Loss of Optimal Performance of the Finite-Horizon Continuous-Time Linear-Quadratic Controller Driven by a Reduced-Order Observer

Radisavljević-Gajić, Verica; Milanović, Miloš

doi:10.1115/1.4038654

Cited by 4 publications

(7 citation statements)

References 10 publications

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“…Implementation of the fulland reduced-order observers in MATLAB/SIMULINK was considered in [13]. Optimal LQ controllers driven by full-and reduced-order observers were considered in [14,15].…”

Section: Design Of Reduced-order Linear Observersmentioning

confidence: 99%

“…It should be emphasized that having unknown initial system conditions is the fundamental assumption of the observer design. If x(t 0 ) is known, then an observer for (14), assuming that value of the input vector is known, will be a computer program that solves the corresponding nonlinear differential Equation (14). Such an observer has no observation error at all times.…”

Section: Remarkmentioning

confidence: 99%

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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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Section: Design Of Reduced-order Linear Observersmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

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

Radisavljevic-Gajic,

Karagiannis,

Gajic

2024

Energies

Self Cite

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“…The LQ optimal performance loss for a reduced-order observer-based controller has been recently derived in Radisavljevic-Gajic and Milanovic. 45 Observer-driven optimal LQ controller design case study: F-15 aircraft…”

Section: Observer-driven Lq Controller Optimal Performancementioning

confidence: 99%

“…This can be done in an optimal manner by minimizing the mean and the variance of the estimation error eðtÞ ¼ xðtÞ Àx KF ðtÞ using the famous Kalman filter 51,52 (see also Kwakernaak and Sivan, 8 Sinha, 15 Gelb, 53 Simon, 54 and Grewal and Andrews 55 ). It is interesting to observe that the Kalman filter has the same structure as the deterministic observer defined in equation (45), that is Note that the choice of the Kalman filter initial condition specified in equation (83), and the fact that white noise processes are assumed to be zero-mean, make the mean value of the estimation error equal to zero at all times, that is EfeðtÞg ¼ eðtÞ ¼ 0; t ! 0.…”

Section: Kalman Filtermentioning

confidence: 99%

Linear–quadratic optimal steady state controllers for engineering students and practicing engineers

Radisavljević-Gajić

2020

International Journal of Mechanical Engineering Education

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This paper is an overview of fundamental linear–quadratic optimal control techniques used for linear dynamic systems. The presentation is suitable for undergraduate and graduate students and practicing engineers. The paper can be used by class instructors as supplemental material for undergraduate and graduate control system courses. The paper shows how to find the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear–quadratic optimal control problem). The solution is obtained by solving a static optimization problem. All derivations done in the paper require only elementary knowledge of linear algebra and state space linear system analysis. The results are presented also for the observer-driven linear–quadratic steady-state optimal controller, output feedback-based linear–quadratic optimal controller, and the Kalman filter-driven linear–quadratic stochastic optimal controller. Having full understanding of derivations of the linear–quadratic optimal controller, observer-driven linear–quadratic optimal controller, optimal linear–quadratic output feedback controller, and optimal linear–quadratic stochastic controller, students and engineers will feel confident to use these controllers in numerous engineering and scientific applications. Several optimal linear–quadratic control case studies involving models of real physical systems, with the corresponding Simulink block diagrams and MATLAB codes, are included in the paper.

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“…The multistage design framework is quite universal and future research directions could include the possible expansion to 4 timescale systems, which is already outlined in [59]. Also, it will be interesting to study how observers affect optimality when optimal controllers are used at subsystem levels [60]. (A5)…”

mentioning

confidence: 99%

Multi-Timescale-Based Partial Optimal Control of a Proton-Exchange Membrane Fuel Cell

Milanović

Radisavljević-Gajić

2019

Energies

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This paper presents a Proton-Exchange Membrane Fuel Cell (PEMFC) transient model in stack current cycling conditions and its partial optimal control. The derived model is used for a specific application of the recently published multistage control technique developed by the authors. The presented control-oriented transient PEMFC model is an extension of the steady-state control-oriented model previously established by the authors. The new model is experimentally validated for transient operating conditions on the Greenlight Innovation G60 testing station where the comparison of the experimental and simulation results is presented. The derived five-state nonlinear control-oriented model is linearized, and three clusters of eigenvalues can be clearly identified. This specific feature of the linearized model is known as the three timescale system. A novel multistage optimal control technique is particularly suitable for this class of systems. It is shown that this control technique enables the designer to construct a local LQR, pole-placement or any other linear controller type at the subsystem level completely independently, which further optimizes the performance of the whole non-decoupled system.

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Loss of Optimal Performance of the Finite-Horizon Continuous-Time Linear-Quadratic Controller Driven by a Reduced-Order Observer

Cited by 4 publications

References 10 publications

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

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

Linear–quadratic optimal steady state controllers for engineering students and practicing engineers

Multi-Timescale-Based Partial Optimal Control of a Proton-Exchange Membrane Fuel Cell

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