Functional Observability and the Design of Minimum Order Linear Functional Observers

Fernando, Tyrone; Trinh, Hieu; Jennings, Leslie

doi:10.1109/tac.2010.2042761

Cited by 127 publications

(120 citation statements)

References 15 publications

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“…A single measurement is only taken from the Linear DC servomotor, i.e., velocity (position is measured and velocity is calculated through a first order lowpass filter with cut-off frequency of 600 rad/s), which is used along with the applied input to calculate the natural feedback effort-force of subsystem P by the effort-force observer (5). The estimated natural feedback effort-force is then injected onto the energy-based state observer (9) to provide estimates of the dynamical state variables of subsystem P. Fig. 6 illus-trates the results of the state variables estimation experiment by the energy-based state observer (9).…”

Section: Resultsmentioning

confidence: 99%

“…4, where x p i represents the estimation error of the ith state variable of subsystem P. It can be shown from Fig. 4 that the stability margins are large enough which allow the energy-based state observer to tolerate with deviations over the nominal parameters of (5) and (9). In addition, the phase margins provide the system with enough stability margin to tolerate with the phase lag induced by the energy-based state observer.…”

Section: Energy-based State Observermentioning

confidence: 98%

“…Further, e s 1 (u, x A ) is the estimated natural feedback effort-force based on the available variables of subsystem A, and e s 1 (x A , x P ) is the natural feedback effortforce based on the Dirac structure of the power-conserving interconnection of subsystems A and P, calculated by the estimated states of subsystem P. Based on (8), the estimated natural feedback effort-force ( e s 1 (u, x A )) will converge to the actual natural feedback effort-force (e s 1 (x A , x P )). Therefore, the actual force is used in (9). The estimation error ( x = x − x) can be calculated by subtracting (6) and (9), this operation yieldṡ…”

Section: Energy-based State Observermentioning

confidence: 99%

“…Trajectory tracking controller for robot with flexible joints was presented in [8], based on feedback linearization and extended state observer, showing robustness in the presence of model uncertainties. The concept of functional observability and detectability were introduced in [9], that ascertains the ability to estimate a given linear function of the state vector using dynamical observer.…”

Section: Introductionmentioning

confidence: 99%

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An energy-based state observer for dynamical subsystems with inaccessible state variables

Khalil

Şabanoviç

Misra

2012

2012 IEEE/RSJ International Conference on Intelligent Robots and Systems

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Abstract-This work presents an energy-based state estimation formalism for a class of dynamical systems with inaccessible/unknown outputs, and systems at which sensor utilization is impractical, or when measurements can not be taken. The power-conserving physical interconnections among most of the dynamical subsystems allow for power exchange through their power ports. Power exchange is conceptually considered as information exchange among the dynamical subsystems and further utilized to develop a natural feedback-like information from a class of dynamical systems with inaccessible/unknown outputs. This information is used in the design of an energybased state observer. Convergence stability of the estimation error for the proposed state observer is proved for systems with linear dynamics. Furthermore, robustness of the convergence stability is analyzed over a range of parameter deviation and model uncertainties. Experiments are conducted on a dynamical system with a single input and multiple inaccessible outputs ( Fig. 1) to demonstrate the validity of the proposed energybased state estimation formalism.

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Section: Resultsmentioning

confidence: 99%

Section: Energy-based State Observermentioning

confidence: 98%

Section: Energy-based State Observermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An energy-based state observer for dynamical subsystems with inaccessible state variables

Khalil

Şabanoviç

Misra

2012

2012 IEEE/RSJ International Conference on Intelligent Robots and Systems

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show abstract

“…In [32]，A reduced-order rotor flux is used to estimate the position of the rotor flux and hence the rotor speed, excellent results verified the performances of the observer. Meanwhile, the minimum-order observer (MOO) has been well studied and applied successively in [33,34]. The MOO has some attractive features, e.g., 1), its order is the minimum second.…”

Section: Introductionmentioning

confidence: 99%

An Improved Predictive Functional Control with Minimum-Order Observer for Speed Control of Permanent Magnet Synchronous Motor

Wang¹,

Fu²,

Yang³

et al. 2017

Journal of Electrical Engineering and Technology

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-In this paper, an improved predictive functional control (PFC) scheme for permanent magnet synchronous motor (PMSM) control system is proposed, on account of the standard PFC method cannot provides a satisfying disturbance rejection performance in the case of strong disturbances. The PFC-based method is first introduced in the control design of speed loop, since the good tracking and robustness properties of the PFC heavily depend on the accuracy of the internal model of the plant. However, in orthodox design of prediction model based control method, disturbances are not considered in the prediction model as well as the control design. A minimumorder observer (MOO) is introduced to estimate the disturbances, which structure is simple and can be realized at a low computational load. This paper adopted the MOO to observe the load torque, and the observations are then fed back into PFC model to rebuild it when considering the influence of perturbation. Therefore, an improved PFC strategy with torque compensation, called the PFC+MOO method, is presented. The validity of the proposed method was tested via simulation and experiments. Excellent results were obtained with respect to the speed trajectory tracking, stability, and disturbance rejection.

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On the Existence and Design of Functional Observers for LTI Systems, with Application to User Modeling

Eskandari¹,

Wang²,

Dumont³

2014

Asian Journal of Control

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Observing the states of a linear system has been an extensively studied topic over the past few decades. Different from full‐state observers and reduced‐order observers which are used to reconstruct the entire state space and the unmeasured states, respectively, functional observers are developed for applications in which only a linear combination of the states is required. For linear time‐invariant (LTI) systems with known and/or unknown inputs and assuming availability of the derivatives of the input and the output signals, we study the existence of a novel stable functional observer. Considering the output to be the extended vector of the output and its derivatives, we derive the existence conditions for a functional observer by making the estimation error asymptotically approach zero. The derived existence conditions are applicable to multi‐input multi‐output (MIMO) systems (e.g., with either known or unknown inputs, and with or without the derivatives of the signals being available). We also provide an estimate of the required observer order for the reconstruction of a desired functional and present how to design this functional observer by modifying certain current techniques. As an application, we apply the designed functional observer to model the stage of information comprehension in the user of a shared/human controlled system.

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Functional Observability and the Design of Minimum Order Linear Functional Observers

Cited by 127 publications

References 15 publications

An energy-based state observer for dynamical subsystems with inaccessible state variables

An energy-based state observer for dynamical subsystems with inaccessible state variables

An Improved Predictive Functional Control with Minimum-Order Observer for Speed Control of Permanent Magnet Synchronous Motor

On the Existence and Design of Functional Observers for LTI Systems, with Application to User Modeling

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