Local State Feedback Controllers Research Articles

Accurate voltage regulation for a DC microgrid using nonlinear state feedback controller

AbstractThe high penetration of distributed generation systems poses challenges in effectively managing both DC bus voltage and power‐sharing in DC microgrids (MGs). To ensure precise voltage regulation across various distributed generation systems and maintain overall system stability, this paper studies the modelling and control of an islanded DC MG described by a set of nonlinear‐nonaffine differential equations. In the proposed DC MG, a battery storage, a photovoltaic (PV) power plant, and a back‐end power converter with DC loads have been connected to a common DC bus. First, a dynamic model of a DC MG was developed. Then, to find the maximum power point of solar PV, a straightforward method based on an artificial neural net is employed. Afterward, a nonlinear local state feedback controller through output regulation theory is applied to achieve voltage stability, overcoming the drawbacks of droop‐based techniques. Moreover, partial state feedback capability simplifies controller design. To verify the effectiveness of the proposed approach, various scenarios, including sudden load variation, illumination change, and changes in the MG configuration, have been examined. Finally, numerical studies were carried out in a simulation environment to demonstrate the superiority of the proposed nonlinear control scheme over constant feedback control.

Novel asymptotic stabilisation conditions of nonlinear fractional-order composite systems via the decentralised control

ABSTRACT In this paper, we consider decentralised control of a nonlinear fractional-order composite system and show novel sufficient conditions for the asymptotic stabilisation of the fractional-order composite system by a set of local state feedback controllers. First, we design a local state feedback controller for each nonlinear fractional-order subsystem and a Lyapunov function that guarantees the stabilisation of the isolated nonlinear fractional-order subsystem by the controller. Then, we construct a vector Lyapunov function from the set of the Lyapunov functions, and show the stabilisation of the nonlinear fractional-order composite system. Finally, two numerical simulation examples of the nonlinear fractional-order composite systems are performed to show the correctness and usefulness of the proposed decentralised control.

Asymptotic Stabilization for a Class of Linear Fractional-Order Composite Systems

In this paper, we present the design for a decentralized control method comprising a series of local state feedback controllers for a class of linear fractional composite systems. In addition, the corresponding asymptotic stabilization criterion is derived. First, we design the local state feedback controllers for each subsystem of the linear fractional composite system. Then, based on the vector Lyapunov function, we combine these local state feedback controllers into a single decentralized controller through which the asymptotic stabilization criterion is proposed for the class of linear fractional composite system. Finally, numerical simulation of a class of linear fractional composite systems is used to verify the accuracy and effectiveness of the decentralized control method.

Voltage Regulation of DC-Microgrid With PV and Battery

This paper studies voltage regulation and maximum power point tracking (MPPT) control for a DC-microgrid that includes a photovoltaic (PV) panel, battery, constant resistance and constant power loads. A dynamic model of the DC-microgrid system described by a multi-input and multi-output nonlinear system with non-affine inputs is derived. Based on this nonlinear dynamic model, we use output regulation theory to design a local state feedback controller that regulates voltages to prescribe set points and maximizes PV power output. Global set point regulation is also studied using passive system theory for non-affine systems and Lyapunov stability theory. The effectiveness of the proposed control schemes is investigated using simulations when changes in both illumination and load occur.

Robust Economic Model Predictive Control Based on a Zonotope and Local Feedback Controller for Energy Dispatch in Smart-Grids Considering Demand Uncertainty

Electrical smart grids are complex MIMO systems whose operation can be noticeably affected by the presence of uncertainties such as load demand uncertainty. In this paper, based on a restricted representation of the demand uncertainty, we propose a robust economic model predictive control method that guarantees an optimal energy dispatch in a smart micro-grid. Load demands are uncertain, but viewed as bounded. The proposed method first decomposes control inputs into dependent and independent components, and then tackles the effect of demand uncertainty by tightening the system constraints as the uncertainty propagates along the prediction horizon using interval arithmetic and local state feedback control law. The tightened constraints’ upper and lower limits are computed off-line. The proposed method guarantees stability through a periodic terminal state constraint. The method is faster and simpler compared to other approaches based on Closed-loop min–max techniques. The applicability of the proposed approach is demonstrated using a smart micro-grid that comprises a wind generator, some photovoltaic (PV) panels, a diesel generator, a hydroelectric generator and some storage devices linked via two DC-buses, from which load demands can be adequately satisfied.

Cooperative control of a flexible manufacturing system

Abstract This paper considers networked discrete-event systems. Local state-feedback controllers enable each subsystem to reach local target states. Due to the physical restrictions between the subsystems, the local target states might not be reachable autonomously, but cooperatively with the help of other subsystems. Therefore, each subsystem is extended by a network unit, which detects and resolves possible physical restrictions. If cooperation is necessary, the network units temporarily modify their local target states while applying situation-dependent communication. The proposed method is applied to the flexible manufacturing system HANS and its applicability to real-life systems is demonstrated by experimental results.

Dual-mode Distributed Model Predictive Control for Platooning of Connected Vehicles with Nonlinear Dynamics

This paper presents a dual-mode distributed model predictive control (DMPC) strategy for platooning of connected vehicles with nonlinear dynamics. A third-order nonlinear model is employed to describe the dynamic characteristics of vehicles. In order to deal with the system nonlinearity and enhance the control precision, a DMPC based optimization problem is formulated for the vehicle platoon control, in which the nonlinear dynamics and the input boundaries are both considered as its constraints. Then, a dual-mode structure with the control scheme from the optimization and a local state feedback controller is proposed to drive the vehicles to the desired platoon. Comparing with other vehicle platoon algorithms, the proposed dual-mode DMPC strategy can significantly reduce the computational burden and save the communication resources. Furthermore, the iterative feasibility and the stability of proposed control system are strictly analyzed. In final, numerical simulations are provided to validate the effectiveness of proposed approaches.

Containment control of high‐order multi‐agent systems with heterogeneous uncertainties, dynamic leaders, and time delay

AbstractThis paper deals with containment control of multi‐agent systems where high‐order canonical controllable linear systems with heterogeneous uncertainties are considered as the agents' dynamics. The leaders are dynamic with polynomial‐type trajectories. In this paper, the control protocol is smooth and it is constructed from a flexible combination of local state feedback controller and a PI‐type protocol. Utilizing this protocol, containment without suffering from chattering phenomena and consideration of any bound on the agents' states is achieved. In addition, the flexibility of this protocol helps the designer to reduce or even discard the inter‐agent communication. Recalling the significant effects of time delay on the performance and stability of multi‐agent systems, in this paper input time delay is also considered. Following a Lyapunov‐Krasovskii stability approach, two linear matrix inequalities (LMIs) are derived, and then solving the LMIs' gains of the protocol are attained such that asymptotic stability of the multi‐agent system under switching graph topology is guaranteed. Finally, the feasibility of the LMIs and the validity of the theoretical results are demonstrated through some numerical examples.

On Exponential Stability of Neural Networks with Proportional Delays and Periodic Distribution Impulsive Effects

This paper is concerned with the problem of generalized exponential stability of impulsive neural networks with a proportional delay. More specifically, the considered network models are subject to both time-varying impulses, whose strengths are in a type of periodic distributions, and a special kind of unbounded time-varying delays called proportional delays. Based on the comparison principle, a unified delay-independent stability criterion is first derived. As an application of the derived stability conditions, the problem of designing a local state feedback control law with bounded controller gains is addressed. Finally, three examples with numerical simulations are given to demonstrate the effectiveness and advantages of the results.

Cooperative Output Regulation for Multi-Agent Systems with EDMD Leader Approximation

This paper presents a distributed output regulation algorithm for the leader-follower heterogeneous multi-agent system with unknown leader dynamics. The unknown nonlinear dynamics of the leader agent are reconstructed based on a data-driven transformation that lifts the nonlinear dynamics to a linear space that approximates it. An adaptive distributed observer algorithm is designed to estimate the leader states and its linear model approximation for each follower agent, since it is considered that the leader communicates only to a subset of followers. To design the output synchronization protocol, a local state feedback control is developed for each agent. The proposed algorithm is validated through simulation studies.

Spatially Piecewise Fuzzy Control Design for Sampled-Data Exponential Stabilization of Semilinear Parabolic PDE Systems

This paper employs a Takagi–Sugeno (T-S) fuzzy partial differential equation (PDE) model to solve the problem of sampled-data exponential stabilization in the sense of spatial $L^\infty$ norm $\Vert \cdot \Vert _\infty$ for a class of nonlinear parabolic distributed parameter systems (DPSs), where only a few actuators and sensors are discretely distributed in space. Initially, a T-S fuzzy PDE model is assumed to be derived by the sector nonlinearity method to accurately describe complex spatiotemporal dynamics of the nonlinear DPSs. Subsequently, a static sampled-data fuzzy local state feedback controller is constructed based on the T-S fuzzy PDE model. By constructing an appropriate Lyapunov–Krasovskii functional candidate and employing vector-valued Wirtinger's inequalities, a variation of vector-valued Poincare–Wirtinger inequality in one-dimensional spatial domain, as well as a vector-valued Agmon's inequality, it is shown that the suggested sampled-data fuzzy controller exponentially stabilizes the nonlinear DPSs in the sense of $\Vert \cdot \Vert _\infty$ , if sufficient conditions presented in term of standard linear matrix inequalities (LMIs) are fulfilled. Moreover, an LMI relaxation technique is utilized to enhance exponential stabilization ability of the suggested sampled-data fuzzy controller. Finally, the satisfactory and better performance of the suggested sampled-data fuzzy controller are demonstrated by numerical simulation results of two examples.

Controller design for nonlinear time delay distributed control systems subjected to input saturation nonlinearity and disturbances

This article proposes a state feedback controller synthesis for nonlinear time-delay distributed control systems subjected to input saturation nonlinearity and disturbances. Nonlinear time-delay distributed control system individual states are without time-delay and the states coming from other subsystems have the communication link time-delay. The coupling states time-delay is presumed to be time-varying within a predefined bound. First, we suggest global state feedback controller design and then, we extend the proposed global design technique to more general local state feedback controller scheme by using an auxiliary region of attraction. Linear matrix inequality (LMI)-based solution is anticipated to synthesis global and local state feedback controller by using global and local sector bounded condition, Lyapunov–Krasovskii function, and Lipschitz condition. Which guarantee global and local asymptotic stability of the complete closed-loop system and $$ L_{2} $$ gain reduction of the mapping from $$ d_{p} (t) $$ to $$ z_{p} (t) $$ . Application results are presented to validate the benefits and effectiveness of the anticipated controller design schemes.

Observer‐based output feedback compensator design for linear parabolic PDEs with local piecewise control and pointwise observation in space

This study presents an observer-based output feedback compensator design for a linear parabolic partial differential equation (PDE), where a finite number of actuators and sensors are active over partial areas and at specified points in the spatial domain, respectively. In the proposed design method, a Luenberger-type PDE observer is first constructed by using the non-collocated pointwise observation to exponentially track the PDE state. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed. By employing a Lyapunov direct method, integration by parts, Wirtinger's inequality and first mean value theorem for definite integrals, sufficient conditions on the exponential stability of the resulting closed-loop coupled PDEs are presented in terms of standard linear matrix inequalities. Furthermore, both open-loop and closed-loop well-posedness analysis results are also established by the C 0 -semigroup method. Numerical simulation results are presented to show the effectiveness of the proposed design method.

Observer‐based dynamic local piecewise control of a linear parabolic PDE using non‐collocated local piecewise observation

This paper employs the observer-based output feedback control technique to study the problem of local piecewise control for a linear parabolic partial differential equation(PDE) using non-collocated local piecewise observation. By the noncollocated local piecewise observation, a Luenberger-type PDE observer is first constructed to exponentially track the state of the PDE in the sense of both ℒ 2 norm and ℋ 1 norm. Based on the estimated state, a collocated local piecewise state feedback controller is then proposed for exponential stabilisation of the PDE. Sufficient conditions on exponential stabilisation of the PDE by the suggested feedback controller in the sense of both ℒ 2 norm and ℋ 1 norm are developed by utilising Lyapunov direct method, integration by parts, Wirtinger's inequality, and first mean value theorem for definite integrals, and presented in terms of standard linear matrix inequalities. The well-posedness is also analysed for both open-loop and resulting closed-loop PDE by using C 0 -semigroup approach. Finally, numerical simulation results are presented to show the effectiveness of the proposed design method.

Multiagent System-Based Distributed Coordinated Control for Radial DC Microgrid Considering Transmission Time Delays

This paper focuses on a multiagent-based distributed coordinated control for radial dc microgrid considering transmission time delays. First, a two-level multiagent system is constructed, where local control is formulated based on local states and executed by means of the first-level agent, and distributed coordinated control law is formulated based on wide-area information and executed by means of the secondary-level agent in order to improve the voltage control performances. Afterward, the research mainly focuses on designing the local controller and the distributed coordinated controller. For the purpose of robust stability, the local control is designed as local state-feedback-based $\text{H}_{\boldsymbol \infty }$ robust controller. It is worth mentioning that the distributed coordinated control consists of local state feedback control and decoupling coordinated control law that only come from adjacent distributed energy resource units. Moreover, the distributed coordinated controller is designed by means of delay-dependent $\text{H}_{\boldsymbol \infty }$ robust control method taking into account transmission time delays. Finally, the validity of the proposed control scheme is demonstrated by means of simulation results.

Decentralised adaptive robust control schemes of uncertain large‐scale time‐delay systems with multiple unknown dead‐zone inputs

A simple design method is presented such that the decentralised adaptive robust control schemes with a relatively simple structure can be synthesised for a class of uncertain large-scale interconnected time-delay systems with multiple dead-zone inputs. It is supposed that any information on dead-zone input non-linearities is completely unknown. On the basis of adaptive technique, a self-tuning control gain function is introduced for each subsystem to construct a simple local state feedback controller which is structurally linear in the local state variables. The simple design method presented in this study might be well understood by engineering designers, and the resulting simple control schemes can be easily implemented in a number of practical engineering control problems. By combining the presented design method with other control methods, one may expect to obtain a number of interesting results for a rather large class of uncertain interconnected dynamical systems with completely unknown dead-zone in the actuators. Finally, the simulations of some numerical examples are provided to show the design procedure of the presented method and to demonstrate the validity of the theoretical results.

Self-Triggered Model Predictive Control for Nonlinear Input-Affine Dynamical Systems via Adaptive Control Samples Selection

In this paper, we propose a self-triggered formulation of Model Predictive Control for continuous-time nonlinear input-affine networked control systems. Our control method specifies not only when to execute control tasks but also provides a way to discretize the optimal control trajectory into several control samples, so that the reduction of communication load will be obtained. Stability analysis under the sample-and-hold implementation is also given, which guarantees that the state converges to a terminal region where the system can be stabilized by a local state feedback controller. Some simulation examples validate our proposed framework.

T-S fuzzy model based adaptive fuzzy current tracking control of three-phase active power filter

This paper proposed an adaptive fuzzy state feedback controller for a three-phase active power filter (APF) based on a Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model is based on the APF dynamic model in the dq frame, which ensures that the current control dynamic and DC capacitor voltage dynamic become decoupled. By using the parallel distributed compensation (PDC), local linear state feedback controller could be designed for each T-S fuzzy sub-model. To deal with the parametric uncertainties and external disturbances, a parameter estimation scheme for tuning the parameters of T-S fuzzy model is designed and the parameters are adjusted online by the adaptive law derived from the Lyapunov stability analysis. Simulation studies demonstrate that the proposed control method exhibit excellent performance in both steady state and transient operation during balanced and unbalanced load, and source voltage.

A novel control algorithm for interaction between surface waves and a permeable floating structure

An analytical solution is undertaken to describe the wave-induced flow field and the surge motion of a permeable platform structure with fuzzy controllers in an oceanic environment. In the design procedure of the controller, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers. A stability analysis is carried out for a real structure system by using Lyapunov method. The corresponding boundary value problems are then incorporated into scattering and radiation problems. They are analytically solved, based on separation of variables, to obtain series solutions in terms of the harmonic incident wave motion and surge motion. The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structure properties including platform width, thickness and mass has been thus drawn with a parametric approach. From which mathematical models are applied for the wave-induced displacement of the surge motion. A nonlinearly inverted pendulum system is employed to demonstrate that the controller tuned by swarm intelligence method can not only stabilize the nonlinear system, but has the robustness against external disturbance.

Output regulation of linear heterogeneous multi-agent systems via output and state feedback

In this paper, we propose output feedback and state feedback controllers for output regulation of linear heterogeneous multi-agent systems. We use a general model for the output regulation problem of linear multi-agent systems which accounts for a general directed and fixed communication graph, heterogeneity of the agents, an arbitrary number of inputs and outputs and both state and output feedback. First, we derive global and local sufficient conditions for the existence of local output feedback and local state feedback controllers. We show that both controllers have an H∞ criterion as a part of their sufficient conditions. Second, we design these controllers locally to insure those sufficient conditions. Third, for the case of output feedback, we show that the design procedure requires a feasible solution to the set of two LMIs and one non-convex algebraic constraint. We provide an existing algorithm to find a feasible solution to this problem. Fourth, for the case of state feedback we prove that the H∞ criterion is satisfied if and only if there exists a feasible solution to an LMI. Moreover, we define an output regulation region such that selecting the state feedback coupling gain from this region ensures that the sufficient condition is always satisfied.