Search

This article addresses the modeling and control of heterogeneous populations of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) schemes at the level of each TCL. It is shown that the dynamics of such TCLs populations can be described by a pair of Fokker–Planck equations coupled via the actions in the domain. The technique of input–output feedback linearization is used in the design of aggregate power control, which leads to a nonlinear system in a closed loop. Well-posedness analysis is carried out to validate the developed control scheme. The closed-loop stability of the system is assessed by rigorous analysis. A simulation study is contacted, and the obtained results confirm the validity and effectiveness of the proposed approach.

The aim of this paper is to introduce a weak maximum principle--based approach for studying the input-to-state stability (ISS) with respect to boundary disturbances and states in certain classes fo...

The aim of this paper is to mitigate the problem of high power demand peak and load oscillations in the operation of a large population of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) at the TCL level. Two desynchronized MPC schemes are introduced: 1) adding random delays in reference signals and 2) extra penalizations on MPC objective functions. For characterizing and validating the proposed desynchronization MPC schemes, a partial differential equation (PDE) model is developed to represent the evolution of the operational states of the TCLs controlled by MPC in a population. The focus of this paper is put on the control of cooling fans in server racks of datacenters, whereas the proposed approach is applicable to other types of TCLs. Numerical simulation studies are carried out and the obtained results confirm the validity and the applicability of the developed approach.

This paper addresses the problem of output regulation control of a Burgers' equation under pointwise in-domain actuation. A dynamic compensator that generates the in-domain control is developed for...

In this paper, we introduce the notion of relative $\mathcal{K}$-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic PDE systems. Based on the RKES, we prove the input-to-state stability (ISS) in the spatial sup-norm for a class of nonlinear parabolic PDEs with either Dirichlet or Robin boundary disturbances. Two examples, concerned respectively with a super-linear parabolic PDE with Robin boundary condition and a $1$-D parabolic PDE with a destabilizing term, are provided to illustrate the obtained ISS results. Besides, as an application of the notion of RKES, we conduct stability analysis for a class of parabolic PDEs in cascade coupled over the domain or on the boundary of the domain, in the spatial and time sup-norm, and in the spatial sup-norm, respectively. The technique of De Giorgi iteration is extensively used in the proof of the results presented in this paper., This is a reduced version of our manuscript written in the summer of 2019, which presents the application of the De Giorgi iteration in the analysis of ISS in $L^\infty$-norm for nonlinear parabolic PDEs with Robin or mixed boundary disturbances

This note establishes the Exponential Input-to-State Stability (EISS) property for a clamped-free damped string with respect to distributed and boundary disturbances. While efficient methods for establishing ISS properties for distributed parameter systems with respect to distributed disturbances have been developed during the last decades, establishing ISS properties with respect to boundary disturbances remains challenging. One of the well-known methods for well-posedness analysis of systems with boundary inputs is the use of a lifting operator for transferring the boundary disturbance to a distributed one. However, the resulting distributed disturbance involves time derivatives of the boundary perturbation. Thus, the subsequent ISS estimate depends on its amplitude, and may not be expressed in the strict form of ISS properties. To solve this problem, we show for a clamped-free damped string equation that the projection of the original system trajectories in an adequate Riesz basis can be used to establish the desired EISS property., Comment: Accepted for publication in IEEE Transactions on Automatic Control as a brief paper

This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid the appearance of time derivatives of the disturbances in ISS estimates, some technical inequalities are first developed, which allow directly dealing with the boundary conditions and establishing the ISS based on the method of Lyapunov functionals. The well-posedness analysis of the considered problem is carried out and the conditions for ISS are derived. Two examples are used to illustrate the application of the developed result., Comment: Manuscript submitted to Automatica

This paper introduces a maximum principle-based approach for the establishment of input-to-state stability (ISS) for parabolic equations with different type of boundary disturbances. A classical result on the estimate of the solutions to linear parabolic partial differential equations (PDEs) has been extended, which enables the application of the maximum principle to ISS analysis of certain linear or nonlinear parabolic PDEs. The effectiveness of this approach is demonstrated through the establishment of the ISS properties of a nonlinear parabolic equation with Dirichlet boundary disturbances in higher dimensional space, a 1-D linear parabolic equation with mixed boundary disturbances, and the Chafee-Infante equation with Robin boundary disturbances.

This paper presents a decentralized model predictive control (MPC) scheme for thermal appliances coordination control in smart buildings. The general system structure consists of a set of local MPC controllers and a game-theoretic supervisory control constructed in the framework of discrete-event systems (DES). In this hierarchical control scheme, a set of local controllers work independently to maintain the thermal comfort level in different zones, and a centralized supervisory control is used to coordinate the local controllers according to the power capacity and the current performance. Global optimality is ensured by satisfying the Nash equilibrium at the coordination layer. The validity of the proposed method is assessed by a simulation experiment including two case studies. The results show that the developed control scheme can achieve a significant reduction of the peak power consumption while providing an adequate temperature regulation performance if the system is $\mathcal{P}$ -observable.

This paper presents a scheme aimed at mitigating the influence of random data transmission delays in networked thermal appliance control systems in smart buildings. The impact of this type of delays is first analyzed, and it is proposed to utilize loose timing synchronization and add blank gaps between the consecutive appliance operations to avoid the possible violation of the given power budget. A cooperative control of thermal appliance operation is developed using a networked model predictive control-based controller to deal with delays. It is also shown that the schedulability of such a control scheme can be assessed online. The performance of the proposed control scheme is assessed by a simulation study based on the thermal dynamics of an eight-room office building. The obtained results show that the proposed solution can achieve an efficient power peaks shaving in the presence of random network delays.

Synchrophasor networks are subject to communication delays and packet dropout that can compromise data integrity and, thus, jeopardize control and monitoring of smart microgrids. This paper proposes an advanced phasor data concentrators (APDC) capable of counteracting the communication impairments and improving the quality of monitoring of distributed energy resources (DERs) in microgrids. The proposed APDC utilizes an adaptive compensation scheme to achieve an effective estimate of missing data elements. Moreover, a monitoring unit is proposed to reliably detect frequency excursions and identify the DERs affected by islanding events. The performance of the proposed APDC is evaluated based on realistic phasor measurement unit data aligned and processed with real-time OpenPDC software. The experimental results confirm a high-level data integrity under both normal and disturbed conditions of microgrids. Moreover, fast and reliable detection of islanding events is achieved due to the significant improvement in detection time even under severe data losses.

This paper addresses the admission control of thermal appliances in the context of smart buildings. The scheduling of thermal devices operation is formulated in the framework of discrete-event systems, which allows for the modeling and design of admission control to be carried out in a systematic manner and ensuring the existence of the feasible scheduling prior to exploring control solutions. Two algorithms are developed for the purpose of peak demand reduction. While the first algorithm validates the schedulability for the control of thermal appliances, the second algorithm may achieve a more efficient use of available capacity by exploring the concept of max–min fairness. Simulation studies are carried out in MATLAB/Simulink platform and the results show a noticeable improvement on peak power reduction.

International audience; This paper presents a novel method for the design of gain-scheduled output feedback controllers in the presence of hidden coupling terms, which naturally arise when endogenous signals are used as scheduling parameters. In this case, the controller gains vary with respect to system variables, leading to inner loops between the system and the linearized gain-scheduled controller dynamics. Such effects, also known as parasitic feedbacks, are inherently difficult to handle in classic gain-scheduling control design and are often omitted, which might result in performance degradations or even destabilization of the closed-loop system. This paper shows how such a pitfall can be avoided through the application of self-scheduling and eigenstructure assignment techniques. In this context, the main contribution of the present work is the extension of eigenstructure assignment-based self-scheduling techniques for explicit hidden coupling terms handling. The viability of the proposed method is illustrated through a pitch-axis missile autopilot benchmark problem.