressed rock in pillars or near the boundary of underground openings, and iterative two- and three-dimensional numerical modelling calibrated with observations. Examples are provided to illustrate how the philosophy of Observational Design Method can be used to infer the in situ stress state.

An intrinsic observer for a class of lagrangian systems

We propose a new design method of asymptotic observers for a class of nonlinear mechanical systems: Lagrangian systems with configuration (position) measurements. Our main contribution is to introduce a state (position and velocity) observer that is invariant under any changes of the configuration coordinates. The observer dynamics equations, as the Euler-Lagrange equations, are intrinsic. The design method uses the Riemannian structure defined by the kinetic energy on the configuration manifold. The local convergence is proved by showing that the Jacobian of the observer dynamics is negative definite (contraction) for a particular metric defined on the state-space, a metric derived from the kinetic energy and the observer gains. From a practical point of view, such intrinsic observers can be approximated, when the estimated configuration is close to the true one, by an explicit set of differential equations involving the Riemannian curvature tensor. These equations can be automatically generated via symbolic differentiations of the metric and potential up to order two. Numerical simulations for the ball and beam system, an example where the scalar curvature is always negative, show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics.

미지의 시간지연을 갖는 비선형 시스템의 이산시간 퍼지 출력 궤환 제어

A new discrete-time fuzzy output feedback control method for nonlinear systems with unknown time-delay is proposed. Ma et al. proposed an analysis and design method of fuzzy controller and observer and Cao et al. extend this result to be applicable fir the nonlinear systems with known time-delay. For the case of unknown time-delay, we derive the sufficient condition f3r the asymptotic stability of the equilibrium Point by applying Lyapunov-Krasovskii theorem and convert this condition into the LMI problem.

A discrete-time design and analysis of perturbation observer for motion control applications

A discrete perturbation observer (DPO) is suggested in state-space form for motion control applications. In existing disturbance observer design methods, the low-pass filter (so-called Q-filter) is central. However, the effect of the Q-filter on performance and robustness has not been clarified, specifically in the discrete-time domain. Considering the discrete Q-filter, with general order and inertia perturbations as a structured model uncertainty, we clarify how the performance and robustness of the perturbation observer are changed according to the variation of the Q-filter parameters and model parameter (i.e., inertia) perturbations in discrete control systems. Experimental results show the validity of the analysis and the effectiveness of the DPO.

Nonlinear discrete-time observer design with linearizable error dynamics

A necessary and sufficient condition for the existence of a discrete-time nonlinear observer with linearizable error dynamics is provided. The result can be applied to any real analytic nonlinear system whose linear part is observable. The necessary and sufficient condition is the solvability of a nonlinear functional equation. Furthermore, the well-known Siegel's theorem on the linearizability of a mapping is naturally reproduced in a corollary. The proposed observer design method is constructive and can be applied approximately to any sufficiently smooth, linearly observable system yielding a local observer with approximately linear error dynamics.

Computation of Controllability and Observability Matrices – Duality and Automatic Differentiation

AbstractDuring the last decades, many new methods for controller and observer design for nonlinear state‐space systems have been developed. Several of these design methods require Lie derivaties and Lie brackets. These derivatives are also needed to compute controllability and observability matrices of nonlinear systems. Up to now, these derivatives have been computed symbolically. An alternative approach based on automatic differentiation is presented.

Position Sensorless Control of PM Motor Using Adaptive Observer on Rotational Coordinate

Position sensorless control system using adaptive observer of PM motor was developed.But the adaptive observer design method of PM motor suggested already has problem in a characteristic at a high-speed region.This paper gives a design method of the adaptive observer to solve this problem.In addition, this paper suggests technique to transform the adaptive observer of PM motor on a standstill coordinate into the observer on a rotational coordinate.Finally, we can confirm by an experiment thatproposed method shows good characteristics.

Locally Convergent Nonlinear Observers

We introduce a new method for the design of observers for nonlinear systems using backstepping. The method is applicable to a class of nonlinear systems slighter larger than those treated by Gauthier, Hammouri, and Othman [IEEE Trans. Automat. Control, 27 (1992), pp. 875--880]. They presented an observer design method that is globally convergent using high gain. In contrast to theirs, our observer is not high gain, but it is only locally convergent. If the initial estimation error is not too large, then the estimation error goes to zero exponentially. A design algorithm is presented.

A note on observers for Lipschitz nonlinear systems

This note deals with the design of reduced-order observers for Lipschitz nonlinear systems. It shows that the conditions under which a full-order observer exists also guarantee the existence of a reduced-order observer. A design method of the reduced-order observer that is dependent on the solution of the Riccati equation is then presented and an example is given to illustrate effects of the design method.

Unknown input observers designed by eigenstructure assignment

A simple and direct method for full-order unknown input observer design is proposed. The procedure is straightforward and no further complex conditions are needed, provided that the solutions exist. The solutions for the observer matrices and for the eigenvectors are represented in parametric forms. Owing to the parametric forms of the solutions, more properties of the observer such as robustness, eigenvalue sensitivity and minimum gain can be considered. The existence condition of the observer is also established.

Unknown Input Observers Designed by Eigenstructure Assignment

A simple and direct method for full-order unknown input observer design is proposed. The procedure is straightforward and no further complex conditions are needed, provided that the solutions exist. The solutions for the observer matrices and for the eigenvectors are represented in parametric forms. Owing to the parametric forms of the solutions, more properties of the observer such as robustness, eigenvalue sensitivity and minimum gain can be considered. The existence condition of the observer is also established.

Observers for Takagi-Sugeno fuzzy systems

We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.

NONLINEAR OBSERVER FOR TAIL-CONTROLLED SKID-TO-TURN MISSILES

This paper presents a nonlinear observer design method for acceleration control of tail-controlled Skid-to-Turn missiles. A nonlinear observer for wind angles (angle of attack and sideslip angle) is designed using a parametric affine missile model developed by the authors. Using the estimated wind angles, a desired acceleration tracking performance can be obtained by a nonlinear control based on a parametric affine missile model. The performance and stability of the proposed observer are analyzed. Simulation results are also included to show that the proposed approach can give a satisfactory performance for missile dynamics.

Design Method of Robust Full-Order Observer to Suppress Axis Deviation for Vector Controlled Induction Motor using γ Positive Real Problem and Gain Scheduled <i>H</i><sub>∞</sub> Control

This paper proposes a novel robust design method of the full-order observer for vector controlled induction motors. The full-order observer has been widely employed to estimate rotor flux, but pole location for robust flux estimation against parameter deviations has not been clear unfortunately.In this paper, robust flux estimation problem is regarded as a phase shaping problem of a transfer function because it is the most important for the vector control to suppress axis deviation. Accordingly, the proposed design method utilizes γ-positive real problem, gain-scheduled H∞ control and linear matrix inequality technique so that axis deviation might be suppressed against parameter deviations at all operating point. Robust performance of the proposed method is evaluated by the frequency response function. Finally, feasibility and effectiveness of the proposed method are shown by experimental results.

On the Design of Robust Disturbance Observers for Mechatronic Systems

High speed and high accuracy mechanical systems pose an increasing demand on the control systems to eliminate the influence of disturbances like cogging and friction. One way to incorporate additional disturbance rejection for linear systems is to extend the controller with a disturbance observer. By virtue of the separation property, the disturbance observer and the controller can be designed separately.In this paper, an overview is given of choices to be made to design a disturbance observer, and the consequences of every step are discussed. It follows that, despite the separation property, knowledge about the feedback controller is needed to design the disturbance observer (and vice versa), in order to guarantee robust stability. Existing disturbance observer design techniques are extended to account for model uncertainty. Experimental results on a linear permanent magnet motor demonstrate the effectiveness and robustness of the disturbance observer design method.

Well-Conditioned Observer Design for Two-Output Systems.

It was shown that the robustness of deterministic observers with respect to modeling errors, measurement bias and round-off errors can be represented by a single performance index, x 2 (P), the condition number of the observer eigenvector matrix. In this paper, based on the performance index, a robust observer design method is proposed for two-output systems where the observer gain can not be determined uniquely with respect to the desired observer poles. Utilizing the pole/zero locations of the observer dynamics, a step-by-step design procedure of the well-conditioned observer is developed. In addition, a new scaling method is developed with employing the eigenvector matrix as a scaling matrix. The proposed method is evaluated and compared with the Kalman filter technique in a spindle-drive simulation example where the load speed needs to be estimated based on the measured signals.

Multirate nonlinear state estimation with application to a polymerization reactor

AbstractA method of multirate nonlinear state observer design, which can use directly a nonlinear process model in the observer design without any linear approximation, is presented. The multirate nonlinear state observer is easy to design and implement, and is computationally efficient. Furthermore, for a number of processes, it is possible to prove the global convergence of the multirate state observer analytically. The design, implementation and performance of the state observer design method are shown by a polymerization reactor in which free‐radical solution polymerization of styrene takes place. The initiator concentration and three leading moments of the molecular weight distribution (MWD) of the polymer product are estimated continuously from: (i) frequent measurements of the reactor temperature, jacket temperature and reacting‐mixture density; (ii) infrequent and delayed measurements of the leading moments of the MWD. Each infrequent measurement has a sampling period and a measurement delay of 0.5 or 1 h. In the presence of model‐plant mismatch and measurement noise, the convergence of the multirate state observer is shown by numerical simulations.

Servo Control of Unstable-wheeled System by Using Virtual Disturbance Torque Observer and its Feedback Compensation.

In this paper, we are concerned with the servo control for a unstable-wheeled system by using virtual disturbance torque observer and its feedback compensation. We consider that unstable behavior of the monowheeled system because of one supported point body is caused by the virtual disturbance torque. For this purpose, this paper proposes a design method of disturbance observer for such virtual disturbance torque in feedback loop and evaluates its effectiveness by experiment. In disturbance observer, ordinary 2nd-order low pass filter for noise attenuation is insufficient to stabilize the whole wheeled system, so more high order filter is designed by H ∞ loop shaping method in view point of the regulator specifications. And the servo controller for the closed loop system including such H ∞ high order filter is also designed by satisfying an H ∞ norm condition.

Realization of Robust Vector Control System using Flux Observer and its Performance Evaluation

A new design method of the flux observer for the vector control is proposed in this paper. The newly designed observer estimates the flux within predetermined flux angle deviations. The characteristics are studied by Frequency Response Function (FRF) and the proposed designed method is shown to realize robust flux estimations. Then, the proposed observer is compared with the adaptive identifier, and they are shown to compensate with each other. Moreover, the proposed designed method is implemented in the vector control system and is shown feasible experimentally.