Robust Nonlinear Feedback Control Research Articles

A Novel Hybrid Robust Control Design Method for F-16 Aircraft Longitudinal Dynamics

This paper presents a hybrid robust control design method for a third-order lower-triangular model of nonlinear dynamic systems in the presence of disturbance. In this paper, a novel control design is presented systematically to synthesize a robust nonlinear feedback controller, called backstepping sliding mode control (BSMC), for the proposed system by a combined approach of backstepping design and sliding mode control. In this approach, a family of the “sliding surface” is introduced in state transformations. Then, a smooth switching function of the sliding surface is introduced and enforced to include in virtual feedbacks and a real control law from the control selection phrases of the backstepping design loop. The achieved control method proves a well-tracking command with asymptotic stability, provides a robustness in the presence of uncertainties, and eliminates completely a chattering phenomenon. The application of flight-path angle control corresponding to the longitudinal dynamics of a high-performance F-16 aircraft simulation model is implemented. Under some assumptions, full nonlinear longitudinal dynamics is reformed into a lower-triangular system for a direct application to formulate a control law. A closed-loop system is achieved for in-flight simulation with different flight profiles for a comparison of the existing methods. Also, an external disturbance on different loading/unloading conditions in flight is applied to verify and validate robustness of the proposed control method.

A finite time adaptive back‐stepping sliding mode control for instantaneous active‐reactive power dynamics based DFIG‐wind generation towards improved grid stability

AbstractIn this paper, a low computational, robust nonlinear feedback control is proposed as independent distributed generation controller (IDGC) for doubly fed induction generator (DFIG) based wind power generation system (WPGS). WPGS integration as distributed generation (DG) to grid point of common coupling (PCC) is reflecting high power loss profile in terms of low frequency oscillations under grid operational contingencies and have high instability hazard under unbounded uncertainties like unintentional islanding operation. Thus, to improve the stability margin of DFIG‐WPGS integration fast DG dynamic relations are obtained, where instantaneous active‐reactive power (P‐Q) formulation is proposed to avoid unnecessary phase locked loop (PLL) angle (ω) estimation. The feedback path is designed with proposed finite time adaptive backstepping sliding mode control (FTABSMC) for IDGC operation according to ISA‐95 standards. The FTABSMC is ensured with bounded/unbounded uncertainty handling capability by incorporating backstepping based dynamic error profile depletion and with enhanced stability margin by finite time sliding surface based error trajectory to equilibrium. Further, the adaptive sliding surface estimation is proposed in terms of dynamic uncertainty (energy fluctuation) for robust unbounded uncertainty handling. The stability improvement is established with small‐signal (SS) based closed loop analysis of considered DFIG‐WPGS. The uncertainty handling capability is presented thought rigorous case studies in MATLAB based simulation environment and TMS 320 digital signal processor (DSP) based processor‐in‐loop (PIL) validation.

Robust Nonlinear State Feedback Control of Bidirectional Interlink Power Converters in Grid-Connected Hybrid Microgrids

In this paper, a new scheme based on state feedback control concept is presented for robust control of bidirectional interlink power converters (BILPCs) in hybrid microgrids (HMGs). The studied grid-connected HMG contains one dc and one ac microgrid, interconnected by BILPCs. To consider uncertainties, the nonlinear uncertain model of the BILPC is derived and linearized based on Lie derivative concept. As a new point of view for dynamic modeling of BILPC, it is indicated that each nonlinear uncertain BILPC model can be represented by two decoupled subsystems. Then, a virtual robust state feedback controller is designed to independently control each of these subsystems with disturbance rejection capability. The gains of the state feedback controllers are obtained using Ackerman pole placement method. To approximate the unknown inputs/unmodeled dynamics, which are needed in the design process of the state feedback controllers, a high-gain proportional-integral (PI) observer is designed. The high gains of this PI observer are determined using linear quadratic regulation method. Simulation results and comparative studies support the efficacy of the proposed control approach.

Quaternion-based Robust Trajectory Tracking Control of a Quadrotor Hover System

This paper presents a robust nonlinear output feedback control method that achieves three degree of freedom (3-DOF) attitude trajectory tracking of a hover system test bed. The proposed control method formally incorporates dynamic model uncertainty in addition to test bed voltage constraints. To reduce the computational requirement in the closed-loop system, constant feedforward estimates of the input-multiplicative parametric uncertainty are utilized in lieu of adaptive parameter estimates. To eliminate the need for angular rate measurements, the control design employs a bank of dynamic filters, which operates as a velocity estimator in the closed-loop system. A rigorous error system development and Lyapunov-based stability analysis are presented to prove asymptotic 3-DOF attitude trajectory tracking control. Computer simulation and experimental results are also included to illustrate the performance of the attitude control method using the Quanser 3-DOF hover system test bed.

Approximate finite‐time control for a class of uncertain nonlinear systems with dynamic compensation

SummaryIn this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite‐time single‐input single‐output nonlinear system with uncertainty. In further tracking the closed‐loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to solve for the finite‐time stability of the closed‐loop system; furthermore, numerical simulations showed that the robust nonlinear feedback controller tracked the uncertainty in a nonlinear Duffing‐type oscillator and has proven the effectiveness of the approximate finite‐time control strategy proposed. By using an approximate finite‐time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled. Copyright © 2017 John Wiley & Sons, Ltd.

Operator-based experimental studies on nonlinear vibration control for an aircraft vertical tail with considering low-order modes

In this paper, a robust nonlinear control design using an operator-based robust right coprime factorization approach is considered for vibration control on an aircraft vertical tail with piezoelectric elements. First, a model of the aircraft vertical tail is derived to describe vibration response using the operator-based approach, where, to stabilize vibration of the tail, piezoelectric elements are used as actuators and a hysteresis nonlinear property of piezoelectric actuators is considered. Simultaneously, positions of the piezoelectric actuators that are stuck on the plate are arranged by using a finite element method. Then based on the obtained operator-based model, a robust nonlinear feedback control design is given by using robust right coprime factorization for the aircraft vertical tail with considering the effect of hysteresis nonlinearity from piezoelectric actuators. In particular, low-order modes are employed to design the control scheme even though vibration is configured by high-order modes. In other words, robustness is considered, and the desired performance of tracking is discussed. Finally, both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.

Adaptive robust nonlinear feedback control of chaos in PMSM system with modeling uncertainty

It has been proved that chaos exists in the permanent-magnet synchronous motor (PMSM) system when its parameters satisfy some condition, and it would degrade the efficiency of the PMSM system dramatically. In this paper, an adaptive robust control method is proposed to eliminate or suppress the chaos in PMSM, based on the mathematical analysis of chaotic property of the PMSM system. It not only accounts for the parametric uncertainties (structured uncertainties) but also takes the external load torque disturbances (unstructured uncertainties) into account. Adaptive control item is designed to deal with the former while robust item is designed to deal with the latter and the parametric estimation error respectively and both of them are integrated together via a feedforward cancellation technique. Numerical simulation results show that this method is more reliable, more accurate, and thus more applicable, compared to the existing control methods.

Controlling a class of chaotic quantum system under disturbances and noisy measurements: Application to 1D Bose-Einstein condensate

In this paper, a robust nonlinear feedback control scheme with adaptive gain is proposed to control the chaotic behavior in a Bose–Einstein condensate (BEC). The control goal concerns the track or regulation purposes. The BEC system is represented as stochastic ordinary differential equations with measured output perturbed by Gaussian noise, which represents the nature of the quantum systems. The convergence of the BEC control law is analyzed under the frame of the Lyapunov stability theory. Numerical experiments show an adequate performance of the proposed methodology under the required conditions. The results are applicable when the shape of the condensate is sufficiently simple.

Using Inverse Nonlinearities in Robust Output Feedback Guaranteed Cost Control of Nonlinear Systems

This paper extends the result of an earlier paper on constructive robust nonlinear output feedback controller design, which is based on the use of IQCs and minimax LQG control. In this paper, in addition to copies of the nonlinearities, we include copies of the inverses of the nonlinearities in the controller. Consequently more IQCs are exploited in the design procedure, which gives a smaller bound on the closed-loop cost function than the earlier result.

Robust nonlinear feedback control of a chaotic permanent-magnet synchronous motor with a load torque disturbance

The permanent-magnet synchronous motor (PMSM) system, which is a nonlinear dynamic system, will demonstrate a variety of chaotic phenomena when its parameters or external inputs fall into a certain area, which will lead to a deterioration of its performance. Thus, chaos should be suppressed or eliminated. In this paper, the property of equilibrium points is analyzed, and the condition for the occurrence of a Hopf bifurcation in a PMSM system is given based on a mathematical model of the PMSM system with a bifurcation diagram, a Lyapunov exponent map and phase plane diagrams given. After the drawbacks of the existing control methods have been analyzed, a robust nonlinear feedback controller is designed to control the chaos in the PMSM system with a load torque disturbance. The object is to eliminate the chaos and to drive the system speed to a desired value, Numerical simulation proves the validity of this control method.

Tensegrity deployment using infinitesimal mechanisms

Kinematic properties of tensegrity structures reveal that an ideal way of motion is by using their infinitesimal mechanisms. For example in motions along infinitesimal mechanisms there is no energy loss due to linearly kinetic tendon damping. Consequently, a deployment strategy which exploits these mechanisms and uses the structure’s nonlinear equations of motion is developed. Desired paths that are tangent to the directions determined by infinitesimal mechanisms are constructed and robust nonlinear feedback control is used for accurate tracking of these paths. Examples demonstrate the feasibility of this approach and further analysis reveals connections between the power and energy dissipated via damping, infinitesimal mechanisms, speed of the motion, and deployment time.

Operator-based robust nonlinear control and its realization for a multi-tank process by using a distributed control system

In this paper, a robust nonlinear control design method using an operator-based robust right coprime factorization approach and its realization based on a distributed control system (DCS) device are considered for a multi-tank process. In detail, for the multi-tank process, consisting of a water-level process and a water-flow process, theoretical models are developed according to the Bernoulli theorem. Based on the obtained models, a robust nonlinear feedback control design is presented by using robust right coprime factorization for the multi-tank process. Further, from a large-scale industrial application viewpoint, the realization of the designed operator-based robust right coprime factorization controllers is considered by using a DCS device. Because there are some nonlinear functions in the designed controllers which cannot be realized straightforwardly in the DCS device such that the designed controllers need to be realized approximately. That is, there exist some parasitic terms for the approximated realization of the controllers in the real system. As a result, the parasitic terms and processes’ unknown uncertainties should be considered simultaneously. In this paper, a robust condition is derived to guarantee robust stability of the nonlinear feedback control system with the parasitic terms and the uncertainties. Moreover, tracking controller design problem for the multi-tank process is discussed. Finally, by using a DCS device (CENTUM CS3000), experimental results are given to confirm the effectiveness of the proposed design scheme.

Adaptive tracking and asymptotic rejection of unknown but bounded disturbances in nonlinear MIMO systems

The goal of this paper is global disturbance rejection in nonlinear systems. An output feed- back controller with disturbance rejection is developed for a class of nonlinear multi input-multi output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance and reference tracking will is guaranteed. By the aid of designing an adaptive ob- server, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. For tracking problem, an adaptive pre-compensator is used. The control methodology is robust against both constant and time varying bounded disturbances, maintaining effective performance. The adaptive laws are derived based on the Lyapunov synthesis method, therefore closed-loop asymptotic stability is also guaranteed. Moreover, for chattering reduction we use a low-pass filter. Consequently, small gain theo- rem is adopted to prove the stability of the closed-loop system. Simulation results are employed to illu- strate the effectiveness of the proposed controller.

Robust non-linear feedback control for BTT missile with NN-based uncertainty estimation

A robust non-linear feedback control strategy combined with neural network (NN) estimator is presented, for the non-linear model of bank-to-turn (BTT) missile with modeling uncertainties. The non-linearities in the missile dynamics are taken into account, including coupling items between three channels. Standard feedback linearisation is implemented to linearise and decouple the nominal system. In the presence of unknown bounded uncertainties, the performance will deteriorate because the precise model cannot be obtained. Then, linear matrix inequality (LMI) based guaranteed cost control (GCC) is adopted to solve the robust control problem for the linearised uncertain models. Further, adaptive neural network estimators, which use Lyapunov based tuning rules, are integrated in the control strategy to eliminate the effect of high-order uncertain terms. Simulation results on a specified BTT missile model are provided to demonstrate the feasibility and effectiveness of the proposed approach, which achieves more improved tracking performance comparing with conventional method.

Dynamic Modelling and Stability Analysis of Model-Scale Helicopters Under Wind Gust

The purpose of this paper is to present the stabilization (tracking) with motion planning of a reduced-order model having 3 Degrees Of Freedom (DOF). This last one represents a scale model helicopter mounted on an experimental platform. It deals with the problem of disturbance reconstruction acting on the autonomous helicopter, the disturbance consists in vertical wind gusts. The objective is to compensate these disturbances and to improve the performances of the control. Consequently, a nonlinear simple model with 3DOF of a helicopter with unknown disturbances is used. Three approaches of robust control are compared via simulations: a robust nonlinear feedback control, an active disturbance rejection control based on a nonlinear extended state observer and backstepping control.

Output feedback control with disturbance rejection of a class of nonlinear MIMO systems

Output feedback control with disturbance rejection is developed for a class of nonlinear multi-input-multi-output (MIMO) systems. The availability of state variables and the bound of disturbances are not required to be known in advance. In the design of an adaptive observer, a robust adaptive nonlinear state feedback controller using the estimated states is proposed. The control methodology is robust to bounded disturbances that are both constant and time-varying, with effective performance. The adaptive laws are derived based on the Lyapunov synthesis method; therefore closed-loop asymptotic stability is also guaranteed. Moreover, chattering can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed controller.

Robust nonlinear output feedback control for brake by wire control systems

This work proposes a nonlinear output feedback control law for active braking control systems. The control law guarantees bounded control action and can cope also with input constraints. Moreover, the closed-loop system properties are such that the control algorithm allows to detect—without the need of a friction estimator—if the closed-loop system is operating in the unstable region of the friction curve, thereby allowing to enhance both braking performance and safety. The design is performed via Lyapunov-based methods and its effectiveness is assessed via simulations on a multibody vehicle simulator.

A Robust nonlinear state feedback control law for a stirred tank chemical reactor with recycling

A nonlinear state feedback control law for a stirred tank chemical reactor with recycling is studied in this paper. The system is described by nonlinear delay differential equations and the projected control law depends on the system variables at present and past times. Such feedback control law drives the output of the system, the reactor temperature, at the desired value, with exponential error decay rate. Moreover, the closed loop system is locally input-to-state stable with respect to a disturbance forcing, as the control law, the jacket temperature. Such disturbance may well describe sensor and actuator errors, as well as errors due to parameters uncertainty such as the time-delay. Copyright @ IFAC, 7th Workshop on Time-Delay Systems, Nantes, September 2007.

Robust Adaptive Transient Stabilization of a Synchronous Generator with Parameter Uncertainty

A robust nonlinear state feedback control achieving transient stabilization is designed on the basis of a third order model of a synchronous generator connected to an infinite bus, relying on the well-understood nonlinearities of the model but not on the parameters which, with the exception of the synchronous speed, are not assumed to be known and are also allowed to be time-varying (within known bounds) to account for unmodelled dynamics. Sudden mechanical power failures, short circuits, infinite bus perturbations may drive the generator outside its stability region and therefore out of step. The proposed robust nonlinear excitation control prevents the machine from going out of step in the presence of mechanical and/or electrical parameter perturbations: when all parameters are equal to their nominal values, the operating condition is the only equilibrium point of the closed loop system with an explicitly computable stability region; boundedness and L ∞ and L 2 disturbance attenuations are guaranteed from the power angle and relative speed regulation errors with respect to time-varying parameter variations from nominal values. An adaptive option can be added to the nonlinear robust controller which guarantees asymptotic speed regulation if the parameter variations from nominal values become constant.

Nonlinear robust temperature–humidity control in livestock buildings

The physical environment of farm animals inside livestock buildings is primarily characterised by hygro-thermal parameters and air quality. These parameters are influenced by the interaction with the outdoor situation on one hand, and the livestock, the ventilation system and the building on the other hand. Livestock housing must ultimately provide environmental conditions favorable to the preservation of animal health and welfare and, consequently, to the efficiency of animal production. To reach the best environmental conditions inside a building, it is necessary to apply advanced control systems and effective control techniques. In this paper, such a new control technique is presented. In particular, the use of robust nonlinear feedback control in conjunction with feedforward action, in order to assure arbitrarily small deviations in the desired temperature and humidity values in an animal building, is described. This method results in a controller whose characteristics depend on knowledge of the bounds of the uncertain elements in the system description. The method is illustrated by simulation studies for a contemporary pig house during summer and winter operation.