A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 4) Distributed Control Based on State-Space Models: <s> Further to results reported by Jiang , this paper investigates delay-dependent stability of load frequency control (LFC) emphasizing on multi-area and deregulated environment. Based on Lyapunov theory and the linear matrix inequality technique, a new stability criterion is proposed to improve calculation accuracy and to reduce computation time, which makes it be suitable for handling with multi-area LFC schemes. The interaction of delay margins between different control areas and the relationship between delay margins and control gains are investigated in details. Moreover, usage of delay margins as a new performance index to guide controller design is discussed, including tuning of the controller for a trade-off between delay tolerance and dynamic response, choosing the upper bound of the fault counter of communication channels and the upper bound of sampling period of a discrete realization of the controller. Case studies are carried out based on two-area traditional, two-area and three-area deregulated LFC schemes, all equipped with PID-type controllers, respectively. Simulation studies are given to verify the effectiveness of the proposed method. <s> BIB001 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 4) Distributed Control Based on State-Space Models: <s> This paper presents an intelligent controller for “load frequency control (LFC)” application in “smart grid (SG)”environment having changes in communication topology (CT) via a multi-agent system (MAS) technology. In this study, network-induced effects, time delay, and change in CT have been addressed to examine the system performance in a closed loop. An event-triggered control method is used to reduce the communication burden in a network. An intelligent controller based on reinforcement learning consists of two levels, estimator agent and controller agent, in each multi-area system. Particle swarm optimization is used to tune the controller parameters. Furthermore, the proposed control strategy and system architecture as MAS for LFC in SG are analyzed in detail, verified for various load conditions and different network configurations. In addition, mean-square error of the power system states with CT is also analyzed. The results of this study validate the feasibility of the proposed control, as well as the capability of the MAS for the operation of LFC in SG with changes in CT. <s> BIB002 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 4) Distributed Control Based on State-Space Models: <s> The purpose of this paper is to explore the applicability of linear time-invariant dynamical systems with polytopic uncertainty for modeling and control of islanded dc microgrids under plug-and-play (PnP) functionality of distributed generations (DGs). We develop a robust decentralized voltage control framework to ensure robust stability and reliable operation for islanded dc microgrids. The problem of voltage control of islanded dc microgrids with PnP operation of DGs is formulated as a convex optimization problem with structural constraints on some decision variables. The proposed control scheme offers several advantages including decentralized voltage control with no communication link, transient stability/performance, PnP capability, scalability of design, applicability to microgrids with general topology, and robustness to microgrid uncertainties. The effectiveness of the proposed control approach is evaluated through simulation studies carried out in MATLAB/SimPowerSystems Toolbox. <s> BIB003 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 4) Distributed Control Based on State-Space Models: <s> Development of microgrids and wide spread deployment of renewable generation and energy storage systems have highlighted the need for distributed control schemes to achieve maximum utilization and coordination among all the connected resources. In DC microgrids, the key goals of system-wide control are droop-based current sharing and network dc-voltage regulation. These may be achieved using a consensus algorithm secondary control that a) averages all the node voltages dynamically and maintains them at a nominal value and b) based on information from neighboring source currents to converge to a consensus in current sharing. Achieving the dynamic consensus may impose significant communication burden when implemented using conventional periodic communication methods. In this paper, an event-triggered communication based dynamic consensus algorithm is proposed that helps achieve both the stated goals of proportional current sharing along with average DC voltage regulation in a DC microgrid. The convergence and stability of the modified dynamic consensus algorithm and event triggering condition is proven using Lyapunov's stability criterion. The proposed control is applied to a DC microgrid system for secondary control of voltage and current regulation, and the performance of the proposed technique is validated under various operating conditions and disturbance in the communication system in both simulation and hardware environment. <s> BIB004 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 4) Distributed Control Based on State-Space Models: <s> This paper proposes an adaptive event-triggered communication-assisted distributed secondary cooperative control strategy using a parameter projection law-based estimate of states to reduce communication burden. It overcomes the drawbacks of operating in an open loop manner between two triggering time instants in traditional zero-order hold-based event triggering schemes using a full state feedback control strategy to update the control input simultaneously. Moreover, real-time precision of information and model uncertainties is well dealt owing to the adaptive mechanism via an event-triggering condition designed using the Lyapunov technique to ensure the stability of the system. This strategy is used in tandem to achieve global average voltage regulation and proportionate load sharing in dc microgrids for various disturbances without sacrificing system performance. The proposed control strategy is simulated in MATLAB/Simulink environment and tested on a 500-W FPGA-based experimental prototype to validate the control approach under different scenarios. <s> BIB005 </s> A Survey on Model-Based Distributed Control and Filtering for Industrial Cyber-Physical Systems <s> 4) Distributed Control Based on State-Space Models: <s> In this paper, a distributed control scheme is proposed for voltage control and power management of coupled microgrids (MGs). The control scheme is implemented in a two-level structure. In the primary level, a voltage–current droop controller is adopted in the $dq$ reference frame to facilitate proportional load sharing among the distributed energy resources (DERs) with fast dynamic response. A novel distributed secondary control scheme is introduced to regulate the power exchange among MGs and restore the average voltage to the nominal value. The secondary controller is comprised of a network of control agents interconnected through low bandwidth communication links. Each control agent alters the offset of $d$ - and $q$ -axis droop characteristics to change the current output of the DERs within each cluster until the current exchanges among the clusters are regulated at the set points and the average voltage is restored to the nominal value. If the load of an MG cluster is increased above its total generation capacity, the secondary controller alters the current exchange among the clusters to prevent overload. Simulation and experimental results are presented to demonstrate the efficacy of the proposed method. <s> BIB006
In addition, by regarding each control area as a single-machine singleload system or using the droop characteristics of power sharing, a state-space model of power systems can be described bẏ  where state vector x i can be selected as T for multiarea power systems BIB002 , BIB001 augmenting the deviation of frequency ω i , generator mechanical power P ti , turbine valve position P gi , and the net tie-line power flow ΔP i tie , or selected as T for dc microgrids BIB003 , BIB004 , BIB005 reflecting the load voltage at point of common coupling, the filter current, the dynamics of primary control (the third and fourth states), and the dynamics of secondary voltage controllers (the last two states). Additionally, n di stands for a load disturbance and A ij represents the coupled matrix of interconnected areas. The adopted distributed control is with the form BIB002 , BIB001  or the form based on consensus control BIB004  wherex i is the estimated state and K i and K ij are two controller gains to be designed. Furthermore, one can obtain a model similar to  by using small signal analysis under the d-q (direct quadrature) reference frame (see BIB006 and the references therein). For large-scale power systems with limited bandwidth constraints, a delay-dependent stability criterion is proposed in BIB001 for systems subject to communication delays, and the relationship between delay margins and control gains is exposed in detail. Furthermore, the impact on the closed-loop system performance from both time delays and varying communication topologies is examined in BIB002 via multiagent technologies, and the dynamic performance under the event-triggered scheme is also analysed via simulations. In order to reduce the communication burden, event-triggered protocols dependent on dynamic consensus algorithms are designed in BIB004 and BIB005 to achieve both voltage regulation and proportional current (or load) sharing. With the help of constructed consensus estimators combined with the Lyapunov stability theory, the desired event-triggering conditions are obtained and the convergence and stability of the proposed dynamic consensus algorithm are discussed. In comparison with the condition in BIB004 , the setup of the adaptive strategy in BIB005 results in a requirement of GPS signal.