Nonlinear state estimation using interval computation in PMSM state observer simulation

Zbranek, Pavel; Veselý, Libor

doi:10.1109/ais.2010.5547030

Cited by 13 publications

(8 citation statements)

References 6 publications

(5 reference statements)

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“…The proposed method of rotor angular speed estimation ω and the angle of rotation θ makes use of the Jacobian matrix [39,40] formulated according to the following dependency (8). The values of magnetic flux derivatives from permanent magnets coupled with stator winding are expressed in a time-invariant system α, β.…”

Section: The Proposed Methods For Estimation Of Rotor Rotation Angle and Speed Of The Designed Machine On The Basis Of The Output Voltagementioning

confidence: 99%

Innovative Construction of the AFPM-Type Electric Machine and the Method for Estimation of Its Performance Parameters on the Basis of the Induction Voltage Shape

Smoleń

Gołębiowski

2021

Energies

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The article presents an innovative construction of the Axial Flux Permanent Magnet (AFPM) machine designed for generator performance, which provides the shape of induced voltage that enables estimation of the speed and rotational angle of the machine rotor. Design solutions were proposed, the aim of which is to limit energy losses as a result of the occurrence of eddy currents. The method of direct estimation of the value of the rotational speed and rotational angle of the machine rotor was proposed and investigated on the basis of the measurements of induced voltages and machine phase currents. The advantage of the machine is the utilization of simple and easy-to-use computational procedures. The acquired results were compared with the results obtained for estimation performed by using the Unscented Kalman Filter (UKF).

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Section: The Proposed Methods For Estimation Of Rotor Rotation Angle and Speed Of The Designed Machine On The Basis Of The Output Voltagementioning

confidence: 99%

Innovative Construction of the AFPM-Type Electric Machine and the Method for Estimation of Its Performance Parameters on the Basis of the Induction Voltage Shape

Smoleń

Gołębiowski

2021

Energies

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“…Proof. With V ∈ R (n−p)×n and L ∈ R (n−p)×n , these error definitions e q (t), e q (t), e z (t), and e z (t) are obtained as e q (t) = q(t) − Vx(t), e q (t) = Vx(t) − q(t), (11) e z (t) = z(t) − Lx(t), e z (t) = Lx(t) − z(t), (12) and it follows from the derivation of (11) that we have…”

Section: Existence Conditionmentioning

confidence: 99%

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Liu

Xie

Zhang

2022

Intl J Robust & Nonlinear

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This article investigates the reduced‐order interval observer (R‐IO) design technique for continuous‐time linear systems with unknown external disturbances and measurement noises. First, we propose a coupled R‐IO structure with more design degrees of freedom, and it can be directly applied not only to solve the difficulty of the error system cooperativity construction but to relax the constraint on the sensor measurement noises. Second, the R‐IO existence condition is derived as a set of matrix equations (MEs), and a complete solution, explicitly showing the available design parameters, to such an R‐IO is further obtained by solving the MEs. Third, using the solution, an integrated optimization indicator of the R‐IO performance is built as the valid selection mechanism of these parameters. Finally, the efficiency of the obtained results is illustrated through a numerical example and a practical example.

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“…where Z(t) ∈ R n×n is a selectable parameter matrix, and R(t) is any Hurwitz and Metzler matrix. Therefore, H(t) can be directly obtained as (21).…”

Section: Respectively the Coefficient Matrices Of N(t S) And D(t S) S...mentioning

confidence: 99%

“…This is exactly what makes it distinct and popular. With the same observation goal as IOs but different mechanisms, the set-membership observers utilize the set theory and the Kalman filtering-like scheme 21 to obtain the approximately feasible solution set of states, which leads to a better-performance observation on the discrete-time systems. [22][23][24][25][26] However, its computational amount is too large for the systems with small-time constants.…”

Section: Introductionmentioning

confidence: 99%

Time‐dependent Luenberger‐type interval observer design for uncertain time‐varying systems

Liu

Xie

Zhang

et al. 2022

Intl J Robust & Nonlinear

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This article investigates the state interval observation problem for a class of continuous and discrete‐time linear time‐varying (LTV) systems with bounded uncertainties separately. First, by utilizing both the LTV transformation and the solutions to a type of time‐varying fully‐actuated Sylvester equations, a time‐dependent standard interval observer (IO) is established in a parametric form with some design degrees of freedom. Second, a new time‐dependent structure of Luenberger‐type IOs is proposed to relax the limitation of the LTV transformation‐based design method. Further, its sufficient existence conditions are given in virtue of positive system theory. Meanwhile, a parametric design technique of such an IO for uncertain LTV systems is also raised under rank conditions. Third, the obtained results are extended to the discrete‐time systems. Finally, the correctness and benefits of the proposed methods are verified using some numerical examples.

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Nonlinear state estimation using interval computation in PMSM state observer simulation

Cited by 13 publications

References 6 publications

Innovative Construction of the AFPM-Type Electric Machine and the Method for Estimation of Its Performance Parameters on the Basis of the Induction Voltage Shape

Innovative Construction of the AFPM-Type Electric Machine and the Method for Estimation of Its Performance Parameters on the Basis of the Induction Voltage Shape

Optimal reduced‐order interval observer design for uncertain continuous‐time linear systems

Time‐dependent Luenberger‐type interval observer design for uncertain time‐varying systems

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