Moving-Horizon Modulating Functions-Based Algorithm for Online Source Estimation in a First-Order Hyperbolic Partial Differential Equation

Abstract

In this paper, an online estimation algorithm of the source term in a first-order hyperbolic partial differential equation (PDE) is proposed. This equation describes heat transport dynamics in concentrated solar collectors where the source term represents the received energy. This energy depends on the solar irradiance intensity and the collector characteristics affected by the environmental changes. Control strategies are usually used to enhance the efficiency of heat production; however, these strategies often depend on the source term which is highly affected by the external working conditions. Hence, efficient source estimation methods are required. The proposed algorithm is based on modulating functions method (MFM) where a moving-horizon strategy is introduced. Numerical results are provided to illustrate the performance of the proposed estimator in open-and closed-loops.

Selection of Modulating Functions’ Design Parameters for Estimation Problems

“…reduce the size of the linear system), and hence reduce the computational load. We propose to use Algorithm IV.1 for constructing modulating functions based 1 If a time-dependent modulating function is used, thenn in the algorithm refers to the temporal derivative's order.…”

“…Thus, solutions of these equations are usually approximated numerically, this increases the difficulty of solving estimation problems in DEs, especially in the case of higher-order nonlinear DEs. Modulating functions-based method (MFBM) is among the recent active and effective methods for real-time estimation of input, states, and parameters of systems governed by DEs [1]- [6]. The MFBM consists of a kernel-based linear integral operator in which the kernel is given by certain functions called modulating functions.…”

Intelligent Proportional–Integral–Derivative Control-Based Modulating Functions for Laser Beam Pointing and Stabilization

“…To estimate F while the system is operating, a movinghorizon strategy is applied [38]. The main idea of this strategy is to implement the MFBM on a time window that moves one sampling time forward.…”

On-line parameter and state estimation of an air handling unit model: experimental results using the modulating function method

“…This offers the additional advantages of giving estimates after a fixed and predetermined amount of time, contrary to usual Kalman-based filtering methods. Originally proposed towards parameter estimation, the modulating function method was more recently extended to include state estimation [23] [19].Many studies considering the modulating function approach showed satisfactory performance, but mostly in simulations using artificial data [19] or sources generated from real profiles [5]. In contrast to that and to the best of our knowledge, not many applications can be found in the literature dealing with experiments done on actual measurements, to the notable exception of [11], where Hartley modulating functions are used to estimate the parameters of a thyristor driven DC-motor.…”

“…Many studies considering the modulating function approach showed satisfactory performance, but mostly in simulations using artificial data [19] or sources generated from real profiles [5]. In contrast to that and to the best of our knowledge, not many applications can be found in the literature dealing with experiments done on actual measurements, to the notable exception of [11], where Hartley modulating functions are used to estimate the parameters of a thyristor driven DC-motor.…”