General Structured Observers for Discrete-Time Linear Systems

Recently, several model-based control designs have been proposed for motion systems and computerized numerical control (CNC) machines to improve motion accuracy. However, in real applications, their performance is seriously degraded when significant disturbances or cutting forces are applied. In this paper, we derive straightforward design procedures for a generalstructured unknown input observer (UIO) which perfectly decouples the effect of the external disturbance from the state estimation. Furthermore, we derive the optimal UIO by minimizing the estimation errors for both the state and the disturbance via the Riccati equation. Experimental results show that the performance of all advanced motion controllers suffers when external loads are applied. By compensating for the disturbance of a servo motor using the proposed optimal-UIO, the original contouring accuracy, which is degraded by the external loading, can be successfully recovered.

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“…For the system in Eq. (1), the generalstructured observer proposed by Cheok et al [3] is as follows:…”

Section: The General-structured Uiomentioning

confidence: 99%

Design of an Optimal Unknown Input Observer for Load Compensation in Motion Systems

Hsu

Houng

Yeh

2001

Asian Journal of Control

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“…(b) current update (CU) observers (Willems 1980); (c) general structured (GS) observers (Cheok et al 1982).…”

Section: Unknown Input Observers For Linear Discrete-time Systemsmentioning

confidence: 99%

Actuator fault detection and isolation in linear systems

Phatak¹,

Viswanadham²

1988

International Journal of Systems Science

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A scheme for the detection and isolation of actuator faults in linear systems is proposed. A bank of unknown input observers is constructed to generate residual signals which will deviate in characteristic ways in the presence of actuator faults. Residual signals are unaffected by the unknown inputs acting on the system and this decreases the false alarm and miss probabilities. The results are illustrated through a simulation study of actuator fault detection and isolation in a pilot plant doubleeffect evaporator.

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“…Notably, Reference 23 developed a straightforward and useful reduced‐order observer applicable to a broad range of nonlinear discrete‐time systems. In Reference 24, a class of general structured deterministic discrete‐time observers was introduced. Over the years, various types of observers have been created, with one of the most commonly used being the full order observer, also known as a proportional observer (PO) (see Reference 25 and references therein).…”

Section: Introductionmentioning

confidence: 99%

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

Naami,

Ouahi

2023

Optim Control Appl Methods

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This study explores the development of dynamic observer (HDO) for discrete‐time nonlinear systems (DTNLS) with time‐varying delay (TVD) and disturbances. The approach is to construct an augmented Lyapunov–Krasovskii function (LKF) with double summation terms, using the generalized reciprocally convex matrix inequality (GRCMI), as well as the Jensen‐based inequality (JBI) and the Wirtinger‐based inequality (WBI). These lead to less conservative time‐dependent conditions, represented as a set of linear matrix inequalities (LMIs) that can be efficiently solved using the LMI or YALMIP toolboxes. In addition, the proposed observer includes the widely used proportional observer (PO) and proportional integral observer (PIO) as specific cases. Two examples are presented to demonstrate the validity and effectiveness of the results.

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General Structured Observers for Discrete-Time Linear Systems

Cited by 7 publications

References 12 publications

Design of an Optimal Unknown Input Observer for Load Compensation in Motion Systems

Design of an Optimal Unknown Input Observer for Load Compensation in Motion Systems

Actuator fault detection and isolation in linear systems

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

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General Structured Observers for Discrete-Time Linear Systems

Cited by 7 publications

References 12 publications

Design of an Optimal Unknown Input Observer for Load Compensation in Motion Systems

Design of an Optimal Unknown Input Observer for Load Compensation in Motion Systems

Actuator fault detection and isolation in linear systems

H∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays

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Product

Resources

About

H_∞ dynamic observer design for a class of Lipschitz nonlinear discrete‐time systems with time varying delays