Minimal-order Observer Research Articles

Design of Observer for Linear Descriptor Systems

This paper is concerned with the problem of designing an observer for linear descriptor systems Ex = Ax + Bu, Y= Cx. At first, an observer is presupposed to have the same structure as Luenberger Observer, and the fundamental equations that the plant and the observer must satify are derived. Based on these equations, it is shown that an observer exists if the system is observable in the sense of Rosenbrock. And the design methods of an identity observer and a minimal-order observer are presented by utilizing the generalized matrix inverse. Secondly, the realizability condition is relaxed by eliminationg the purely static modes of the system, and it is shown that the observer can be realized if the system is observable in the sense of Verghese.

Observer Synthesis by Eigenstructure Assignment – An Application to "Loop Transfer Recovery"

In this paper we give, in an eigenstructure assignment setting, a geometric approach to the synthesis of observers. This formulation allows to exhibit all the degrees of freedom and to give them a physical meaning. The problem of exact loop transfer recovery by mean of observers, more specifically by mean of minimal order observers, is then examined. The choice of the free parameters appearing for solving this problem reduces to a classical eigenstructure assignment problem.

An Observer-based Robust Stabilization of 3-axes Controlled Type Magnetic Bearings Using a Digital Signal Processor

This paper deals with an effective stabilization of 3-axes controlled type magnetic bearings. All the five degrees of freedom of the motion for the suspended rotor are stabilized completely by using only three pairs of electromagnets with permanent magnets. We employ a minimal-order observer in order to estimate the motion of the rotor which can not be measured by the position sensors. First, the state-space equation of the magnetic bearing is derived on the assu mption that t he rotor is rigid and well-balanced. Next, an observer-based discrete-time control system is designed. In particular, we make use of an attractive design method: the turn-over method, to place all the closed-loop poles in a desirable stability region. Moreover, the robust stability of the system is investigated against the perturbations caused by the rotation of the rotor. Then, a digital signal processor-based controller is actually implemented. Finally, several experimental results show that the designed control system achieves excellent stability and good performance.

A pedagogical approach to minimal order observers

The minimal-order observer is derived by viewing the system output as a constraint on the full-order observer. The use of a special set of coordinates for the system realization is avoided. The approach relies on an orthogonal decomposition of the state space.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

指定した回復度を満たすLoop Transfer Recovery設計法による最小次元オブザーバの設計

指定した回復度を満たすLoop Transfer Recovery設計法による最小次元オブザーバの設計

Doubly coprime factorizations, reduced-order observers, and dynamic state estimate feedback

Doubly coprime factorizations of the transfer function of a lumped linear time-invariant system are a starting point for many of the results in the factorization approach to multivariabie control system analysis and synthesis. In work by Nett et al. (1984), explicit state-space realizations of these factorizations are derived using results from state estimation/state feedback theory. Here new doubly coprime factorizations are developed based on minimal-order observers. Following on from this, various extensions are noted, and it is proved that the class of all proper stabilizing controllers for a given plant can be generated by dynamic feedback of the reduced-order state estimate.

Design of a helicopter output feedback control law using modal and structured-robustness techniques

A procedure is described for designing output-feedback control laws based on a mixture of modal and frequency domain approaches. In the first step of this procedure, a state-feedback control law is synthesized. The modal approaches are used for dealing with dynamic performances whilst the robustness is optimized by using frequency domain criteria. Note that the robustness measure adopted here is based on structured singular values in such a way that not only the stability but also the damping ratio are robust against uncertainties. In the second step, a minimal-order observer output-feedback control law, defined in an eigenstructure setting, is performed in such a way that both modal and robustness properties are recovered. The robustness of the technique is illustrated using a realistic helicopter problem.

Observers for descriptor systems

Abstract The design of observers is investigated for the estimation of the descriptor vector x(t) of descriptor systems of the form Ex(t) = Ax(t) + Bu(t), y(t) = Cx(t). Such systems are divided into two categories: non-causal (impulsive) systems and causal (impulse- free) systems. For non-causal systems, an observer of order rank [E] is proposed and termed a full-order observer, since the dynamical order of a descriptor system is regarded as rank [E]. For causal systems, it is shown that the number of independent outputs m does not exceed rank [E], and an observer of order (rank [E] — m) is introduced and termed a minimal-order observer. The approach is based on the transformation of the system into particular design coordinates via a singular value decomposition of the matrix E. Illustrative examples are included.

Observers for descriptor systems

Abstract The design of observers is investigated for the estimation of the descriptor vector x(t) of descriptor systems of the form Ex(t) = Ax(t) + Bu(t), y(t) = Cx(t). Such systems are divided into two categories: non-causal (impulsive) systems and causal (impulse- free) systems. For non-causal systems, an observer of order rank [E] is proposed and termed a full-order observer, since the dynamical order of a descriptor system is regarded as rank [E]. For causal systems, it is shown that the number of independent outputs m does not exceed rank [E], and an observer of order (rank [E] — m) is introduced and termed a minimal-order observer. The approach is based on the transformation of the system into particular design coordinates via a singular value decomposition of the matrix E. Illustrative examples are included.

Model-following repetitive control.

A design method for a new type of repetitive control system is proposed. By considering a reference signal generator to be a model which a controlled system should track in a typical repetitive control system, a model-following structure is derived. It is shown that state feedback can further be added in this repetitive control system without affecting the repetitive control. The tracking error of the proposed repetitive control system can be made extremely small by adjusting the gains in the feedback loop. In case that there are inaccessible state variables, a minimal order observer is useful to construct the repetitive control system although the observer does not estimate the exact states of the system due to disturbances.

Parallel procedure for the design of observers in high-order multivariable systems

This paper considers the design of minimal-order observers for reconstructing the state of high-order multivariable systems. The given system is first transformed to a lower block Hessenberg form by means of orthogonal state coordinate transformations. Then the transformed system matrices along with certain assumed block forms for the observer matrices enable the constraint equations to be decomposed and solved effectively. It is shown that a parallel procedure can be used to solve certain chain equations arising from this block decomposition.

A Novel Induction Machine Flux Observer and its Application to a High Performance AC Drive System

Abstract We proposed an induction machine flux observer based on Gopinath’s minimum order observer theory. In this paper, we generalize the design methods showing that up to 10 different kinds can be constructed and that they can be categorized into 4 groups. We construct a flux feedback type vector controller incorporating the proposed flux observer, and confirm its effectiveness with both numerical simulations and experiments. Finally, we introduce a novel approach to reducing parameter sensitivity based on using all degrees of freedom inherent in the flux observer’s gain matrix.

Design of a minimal-order observer for singular systems

This paper considers the design of an observer for generalized state-space systems using the concept of generalized inverses. In contrast to the Luenberger observer theory, a new method is proposed which does not presuppose the observer structure. It is shown that under certain conditions it is possible to construct a minimal-order observer for this class of systems. Illustrative examples are included.

Two-dimensional disturbance decoupled observers†

A procedure is developed for the design of a minimal-order observer capable of estimating the states of a two-dimensional system in the presence of unknown inputs. This is done using singular-value decomposition. The assignment of eigenvalues to the observer is facilitated by choosing the observer structure.

Minimal-order observer designs for linear time-varying multivariable systems

This note presents two simple approaches for the design of minimal-order observer for linear time-varying systems. Both techniques rely on canonical transformations of the given system. As a consequence, simple expressions are obtained which permit the observer constraint equation to be solved effectively. The observers possess the desirable property of having a time-invariant observer coefficient matrix with arbitrary eigenvalues. A comparison is made between the proposed methods from which conclusions are drawn. An illustrative example is also included.

Delayless observers for systems with delay

The design of minimal-order observers for linear systems having a time-delay in the state variables is considered. Necessary and sufficient conditons are established for the existence of delayless observers for these systems.

NEAR OPTIMAL GUIDANCE FOR SHORT RANGE HOMING MISSILE,USING THE MINIMAL ORDER OBSERVER

This paper brought a new trend giving a baseline algorithm which yield an approach for the design of the near optimal controller for the short range homing, guided missile. This new trend is based on the minimal order observer as state estimator. The problem is studied based on a linear discrete model taking into consideration the dynamics of the missile motion, the target manuvering capability, errors of measuring sensors and launch initial conditions. Quadratic criterion penalizing the state trajectory as well as the control is used. The near optimal control is derived through the linear quadratic Gaussian technique (L.Q.G.) and the minimal order observer as stato estimator. The derived control accounts for bounded control variable, Limited missile manuvering capability and bounded minimum terminal miss-distance at the intercept point.

Microcomputer as a Programmable Controller for State Feedback Control of a DC Motor Employing Thyristor Amplifier

A microprocessor-based state feedback control of a single-phase thyristor bridge/dc motor drive system is presented. Considering the drive system as a regulator problem in multivariable system theory, suitable control laws are developed using a state space model and applying a pole placement technique for fast regulation coupled with system stability by state feedback. To improve the response further, feedforward control is included in the control law so that the output follows the reference with minimum delay. A minimal order observer is also incorporated to make a quick estimate of the armature current (assumed to be inaccessible) from the knowledge of output speed and inputs of the system. Finally, the controller including the feedback control, feedforward control, and minimal order observer has been implemented in real time using an Intel 8085 microprocessor kit with suitable interfacing and standard software package. The experimental setup is fabricated and tested, and the test results are compared with digital simulation results for step changes in reference and load torque.

Minimal Order State Observer for Two-Dimensional Systems

This paper is concerned with the construction of the state observer for Roesser-type two-dimensional systems. It is shown that the existence problem of a state observer reduces to a stability problem of two-dimensional systems. Using the results on such a stability problem, a sufficient condition for the existence of a full order observer is derived. Similar results for a minimal order state observer are also derived, and the design procedure is presented. Further it is shown that if a full order observer can be realized, then a minimal order observer can also be realized. These conditions make it possible to design an observer for a class of two-dimensional systems, which has no observer by any other method.

Automotive Power Train Control Using Minimum-Order Observers

A minimum-order observer was designed and applied to the problem of shift quality control of an automotive power train. When compared with the full-order observer, the present observer resulted in ~ 70% reduction in on-line computational requirements. The performance of the observer was investigated through computer simulations of linear and nonlinear power train models.