Nonlinear Dynamic Feedback Research Articles

Nonlinear modelling and control of the flow over aerofoils using CFD simulations

A simulation based approach for nonlinear dynamical modelling and feedback control of the drag to lift ratio for aerofoils is investigated through case studies involving NACA 23012, ag13 and b737a aerofoils. The flow around the aerofoils is studied via numerical solutions of the 2D Navier–Stokes (NS) equations. A standard computational fluid dynamics (CFD) solver is extended to be able to measure desired feedback values and to apply a control input to the flow field. The proposed modelling and control approach is based on first determining the measurement points and injection points on the aerofoil for the control input. Then, to estimate the dynamical model, some input–output data are collected by injecting a chirp input flow to the field and saving the measurement data. Next a Hammerstein–Wiener (HW) type nonlinear dynamical model of the flow field is estimated using system identification. For control design, the nonlinear part of the model is eliminated by means of inverse functions, followed by the application of automated tuning methods to the linear part to obtain the closed-loop system. The results show that the designed feedback control system can reduce the drag to lift ratio considerably as compared to the unactuated case.

Dynamic anti-windup design for a class of nonlinear systems

ABSTRACTThis work addresses the dynamic anti-windup design problem for a class of nonlinear systems subject to actuator saturation. The considered class regards the systems that can be cast in a differential algebraic representation (DAR), such as rational and polynomial systems. Considering that a nonlinear dynamic output feedback controller, which can also be written as a DAR, has been designed to stabilise the nonlinear system disregarding the saturation effects, LMI-based conditions are proposed to compute a stabilising dynamic anti-windup compensator. Two problems are considered: the first one regards the regional internal stabilisation; and the second one, assuming that an energy-bounded disturbance acts on the system, concerns the input-to-state stability. The derived conditions can therefore be incorporated in convex optimisation problems that allow to compute the anti-windup compensator in order to maximise the region of guaranteed asymptotic stability, to maximise a bound on the admissible -norm of the disturbance or even to minimise a bound on the -gain between the disturbance and the output. Numerical examples illustrate the proposed methods.

An adaptive control for a variable speed wind turbine using RBF neural network

In this work, a controller based on Radial Basis Functions (RBF) for network adaptation is considered. The adaptive Neural Network (NN) control approximates the nonlinear dynamics of the wind turbine based on input/output measurement and ensures smooth tracking of optimal tip speed-ratio at different wind speeds. The wind turbine system and this controller were modeled and a program to integrate the obtained coupled equations was developed under Matlab/Simulink software package. Then, performance of the controller was studied numerically. The proposed controller was found to effectively improve the control performance against large uncertainty of the wind turbine system. comparison with nonlinear dynamic State feedback control with Kalman filter controller was performed, and the obtained results have demonstrated the relevance of this RBFNN based controller.

Structural Identification of Nonlinear Dynamic Biomolecular Feedback and Feedforward Loops

Many biomolecular networks are still widely unknown. With high structural uncertainties, bottom-up identification based on model discrimination tends to fail because of combinatorially many possible model structures. Top-down approaches, in contrast, describe general signal processing properties, rather than specific mechanisms. Most of these approaches originated in engineering disciplines where linearity is commonly (approximately) given, but naturally evolved networks exhibit a rather high degree of nonlinearity. Here, we present a top-down structural identification method that is not only applicable to nonlinear biomolecular networks, but indeed requires the network under study to be nonlinear. Similar to traditional frequency domain analysis, we apply an oscillatory input signal to a biomolecular network. However, instead of varying the frequency, we vary the mean value of the oscillatory signal to detect, discriminate, and partly characterize single feedback and feedforward loops in nonlinear networks.

Nonlinear dynamic output-feedback power-level control for PWRs: A shifted-ectropy based design approach

Nuclear fission energy is currently the sole energy that can substitute fossil in a centralized way and great amount with commercial availability and economic competitiveness. Power-level control is one of the key techniques which provide safe, stable and efficient operation for nuclear power plants. The physically-based regulation theory is definitely a promising trend of modern control theory, which can provide a control design method that suppresses the unstable part of the system dynamics and remains the stable part. Usually, control laws designed by the physically-based control theory have a simple form and high performance. Stimulated by this, a novel nonlinear dynamic output feedback power-level control law is established in this paper for the pressurized water nuclear reactors (PWRs) based upon its natural dynamic features. This newly-developed controller guarantees not only the globally asymptotic closed-loop stability but also the satisfactory transient performance through properly adjusting the feedback gains. Furthermore, this controller has the L2 disturbance attenuation performance. Numerical simulation results not only verify the correctness of the theoretical results but also illustrate the high control performance.

Design of Anti-Windup Compensators for a Class of Nonlinear Control Systems with Actuator Saturation

This paper addresses the design of static anti-windup compensators for a class of nonlinear systems subject to actuator saturation. Considering that a (possibly nonlinear) dynamic output feedback control law has been previously designed disregarding the saturation, a method to compute a static anti-windup gain which ensures the local stability of the closed-loop system is proposed. The results are based on a differential algebraic representation of rational systems and on a modified version of the generalized sector condition to deal with the saturation effects. From these elements, an algorithm based on the solution of LMIs is proposed to calculate an anti-windup gain to enlarge the region of attraction of the closed-loop system. Moreover, extensions of the results are presented to deal with parameter uncertainty and the presence of energy bounded disturbances. A numerical example is presented to illustrate the proposed method.

Lyapunov-based hybrid loops for stability and performance of continuous-time control systems

We construct hybrid loops that augment continuous-time control systems. We consider a continuous-time nonlinear plant in feedback with a (possibly non stabilizing) given nonlinear dynamic continuous-time state feedback controller. The arising hybrid closed loops are guaranteed to follow the underlying continuous-time closed-loop dynamics when flowing and to jump in suitable regions of the closed-loop state space to guarantee that a positive definite function V of the closed-loop state and/or a positive definite function Vp of the plant-only state is non-increasing along the hybrid trajectories. Sufficient conditions for the construction of these hybrid loops are given for the nonlinear case and then specialized for the linear case with the use of quadratic functions. For the linear case we illustrate specific choices of the functions V and Vp which allow for the reduction of the overshoot of a scalar output. The proposed approaches are illustrated on linear and nonlinear examples.

Physically-Based Power-Level Control for Modular High Temperature Gas-Cooled Reactors

Because of its strong inherent safety, the modular high temperature gas-cooled nuclear reactor (MHTGR) has been regarded as the central part of the next generation nuclear plants (NGNPs). Power-level control is one of the key techniques which provide safe, stable and efficient operation for the MHTGRs. The physically-based regulation theory is definitely a promising trend of modern control theory and provides a control design method that can suppress the unstable part of the system dynamics and remain the stable part. Usually, the control law designed by the physically-based control theory has a simple form and high performance. Stimulated by this, a novel nonlinear dynamic output feedback power-level control is established in this paper for the MHTGR based upon its own dynamic features. This newly-built control strategy guarantees the globally asymptotic stability and provides a satisfactory transient performance through properly adjusting the feedback gains. Simulation results not only verify the correctness of the theoretical results but also illustrate the high control performance.

Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems

This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.

Simultaneous external and internal stabilization of linear systems with input saturation and non-input-additive sustained disturbances

In this paper, we study simultaneous external and internal stabilization of the linear system under input saturation and non-input additive sustained disturbances. For systems that are asymptotic null controllable with bounded control, it is shown that a nonlinear dynamic feedback controller can be designed so that the closed-loop states remain bounded for any initial condition and for two classes of sustained disturbances, and that the equilibrium in the absence of disturbances is globally asymptotically stable.

Online Trajectory Generation for Mobile Robots with Kinodynamic Constraints and Embedded Control Systems

The paper describes trajectory generation and tracking control algorithms, respectively based on nonlinear filtering and dynamic feedback linearization, for mobile robots. A main feature of proposed algorithms is that they are suitable for the implementation on embedded systems with limited computational resources. The trajectory generator is based on nonlinear filters and logic-based management of reference inputs and dynamic constraints, allowing online smoothing of straight-line reference paths. Sparse via-points along a path can be assigned by a global planner based on obstacle avoidance algorithms and can be changed at any time during motion. Moreover, the trajectory generated by the nonlinear filter can be fed into a control loop based on the dynamic model of the robot, so that accurate tracking can be achieved. The paper includes practical remarks for efficient fixed-point implementation of the proposed trajectory generator.

Anti-windup Design for a Class of Nonlinear Control Systems

AbstractThis paper focuses on the problem of static anti-windup design for a class of nonlinear systems subject to actuator saturation. Considering that a nonlinear dynamic output feedback controller has been designed to stabilize the nonlinear system, a method is proposed to compute a static anti-windup gain which ensures the local stability of the the closed-loop system while providing an estimate of the region of attraction. The results are based on a differential-algebraic representation of rational systems and a modified sector bound condition to deal with the saturation effects. From these elements, LMI based conditions are proposed to compute an anti-windup gain for enlarging the size of the closed-loop region of attraction. A numerical example is given to illustrate the proposed method.

Finite-time semistability, Filippov systems, and consensus protocols for nonlinear dynamical networks with switching topologies

This paper focuses on semistability and finite-time semistability for discontinuous dynamical systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we extend the theory of semistability to discontinuous autonomous dynamical systems. In particular, Lyapunov-based tests for strong and weak semistability as well as finite-time semistability for autonomous differential inclusions are established. Using these results we then develop a framework for designing semistable and finite-time semistable protocols for dynamical networks with switching topologies. Specifically, we present distributed nonlinear static and dynamic output feedback controller architectures for multiagent network consensus and rendezvous with dynamically changing communication topologies.

High order sliding-mode dynamic control for chaotic intracellular calcium oscillations

In this article the closed-loop stability conditions and the control design of a class of biological system that exhibit chaotic oscillations are addressed. It is proved that the biological system is minimum phase. A class of nonlinear dynamic feedback control is designed using sliding-mode control ideas, which can be used for regulation, tracking and synchronization tasks. Numerical experiments illustrate the satisfactory performance of the proposed control methodology.

Dynamic arrest within the self-consistent generalized Langevin equation of colloid dynamics

This paper presents a recently developed theory of colloid dynamics as an alternative approach to the description of phenomena of dynamic arrest in monodisperse colloidal systems. Such theory, referred to as the self-consistent generalized Langevin equation (SCGLE) theory, was devised to describe the tracer and collective diffusion properties of colloidal dispersions in the short- and intermediate-time regimes. Its self-consistent character, however, introduces a nonlinear dynamic feedback, leading to the prediction of dynamic arrest in these systems, similar to that exhibited by the well-established mode coupling theory of the ideal glass transition. The full numerical solution of this self-consistent theory provides in principle a route to the location of the fluid-glass transition in the space of macroscopic parameters of the system, given the interparticle forces (i.e., a nonequilibrium analog of the statistical-thermodynamic prediction of an equilibrium phase diagram). In this paper we focus on the derivation from the same self-consistent theory of the more straightforward route to the location of the fluid-glass transition boundary, consisting of the equation for the nonergodic parameters, whose nonzero values are the signature of the glass state. This allows us to decide if a system, at given macroscopic conditions, is in an ergodic or in a dynamically arrested state, given the microscopic interactions, which enter only through the static structure factor. We present a selection of results that illustrate the concrete application of our theory to model colloidal systems. This involves the comparison of the predictions of our theory with available experimental data for the nonergodic parameters of model dispersions with hard-sphere and with screened Coulomb interactions.

Planetary and synoptic scale adjustment of the Arctic atmosphere to sea ice cover changes

By means of unforced simulations with a global coupled circulation model it is shown that naturally occurring changes between high and low sea ice cover phases of the Arctic Ocean exert a strong influence on the Northern Hemisphere storm tracks. This work emphasizes the nonlinear dynamical feedback between Arctic sea ice cover and the Arctic Oscillation (AO) such as atmospheric response depending upon the wintertime sea ice distribution. Two seven year long time slices, with high and low sea ice cover, were analyzed with respect to the feedbacks between the time‐mean flow, the quasi‐stationary planetary and the baroclinic waves. The wave energy fluxes on time scales of 2 to 6 days increase in the middle troposphere between 30 and 60°N during the high sea ice phase and increase the zonal wind. This increase is compensated by a strong reduction in the Eliassen‐Palm fluxes on time scales from 10 to 90 days between 60 and 70°N during high sea ice phases, accompanied by reduced zonal winds. High sea ice cover phases are related to the zonal wind changes during the positive phases of the AO, especially over the northern part of the Atlantic Ocean.

Unified stabilizing controller synthesis approach for discrete-time intelligent systems with time delays by dynamic output feedback

A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems composed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.

Multivariable control strategy for variable speed, variable pitch wind turbines

Reliable and powerful control strategies are needed for wind energy conversion systems to achieve maximum performance. A new control strategy for a variable speed, variable pitch wind turbine is proposed in this paper for the above-rated power operating condition. This multivariable control strategy is realized by combining a nonlinear dynamic state feedback torque control strategy with a linear control strategy for blade pitch angle. A comparison with existing strategies, PID and LQG controllers, is performed. The proposed approach results in better power regulation. The new control strategy has been validated using an aeroelastic wind turbine simulator developed by NREL for a high turbulence wind condition.

Nonlinear Control of Variable-Speed Wind Turbines for Generator Torque Limiting and Power Optimization

To maximize wind power extraction, a variable-speed wind turbine (VSWT) should operate as close as possible to its optimal power coefficient. The generator torque is used as a control input to improve wind energy capture by forcing the wind turbine (WT) to stay close to the maximum energy point. In general, current control techniques do not take into account the dynamical and stochastic aspect of both turbine and wind, leading to significant power losses. In addition, they are not robust with respect to disturbances. In order to address these weaknesses, a nonlinear approach, without wind speed measurement for VSWT control, is proposed. Nonlinear static and dynamic state feedback controllers with wind speed estimator are then derived. The controllers were tested with a WT simple mathematical model and are validated with an aeroelastic wind turbine simulator in the presence of disturbances and measurement noise. The results have shown better performance in comparison with existing controllers.

NONLINEAR OUTPUT FEEDBACK CONTROL OF A 5DOF AMB SYSTEM

A nonlinear dynamic output feedback control method for a 5-degree-of-freedom AMB is presented in this paper. This method is based on the system structure of AMB and a quadratic-like Lyapunov function. It is shown that backstepping and completing square techniques enable the construction of the voltage input by using measured output only. The control law guarantees the asymptotic stability of the closed loop system.