Nonlinear Dynamic Control Research Articles

Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations

A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton--Jacobi--Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The...

Nonlinear dynamic characteristics and control of planar linear array deployable structures consisting of scissor-like elements with revolute clearance joint

This paper comprehensively deals with the parametric effects of the joint clearance and friction coefficient on the dynamics of planar deployable structures consisting of scissor-like elements (SLEs). The dynamic model for scissor deployable structure is based on a comprehensive consideration of the symmetry and array characteristics of this mechanism and on a Lagrange method, which represents the motion equations. A modified nonlinear contact-force model is employed to evaluate the intrajoint contact force, and the incorporation of the friction effect between the inter-connecting bodies is included in this study. The total impact forces produced in the real mechanical joint are embedded into the dynamics and the differential equations of motion are solved numerically based on a set of initial conditions. The clearance size, angle velocity, and friction coefficient are analyzed and discussed separately. Using Poincaré map, the regular and irregular responses of the deployable mulitibody systems are observed. Next, a control scheme is evaluated to maintain a more stable behavior and continuous contact between the clearance joints. The controlled results are compared with those without control, concluding that some undesired effects caused by the clearance joints can be prevented or reduced, resulting in continuous contact at the clearance joint.

Distributed non-fragile containment control of nonlinear multi-agent systems with time-varying delays

ABSTRACT Distributed containment control for multi-agent systems with time delay is investigated, where the communication topology is directed. Different from the existing literature which mainly focuses on general linear dynamics with time delay, containment control of nonlinear dynamics is discussed with the help of a new follower-based time-varying delays control protocol. Furthermore, there always exist uncertainties in the controller and observer gain matrices, a novel class of non-fragile containment control with time delay is addressed for the first time, which can be more applicable and more significant to real physical systems. By making use of the convex analysis, algebraic graph theory, matrix transformation and Lyapunov theory, it is derived that the obtained results are cast as feasible linear matrix inequalities and the states of the followers finally converge to the convex hull formed by the leaders. Finally, two simulation examples of nine-agents topology are presented to verify the validity of obtained theoretical analysis.

Nonlinear dynamic characteristics and control of Galfenol-Shape Memory Alloy composite plate subjected to stochastic excitation

In this paper, the nonlinear dynamic characteristics and control of a Galfenol-shape memory alloy (SMA) composite plate under stochastic excitation are studied. New nonlinear differential terms are applied in the constitutive modeling of Galfenol alloy and SMA, and the nonlinear dynamic model of the composite system is developed. The drift coefficient and the diffusion coefficient are calculated to obtain the steady-state probability density function of the system, and finally the optimal control strategy is proposed to improve the effects of vibration reduction. Numerical simulation and experiments results show that the system has abundant nonlinear dynamic characteristics, including stochastic Hopf bifurcation and limit cycle bifurcation. The stochastic optimal control strategy can improve the effects of vibration reduction efficiently. These results are helpful for the application of Galfenol-SMA composite structures.

Semigroup applications everywhere.

Most dynamical systems arise from partial differential equations (PDEs) that can be represented as an abstract evolution equation on a suitable state space complemented by an initial or final condition. Thus, the system can be written as a Cauchy problem on an abstract function space with appropriate topological structures. To study the qualitative and quantitative properties of the solutions, the theory of one-parameter operator semigroups is a most powerful tool. This approach has been used by many authors and applied to quite different fields, e.g. ordinary and PDEs, nonlinear dynamical systems, control theory, functional differential and Volterra equations, mathematical physics, mathematical biology, stochastic processes. The present special issue of Philosophical Transactions includes papers on semigroups and their applications. This article is part of the theme issue 'Semigroup applications everywhere'.

A New Type-2 Fuzzy Sliding Mode Control for Longitudinal Aerodynamic Parameters of a Commercial Aircraft

Although sliding mode control has many advantages such as stability and robustness but there are two important disadvantages as follow: Chattering phenomenon and mathematical nonlinear dynamic equivalent controller part. So, this paper presents a new method of adaptive sliding mode control based on general type-2 fuzzy logic to overcome on the mentioned problems. First, the longitudinal motion equations of a commercial aircraft and the upper limits of the unknown functions are introduced, which include the driving errors and uncertain parameters of the model. Then, a general type-2 fuzzy neural network (GT2FNNs), with adaptive rules, estimates these limits. Estimating the limits can reduce the computational load with less rules and weight than the dynamic matrix. The Boeing 747 is being studied and an attempt has been made to use a model very close to this aircraft. The stability of the control system has been proven. The simulation results show that by applying three models of faults to the aircraft system, the proposed type-2 fuzzy-based sliding mode control has excellent performance, especially in controlling the Aileron and Rudder angles.

Bifurcation of Periodic Solutions and Its Maximum Number in a Circular Mesh Antenna System with 1:2 Internal Resonance

In this paper, we study the bifurcation of periodic solutions for a four-dimensional deployable circular mesh antenna system. The tools for proving these results are the averaging theory and Brouwer degree theory. Based on constructing displacement maps, we study the bifurcation of the periodic solutions of linear center, and to discuss the maximum number of periodic solutions in certain parameter control conditions. The results in this paper are helpful to the study of nonlinear dynamic characteristics and vibration control of deployable circular mesh antenna model.

Consensus of Heterogeneous Second-Order Nonlinear Uncertain Multiagent Systems Under Switching Networks

The consensus problem of heterogeneous second-order nonlinear uncertain multiagent systems under switching networks is addressed by a distributed control approach. The network communication of all systems is subject to arbitrarily bounded and nonuniform time-varying delays. Based on the internal model principle, a nonlinear distributed dynamic controller is developed to solve the problem. By means of Lyapunov analysis, consensus of heterogeneous second-order nonlinear multiagent systems is achieved in the presence of system uncertainties, disturbances, and uniformly connected topologies as well as arbitrarily bounded and nonuniform time-varying communication delays.

Beetle antenna strategy based grey wolf optimization

Finding feasible solutions to real-world problems is a crucial task. Metaheuristic algorithms are widely used in many fields due to the variety of solutions they can produce. The grey wolf optimizer (GWO) is a relatively novel population-based metaheuristic algorithm that has been shown to have good optimization performance. However, due to the insufficient diversity of wolves in some cases, this approach can lead to locally optimal situations. Therefore, this paper proposes a grey wolf optimization method based on a beetle antenna strategy (BGWO) that gives the leader wolf a sense of hearing to improve the global search ability and reduce unnecessary searches. In addition, to balance exploration and exploitation, a nonlinear dynamic control parameter update strategy based on the cosine function is proposed. To evaluate the performance of the proposed BGWO, this paper uses 23 standard benchmark functions to test the method in different dimensions. Moreover, four well-known engineering problems are used to evaluate the ability of the proposed algorithm to obtain real-world problem solutions. The experimental results show that BGWO has superior performance and is competitive with many state-of-the-art algorithms in terms of solution accuracy, convergence rate, and stability.

A Non-linear Dynamic Controller for Differential Drive Mobile Robot Trajectory Tracking

A Non-linear Dynamic Controller for Differential Drive Mobile Robot Trajectory Tracking

Extremum seeking control of nonlinear dynamic systems using Lie bracket approximations

SummaryIn this article, we consider extremum seeking problems for a general class of nonlinear dynamic control systems. The main result of the article is a broad family of control laws which optimize the steady‐state performance of the system. We prove practical asymptotic stability of the optimal steady‐state and, moreover, propose sufficient conditions for the asymptotic stability in the sense of Lyapunov. The results generalize and extend existing results which are based on Lie bracket approximations. In particular, our approach does not rely on singular perturbation theory, as commonly used in extremum seeking of nonlinear dynamic systems.

Uniqueness Solution Of Abstract Fractional Order Nonlinear Dynamical Control Problems

The aim of this paper is to investigate the Uniqueness solution of Cauchy Problem represented for fractional order nonlinear dynamical control system involving certain control input and their approach of investigated depended on commutative composite semigroup and some certain conditions in certain space.

Unsteady flow simulation of a variable-sweep morphing aircraft coupled with flight control system

Morphing aircraft has adjustable aerodynamic shapes and is suitable for variable flight conditions. And there have been growing interests in recent years. However, the forces and moments are highly nonlinear, bringing challenges in design and modeling of flight control system (FCS). In this paper, unsteady Computational Fluid Dynamics (CFD) simulations are performed by solving the Arbitrary Lagrangian–Eulerian (ALE) governing equations on unstructured dynamic mesh, then unsteady aerodynamic characteristics of a variable-sweep morphing aircraft at hypersonic speed are acquired. The nonlinearity index theory is employed to analyze the nonlinearity of pitching moments. FCS is designed using nonlinear dynamic inversion control, taking attitude angles and sweep angle into consideration. Unsteady flow simulation is performed using unsteady CFD coupled with FCS. Cases of open and close loop morphing flight over the variation of sweep angle corresponding to flight conditions are studied. Results show that the nonlinearity of unsteady forces and moments are significant. The combination of unsteady CFD and FCS provides a powerful approach to the study of morphing aircraft.

Efficient neural learning control of nonlinear dynamics with applications

The control of nonlinear dynamics is gaining increasing attention since many practical systems are with such kind of characteristics. To deal with the system uncertainty, in this paper, the efficient learning control using neural network is proposed for the nonlinear strict-feedback system. The whole scheme is with the back-stepping design, while the novel learning is proposed for the neural network weights update. To deal with the approximation error, the robust item is added. The stability of the closed-loop dynamics is analysed and the effectiveness of the design is verified through flight simulation.

Robust proportional incremental nonlinear dynamic inversion control of a flying-wing tailsitter

Tailsitter unmanned aerial vehicles are utilized extensively nowadays since they merge advantages of both fixed-wing unmanned aerial vehicles and rotary-wing unmanned aerial vehicles. However, their attitude control suffers from unknown nonlinearities and disturbances due to the wide flight envelope. To solve the problems, a robust attitude controller based on a newly designed flying-wing tailsitter is proposed in this paper. By employing the angular acceleration feedback to compensate unmodeled dynamics, the proportional incremental nonlinear dynamic inversion control law is first developed. The proportional incremental nonlinear dynamic inversion strengthens the conventional nominal gain incremental nonlinear dynamic inversion with a proportional term to reflect the change of the angular acceleration more directly. Therefore, the tailsitter has a quicker response and performs better in suppressing model uncertainties and external disturbances. Since the angular acceleration is difficult to measure in practice, an angular acceleration estimation method is then established to provide accurate signals for the proportional incremental nonlinear dynamic inversion. The signals are derived as complementary results of model prediction method and direct differential method. Theoretical analysis and systematic simulations are conducted to corroborate the effectiveness of the developed estimation method as well as the robustness of the proposed controller.

Guidance command generation and nonlinear dynamic inversion control for reusable launch vehicles

Future launch vehicle concepts and technologies for expendable and reusable launch vehicles are currently investigated by the DLR research projects Akira and X-tras. In particular, the winged Liquid Fly-back Booster concept Lfbb based on an LOX/LH2 propellant combination for vertical takeoff and vertical landing (VTVL), as well as the delta-winged horizontal takeoff and horizontal landing (HTHL) concept Aurora based on an LOX/Kerosene propellant combination are considered in these projects. Because of the complexity and risks involved in on-line trajectory optimization, off-line reference trajectories are still considered important for tracking purposes. In that sense, the goal of this paper is to investigate an off-line and general-purpose guidance and control (G&C) architecture for preliminary studies of reusable launch vehicles. This is done by using trajectory optimization combined with Modelica models for the generation of optimal guidance commands, and then trajectory tracking is performed by means of inner-loop feedback controls in terms of nonlinear dynamic inversion with prescribed desired dynamics. We showcase the advantages of this baseline G&C architecture in terms of early stability and controllability aspects during the preliminary design studies of an example configuration of a reusable launch vehicle investigated in the context of the research projects above mentioned.

Fault Ride Through Capability Improvement of DFIG Based Wind Farm Using Nonlinear Controller Based Bridge-Type Flux Coupling Non-Superconducting Fault Current Limiter

High penetration of Doubly Fed Induction Generator (DFIG) into existing power grid can attribute complex issues as they are very sensitive to the grid faults. In addition, Fault Ride Through (FRT) is one of the main requirements of the grid code for integrating Wind Farms (WFs) into the power grid. In this work, to enhance the FRT capability of the DFIG based WFs, a Bridge-Type Flux Coupling Non-Superconducting Fault Current Limiter (BFC-NSFCL) is proposed. The effectiveness of the proposed BFC-NSFCL is evaluated through performance comparison with that of the Bridge-Type Fault Current Limiter (BFCL) and Series Dynamic Braking Resistor (SDBR). Moreover, a dynamic nonlinear controller is also proposed for controlling the operation of the BFC-NSFCL. Extensive simulations are carried out in the MATLAB/SIMULINK environment for both symmetrical and unsymmetrical temporary as well as permanent faults. Based on the simulation results and different numerical analysis, it is found that the proposed nonlinear controller based BFC-NSFCL is very effective in enhancing the FRT capability of the WF. Also, the BFC-NSFCL outperforms the conventional BFCL and SDBR by maintaining a near-seamless performance during various grid fault situations.

Performance of SMES system with non‐linear dynamic evolution control approach for pulsed power load compensation

Superconducting magnetic energy storage (SMES) system is one of the efficient pulsed power compensators. Its response to the load fluctuations is faster and competent. This study proposes a non-linear dynamic evolution control (NDEC) approach for SMES system. The control approach is implemented to regulate the error of three-phase compensating current and DC-link voltage. The control functions required for voltage source inverter (VSI) and bi-directional DC–DC converter of the SMES system are derived using the NDEC control approach. A proportional–integral (PI) controller is replaced by the NDEC in the inner loop of a traditional pulse-width-modulation control strategy of VSI for the quick response and effective energy exchange. The elementary idea of implementing NDEC is to govern the system dynamics by maintaining a zero-error state irrespective of load uncertainties quickly. Detrimental high rating stress on the system due to pulsed power load is substantially reduced with the proposed NDEC strategy. Source current is maintained almost balanced and harmonic-free in order to ensure a quality and reliable supply to surrounding loads. The variation in source current is drastically reduced from 260 to 6% using the proposed system. Moreover, a comparative study between PI and NDEC-based control scheme is presented using MATLAB simulation and experimental results.

Flower Pollination Optimization Based PID Controller Tuning Scheme With Robust Stabilization of Gain Scheduled CSTR

In the area of chemical and control engineering, Continuous Stirred Tank Reactor (CSTR) has been deliberated as a most important topic in temperature process control and it is a extremely nonlinear process, which displays stability only in definite regions and unsteadiness in other regions. In this CSTR, Proportional Integral Derivative (PID) controller has been used to minimize the Integral SquareError (ISE) by adjustment of control parameters like k_p,k_i and k_d.But, this conventional controller has high computational complexity, so to reduce this, the optimization based tool has been designed for PID and it was conceptually simple.Earlier, the Genetic Algorithm (GA) optimization has been focused, but it was not guarantee for good fitness and global optimal solution. So to overcome this, here, Flower Pollination based Global Optimization Algorithm (FPGOA) with Gain scheduling based PID controller is proposed for CSTR. When a plant is exposing to big changes in its operational state, the Gain scheduling has been used. The FPGOA is used for tuning the parameters of PID controller for each region to reduce the ISE. The fuzzy gain scheduler has been combined with multiple local linear PID controllers to check the stability of loop for entire regions with various levels of temperatures. This scheduling is an exceptional form of fuzzy control, which customs linguistic rules and fuzzy perceptive to establish the controller factor transition strategy for the dynamic plant dependent on high changes in its operational state to improve the optimization. MATLAB results demonstrate that the feasibility of using the proposed PID controller compared than existing controller, and it shows the FPGOA attained better results, due to the effectual fitness and global optimal solution for the dynamical nonlinear control of CSTR. The response curves of these systems has been generated and compared with existing schemes.

Adaptive-Event-Trigger-Based Fuzzy Nonlinear Lateral Dynamic Control for Autonomous Electric Vehicles Under Insecure Communication Networks

This article presents a novel adaptive-event-trigger-based fuzzy nonlinear lateral dynamic control algorithm for autonomous electric vehicles under insecure communication networks. The integration of path following control and direct yaw moment control is considered to acquire a better lateral dynamic performance. To effectively tackle inherent nonlinearities of lateral dynamics, the Takagi-Sugeno fuzzy model approach is employed to approximate the nonlinear lateral dynamics. To avoid the infeasibility of state-feedback control due to the immeasurability of sideslip angle, a fuzzy output feedback control strategy is proposed via a useful transformation. To improve resource utilization of the band-limited communication networks, an adaptive event-triggered communication mechanism is proposed to save communication resource. Moreover, to enhance the robustness of the proposed controller, the insecure communication link is considered, which is described by the Bernoulli random distributed process. Finally, simulation results show the proposed adaptive-event-trigger-based fuzzy controller not only can save communication resource, but also achieve the perfect control performance.