Linear Time-Invariant Discrete Delay Systems in Laguerre Domain

The mathematical modeling of the human smooth pursuit system from eye-tracking data is considered. Recently developed algorithms for the estimation of Volterra-Laguerre (VL) models with explicit time delay are applied in continuous and discrete time formulations to experimental data collected from Parkinsonian patients in different medication states and healthy controls. The discrete VL model with an explicit time delay and the method for its estimation are first introduced in this paper. The estimated parameters of a second-order VL model are shown to capture the ocular dynamics both in health and disease. The possibility of including the estimated time delay, along with the VL kernel parameters, into the set of the model parameters is explored. The results obtained in continuous VL modeling are compared with those in discrete time to discern the effects due to the sampling enforced by the eye tracker used for data acquisition.

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“…The properties of the polynomials Ł (τ ) m (•) are studied in detail in [29]. Assuming kernel separability leads to…”

Section: The Vl Model With Time Delaymentioning

confidence: 99%

Continuous and Discrete Volterra-Laguerre Models With Delay for Modeling of Smooth Pursuit Eye Movements

Bro

Medvedev

2023

IEEE Trans. Biomed. Eng.

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“…Here, the slight error of the u(k) expansion with a small value of N highlights the applicability of Laguerre functions in this work. Thus, z-transform of the discrete-time Laguerre functions can be expressed as [31], [32]:…”

Section: B Operational Principle Of the Gpc With Laguerre Functionsmentioning

confidence: 99%

A New Proposal Generalized Predictive Control Algorithm With Polynomial Reference Tracking Applied for Sodium Fast Reactors

et al. 2023

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This paper proposes a generalized predictive control (GPC) with constraints and orthonormal Laguerre functions using the simplified model of the primary system (reactor core and intermediate heat exchanger (IHX)) of a prototypical sodium fast reactor (SFR). This paper develops a multiple-input multiple-output (MIMO) GPC with input constraints able to track polynomial references of any degree applied in coolant temperature difference across the core and fractional power. The manipulated variables of the GPC-SFR are the reactivity and the sodium flow rate of the primary and secondary pipes. Moreover, orthonormal Laguerre functions and step down condition number techniques were also applied to avoid the numerical ill-conditioning issue in quadratic programming of large systems. Thus, a GPC type-2 was designed to control fractional power, coolant temperature difference across the core and sodium tank temperature of the SFR primary system when temperature references change according to a linear ramp after reaching their steady-state operation, sustaining 100% power operation on the reactor. In order to analyze the load tracking capability of the GPC-SFR type-2, the load following from 100% fractional power (FP) to 60% FP at 0.8% FP/min rate is simulated. Constraints on the rate of coolant temperature difference across the core and reactivity were applied for the design safety. For comparison criteria, this paper compares the GPC-SFR type-2 with the GPC-SFR type-1, i.e, standard model predictive control (MPC), to verify the viability and superior performance of the proposal regarding: (a) ramp-tracking capability of temperature and load; (b) the rejections of a reactivity disturbance of -1 cent and a secondary sodium inlet temperature disturbance of +10 o F ; and (c) a simulation with uncertainty in reactor design. The simulations show that the GPC-SFR type-2 overcome the GPC-SFR type-1 robustness and performance.

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Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra

Medvedev

2024

Automatica

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Linear Time-Invariant Discrete Delay Systems in Laguerre Domain

Cited by 5 publications

References 23 publications

Continuous and Discrete Volterra-Laguerre Models With Delay for Modeling of Smooth Pursuit Eye Movements

Continuous and Discrete Volterra-Laguerre Models With Delay for Modeling of Smooth Pursuit Eye Movements

A New Proposal Generalized Predictive Control Algorithm With Polynomial Reference Tracking Applied for Sodium Fast Reactors

Closed-form expressions for the pure time delay in terms of the input and output Laguerre spectra

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