A Pairwise Growing RBF Neural Network with Sparsely Direct Connections for Nonlinear System Modelling

An effective nonlinear model reduction approach, empirical Gramians balanced reduction approach, is studied, in order to reduce the computation complexity in nonlinear power system model application. The realization procedure is: firstly, computing the empirical controllable and observable Gramians matrices, secondly, computing the balance transformation matrix to obtain the balanced system model of the original model, then, and obtaining the diagonal Hankel singular values of balance transformation matrix. Finally, deciding the lower-order subspace to obtain the reduced model. A 15-machine nonlinear power system model is taken as an example to perform the reduction simulation analysis. Simulation result shows that, under the condition to maintain the stability and input-output dynamic behavior of the original system, the order of the reduced system model could be as low as 1/5 of that of the original system model, verifying the effectiveness of the proposed approach.

The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W) model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Aiming at the complexity of data processing in Weigh-In-Motion (WIM) system, a nonlinear system model is built for the WIM system with radical basic function (RBF) neural network. To achieve more accurate network weights of RBF and improve the model detection precision, a novel chaos immune algorithm is presented to optimize the RBF network weights. In this paper, the logistic equation is used to generate the initial population and the chaos disturbance is used to improve the searching efficiency of immune algorithm. Experiment results show that this nonlinear model is effective, and it can reduce the detection error for nonlinearity and time-varying of WIM system and improve the detection precision. Compared to the simple RBF network model, the proposed RBF network optimized by chaos immune algorithm owns high measuring precision.

Ultra-low-frequency oscillation with almost constant amplitude is a kind of frequency oscillation in power system. It has occurred in several hydro-dominant islanded power systems. With the nonlinearity of hydraulic turbines, a nonlinear model of power system is built in the paper. Stability and performance of both linear and nonlinear models are analyzed and compared. Particularly stable limit cycle could appear in the nonlinear dynamic model. Within a range of parameters, the equilibrium point of the dynamic system is unstable, while there is a stable limit cycle around it. System trajectories converge to this attractor and oscillate with constant amplitude. Limit cycle in the nonlinear model can explain the ultra-low-frequency oscillation of an island power system with ±800kV HVDC transmission to other grids in China and provides a new mechanism of frequency oscillation in islanded hydro-dominant power systems.

The parallel ac and dc nature of most the distributed energy sources and loads, enforces the idea of forming hybrid ac/dc distributed generation (DG) systems. Such a hybrid structure demonstrates the main advantages of ac and dc distribution networks, such as easier renewable energy integration and less power conversion losses. A typical hybrid ac/dc DG system consists of: a dc-side, an ac-side and an interlinking voltage source inverter (VSI) as power interface between the two sides. Dc and ac resistive and constant power loads, as well dc and ac distributed energy resources (DERs) are incorporated. To enhance system reliability and dynamic performance, energy storage devices are connected to the dc link, allowing the power to flow in both directions, via a bidirectional boost converter. A challenging issue in the design of a hybrid ac/dc DG system is to apply effective, reliable and robust control in order to ensure stable operation at the desired conditions and to avoid adverse impacts between the different parts. In this frame, opposite to the small signal analysis, existing in the literature, in this paper, a nonlinear control design and analysis of the complete hybrid system is deployed. Based on the accurate system model, cascaded-mode proportional-integral (PI) controllers are designed and suitably implemented to the power electronic interfaces in order to regulate both the ac and dc voltages as well as the ac-side frequency. The stability analysis conducted on the nonlinear system model with the inner-loop current controllers involved, is based on advanced Lyapunov techniques and as proven in the paper guarantees closed-loop stability and convergence to the desired nonzero equilibrium. The entire hybrid system is simulated under DER and load rapid changes with the results to verify the smooth and robust behavior.

Nonlinear modeling and identification of proton exchange membrane fuel cell (PEMFC)

Estimation of high-spatial resolution clear-sky longwave downward and net radiation over land surfaces from MODIS data

Trajectory tracking is extremely difficult for rotorcrafts based on the nonlinear model and taking into account all the parameters of the system and especially considering the effects of flapping and the main rotor and its control tail in all directions. This paper describes the tracking route, based on nonlinear model and velocity control and feedback mode and Polytopic linear parameter varying (LPV) modeling with the help of solving linear matrix inequalities (LMI) equations for different conditions and complex maneuvers for an unmanned rotorcraft that has been examined in all directions including, longitudinal, altitudinal, latitudinal directions. Based on the different operating points of the system and the different flight conditions, first a Polytopic modeling of the system is performed, and then the control signal is generated based on the state feedback and solution of the linear matrix inequalities (LMI) equations. The final control signal consists of feedback of changes of the state variables around the nominal trajectory under the designed feedback gains, in addition to the nominal control signal for the desired trajectory. In calculating the nominal control signal for the optimum trajectory, the Polytopic system model is used instead of the nonlinear system model. Therefore, the final control signal does not require a dynamic system model and all control calculations are performed using a Polytopic system model and have high computational speed. System simulation shows the capabilities of the proposed control system in different operating conditions.

Interpretable linear and nonlinear quantitative structure-selectivity relationship (QSSR) modeling of a biomimetic catalytic system by particle swarm optimization based sparse regression

PurposeThis study aims to design a robust Fractional Order Set-Point Weighted PID (SWPIλDμ) controller for a 3-DOF nonlinear helicopter system, minimizing error in the presence of parametric uncertainties and sensor faults.Design/methodology/approachA CIFER-based nonlinear helicopter model, renowned for its high accuracy, was utilized to validate the proposed approach. The parameters of the c onventional PID and SWPIλDμ controllers, designed for the nonlinear model, were optimized using the MATLAB Response Optimizer Toolbox.FindingsThe results demonstrate that the SWPIλDμ controller outperforms the PID controller in handling parameter uncertainties and sensor faults, as evidenced by superior performance across the integral time absolute error, mean square error, mean absolute error and mean absolute percentage error indices.Research limitations/implicationsIn the nonlinear model, eight terms representing parameter uncertainties were randomly varied within a range of ±40% from their nominal values, resulting in the generation of 50 distinct faulty models.Practical implicationsThe proposed approach is versatile and can be seamlessly implemented on any aerial platform or system.Originality/valueTo the best of the authors’ knowledge, this study presents the first documented application of the cascade SWPIλDμ controller to the specific system examined. The results highlight the method’s strong potential for broader applicability to a wide range of other systems.

An incremental neuronal-activity-based RBF neural network for nonlinear system modeling

Efficient self-organizing multilayer neural network for nonlinear system modeling

Based on actual hydraulic structure, the linear and nonlinear hydro power system model with surge tank was established for the first time. The simulation results of model demonstrate that the linear model with surge tank and that of individual penstock exists essential difference. The step response of individual penstock model is monotonic rising up to stable state, but that of model with surge tank is vibrating badly. The nonlinear model with surge tank is dynamic stable.

As large-scale renewable energy sources are increasingly integrated into AC grids via voltage source converters (VSCs), the transient synchronization stability of phase-locked loop (PLL)-based VSCs during fault ride-through is gaining more attention. Most existing studies assume that the positive and negative sequence separation and current control dynamics are much faster than the PLL dynamics, thereby neglecting their impact on the transient synchronization stability of the system. However, when the PLL bandwidth is relatively large, ignoring the positive and negative sequence separation and current control dynamics may result in incorrect stability assessments. To address this issue, this paper first considers the multiple control loop coupling, including positive and negative sequence separation, current control, and PLL, to construct a full-order nonlinear mathematical model of the VSC grid-connected system under asymmetric fault conditions. Based on this, the phase trajectory method is employed to analyze the transient synchronization stability of the system. Additionally, this full-order mathematical model is used to determine the PLL bandwidth boundary beyond which the effects of positive and negative sequence separation and current control dynamics cannot be neglected. Finally, PSCAD/EMTDC simulation results validate the effectiveness of the theoretical analysis presented in this paper.

Development and testing of a pintle-style throttle valve and control system for a solid-propellant gas generator (GG), to be used in an Air Turbo-Rocket (ATR) engine, are described. Experimental results from a GG firing program using a non-flight-wei ght throttle valve and open-loop control system to throttle over a 3:1 pressure ratio are presented. A non-linear mathematical model of the gas generator system, incorporating empirical data from the GG test program, and sub-scale test data, is derived. The model accurately reproduces the gas generator pressure and downstream pressures, including the classical nonminimum phase, over- and under- shoots in the downstream pressures. Linear transfer functions of GG pressure and nozzle pressure are derived from the nonlinear model. The existence of a right hand plane pole in the linear transfer function of the downstream nozzle pressure is consistent with the nonminimum phase behavior of the test program. Both mathematical models will be crucial for the design of future closedloop control systems. The models can also be applied, with small modifications, to the development of controllers for other solid-propellant GG-based systems. The design of a pintle valve to be used in an upcoming test series is described. Based on high-pressure water testing, the force requirements of the pressure-balanced valve are expected to be approximately 4% of that of the original non-pressure balanced design.