Nonlinear Dynamic Feedback Research Articles

Nonlocal strain gradient‐based nonlinear dynamics of sinusoidal impulsive actuated porous/piezoelectric multilayer energy nanoharvesters

AbstractThe applications of nanoelectromechanical systems integrating simultaneously the mechanical and electrical functionalities at nanoscale have been gotten wider in the last decade. The main objective of this exploration is to analyze the small scale‐dependent nonlinear dynamical feedback of multilayer energy nanoharvesters containing a graded porous passive core coated by piezoelectric facesheets under a sinusoidal impulsive external actuation. For this purpose, the technique of meshless collocation is constructed at the same time the nonlocal stress and strain gradient tensors without any necessary background meshes and integration procedure. It is found that by taking the nonlocal stress tensor into account, the average of extremum points of maximum lateral deflection increases from to , and from to for simply supported and clamped multilayer nanoharvesters, respectively. On the contrary, through considering the strain gradient tensor, the average of extremum values of the maximum lateral deflection reduces from to for the simply supported nanoharvester, and from to for the clamped one.Highlights Development a third‐order shear flexible nonlocal strain gradient (NSG)‐based plate‐type nanoharvester model Incorporating the role of nonlocal stress and strain gradient tensors in nonlinear dynamics of nanoharvesters Time‐histories of achieved voltage of sinusoidal impulsive loaded plate‐type nanoharvesters Influence of porosity on the NSG‐based nonlinear dynamic performance.

A synergy of the adaptive whale optimization algorithm and differential evolution for abrupt motion tracking

Aiming at the problem that conventional trackers are difficult to adapt to abrupt motion, a tracking algorithm based on a synergy of the adaptive whale optimization algorithm and differential evolution (AWOA-DE) is proposed in this paper. Firstly, the non-linear dynamic feedback strategy based on the one-fifth principle is employed to replace the linear mechanism, which is the variation of exploring step in the basic whale optimization algorithm (WOA), and an adaptive WOA (AWOA) is generated to improve the global optimization ability of the WOA. Secondly, AWOA adopts a random sampling strategy to generate new samples, which could ensure the diversity of solutions, but may lead to instability. By mixing AWOA and DE algorithms, the population is divided into two groups, which are updated by AWOA and DE algorithms respectively, to ensure the diversity of the populations and improve the optimization accuracy of the algorithm. Finally, a visual tracker based on AWOA-DE is proposed, which can deal with the problem of abrupt motion in tracking. In addition, the effectiveness of the hybrid optimization algorithm is evaluated using 23 benchmark functions. In the experiment of visual tracking, extensive experimental results show that the AWOA-DE tracker (AWOADET) has much stronger competitiveness compared to the WOA tracker (WOAT) and the other 10 state-of-the-art trackers, especially for abrupt motion tracking.

Design of a nonlinear dynamic output feedback controller based on a fixed-time RBF disturbance observer for a PEMFC air supply system

The efficiency and service life of proton exchange membrane fuel cells (PEMFCs) are critically related to the control performance of the air supply system. The unmeasured state variables and system disturbances seriously affect the control performance of the air supply system. This research focuses on developing a nonlinear dynamic output feedback controller to address the multivariable, nonlinear and unmeasurable state of the air supply system. First, a simplified control-oriented model of the air supply system dynamic behavior is developed, and the modeling uncertainties are estimated and compensated using two fixed-time radial basis function neural network disturbance observers (FRBFNN-DOBs). Second, a nonlinear reduced-order cathode pressure observer is designed, and the observer error is bounded for the unknown bounded disturbance. Third, an observer-based nonlinear cathode pressure tracking controller and supply manifold pressure tracking controller are designed using backstepping method. Considering the estimation error of the FRBFNN-DOBs, the robustness of the closed-loop system is proven using the input-to-state stability theory; furthermore, the upper bound of the tracking error and the convergence rate of the initial error are obtained, which is useful to design the controller parameters. Finally, simulation results demonstrate that the designed controller is more advantageous and effective than the PID and MPC.

On the Linear Control of a Dynamically Feedback Linearizable Rocket System: An ADRC Approach

This work illustrates the use of an Active Disturbance Rejection Control (ADRC) scheme for flat multivariable nonlinear systems. After a preliminary suitable dynamic extension of the system's control inputs, guided by the flatness property, we focus on the resulting input-output coupling matrix simplification that preserves the required closed-loop performance. A rather general methodology is presented that simplifies the severe nonlinearities commonly appearing in the dynamic feedback linearization control scheme; linear ADRC controllers are proposed to achieve robustness. Numerical simulations of a non-trivial rocket control example are presented; a clear simplification of the nonlinear dynamic feedback controller is achieved without compromising the performance of a rest-to-rest trajectory tracking task.

Multiple delay-dependent finite-time fault-tolerant control for switched fuzzy systems

The work is concerned with this issue of multiple delay-dependent finite-time fault-tolerant control (FTC) for uncertain switched Takagi-Sugeno (T-S) fuzzy systems against state and input constraints. There exist intermittent faults (IFs), exogenous disturbances along with measurement noise in the models. There are few attempts for this theme. A nonlinear dynamic output feedback controller is explored for these uncertain switched T-S fuzzy systems first. And an augmented system with respect to realizing FTC is acquired. Moreover, sufficient conditions of robust finite-time H∞ control are constructed by piecewise fuzzy Lyapunov function. At the same time, finite-time boundedness (FTB) as well as input-output finite-time stability (IO-FTS) is achieved. The effectiveness as well as feasibility of this approach is verified through an example.

A backstepping disturbance observer control for multirotor UAVs: theory and experiment

This paper presents a backstepping disturbance observer based control (DOBC) for trajectory tracking motion control of multirotor Unmanned Aerial Vehicles (UAVs). Two disturbance observers (DO) estimate external force and torque disturbances acting on the UAV. A nonlinear backstepping dynamic state feedback is proposed which uses the DO estimates to achieve exponential stability for the closed-loop tracking error under constant disturbances. The stability analysis accounts for the entire nonlinear vehicle model which includes translational and rotational dynamics. Software-in-the-loop simulation and experimental results are presented showing the effectiveness of the proposed method using the commonly used PX4/Pixhawk development framework.

New Electrosurgical Technologies for High Amputations of the Lower Limbs

We present here results obtained using hightech bipolar instruments with an electrosurgical device and a non-linear dynamic feedback system for excision of large tissue blocks. The effectiveness of using bipolar scissors with blades made of nanostructured zirconium dioxide and thermostabilized bipolar forceps was assessed using high amputation of the lower limbs as an example. Significant results were obtained showing that the use of innovatory electrosurgical technologies for transfemoral amputation in patients with terminal-stage peripheral arterial disease increases the typical clinical measures of efficacy by an average of 39%. The results can be taken as the basis for a new method of using electrosurgical technology for high amputations of the lower limbs.

One Step Anti-Windup Design for Nonlinear Systems: An Indirect LMI-Based Approach

This paper proposes an indirect linear matrix inequality (LMI) approach to design one step anti-windup dynamic output feedback compensator for a class of nonlinear systems subject to actuator saturation. When the system state satisfies certain conditions, the nonlinear system can be reconstructed accurately by T-S fuzzy model, based on Lyapunov stability analysis and a result about matrix inequality, we show that the feasibility of an LMI guarantees the solvability of the corresponding one step anti-windup compensator. Once the solvability issue is determined, then we give an algorithm of one step anti-windup nonlinear dynamic output feedback compensator. The effectiveness of the proposed method is illustrated with numerical example.

Dynamic Output Controllers for Exponential Stabilization of Periodic Orbits for Multidomain Hybrid Models of Robotic Locomotion

Abstract The primary goal of this paper is to develop an analytical framework to systematically design dynamic output feedback controllers that exponentially stabilize multidomain periodic orbits for hybrid dynamical models of robotic locomotion. We present a class of parameterized dynamic output feedback controllers such that (1) a multidomain periodic orbit is induced for the closed-loop system and (2) the orbit is invariant under the change of the controller parameters. The properties of the Poincaré map are investigated to show that the Jacobian linearization of the Poincaré map around the fixed point takes a triangular form. This demonstrates the nonlinear separation principle for hybrid periodic orbits. We then employ an iterative algorithm based on a sequence of optimization problems involving bilinear matrix inequalities to tune the controller parameters. A set of sufficient conditions for the convergence of the algorithm to stabilizing parameters is presented. Full-state stability and stability modulo yaw under dynamic output feedback control are addressed. The power of the analytical approach is ultimately demonstrated through designing a nonlinear dynamic output feedback controller for walking of a three-dimensional (3D) humanoid robot with 18 state variables and 325 controller parameters.

Design an anti-windup controller for a PWR power-level control in the presence of control rod speed saturation

Control input saturation can cause severe performance degradation and possible instability in a Pressurized Water Reactor (PWR). Therefore, some form of limit protection is needed. This study proposes a dynamic compensation design problem for a PWR subject to control rod speed saturation. Design of this dynamic compensator is based on minimization of a performance index. First, a nonlinear dynamic feedback controller is designed based on feedback linearization. Then based on Parseval's theorem, the dynamic compensator is design such that the auxiliary control law is the same as that without control rod speed saturation. The proposed control approach is applied to a PWR. Simulation results show that the proposed anti-windup scheme is quite effective in presence of input saturation and it has a remarkable performance for tracking reference trajectory.

System dynamics simulation of the thermal dynamic processes in nuclear power plants

Abstract A nuclear power plant (NPP) is a highly complex system-of-systems as manifested through its internal systems interdependence. The negative impact of such interdependence was demonstrated through the 2011 Fukushima Daiichi nuclear disaster. As such, there is a critical need for new strategies to overcome the limitations of current risk assessment techniques (e.g. the use of static event and fault tree schemes), particularly through simulation of the nonlinear dynamic feedback mechanisms between the different NPP systems/components. As the first and key step towards developing an integrated NPP dynamic probabilistic risk assessment platform that can account for such feedback mechanisms, the current study adopts a system dynamics simulation approach to model the thermal dynamic processes in: the reactor core; the secondary coolant system; and the pressurized water reactor. The reactor core and secondary coolant system parameters used to develop system dynamics models are based on those of the Palo Verde Nuclear Generating Station. These three system dynamics models are subsequently validated, using results from published work, under different system perturbations including the change in reactivity, the steam valve coefficient, the primary coolant flow, and others. Moving forward, the developed system dynamics models can be integrated with other interacting processes within a NPP to form the basis of a dynamic system-level (systemic) risk assessment tool.

Memantine produces antidepressant effect through the enhancement of hippocampal neurogenesis in olfactory bulbectomized mice

The work is concerned with this issue of multiple delay-dependent finite-time fault-tolerant control (FTC) for uncertain switched Takagi-Sugeno (T-S) fuzzy systems against state and input constraints. There exist intermittent faults (IFs), exogenous disturbances along with measurement noise in the models. There are few attempts for this theme. A nonlinear dynamic output feedback controller is explored for these uncertain switched T-S fuzzy systems first. And an augmented system with respect to realizing FTC is acquired. Moreover, sufficient conditions of robust finite-time H∞ control are constructed by piecewise fuzzy Lyapunov function. At the same time, finite-time boundedness (FTB) as well as input-output finite-time stability (IO-FTS) is achieved. The effectiveness as well as feasibility of this approach is verified through an example.

Adaptive active fault-tolerant MPPT control for wind power generation system under partial loss of actuator effectiveness

In order to improve the dynamic performance and reliability of the maximum power point tracking (MPPT), this paper proposes an adaptive active fault-tolerant control (AFTC) strategy of the wind power generation system to overcome uncertain problems, including potential partial loss of actuator effectiveness, unknown modeling errors and external disturbances. The AFTC method is designed according to a new dynamic model of angular speed tracking for wind power generation system based on generalized perturbation. It neither requires the actuator fault information detection, nor relies on the system model parameters and external disturbance identification. In terms of the on-line estimation of the disturbance boundary amplitude and the nonlinear state feedback based on MPPT tracking error, the gain of the switching control is adaptively adjusted to speed up the convergence of the system and reduce the delay of the fault compensation. A first-order integral process is involved in the AFTC law to further weaken the chattering of output signal amplitude, hence smooth the torque and improve the tracking accuracy during generation. In addition, the global stability of the closed-loop control system based on AFTC is proved by the Lyapunov approach. By comparing with the conventional linear PID control and the nonlinear dynamic state feedback control (NDSFC), the case studies simulation results validate the great MPPT fault-tolerant capability even subject to partial loss of actuator effectiveness, and separately show the strong robustness and self-adaptation of the proposed adaptive AFTC method.

Fault-Tolerant Control of a Nonlinear System Based on Generalized Fuzzy Hyperbolic Model and Adaptive Disturbance Observer

This paper focuses on the problem of fault-tolerant control for a class of nonlinear systems with unknown nonlinear dynamic. The generalized fuzzy hyperbolic model is used to approximate the unknown nonlinear function. A novel fuzzy adaptive descriptor observer and an adaptive disturbance observer are designed simultaneously to estimate the system state, actuator fault, sensor fault, and disturbance. In this paper, the disturbance is assumed to be generated from an unknown exogenous system. Compared with the existing results, in which the disturbance is generated from known exogenous system, the proposed adaptive disturbance observer is more applicable in practice, since the exogenous system is independent of the controlled system and its parameter matrix is difficult to be measured. Furthermore, using the estimation information, a novel nonlinear dynamic output feedback controller is designed. The controller can stabilize the nonlinear system, which is subjected to the unknown nonlinear dynamic, actuator fault, sensor fault, and mismatched disturbance, simultaneously. Finally, simulation results are provided to illustrate the effectiveness of the proposed techniques.

Dynamic controller design for synchronization of Lur’e type systems subject to control saturation

This paper addresses the synchronization problem between two nonlinear Lur’e systems subject to control saturation. Assuming that only the output of master and slave systems are measurable, the design of a nonlinear dynamic feedback controller is considered. Based on Lyapunov arguments and a sector-based approach to deal with the system nonlinearities, linear matrices inequalities (LMI) to ensure the local asymptotic convergence of the slave state to the master one (i.e. to ensure null synchronization error) are derived. The design of the controller parameters is then carried out by the solution of a convex optimization problem aiming to maximize a set of initial conditions for which the synchronization is guaranteed. A numerical example considering the synchronization of a Chua’s circuit illustrates the proposed method.

A nonlinear switching control strategy of regulation and safety protection for aero-engines based on the equilibrium manifold expansion model

This article proposes a nonlinear switching control strategy to solve the regulation control problem with safety constraint for aero-engines based on the equilibrium manifold expansion model. That is a kind of nonlinear model with satisfactory accuracy. The design procedure includes design of sub-controllers such as the nonlinear high-pressure spool speed tracking controller, high pressure turbine outlet temperature safety protection controller and the nonlinear dynamic feedback recovery controller. Also, switching law and dynamic controller state reset law are properly designed. Under the proposed strategy, system trajectory starting from temperature safety boundary will never return to the safety boundary. The designed reset law ensures a smooth switching from protection mode to recovery mode. Switch-off moment of the protection controller can be arbitrarily selected according to the tracking performance requirement. Freedom degree of selection is enlarged. The sub-controllers corresponding to objectives of regulation and safety protection are designed separately with more freedom degree and less conservatism. The effectiveness and the robustness of the proposed strategy are verified through a case study for a two-spool turbofan engine.

Energy Based Limit Cycle Control of Elastically Actuated Robots

A new control law for elastic joint robots that allows to regulate an energy function of the system to a desired value is presented in this technical note. Being able to either remove energy from the system or inject into it, oscillations can be both damped out and induced. The proposed nonlinear dynamic state feedback controller forces the system to evolve on a submanifold of the configuration space. The reduced dynamics of the system and of the controller itself are similar to a single elastic joint, for which an asymptotically stable limit cycle is obtained regulating an energy function to a positive desired value. When the desired value of the energy function is chosen to be zero, then the asymptotically stable limit cycle reduces to an asymptotically stable equilibrium point. In this case the oscillations are damped out and the desired task-space configuration is reached. The design of the controller extensively uses the concept of conditional stability, so that the limit cycle can be designed for a lower dimensional dynamical system, although it will result to be a limit cycle for the whole system.

An Interval-Valued Fuzzy Cerebellar Model Neural Network Based on Intuitionistic Fuzzy Sets

An interval-valued fuzzy cerebellar model neural network (IV-FCMNN) is proposed for the identification and control of uncertain systems. It is a more general model that uses the framework of a cerebellar model neural network (CMNN) and Atanassov intuitionistic fuzzy sets (AIFSs), so that the mathematical representation of a fuzzy event is more complete and the fuzzy neural network is more general. In some special cases, this neural network can be reduced to an interval-valued fuzzy neural network (IV-FNN), a fuzzy neural network (FNN), a fuzzy cerebellar model neural network (FCMNN) or a CMNN. Since the interval-type input data are used to realize this algorithm, the IV-FCMNN copes better with uncertainty and allows greater freedom of design. Therefore, the ability to learn, the approximation precision and the fuzzy semantic description of this network are much better than those of other models. In the proposed IV-FCMNN, a training algorithm that uses a gradient descent method is proposed to adjust the parameters and convergence is proved using the Lyapunov stability theorem. The variable learning rates are analyzed and the optimal learning rates are also determined. For demonstrating the effectiveness of the proposed IV-FCMNN, three types of applications, including multiple functions approximation, multi-dimensional classification and nonlinear dynamic system feedback control, are performed and the comparison with other models are also provided.

Nonlinear robust state feedback control system design for nonlinear uncertain systems

SummaryThis paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.

Stability of an Euler-Bernoulli Beam With a Nonlinear Dynamic Feedback System

This paper is concerned with the stability analysis of a lossless Euler-Bernoulli beam that carries a tip payload which is coupled to a finite-dimensional nonlinear dynamic feedback system. The latter comprises dynamic systems satisfying the nonlinear KYP lemma, which may represent the closed-loop dynamics of subordinate controlled actuators, as well as the interaction with a nonlinear passive environment. Global-in-time wellposedness and asymptotic stability is rigorously proven for the resulting closed-loop partial differential equation–ordinary differential equation (PDE–ODE) system. The analysis is based on semigroup theory for the corresponding first order evolution problem. For the large-time analysis, precompactness of the trajectories is shown by deriving uniform-in-time bounds on the solution and its time derivatives.