Observer-based bilinear control of first-order hyperbolic PDEs: Application to the solar collector

Mechhoud, Sarah; Laleg‐Kirati, Taous‐Meriem

doi:10.1109/cdc.2015.7402986

Cited by 3 publications

(7 citation statements)

References 19 publications

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“…To satisfy 𝑉 ̇2(𝑡) < 0, select 𝜃 = −sign(𝑤) max (𝑑). Substitute 𝜃 = −sign(𝑤) max(𝑑) into ( 16) so that the final form of the derivative of the Lyapunov function is obtained that is (17).…”

Section: Control Design For the System With Exact Linearisationmentioning

confidence: 99%

“…Some examples of the use of other bilinear control systems can be seen in the boost converter problem in [11], [12], on controlling the spread of disease in [13], [14], on directing ship motion in [15], on regulating hot water storage in [16], on the diesel engine fuel collector in [17]. The application of control to the Hilbert chamber using finite feedback has also been carried out [18].…”

Section: Introductionmentioning

confidence: 99%

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Tracking control for planar nonminimum-phase bilinear control system with disturbance using backstepping

Mu’tamar

Naiborhu

Saragih

et al. 2022

IJEECS

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This article <span>presents the design control of a tracking problem for a non-minimum phase bilinear control system containing disturbance. The bilinear control system is assumed to have a relative degree one and non-minimum phase, which means it has unstable internal dynamics. The disturbance exists only in state variables corresponding to the control function in external dynamics. The control design was carried out using the backstepping method, which was applied to the normal form of the bilinear control system. Internal dynamics will be stabilised using virtual control to overcome unstable internal dynamics. The last step will stabilise the external dynamics and disturbance using the original control function. The simulation results show that the proposed control method can rapidly drive the output to the given trajectory. Control performance varies depending on the control parameter setting. The higher the control parameter, the better the control performance, evaluated using integral absolute error.</span>

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Section: Control Design For the System With Exact Linearisationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tracking control for planar nonminimum-phase bilinear control system with disturbance using backstepping

Mu’tamar

Naiborhu

Saragih

et al. 2022

IJEECS

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show abstract

“…Whereas, the optimal control problem in bilinear systems is complex and leads in practice to suboptimal control laws. In [15], a new observer-based bilinear control approach was proposed for the solar collector model. It was able to guarantee the exponential convergence of the tracking error using direct measurements of the solar irradiance.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…Moreover as it was presented, the convergence result was only established for δ(t) and not for the tracking error. In [15] the control strategy proposed in [16] was enhanced by developing conditions under which the stabilization of δ(t)…”

Section: Adaptive Control Designmentioning

confidence: 99%

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Adaptive energy-based bilinear control of first-order 1-D hyperbolic PDEs: Application to a one-loop parabolic solar collector trough

Mechhoud

Laleg‐Kirati

2018

Journal of the Franklin Institute

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In this paper, the adaptive bilinear control of a first-order 1-D hyperbolic partial differential equation (PDE) with an unknown time-varying source term is investigated where only boundary measurements are available. By means of boundary injection, the bilinear adaptive law is developed in the Lyapunov approach. It consists of a state observer and an input adaptation law combined with a bilinear control method derived using an energy-like principle. Both global asymptotic practical convergence of the tracking error and input-to-state stability of the system are guaranteed. A potential application of this control strategy is the one-loop solar collector parabolic trough where the solar irradiance is the unknown input (source term) and the flow rate is the control variable. The objective is to drive the boundary temperature at the outlet to track a desired profile. Simulation results are provided to illustrate the performance of the proposed method.

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Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

Radisavljevic-Gajic,

Karagiannis,

Gajic

2024

Energies

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Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

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Observer-based bilinear control of first-order hyperbolic PDEs: Application to the solar collector

Cited by 3 publications

References 19 publications

Tracking control for planar nonminimum-phase bilinear control system with disturbance using backstepping

Tracking control for planar nonminimum-phase bilinear control system with disturbance using backstepping

Adaptive energy-based bilinear control of first-order 1-D hyperbolic PDEs: Application to a one-loop parabolic solar collector trough

Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

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