Nonlinear Steady-state Model Research Articles

Predicting the Performance Deterioration of a Three-Shaft Industrial Gas Turbine.

The gas turbine was one of the most important technological developments of the early 20th century, and it has had a significant impact on our lives. Although some researchers have worked on predicting the performance of three-shaft gas turbines, the effects of the deteriorated components on other primary components and of the physical faults on the component measurement parameters when considering the variable inlet guide valve scheduling and secondary air system for three-shaft gas turbine engines have remained unexplored. In this paper, design point and off-design performance models for a three-shaft gas turbine were developed and validated using the GasTurb 13 commercial software. Since the input data were limited, some engineering judgment and optimization processes were applied. Later, the developed models were validated using the engine manufacturer’s data. Right after the validation, using the component health parameters, the physical faults were implanted into the non-linear steady-state model to investigate the performance of the gas turbine during deterioration conditions. The effects of common faults, namely fouling and erosion in primary components of the case study engine, were simulated during full-load operation. The fault simulation results demonstrated that as the severity of the fault increases, the component performance parameters and measurement parameters deviated linearly from the clean state. Furthermore, the sensitivity of the measurement parameters to the fault location and type were discussed, and as a result they can be used to determine the location and kind of fault during the development of a diagnosis model.

Assessing the impact of cornering losses on the energy consumption of electric city buses

In view of the increasing electrification of public city transport, an accurate energy consumption prediction for Battery Electric Buses (BEBs) is essential. Conventional prediction algorithms do not consider energy losses that occur during turning of the vehicle. This is especially relevant for electric city buses, which have a limited battery capacity and often drive curvy routes.In this paper, the additional energy consumption during steering of a BEB is modeled, measured, and assessed. A nonlinear steady-state cornering model is developed to establish the additional energy losses during cornering. The model includes large steer angles, load transfer, and a Magic Formula tire model. Model results show that both cornering resistance and tire scrub of the rear tires cause additional energy losses during cornering, depending on the corner radius and vehicle velocity.The energy consumption model is validated with full scale vehicle tests and shows an average deviation of 0.8kW compared to the measurements. Analysis of recorded real-world bus routes reveals that on average these effects constitute 3.1% of the total powertrain energy. The effect is even more significant for routes crossing city centers, reaching values up to 5.8%. In these cases, cornering losses can be significant and should not be neglected in an accurate energy consumption prediction.

Modelovanje simulacija i upravljanje postrojenja za desalinizaciju vode

In this paper, modelling, simulation and control of water desalination plant is presented. The desalination plant is based on vapour compression method acquired utilizing a liquid jet ejector. Nonlinear steady-state model is developed in order to verify simplified dynamic model for control purposes. Furthermore, to design PI controller capable of guiding the system through desired states under the influence of disturbances, the linearized model of the plant has been developed and verified applying the nonlinear dynamical model. It is shown that presented approach can deliver satisfying model and tracking results.

Gas Turbine Gas Path Fault Diagnosis based on Adaptive Nonlinear Steady-State Thermodynamic Model

Gas Turbine Gas Path Fault Diagnosis based on Adaptive Nonlinear Steady-State Thermodynamic Model

Modelling and analysis of an open-loop induction motor drive incorporating the effect of inverter dead-time

The objective of this paper is to study the influence of inverter dead-time on steady as well as dynamic operation of an open-loop induction motor drive fed from a voltage source inverter (VSI). Towards this goal, this paper presents a systematic derivation of a dynamic model for an inverter-fed induction motor, incorporating the effect of inverter dead-time, in the synchronously revolving dq reference frame. Simulation results based on this dynamic model bring out the impact of inverter dead-time on both the transient response and steady-state operation of the motor drive. For the purpose of steady-state analysis, the dynamic model of the motor drive is used to derive a steady-state model, which is found to be non-linear. The steady-state model shows that the impact of dead-time can be seen as an additional resistance in the stator circuit, whose value depends on the stator current. Towards precise evaluation of this dead-time equivalent resistance, an analytical expression is proposed for the same in terms of inverter dead-time, switching frequency, modulation index and load impedance. The notion of dead-time equivalent resistance is shown to simplify the solution of the non-linear steady-state model. The analytically evaluated steady-state solutions are validated through numerical simulations and experiments.

Non-Linear Steady-State Electrical Current Modeling for the Electropermeabilization of Biological Tissue

We propose a non-linear steady-state model of irreversible electropermeabilization in a biological tissue. The non-linear problem is solved using a modified fixed point iteration. The unknown parameters are experimentally estimated from the observation of the necrosis on a potato tissue for different applied voltages. A variability study of the parameters involved in the model is performed.

Nonlinear Steady-State Model Based Gas Turbine Health Status Estimation Approach with Improved Particle Swarm Optimization Algorithm

In the lifespan of a gas turbine engine, abrupt faults and performance degradation of its gas-path components may happen; however the performance degradation is not easily foreseeable when the level of degradation is small. Gas path analysis (GPA) method has been widely applied to monitor gas turbine engine health status as it can easily obtain the magnitudes of the detected component faults. However, when the number of components within engine is large or/and the measurement noise level is high, the smearing effect may be strong and the degraded components may not be recognized. In order to improve diagnostic effect, a nonlinear steady-state model based gas turbine health status estimation approach with improved particle swarm optimization algorithm (PSO-GPA) has been proposed in this study. The proposed approach has been tested in ten test cases where the degradation of a model three-shaft marine engine has been analyzed. These case studies have shown that the approach can accurately search and isolate the degraded components and further quantify the degradation for major gas-path components. Compared with the typical GPA method, the approach has shown better measurement noise immunity and diagnostic accuracy.

A Novel Neural Network Based Modeling for Control of NO<sub>x</sub> Emission in Power Plant

A novel neural network based modeling for non-linear model identification technique is proposed. It combines a nonlinear steady state model with a linear one, to describe the disturbance and dynamics in the coal-fired power plant. The modeling and training algorithm is used to develop a model of nitrogen oxides (NOx) emitted from the process where one-step ahead optimal prediction formula are developed. Two cases show that the resulting model provides a better prediction of NOx and fitting capabilities.

Steady-state target optimization designs for integrating real-time optimization and model predictive control

In industrial practice, the optimal steady-state operation of continuous-time processes is typically addressed by a control hierarchy involving various layers. Therein, the real-time optimization (RTO) layer computes the optimal operating point based on a nonlinear steady-state model of the plant. The optimal point is implemented by means of the model predictive control (MPC) layer, which typically uses a linear dynamical model of the plant. The MPC layer usually includes two stages: a steady-state target optimization (SSTO) followed by the MPC dynamic regulator. In this work, we consider the integration of RTO with MPC in the presence of plant-model mismatch and constraints, by focusing on the design of the SSTO problem. Three different quadratic program (QP) designs are considered: (i) the standard design that finds steady-state targets that are as close as possible to the RTO setpoints; (ii) a novel optimizing control design that tracks the active constraints and the optimal inputs for the remaining degrees of freedom; and (iii) an improved QP approximation design were the SSTO problem approximates the RTO problem. The main advantage of the strategies (ii) and (iii) is in the improved optimality of the stationary operating points reached by the SSTO-MPC control system. The performance of the different SSTO designs is illustrated in simulation for several case studies.

Sensitivity Analysis of Optimal Operation of an Activated Sludge Process Model for Economic Controlled Variable Selection

This paper describes a systematic sensitivity analysis of optimal operation conducted on an activated sludge process model based on the test-bed benchmark simulation model no. 1 (BSM1) and the activated sludge model no. 1 (ASM1). The objective is to search for a control structure that leads to optimal economic operation, while promptly rejecting disturbances at lower layers in the control hierarchy avoiding thus violation of the more important regulation constraints on effluent discharge. We start by optimizing a steady-state nonlinear model of the process. Here, a new steady-state secondary settler mathematical model is developed based on the theory of partial differential equations applied to the conservation law with discontinuous fluxes. The resulting active constraints must be chosen as economic controlled variables. These are the effluent ammonia from the bioreaction section and the final effluent total suspended solids at their respective upper limits, in addition to the internal recycle flow rate ...

A New MTSA and its Application for Model Optimization

In this paper, a modified two-step algorithm (MTSA) is applied to an optimization problem in which the objective function is a multi-input single-output nonlinear steady-state model. An on-line searching method for gain-keeping in MTSA is proposed. The simulation results show that the method is effective.<strong></strong>

Systematic Approach to the Design of Operation and Control Policies in Activated Sludge Systems

This article describes the systematic design of a control structure for a biological wastewater treatment process as given by the test-bed Benchmark Simulation Model No. 1 (BSM1) and Activated Sludge Model No. 1 (ASM1). The objective of this work was to formalize and implement a systematic and yet simple procedure for the selection of control structures in wastewater treatment plants (WWTPs) and to show that the application of the proposed methodology agrees with the “empirical”’ findings regarding the operation of this process. The motivation underlying this endeavor was to search for a control configuration that leads to optimal economic operation while promptly rejecting disturbances at lower layers in the control hierarchy, thus avoiding violation of the more important regulatory constraints on effluent discharge. We started by optimizing a steady-state nonlinear model of the process for various important disturbances. The results confirmed that it is economically optimal to control the oxygen concent...

MULTILAYER AND INTEGRATED STRUCTURES FOR PREDICTIVE CONTROL AND ECONOMIC OPTIMISATION

The problem of co-operation of model predictive control (MPC) algorithms with nonlinear economic optimisation is considered. It is important when dynamics of disturbances is comparable with dynamics of the process, thus when application of the classical multilayer approach may be not efficient. Two main approaches are discussed and their features studied. The first one consists in approximate linear, linear-quadratic or piecewise-linear formulations of the target set-point optimisation depending on problem properties. The idea of the second approach consists in integrating the economic optimisation and manipulated variables calculation by MPC algorithm into one optimisation problem. The nonlinear steady-state model used in economic optimisation is approximated on-line. The resulting optimisation problem is then integrated with the MPC optimisation task and a computationally efficient quadratic programming problem is obtained.

A nonlinear diffusion model incorporating edge and surface texture effects to predict absorption behaviour of composites

A nonlinear steady-state diffusion model has been proposed that accounts for various effects, including different surfaces profiles. Alternating current analogy has been employed to study the effects of sinusoidal and saw-tooth surface textures on absorption and diffusivity. Expressions have been presented by incorporating the parameters, such as time shift factor, swelling stress dependence factor, moisture sensitive diffusion factor and roughness coefficient. A glass fibre–epoxy composite has been fabricated and real effect experiments preformed on seven specimens under varying conditions of edge, texture, loading and temperature. The outcomes of the proposed model have been compared with those of the classical model.

Frequency shift of a rotating-imbalance vibration source caused by radiative damping in the surrounding medium

The motion of vibrating bodies in a surrounding fluid is often used to infer the transport properties of the fluid. A new sensor configuration is presented that consists of a rotating imbalance source radiating into an unbounded fluid medium. Under these circumstances, the reaction of the fluid medium onto the vibration source includes a steady state torque that opposes the applied torque required to sustain the rotating imbalance. This reaction torque causes a shift in frequency of the vibration source. The frequency shift is related to the density of the surrounding fluid medium and vibration source characteristics. A description of measurements taken with a rotating-imbalance source located in unbounded water and air is provided. The total mass, eccentricity, and length of the source were 4.1 kg, 3.28(10−4) kg<th>m, and 0.432 m, respectively. Motive torque to drive the imbalance was provided by a permanent-magnet dc motor. For an applied dc voltage that caused the source to operate at a nominal frequency near 150 Hz, a frequency shift of approximately 11 Hz was observed when the source was moved from air to water. Experimentally measured frequency shifts compared favorably with predictions provided by a nonlinear steady state model of the source and surrounding medium.

On the operability of continuous processes

This paper offers a brief overview of past work as well as a comprehensive summary of our efforts based on the operability framework introduced by Vinson and Georgakis (in: C. Georgakis (Ed.), DYCOPS-5, Proceedings of the fifth IFAC symposium on dynamics and control of process systems, 1998, pp. 700–709; J. Proc. Control 10, 200, 10, pp. 185–194). This framework aims to quantify the inherent operability of a process without having to specify the control structure. It enables the identification of inoperable processes, regardless of the feedback controller selected, necessitating process rather than controller changes. Evaluation of steady-state operability is a necessary first step which should subsequently be complemented by the examination of the dynamic operability. The defined concepts are based on some key operating spaces. These spaces define the available ranges of input variables, the desired ranges of output variables, and the expected ranges of disturbance variables of the process. The calculation of the operability index is demonstrated for linear and the more general case of nonlinear models. This is achieved by mapping the defined input and output spaces onto each other using the nonlinear steady-state model of the process. Dynamic operability is examined by solving an optimal control problem to find the minimum time within which the process can respond to a disturbance or move to a new operating point with the available ranges of inputs.

A Symbolic Derivation Approach for Redundancy Analysis

Redundancy analysis is an important stage in plant instrumentation design that consists of classifying the measurements so as to determine the redundant ones. In this work, we propose a new method based on the symbolic derivation of the equations that constitute the nonlinear steady-state model of the plant under study. The strategy succeeds in overcoming the limitations of existing techniques with respect to accuracy as well as model size and complexity. The approach is nonnumeric, thus allowing independence from the operating point. No linearization is required because the method works directly on the original model equations. Another advantage is that there is no need to solve for the observable variables. The prototype was implemented in Matlab, and its performance was assessed for several academic and industrial case studies with accurate results.

Gas Turbine Engine and Sensor Fault Diagnosis Using Optimization Techniques

A diagnostic system is described for performance analysis of gas turbine engine components and sensors. The system estimates the performance parameters expressing the fault condition of the engine components in the presence of measurement noise and biases. The measurement uncertainty is supposed to affect even the parameters setting the operating condition of the engine. Estimation is performed through bptimization of an objective function by means of an ad hoc genetic algorithm. The genetic algorithm uses an accurate nonlinear steady-state performance model of the engine. The only statistical assumption required by the technique concerns the measurement noise and the maximum allowed number of faulty sensors and engine components, which is enclosed as a constraint. The technique has been thoroughly tested with the model of a low bypass ratio turbofan, and the results show the high level of accuracy achieved.

Northern Winter Stationary Waves: Theory and Modeling

A review is provided of stationary wave theory, the theory for the deviations from zonal symmetry of the climate. To help focus the discussion the authors concentrate exclusively on northern winter. Several theoretical issues, including the external Rossby wave dispersion relation and vertical structure, critical latitude absorption, the nonlinear response to orography, and the interaction of forced wave trains with preexisting zonal asymmetries, are chosen for discussion while simultaneously presenting a decomposition of the wintertime stationary wave field using a nonlinear steady-state model.

Simple and Accurate Scheme for Nonlinear Convection–Diffusion Equation

A simple nonlinear scheme for iterative solution of nonlinear convection–diffusion equation is described. The scheme is tested by solutions of three nonlinear steady-state model equations and linear nonstationary transport equation. The feature of the scheme is transition from a second-order accuracy on coarse grids to a first-order on fine grids.