Nonlinear Dynamic Plants Research Articles

Stability in small signals investigation of nonlinear dynamic power systems

The new technique of Frobenius norm calculation of Gramians, sub-Gramians and transfer functions of electric power systems (EPS) is suggested. It is based on spectral expansion of gramian by combinational modes of dynamic matrix of EPS predicting model. It is more effective comparing to modal analysis as it allows to prescribe the criterion of EPS stability loss risk, and also to evaluate the interaction of ill-stable system modes. The suggested approach has a transparent physical interpretation, i.e., stability loss risk corresponds to the energy of ill-stable modes group. The predicting model is formed basing on associative search technique for nonlinear dynamic plants.

Improving Quality of Regulation of a Nonlinear MIMO Dynamic Plant

The paper presents a robust two-degrees of freedom control system for a multi-input, multi-output (MIMO) nonlinear dynamic process. There are discussed the advantages of the model following control (MFC) structure for MIMO systems, its stability and robustness properties and a method for synthesis of a multi-controller structure of the MFC model loop. The problems under study are exemplified by synthesis of a position and yaw angle control system for a 3DOF nonlinear mathematical model of a drillship, where the MFC structure is used to reduce effects of the impact of the sea current and wind forces on the ship's hull. perturbations, as well as great disturbances dumping at the input and at the output of the plant to be controlled (10)- (12). In the paper we fully utilize this theory and adopt the MFC advantages to synthesize a robust control system of improved quality for a class of nonlinear MIMO systems. The problems under study are exemplified by synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low- frequency motions over the drilling point. The effectiveness of the proposed MFC structure is shown by its use to compensate the environmental disturbances, the impact of

NARX model based nonlinear dynamic system identification using low complexity neural networks and robust H∞ filter

This paper proposes NARX (nonlinear autoregressive model with exogenous input) model structures with functional expansion of input patterns by using low complexity ANN (artificial neural network) for nonlinear system identification. Chebyshev polynomials, Legendre polynomials, trigonometric expansions using sine and cosine functions as well as wavelet basis functions are used for the functional expansion of input patterns. The past input and output samples are modeled as a nonlinear NARX process and robust H∞ filter is proposed as the learning algorithm for the neural network to identify the unknown plants. H∞ filtering approach is based on the state space modeling of model parameters and evaluation of Jacobian matrices. This approach is the robustification of Kalman filter which exhibits robust characteristics and fast convergence properties. Comparison results for different nonlinear dynamic plants with forgetting factor recursive least square (FFRLS) and extended Kalman filter (EKF) algorithms demonstrate the effectiveness of the proposed approach.

Linear adaptive structure for control of a nonlinear MIMO dynamic plant

In the paper an adaptive linear control system structure with modal controllers for a MIMO nonlinear dynamic process is presented and various methods for synthesis of those controllers are analyzed. The problems under study are exemplified by the synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system, use is made of a set of (stable) linear modal controllers that create a linear adaptive controller with variable parameters tuned appropriately to operation conditions chosen on the basis of two measured auxiliary signals. These are the ship’s current forward speed measured in reference to the water and the systematically calculated difference between the course angle and the sea current (yaw angle). The system synthesis is carried out by means of four different methods for system pole placement after having linearized the model of low-frequency motions made by the vessel at its nominal “operating points” in steady states that are dependent on the specified yaw angle and the sea current velocity. The final part of the paper includes simulation results of system operation with an adaptive controller of (stepwise) varying parameters along with conclusions and final remarks.

Disturbance observer assisted robust control of wing rock motion based on contraction theory

A nonlinear robust control strategy is proposed in this paper to deal with wing rock motion. The method is based on the disturbance observer enforced contraction theory results. The disturbance observer calculates and robustly cancels system uncertainties and input disturbances. The information regarding the known part of the nonlinear plant dynamics is used by the controller, while the uncertainties and disturbances are treated as an additional input to the system and dealt with by the disturbance observer. The algorithm demonstrates good performance in damping the oscillations while rejecting the disturbances. Simulations are provided to demonstrate the effectiveness of the proposed method via an application to an experimentally derived delta wing rock model operating in both nominal and uncertain environments.

Local control gradients criterion for selection of neuroemulators for model reference adaptive neurocontrol

We discuss neural identification and control of nonlinear dynamic plant. We analyze a problem of selection of a proper neuroemulator for training neurocontrollers, and we propose a new effective criterion based on the analysis of local gradients of neuroemulator's input neurons. We present results of numerical simulations of neurocontroller training by a gradient descent method and by an Extended Kalman Filter method.

Neural Internal Model Control for tracking Unknown Nonaffine Nonlinear Discrete-time Systems under External Disturbances

of nonlinear dynamic plants under external disturbances is presently an active area of research. The main difficulty felt in the tracking of nonlinear dynamic plants under external disturbances is the computational complexity in control design. This paper presents a simple neural network internal model control (IMC) approach for off-line tracking of unknown nonaffine nonlinear discrete time systems subject to external disturbances. The proposed control scheme is based on the neural network plant model and the inverse model. These models are determined using input output data. The final neural network IMC approach, including network plant model and the inverse model, is work off-line for tracking nonaffine nonlinear discrete time systems subject to external disturbances. Simulation results have been presented toward the end of the paper to illustrate the effectiveness of the proposed control strategy for tracking unknown nonaffine nonlinear discrete-time systems with and without external disturbances.

WSVR-based fuzzy neural network with annealing robust algorithm for system identification

This paper proposes a fuzzy neural network (FNN) based on wavelet support vector regression (WSVR) approach for system identification, in which an annealing robust learning algorithm (ARLA) is adopted to adjust the parameters of the WSVR-based FNN (WSVR-FNN). In the WSVR-FNN, first, the WSVR method with a wavelet kernel function is used to determine the number of fuzzy rules and the initial parameters of FNN. After initialization, the adjustment for the parameters of FNNs is performed by the ARLA. Combining the self-learning ability of neural networks, the compact support of wavelet functions, the adaptive ability of fuzzy logic, and the robust learning capability of ARLA, the proposed FNN has the superiority among the several existed FNNs. To demonstrate the performance of the WSVR-FNN, two nonlinear dynamic plants and a chaotic system taken from the extant literature are considered to illustrate the system identification. From the simulation results, it shows that the proposed WSVR-FNN has the superiority over several presented FNNs even the number of training parameters is considerably small.

Adaptive multi-controller TSK Fuzzy Structure for Control of Nonlinear MIMO Dynamic Plant

In the paper an adaptive multi-controller control system utilizing a TSK fuzzy rules for a MIMO nonlinear dynamic plant is presented. The problems under study are exemplified by synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system use is made of a set of linear modal controllers that create a multi-controller structure from which a group of controllers appropriate to given operation conditions is chosen and used to calculate, by using TSK fuzzy rules, control signals. The final part of the paper includes simulation results of system operation with an adaptive controller of (stepwise) varying parameters along with conclusions and final remarks.

Direct design of a U-model-based generalized predictive controller for a class of non-linear (polynomial) dynamic plants

Facing the big challenge of directly designing a generalized predictive controller (GPC) for a class of smooth non-linear dynamic plants described with polynomial models, this study reformulates the classical GPC into a U-model-based implementation. Mathematically, the final solution of the controller output is converted into resolving a polynomial equation in terms of current controller output u( k), which dramatically reduces the difficulties and complexity encountered in non-linear control system synthesis, algorithm development, and online implementation. It is believed that the integrated procedure provides a straightforward methodology to apply linear control system design techniques to design non-linear control systems without any enforced linearization of plant models. For a demonstration of the feasibility and effectiveness of the designed procedure, a continuously stirred tank reactor, and the other simulated example to represent chemical kinetics, are selected for the initial bench tests. The key contribution of the study is to derive and demonstrate feasibility and effectiveness of the U-model approach to GPC of non-linear systems. This is further evidence to support the author’s insight on the U-model approach that was previously used to design pole placement controller (PPC).

Simulation of a high-agility model airplane in the presence of severe structural damage and failures, and design of a dynamic inversion controller

The simulation of the aircraft dynamics and behavior of the open loop as well as the closed loop system is a central part in the development of controllers for real flight tests. This paper presents an approach for the systematic development of a nonlinear simulation model in MATLAB/Simulink for a high-agility model airplane, with a total of 16 different control inputs, together with the design of an appropriate rate command attitude hold (RCAH) controller. The simulation model is capable to represent the behavior of the aircraft, including the dynamics of the motors, the actuators and the sensors, for the nominal case as well as in the case of severe structural damage and failures. The highly sophisticated model of the aircraft is used subsequently for the design of a controller. Dynamic inversion (DI) uses the knowledge of the nonlinear plant dynamics to transform the nonlinear dynamics into a chain of integrators, and after this transformation, a controller can be designed using methods from classical or robust control. A relative degree 1 (RD 1) rate command attitude hold controller, based on dynamic inversion, will be presented together with a semi-analytical approach to select and adjust the appropriate controller gains. The paper is completed by some simulation results encountering severe structural damage and failures. The derived controller can either serve as a stand-alone controller or as a baseline controller for more sophisticated control approaches.

A neuro-fuzzy online fault detection and diagnosis algorithm for nonlinear and dynamic systems

This paper presents a new fault detection and diagnosis approach for nonlinear dynamic plant systems with a neuro-fuzzy based approach to prevent developing of fault as soon as possible. By comparison of plants and neuro-fuzzy estimator outputs in the presence of noise, residual signal is generated and compared with a predefined threshold, the fault can be detected. To diagnose the type, size, time and fault conditions, are used analytical approach and neural network for tracking fault developing online. The neuro-fuzzy nets are compared with some other identification methods in application of power plant gas turbine. Faults are considered in two forms, step, and ramp shape. This work was implemented with real data from gas turbine of Kazeroun (Iran) power plant (Mitsubishi unit) and result is presented to demonstrate the benefits of the proposed method.

RBF Neural Network Based Adaptive Tracking Control for a Class of Nonlinear Plant Using Stochastic U-Model

In this paper an adaptive tracking control algorithm and its step by step implementation procedure are developed for a class of nonlinear plants within a U-model framework with unknown parameters. With the author’s previous justification, not only the control oriented model represents a wide range of smooth (polynomial) nonlinear dynamic plants (without using linearisation approximation at all), but also make almost all linear control system design techniques directly applicable (with a root solver bridging the linear design and calculation of controller output). A new technique is proposed to design an online control algorithm using the Radial Basis Functions Neural Network (RBFNN). The plant parameters are estimated online and are used to update the weights of the RBFNN. The weights update equations are derived based on the well known LMS (least mean square). A number of simulated case studies are conducted to illustrate the efficiency of the claimed insight and design procedure.

U-model-based adaptive control for a class of stochastic non-linear dynamic plants with unknown parameters

In this paper, an adaptive control algorithm within a U-model framework is developed for controlling a class of stochastic non-linear discrete-time models with unknown parameters. With the authors' previous justification, the control-oriented model not only represents a wide range of smooth (polynomial) non-linear dynamic plants (without using linearisation approximation at all), but also makes almost all linear control system design techniques directly applicable to non-linear dynamic plants (with a root solver bridging the linear design and calculation of controller output). A new recursive least squares algorithm is derived and its convergence is proved for the online estimation of time-varying parameters. For initial bench test, a pole placement controller for non-linear stochastic polynomial models is designed using the corresponding linear design technique. Accordingly a step by step procedure is listed to implement the adaptive control operation. A number of simulated case studies are conducted to illustrate the efficiency of the claimed insight and design procedure.

A harmonic balance approach to robust neural control of MIMO nonlinear processes applied to a distillation column

Robust stability and performance are the two most basic features of feedback control process. The harmonic balance analysis based on the describing function technique enables to analyze the stability of limit cycles arising from a closed loop control process operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural network controller in series with a dynamic multivariable nonlinear plant under generic Lur’e configuration. The neural controller is replaced by its sinusoidal input describing function while a linearized model is derived to represent the nonlinear plant dynamics. The uncertainty induced by the high harmonics effect for the neural controller, together with the neglected nonlinear dynamics due to plant linearization are incorporated in the robustness analysis as structured norm bounded uncertainties. Stability and robustness conditions for the neural closed loop control system are discussed using the harmonic balance equation together with the structured singular values of the uncertainty. The application to a multivariable binary distillation column under feedback neurocontrol illustrates the usefulness of the robustness approach here developed to predict the absence of limit cycles, which of course is subject to the usual restrictions of the describing function method.

Robust identification of nonlinear complex systems using low complexity ANN and particle swarm optimization technique

The paper introduces a novel method of adaptive robust identification of complex nonlinear dynamic plants including Box Jenkin, Mackey Glass and Sunspot series under the presence of strong outliers in the training samples. The identification model consists of a low complexity single layer functional link artificial neural network (FLANN) in the feed forward path and another on the feedback path. The connecting weights are iteratively adjusted by a population based particle swarm optimization technique so that a robust cost function (RCF) of the model-error is minimized. To demonstrate robust identification performance up to 50% random samples of the plant output is contaminated with strong outliers and are employed for training the model using PSO tool. Identification of wide varieties of benchmark complex static and dynamic plants is carried out through simulation study and the performance obtained are compared with those obtained from using standard squared error norm as CF. It is in general observed that, the Wilcoxon norm provides best identification performance compared to squared error and other RCFs based models.

Tase Tsk Model Based Inverse Model Controller And Its Application

Abstract This paper presents a new approach of achieving inverse model control (IMC) of nonlinear plants with TaSe Takagi-Sugeno-Kang (TSK) fuzzy system. The inverse control law, designed for the control of nonlinear plant dynamics, is derived directly based on approximate model method and it is implemented using TaSe TSK fuzzy system modeling. The robust stability of the IMC is analyzed using Lyapunov function. The proposed IMC strategy is applied to the control of electronic throttle, and simulations demonstrate the effectiveness of this controller.

Trajectory-tracking control of underwater inspection robot for nuclear reactor internals using Time Delay Control

This paper addresses the trajectory control problem of an underwater inspection robot for nuclear reactor internals. From the viewpoint of control engineering, the trajectory control of the underwater robot is a difficult task due to its nonlinear dynamics, which includes various hydraulic forces such as buoyancy and hydrodynamic damping, the difference between the centres of gravity and buoyancy, and disturbances from a tether cable. To solve such problems, we applied Time Delay Control to the underwater robot. This control law has a very simple structure not requiring nonlinear plant dynamics, and was proven to be highly robust against nonlinearities, uncertainties and disturbances. We confirmed its effectiveness through experiments.

Development of efficient identification scheme for nonlinear dynamic systems using swarm intelligence techniques

This paper outlines the basic concept and principles of two simple and powerful swarm intelligence tools: the particle swarm optimization (PSO) and the Bacterial Foraging Optimization (BFO). The adaptive identification of an unknown plant has been formulated as an optimization problem and then solved using the PSO and BFO techniques. Using this new approach efficient identification of complex nonlinear dynamic plants have been carried out through simulation study.

Reduced Order Robust Gain-Scheduling Control Of The Diesel Apu For Series Hybrid Vehicles

This paper presents a reduced order robust gain-scheduling approach for the control of the diesel auxiliary power unit (APU) for series hybrid vehicles. The nonlinear plant dynamics are converted into a linear parameter-varying (LPV) form with parametric uncertainties, in which only partial information of the plant states is available. For this type of LPV system, a new reduced order robust gain-scheduling synthesis method is proposed based on partial state feedback. The parametric uncertainties are considered using multipliers to reduce the conservatism. The reduced order synthesis problem is solved offline by means of linear matrix inequalities (LMIs), and the synthesis result requires much simpler online computation than the explicit controller formulas do. The synthesis method is applied to the diesel APU controller design, and simulation results are given to demonstrate the controller performance.