Closed-loop Dynamics Research Articles

Optimal power distribution with mitigation of DC voltage fluctuations using artificial intelligent droop control scheme for MTDC grid

Optimal power share contribution with minimum DC voltage deviations is highly recommended in voltage source converter multi-terminal DC (VSC-MTDC). Hence, in this study, an artificial neural network based intelligent adaptive droop control proposes to enhance MTDC closed-loop system dynamics in terms of optimal power share and small redistribution of terminal DC voltages with negligible oscillations even in the presence of AC grid load demand change, admittance matrix uncertainty, outage of terminals and integration of wind farms. This is achieved via three-layer neural network and its weights are adaptively updated using error-back propagation algorithm. The asymptotic convergence of proposed control is derived using the Lyapunov’s stability theorem. Thus, the proposed intelligent adaptive droop control strategy not only guarantees to improve power share contribution with minimum voltage but also improved power quality and service continuity of MTDC grid. The robustness of proposed intelligent adaptive droop control is demonstrated on five terminal multi-terminal DC grid via MATLAB®.

Optimal Control of Nonlinear Systems With Unsymmetrical Input Constraints and its Application to the UAV Circumnavigation Problem

In this article, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of the constructed optimal control policy, we remove the assumption in the current study for the adaptive optimal control, that is, the internal dynamics should hold zero when the state of the system is in the origin. Particularly, nonlinear control systems with partially unknown dynamics are investigated and the procedure to acquire the corresponding optimal control policy is presented. The stability for the closed-loop dynamics and the optimality of the obtained control policy are both proved. Besides, we apply the proposed control design framework to solve the optimal circumnavigation problem based on the accumulative Fisher information for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our algorithm is compared with that of the existing circumnavigation control policy in a numerical simulation.

Leaderless and Leader-Following Bipartite Consensus of Multiagent Systems With Sampled and Delayed Information.

This article proposes a hybrid systems approach to address the sampled-data leaderless and leader-following bipartite consensus problems of multiagent systems (MAS) with communication delays. First, distributed asynchronous sampled-data bipartite consensus protocols are proposed based on estimators. Then, by introducing appropriate intermediate variables and internal auxiliary variables, a unified hybrid model, consisting of flow dynamics and jump dynamics, is constructed to describe the closed-loop dynamics of both leaderless and leader-following MAS. Based on this model, the leaderless and leader-following bipartite consensus is equivalent to stability of a hybrid system, and Lyapunov-based stability results are then developed under hybrid systems framework. With the proposed method, explicit upper bounds of sampling periods and communication delays can be calculated. Finally, simulation examples are given to show the effectiveness.

A Simple Learning Approach for Robust Tracking Control of a Class of Dynamical Systems

This paper studies the robust tracking control problem for a class of uncertain nonlinear dynamical systems subject to unknown disturbances. A robust trajectory tracking control law is designed via a simple learning-based control strategy. In the developed design, the cost function based on the desired closed-loop error dynamics is minimized by means of gradient descent technique. A stability proof for the closed-loop nonlinear system is provided based on the pseudo-linear system theory. The learning capability of the developed robust trajectory tracking control law allows the system to mitigate the adverse effects of the uncertainties and disturbances. The numerical simulation results for a planar PPR robot are included to illustrate the effectiveness of the developed control law.

Stabilization of a chaotic oscillator via a class of integral controllers under input saturation

This work presents the straightforward design of an integral controller with an anti-windup structure to prevent undesirable behavior when actuator saturation is considered, and the proposed controller improves the performance of the closed-loop dynamics of a class of nonlinear oscillators. The proposed integral controller has an adaptive control gain, which includes the absolute value of the named control error to turn off the integral action when it is saturated. Closed-loop stability analysis is performed under the Lyapunov theory framework, where it can be concluded that the system behaves in an asymptotically stable way. The proposed methodology is successfully applied to a Rikitake-type oscillator, considering a single input-single output (SISO) structure for regulation and tracking trajectory purposes. For comparison, an equivalent fixed gain integral controller is also implemented to analyze the corresponding anti-windup properties of the proposed control structure. Numerical experiments are conducted, showing the superior performance of the proposed controller.

Formula omitted] control for singularly perturbed jumping delayed systems and its application in a tunnel diode circuit model

This paper investigates the slow state variable feedback control issue for a group of singularly perturbed Markov jump systems with time-varying state delay in the discrete-time domain. The primary goal of this paper is to propose a slow state controller design approach that ensures the closed-loop dynamics attain stochastic stability with an H∞ performance. First, the time-varying delay is introduced into system state and Markov jump chain is employed to depict system topological change. Secondly, by resorting to the Lyapunov functional theory and matrix analysis method, several necessary criteria are provided to guarantee the desired control performance. The derived conditions rely not only on the size of time-varying state delay and the upper bound of the singular perturbation parameter, but also on the order of the generated Markov jump mode sequence. Based on the established conditions, the gains of the desired slow state controller are obtained by means of the feasibility of a set of linear matrix inequalities. Eventually, a numerical simulation and a tunnel diode circuit model are presented to demonstrate the efficiency of the proposed technique.

Adaptive Artificial Neural Network-Based Control Through Attracting-Manifold Design and Lipschitz Constant Projection

Abstract This article presents an adaptive artificial neural network-based control scheme that strategically integrates the attracting-manifold design and a smooth Lipschitz-constant projection operator. The essence of the scheme is elaborated through the design of the reference-command-tracking control law of an nth-order single-input uncertain nonlinear system that can be transformed into the Brunovsky form. The method offers two major advantages: First, by employing the attracting-manifold design, it is possible to achieve asymptotic recovery of the ideal (deterministic) closed-loop dynamics. In other words, the perturbation caused by parametric uncertainties will be driven to zero asymptotically as a result of such a design, fostering a superior control performance. Second, the established smooth projection operator ensures the Lipschitz constant of the adaptive artificial neural network is bounded from above, thereby providing a certain degree of robustness against adversarial perturbations. The proposed method is validated through a numerical simulation example and compared with a standard certainty-equivalent neural-adaptive control method to demonstrate its superior performance.

Finite-time Synchronization of the 4-D Hyper-chaotic Chen-Qi-like System

For Chen-Qi-like four-dimensional hyper-chaotic system, controllers designed with Lyapunov stability theory to achieve synchronous/anti- synchronous control of chaos are found that sometimes synchronization errors do not decrease to zero in finite time. To solve it, a new controller and parameter estimation law are proposed to achieve finite-time synchronization. The stability analysis of the closed-loop dynamics is derived and the effectiveness of the theoretical results is testified. Taking the parameters L=2, μ=0.5, the state time history diagram and the synchronous error curve are investigated via numerical simulation, which show that the synchronization errors are zero in finite time while two systems in chaotic motion, but synchronization error of the state with cubic nonlinearity is not zero in finite time while two systems in periodic motion; Adjust L=200,μ=0.5, numerical simulation again, then all the errors are zero in finite time. Thus the effectiveness is verified.

Robust adaptive sliding mode control for path tracking of unmanned agricultural vehicles

In this paper, a novel adaptive sliding mode control (ASMC) for path tracking of unmanned agricultural vehicles is proposed. It is shown that the designed ASMC is capable of driving the closed-loop lateral position error dynamics to converge to zero asymptotically, where the sliding mode observer (SMO) is designed to estimate the system state so as to adaptively adjust the uncertain bounds of cornering stiffness. Compared with the classical sliding mode control technique, the proposed ASMC not only guarantees strong robustness with respect to parameter uncertainties, disturbance and varying road conditions, but also requires no prior knowledge of the road information. Simulation and experimental results from a typical agricultural wheeled vehicle are provided to verify the excellent performance of the proposed scheme.

Event-Based Pinning Synchronization Control for Discrete-Time Delayed Complex Cyber-Physical Networks Under All-Around Attacks

This paper is concerned with the problem of pinning synchronization control for a class of nonlinear discrete-time delayed complex cyber-physical networks under all-around attacks. To handle the all-around attacks, a constrained hybrid attacks model is established, which incorporates the pattern feature of false data injection attacks and physical attacks. By utilizing the Lyapunov stability theory and the linear matrix inequality technique, a novel dynamic event-triggering pinning synchronization control scheme is developed to cope with the synchronization control task. Subsequently, sufficient conditions are obtained to guarantee that the closed-loop error dynamics are ultimately exponentially bounded. Furthermore, the design procedure of the synchronization controller is presented for the considered complex cyber-physical networks subject to all-around attacks. Finally, an illustrative example is delivered to demonstrate the effectiveness of the proposed method.

On the closed-loop stochastic dynamics of two-state nonlinear exothermic CSTRs with PI temperature control

Fokker-Planck (FP) partial differential equation (PDE) theory is applied to characterize the stochastic dynamics of a class of open-loop (OL) 2-state nonlinear exothermic continuous reactors with: (i) zero and time-varying mean noise disturbances, and (ii) linear proportional-integral (PI) temperature control. The characterization includes: (i) the stochastic on deterministic dynamics dependency, (ii) gain condition for robust probability density function (PDF) stability over deterministic-diffusion time biscale with stationary monomodality at prescribed most probable (MP) state, (iii) evolutions of along nearly deterministic time scale of MP state and control and their variabilities, (iv) attainment of random motion in-probability (IP) stability over deterministic-diffusion time biscale, and (v) identification of the compromise between MP state regulation speed, robustness, and control effort. The methodological developments and findings are illustrated with three indicative examples with OL complex (bimodal and vulcanoid) stationary state PDFs, including analytic assessment as well as state PDF and random motion numerical simulation.

Seismic response evaluation of spring-based piston braced frames by employing closed-loop dynamic (CLD) testing

This paper employs the Closed-Loop Dynamic (CLD) testing method for evaluating the seismic response of Spring-Based Piston Braced Frames (SBPBF) by utilizing a combination of experimental and numerical approaches. The CLD testing procedure is an iterative process, which is initiated by conducting cyclic tests on a reduced-scale bracing element and followed by computational simulations of a full-scale braced frame. To this end, a hysteresis model is developed, based on testing the Spring-Based Piston Bracing (SBPB) element, which is incorporated into a simulated multi-story SBPBF. The time-dependent deformations of SBPBs under earthquake loadings are scaled down using similitude law, serving as a loading protocol for further testing and refining the hysteresis model. The developed model is then calibrated, scaled up, and integrated into the computational model to generate more precise deformation histories of the SBPB. The refined model is validated through aniterative process that combines experimental and numerical results. An illustrative example is presented to demonstrate the feasibility of the CLD testing method for SBPB archetypes. The efficiency of this approach is demonstrated by the remarkable match between the experimental and computational results. Additionally, a comparative numerical assessment is conducted on braced frames equipped with non-compressed and pre-compressed SBPBs, revealing their superior performance compared to the Buckling-Restrained Braced Frames (BRBFs).

A Dual-Level Model Predictive Control Scheme for Multitimescale Dynamical Systems

So far, many control algorithms have been developed for singularly perturbed systems. However, in many industrial processes, enforcing closed-loop fast-slow dynamics for peculiarly nonseparable ones is a prior request and a crucial issue to be resolved. Aiming at the above problem, this article presents two dual-level model predictive control (MPC) algorithms for multitimescale dynamical systems with unknown bounded disturbances and input constraints. The proposed algorithms, each one composed of two regulators working in slow and fast time scales, are designed to generate closed-loop separable dynamics at high and low levels. As a prominent feature, the proposed algorithms are not only suitable for singularly perturbed systems but also capable of imposing separable closed-loop performance for dynamics that are nonseparable and strongly coupled. The recursive feasibility and convergence properties are proven under suitable assumptions. The simulation results on controlling a boiler turbine (BT) system, including the comparisons with other classic controllers, are demonstrated, which show the effectiveness of the proposed algorithms.

SMC for Discrete-Time Networked Semi-Markovian Switching Systems With Random DoS Attacks and Applications

This article concentrates on the discrete-time sliding mode control (DTSMC) problem for uncertain networked semi-Markovian switching systems (S-MSSs) under random denial-of-service (DoS) attacks. The semi-Markovian kernel (SMK) approach is utilized such that the switching among different modes is mutually governed by the transition probability and the sojourn-time distribution function. Considering randomly occurring DoS attacks, a sliding mode function related to the attack probability is constructed to analyze the impact of malicious attacks. Then, sufficient conditions under the equivalent DTSMC law are derived in view of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -error mean square stability criterion. Furthermore, the synthesis problem of the proposed DTSMC law ensures that the resulting closed-loop system dynamics can be driven onto the prespecified sliding region within a limited time. Finally, an electronic throttle control system is shown to validate the proposed algorithm.

Time Parameter Mapping and Contour Error Precompensation for Multiaxis Input Shaping

When the trajectory with high speed and high acceleration contains frequency contents matching with the structure mode, the inertial vibration of the structure is easily excited, reducing machining accuracy and surface finish. Input shaping can avoid vibration, but it introduces time-delay that causes multiaxis trajectory distortion and affects the accuracy of contour error estimation. This article presents time parameter mapping and contour error precompensation for multiaxis input shaping to suppress vibration. The mapping of time parameter domain of trajectories is established by deducing the relation between the local curvature extremums of the trajectories before and after shaping, which provides reference points for contour error estimation. The actual trajectory is predicted by the closed-loop servo dynamics model and reference trajectory, and then the Newton iterative algorithm based on time parameter mapping is used to seek the contour error point. Finally, the calculated contour error is low-pass filtered and projected to each axis, and then the shaped trajectory is precompensated to simultaneously reduce the contour error and avoid structural vibration. Comparative experiments are conducted to validate the effectiveness of the proposed method. Experimental results illustrate that the proposed method not only suppresses structural vibration, but also significantly improves the estimation accuracy and contouring performance by time parameter mapping.

Distributed Event-Triggered Secondary Control for Islanded Microgrids With Disturbances: A Hybrid Systems Approach

This paper focuses on the event-triggered secondary control problem of islanded microgrid with nonlinear dynamics and unknown external disturbances. Distributed secondary control law is proposed to compensate for frequency and voltage deviation caused by primary control, and to realize accurate active power sharing. In order to save communication resources, a novel hybrid event-triggering mechanism (ETM) is proposed to schedule the information transmission for each distributed generator. A hybrid model is constructed to describe the closed-loop dynamics and incorporate the ETM into flow and jump sets. Based on this model, Lyapunov stability conditions and ETM design are developed. Compared with the existing results, the proposed hybrid event-triggered control strategy not only has potential to reduce triggering number, but also guarantee a strictly positive minimum event-triggering interval even in the presence of external disturbances, that is important for physical implementation. Finally, simulation results are provided to illustrate the proposed method.

Terminal sliding mode attitude-position quaternion based control of quadrotor unmanned aerial vehicle

In this paper is presented the development of a terminal sliding mode attitude-position quaternion based control of a quadrotor unmanned aerial vehicle UAV. First, the dynamics of this UAV is divided into an attitude and position loop in order to design suitable independent control laws. The type of control law implemented for each loop is of the kind of hybrid terminal sliding mode and quaternion controller. The advantages of these control strategies over other techniques found in the literature are that the implementation of a quaternion based control strategy provides a relatively simple approach considering that the dynamics for the attitude and position loops can be described in this way. The quaternion based control strategy is suitable considering the kinematic and dynamic model of a quadrotor UAV, meanwhile the sliding mode controller part provides a relativelly simple control strategy taking into consideration that is reliable against uncertainties and provide a fast and accurate attitude-position tracking considering a reference to be followed by each loop. It is important to take into consideration that when an attitude command is given, the closed loop dynamics of the attitude block is stabilized generating at the same time the reference for the position loop. The terminal sliding mode controller part is obtained by selecting an appropriate sliding surface in order that the control law for each loop would be drove to the reaching phase faster and accurately. It is worthy to mention that both control loops posses feedforward neural networks as compensators in order that the tracking error will be reduced by both control strategies. Finally, a numerical experiment is conducted in order that the theoretical results are validated offering the appropriate discussion and conclusions about this research study.

ROBUST CONTROL OF LOW-COST DIRECT DRIVES BASED ON INTERIOR PERMANENT MAGNET SYNCHRONOUS MOTORS

Torque ripple compensation problem is considered for electrical drives, based on low-cost direct drive interior perma-nent magnet synchronous motors. Robustness properties of the speed and position control systems have been studied using time scale separation properties of the current, speed and position control loops. It is shown that system closed-loop dynamics according to new controller design has cascaded properties with speed and position control loops con-nected in series and therefore has potential of high frequency torque ripple compensation by increasing controllers gains. Experimental results are presented for two motors with similar rated data but significantly different level of the torque ripple. It is shown that despite of significand difference in parasitic torque amplitude, the similar position con-trol performance can be achieved. It makes proposed control algorithms suitable for both high dynamic performance and low-cost direct drive applications with medium performance requirements. References 13, figures 7.

An optimal control approach to particle filtering

We present a novel particle filtering framework for the continuous-time dynamical systems with continuous-time measurements. Our approach is based on the duality between estimation and optimal control, which allows for reformulating the estimation problem over a fixed time window into an optimal control problem. The resulting optimal control problem has a cost function that depends on the measurements, and the closed-loop dynamics under optimal control coincides with the posterior distribution over the trajectories for the corresponding estimation problem. By recursively solving these optimal control problems approximately as new measurements become available, we obtain an optimal control based particle filtering algorithm. Our algorithm uses path integrals to compute the weights of the particles and is thus termed the path integrals particle filter (PIPF). A distinguishing feature of the proposed method is that it uses the measurements over a finite-length time window instead of a single measurement for the estimation at each time step, resembling the batch methods of filtering, and improving fault tolerance. The efficacy of our algorithm is illustrated with several numerical examples.

Global Versus Local Lyapunov Approach Used in Disturbance Observer-Based Wind Turbine Control

This contribution presents a Lyapunov-based controller and observer design method to achieve an effective design process for more dedicated closed-loop dynamics, i.e., a maximal flexibility in an observer-based controller design with a large consistency in desired and achieved closed-loop system dynamics is intended. The proposed, pragmatic approach enhances the scope for controller and observer design by using local instead of global Lyapunov functions, beneficial for systems with widely spaced pole locations. Within this contribution, the proposed design approach is applied to the complex control design task of wind turbine control. As the mechanical loads that affect the wind turbine components are very sensitive to the closed-loop system dynamic, a maximum flexibility in the control design is necessary for an appropriate wind turbine controller performance. Therefore, the implication of the local Lyapunov approach for an effective control design in the Takagi-Sugeno framework is discussed based on the sensitivity of the closed-loop pole locations and resulting mechanical loads to a variation of the design parameters.