Nonlinear Engine Model Research Articles

Fault detection and isolation of gas turbine engine using inversion-based and optimal state observers

This paper aims to design, develop and compare fault detection and isolation (FDI) schemes including inversion-based fault reconstruction and optimal state observers for a class of nonlinear system subject to concurrent faults and unknown disturbances that represents the nonlinear dynamic model of a gas turbine engine. Towards this end, for each fault, utilizing an existing coordinate transformation, the original system is transformed into a new form in which both observers are applied for fault diagnosis. The coordinate transformation comes from observability concept in differential geometry. The inversion-based observer is highly beneficial for straightforward detection and directly isolating the faults, and the state observer is optimal with respect to the magnitude of observer gain and convergence time. The mentioned approaches are implemented for FDI of a gas turbine model subject to compressor efficiency, compressor mass flow capacity, and actuator faults in addition to an unknown disturbance. The simulation results illustrate that the proposed FDI schemes are a promising tool for the gas turbine diagnostics.

Parameter Set Reduction and Ensemble Kalman Filtering for Engine Model Calibration

Abstract A novel methodology is presented in this paper to reduce the burden of calibrating an engine model associated with a high number of parameters and nonlinear equations. The proposed idea decreases the calibration candidate parameters by detecting the most influential ones in an engine air-charge path model and then using them as a reduced parameter set for further model calibration. Since only the most influential parameters are tuned at the final calibration stage, this approach helps to avoid over-parameterization associated with tuning highly nonlinear engine models. Detection of the influential parameters is proposed using sensitivity analysis followed by principal component analysis (PCA) as an early off-line stage in the model tuning process. Then, an ensemble Kalman filter (EnKF) is used for tuning the detected influential parameters. The Jacobian-free suboptimal filtering approach of EnKF allows tuning parameters either with off-line recorded data or during on-line engine testing. Using EnKF along with parameter set reduction presents an approach for decreasing the complexity of parameter tuning for online model calibration. Results from experiments on a heavy duty diesel engine show an average of 50% improvement of the model accuracy after calibrating the engine model using the proposed reduced parameter set tuning methodology.

Sensor Fault Tolerant Control for Aircraft Engines Using Sliding Mode Observer

This paper investigated the problem of fault estimation and fault-tolerant control (FTC) against sensor faults for aircraft engines. By applying a second order sliding mode observer (SOSMO) to the engine on-board model, estimations of the system states and sensor faults could be obtained simultaneously, and the result of state estimation was unaffected when using the reduced-order sliding mode system. This result gave rise to the idea to use the estimated states instead of physical sensor signal in the engine close-loop feedback control. Unlike those using passive FTC concepts, the tradeoff between control performance and robustness was inherently unnecessary. Meanwhile, compared to active FTC approaches, because any classical state/output feedback method can be directly applied to the proposed scheme without any controller reconfiguration, extra undesired dynamic responses caused by parameter reconfiguring were avoided. In this paper, the proposed FTC scheme was tested on the nonlinear model of a civil aircraft turbofan engine, and numerical simulation results showed satisfactory sensor FTC performance.

An Output-Based Limit Protection Strategy for Turbofan Engine Propulsion Control with Output Constraints

To accomplish the limit protection task, the Min-Max selection structure is generally adopted in current aircraft engine control strategies. However, since no relationship between controller switching and limit violation is established, this structure is inherently conservative and may produce slower transient responses than the behavior by engine nature. This paper proposes an output-based limit management strategy, which consists of the safety margin module and the parameter prediction module to monitor system responses, plus the switching logic to govern switches between the main controller and limiters, and, in this way, a faster transient performance is achieved, and the limit protections in transient states become more effective. To realize smooth switching control, the linear-quadratic bumpless transfer method is developed. The design principle of the multi-loop switching control and bumpless compensator is detailed, and the effect—on limit protection control performance—of the design parameters in the safety margin and parameter prediction modules are also analyzed. The proposed approach is tested using simulations covering the whole flight envelope on the nonlinear component-level model of a turbofan engine, and the superiority over the Min-Max architecture is also validated.

Design and implementation of MPC for turbofan engine control system

The objective of an aircraft engine control system is to provide required thrust as well as protection against the physical and operational limits. Model predictive control (MPC) technique is an attractive approach that incorporates input/output constraints in its optimization process to fulfill the control requirements of an aircraft engine. However, due to heavy computational burden of MPC, the real-time implementation of this algorithm is challenging and selection of MPC design parameters is crucial. This paper presents the design and hardware implementation of MPC algorithm as well as its HIL testing for turbofan engine control. In addition, a feedback correction technique is employed to compensate the effect of plant-model mismatch. For this purpose, a thermodynamic nonlinear engine model is firstly developed. A multivariable model predictive controller is then designed based on a discrete-time linearized state-space model where the horizons are obtained through a genetic algorithm optimization procedure. Moreover, this controller is implemented on an appropriate hardware taking the real-time aspects into account. Finally, an HIL platform is developed for testing the turbofan engine electronic control unit (ECU). For this purpose, a multi-level throttle command is applied to the ECU and the performance of the engine is evaluated. The results indicate that the controller satisfies all the engine constraints, and confirm the successful software and hardware implementation of the control algorithm in real-time.

Fault detection and diagnosis algorithms for transient state of an open-cycle liquid rocket engine using nonlinear Kalman filter methods

This paper deals with an application of the fault detection and diagnosis algorithm based on nonlinear Kalman filter methods for transient state of an open-cycle liquid propellant rocket engine. In order to develop the algorithm, we designed two types of the nonlinear Kalman filter which are the extended Kalman filter and unscented Kalman filter with non-linear model of the liquid propellant rocket engine. Then using the measurement data of some important parameters of the engine, the residuals from the nonlinear Kalman filters are obtained. Using the residuals, we can detect and diagnose faults in the components of the engine by using the multiple model method. To confirm the fault detection and diagnosis algorithm, we developed mathematical model of an open-cycle liquid propellant rocket engine and artificially injected various faults such as decreasing turbopump efficiency. And then, perform the fault detection and diagnosis algorithm and check the performance of the algorithm. This process is numerically demonstrated for the open-cycle liquid propellant rocket engine under start-up process by using the simulated measurement data from the mathematical model of the engine.

Variable Sampling Rate based Active Disturbance Control for a Marine Diesel Engine

In this paper, in order to handle the high nonlinearity and the sophisticated disturbance in marine engines, a variable sampling rate based active disturbance rejection controller is developed for engine speed control. In the proposed method, the Active Disturbance Rejection Control (ADRC) is designed with the consideration of the practical application in engine speed control that is known as the Crank-angle (CA) based or event-based sampling and control, which means the sampling interval varies with the engine speed. Such a problem has not been discussed in any previous study regarding the application of ADRC in engine control. To this end, this paper discusses the convergence of the variable sampling rate based Extended State Observer (ESO), as well as its parameters that guarantee stability. To verify the proposed control scheme more properly, a cycle-detailed hybrid nonlinear engine model is employed. Finally, simulations are carried out on the Hardware-in-the-loop (HIL) system to assess the superiority of the proposed strategy. The comparative results with a Fuzzy-Proportional-Integral-Derivative (PID) controller demonstrate that the proposed control scheme has better adaptation to engine speed, load disturbances, and stronger robustness towards model uncertainties, which indicates a promising reduction of time and burden for calibrating the controller. It also proved that the proposed CA based ADRC by variable sampling rate method outperforms the general fixed sampling rate ADRC, which is widely used in previous works. Moreover, the successful application of the proposed algorithm via CA based strategy in a real Engine Control Unit (ECU) indicates its huge potential in practical engine control.

Analyzing different numerical linearization methods for the dynamic model of a turbofan engine

State equations of aircraft engine dynamics usually required for controller design, are not available in closed form, so the dynamic models are commonly linearized numerically. Development of model-based controllers for aeroengine in the recent years necessitates the use of accurate linear models. However, there is no comprehensive study about the accuracy of the linear models obtained from nonlinear engine models. In this paper, the accuracy of different numerical linearization methods for linearizing the dynamic model of a turbofan engine is investigated. For this objective, a thermodynamic model of a two-spool turbofan engine is considered and three various numerical linearization methods are defined. The first method is based on the perturbation technique, including ordinary and central difference perturbation. The second one is a system identification method and the third one is tuning the elements of the matrices of the linear state-space model using genetic algorithm. The accuracy analysis of the presented procedures is performed for both single-input and double-input cases. In the single-input case, the fuel mass flow rate and in the double-input, in addition to the fuel, the bleed air taken from between the two compressors are considered as control variables. Finally, by defining different error criterions, the accuracy of the linearization methods is evaluated. The results show that the linear model obtained from system identification and central difference perturbation methods have higher percentage of compliances compared to the others.

A Linearization Model of Turbofan Engine for Intelligent Analysis Towards Industrial Internet of Things

Big data processing technologies, e.g., multi-sensor data fusion and cloud computing are being widely used in research, development, manufacturing, health monitoring and maintenance of aero-engines, driven by the ever-rapid development of intelligent manufacturing and Industrial Internet of Things (IIoT). This has promoted rapid development of the aircraft engine industry, increasing the aircraft engine safety, reliability and intelligence. At present, the aero-engine data computing and processing platform used in the industrial Internet of things is not complete, and the numerical calculation and control of aero-engine are inseparable from the linear model, while the existing aero-engine model linearization method is not accurate enough to quickly calculate the dynamic process parameters of the engine. Therefore, in this paper, we propose a linear model of turbofan engine for intelligent analysis in IIoT, with the aim to provide a new perspective for the analysis of engine dynamics. The construction of the proposed model includes three steps: First, a nonlinear mathematical model of a turbofan engine is established by adopting the component modeling approach. Then, numerous parameters of the turbofan engine components and their operating data are obtained by simulating various working conditions. Finally, based on the simulated data for the engine under these conditions, the model at the points during the dynamic process is linearized, such that a dynamic real-time linearized model of turbofan engine is obtained. Simulation results show that the proposed model can accurately depict the dynamic process of the turbofan engine and provide a valuable reference for designing the aero-engine control system and supporting intelligent analysis in IIoT.

LPV/PI Control for Nonlinear Aeroengine System Based on Guardian Maps Theory

The requirement of fighter’s maneuverability puts forward higher indexes for the control performance of aeroengine. It is generally recognized that the proportion integration (PI) control is the most commonly used control method of aeroengine. However, due to the high nonlinearity and performance requirements of aeroengine, the selection of PI parameters needs more accurate methods to satisfy higher performance requirements. In this paper, the linear parameter varying (LPV) model is established according to a nonlinear mathematical model of a turbofan engine. Then, the LPV/PI control based on guardian maps theory is proposed to solve the highly nonlinear aeroengine control problem which improves the response characteristics of aeroengine without changing the control method in the range of the scheduling parameters. In the process of design, a set of controller parameters satisfying the performance requirements is automatically generated by a given initial controller parameter, so designing the controllers at multiple equilibrium points is avoided. Finally, the simulations are performed by the integral separation of PI control at different points in the flight envelope for the nonlinear model. The results illustrate that the control method based on guardian maps theory can contribute significantly to solving the nonlinear problems of aeroengine control system.

Speed Control for a Marine Diesel Engine Based on the Combined Linear-Nonlinear Active Disturbance Rejection Control

In this paper, a compound control scheme with linear active disturbance rejection control (LADRC) and nonlinear active disturbance rejection control (NLADRC) is designed to stabilize the speed control system of the marine engine. To deal with the high nonlinearity and the complex disturbance and noise conditions in marine engines, the advantages of both LADRC and NLADRC are employed. As the extended state observer (ESO) is affected severely by the inherent characteristics (cyclic speed fluctuation, cylinder-to-cylinder deviations, etc.) of the reciprocating engines, a cycle-detailed hybrid nonlinear engine model is adopted to analyze the impact of such characteristics. Hence, the controller can be evaluated based on the modified engine model to achieve more reliable performance. Considering the mentioned natural properties in reciprocating engines, the parameters of linear ESO (LESO), nonlinear ESO (NLESO), and the switching strategy between LADRC and NLADRC are designed. Finally, various comparative simulations are carried out to show the effectiveness of the proposed control scheme and the superiority of switching strategy. The simulation results demonstrate that the proposed control scheme has prominent control effects both under the speed tracking mode and the condition with different types and levels of load disturbance. This study also reveals that when ADRC related approaches are employed to the reciprocating engine, the impact of the inherent characteristics of such engine on the ESO should be considered well.

Torsional system dynamics of low speed diesel engines based on instantaneous torque: Application to engine diagnosis

Abstract Low speed large engines such as those found in marine applications or power plants present large and flexible crankshafts. These elements as well as all the others linked to them, such as the pistons, connecting rods, camshaft and the flywheel, form a torsional system of nonlinear nature for which it is very worthwhile to identify and solve relevant anomalies such as efficiency losses, power imbalance or injection system malfunctions. This work presents a torsional nonlinear model of a two-stroke low speed diesel engine that has been developed and validated through experiments, using the instantaneous torque (IT) between the generator and engine as the validation magnitude. The analysed system loads covered the whole operational range of the system, i.e. 55%, 70%, 85% and 100% of the engine’s attainable power. The lumped torsional system was modelled with 16 degrees of freedom and was solved applying Fourier series expansion for the linear part of the system and with an iterative procedure for the nonlinear character of the system dynamics, which requires up to 12 iterations. A parameter model identification process was performed in Section 4 due to the uncertainty between the data supplied by the manufacturer and real data. As a result, the maximum error between the model and experimental data was reduced to 1.5%. In Section 5 a parametric study was developed that made it possible to establish the relationship between the in-cylinder combustion process and IT. This knowledge is taken into account in Section 6 to generate a proper set of inputs and outputs which is used to train an artificial neural network (ANN). Once trained, this network simulates the indicated mean power (WMI) at each cylinder with an error less than 1% for any load and engine condition. The main goal of the work is to develop a diagnostic tool for the identification and quantification of combustion-related anomalies that can contribute to maintaining the system efficiency as new.

Simulation-based dynamic model and speed controller design of a small-scale turbojet engine

PurposeThis paper aims to present a nonlinear mathematical model of a small-scale turbojet aeroengine and also a speed controller design that is conducted for the constructed nonlinear mathematical model.Design/methodology/approachIn the nonlinear mathematical model of the turbojet engine, temperature, rotational speed, mass flow, pressure and other parameters are generated using thermodynamic equations (e.g. mass, energy and momentum conservation laws) and some algebraic equations. In calculation of the performance parameters, adaptive neuro fuzzy inference system (ANFIS) method is preferred in related components. All calculated values from the mathematical model are then compared with the cycle data of the turbojet engine. Because of the single variable control need and effect of noise factor, modified proportional–integral–derivative (PID) controller is treated for speed control. For whole operation envelope, various PID structures are designed individually, according to the operating points. These controller structures are then combined via gain-scheduling approach and integrated to the nonlinear engine model. Simulations are performed on MATLAB/Simulink environment for design and off-design operating points between idle to maximum thrust levels.FindingsThe cascade structure (proposed nonlinear engine aero-thermal model and speed controller) is simulated and tested at various operating points of the engine and for different transient conditions. Simulation results show that the transitions between the operating points are found successfully. Furthermore, the controller is effective for steady-state load changes. It is suggested to be used in real-time engine applications.Research limitations/implicationsBecause of limited data, only speed control is treated and simulated.Practical implicationsIt can be used as an application in the industry easily.Originality/valueFirst point of novelty in the paper is in calculation of the performance parameters of compressor and turbine components. ANFIS method is preferred to predict performance parameters in related components. Second novelty in the paper can be seen in speed controller design part. Because of the single variable control need and effect of noise factor, modified PID is treated.

Nonlinear dynamics analysis of a low-temperature-differential kinematic Stirling heat engine

The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature difference. The rotational state and the stationary state of the engine are described as a stable limit cycle and a stable fixed point of the dynamical equations, respectively. These two states coexist under a sufficient temperature difference, whereas the stable limit cycle does not exist under a temperature difference that is too small. Using a nonlinear bifurcation analysis, we show that the disappearance of the stable limit cycle occurs via a homoclinic bifurcation, with the temperature difference being the bifurcation parameter.

A Min-Max selector controller for turbofan engines with improvement of limit management and low computational burden

Recent studies show that there is no guarantee for conventional Min-Max structure containing linear compensators to keep engine limitations in transient state, while limit violation can make dangerous events. Careful analysis indicates that despite the design of limitation loops overshoot-free to reduce the possibility of limit violation, exceeding the limits can occur for some variables affected by engine acceleration or deceleration, when other loop controllers are active. In this study, the limit values of these variables are taken into account in controller design of other loops using state feedback techniques and convex optimization problems, and their dynamic compensators are removed from the Min-Max structure. Thus, in addition to improvement of Min-Max limit protection, computational burden also decreases owing to loop reduction. The condition for limit protection in steady state and thrust tracking assurance is also specified. Simulations carried out with linear and nonlinear turbofan engine model show efficient performance of the proposed methodology in comparison with traditional Min-Max and Min-Max/sliding mode control (SMC) approaches.

SPIKING NEURAL NETWORKS BASED PID LIKE FLC DESIGN FOR AN IDLE SPEED CONTROL OF AN AUTOMOTIVE ENGINE

Automatic control of automotive engines provides benefits in the engines performance like emission reduction and fuel economy. The drop in idle speed problem can be seen as the disturbance rejection problem in the main engine speed. In this paper, a PID-like Fuzzy Logic Control (PIDFC) with minimum structure for the four strokes, four cylinders, gasoline engine is designed and simulated to maintain the engine speed at nominal value in idle speed mode. The speed performance must satisfy minimize fuel consumption, and as a result reduces the fuel emissions. A spiking Neural Network (SNN) trained by Particle Swarm Optimization (PSO) algorithm is proposed to online-adapt the inputs and output gains of the PID fuzzy controller in order to achieve the required speed performance. A Mean Value Engine Model (MVEM) is used to simulate nonlinear model of engine. .Results of simulation for this controller showed good improvements over the PIDFC in the idle speed response. .The peak overshoot is reduced about (70 %), the undershoot is reduced about (50 %), the settling time is. .reduced about (83%) and the fuel consumed is reduced about (53%).

Multiple Model Predictive Functional Control for Marine Diesel Engine

A novel control scheme based on multiple model predictive functional control (MMPFC) is proposed to solve the cumbersome and time-consuming parameters tuning of the speed controller for a marine diesel engine. It combines the MMPFC with traditional PID algorithm. In each local linearization, a first-order plus time delay (FOPTD) model is adopted to be the approximate submodel. To overcome the model mismatches under the load disturbance conditions, we introduce a method to estimate the open-loop gain of the speed control model, by which the predictive multimodels are modified online. Thus, the adaptation and robustness of the proposed controller can be improved. A cycle-detailed hybrid nonlinear engine model rather than a common used mean value engine model (MVEM) is developed to evaluate the control performance. In such model, the marine engine is treated as a whole system, and the discreteness in torque generation, the working imbalance among different cylinders, and the cycle delays are considered. As a result, more reliable and practical validation can be achieved. Finally, numerical simulation of both steady and dynamic performances of the proposed controller is carried out based on the aforementioned engine model. A conventional well-tuned PID with integral windup scheme is adopted to make a comparison. The results emphasize that the proposed controller is with stable and adaptive ability but without needing complex and tough parameters regulation. Moreover, it has excellent disturbance rejection ability by modifying the predictive multimodels online.

Explicit MIMO Model Predictive Boost Pressure Control of a Two-Stage Turbocharged Diesel Engine

In this paper, explicit model predictive control (MPC) of a two-stage turbocharged diesel engine is presented. MPC provides superior performance over conventional map-based PID boost pressure control. It can be easily adapted to multivariable control and is relatively easy to tune. A control-oriented multiple-input multiple-output model of a turbocharged diesel engine was derived using system identification methods. As MPC control design is based on a linear model, validation of the controller was carried out using a high-fidelity nonlinear engine model. Using the high-fidelity simulation model provides the opportunity to fine-tune the controller before the real-time testing. The experimental real-time tests demonstrate a superior control performance in a wider range compared with the performance obtained using conventional control.

Identification Method for Nonlinear Dynamic Models of Gas Turbine Engines on Acceleration Mode

The form and identification method of nonlinear dynamic gas turbine models on acceleration mode on the base of experimental transition processes is proposed. The nonlinear dynamic model of a gas turbine engine is represented as a system of nonlinear differential equations as in the normal form of Cauchy. The parameters of the system of differential equations are presented as a function of the acceleration parameter α, and the identification method is based on the determination of parameter α using numerical optimization method, allowing to simulate an acceleration mode with high accuracy. The experimental data are approximated by cubic splines for reduction of identification errors. The developed fast-calculating real-time nonlinear dynamic model is approved to implement in the software for hardware-in-the-loop test-beds and in the on-board software for automatic control systems of gas turbines.

Gas-Path Health Estimation for an Aircraft Engine Based on a Sliding Mode Observer

Aircraft engine gas-path health monitoring (GPHM) plays a critical role in engine health management (EHM). Among model-based approaches, the Kalman filter (KF) has been widely employed in GPHM. The main shortcoming of KF-based scheme lies in the lack of robustness against uncertainties. To enhance robustness, this paper describes a new GPHM architecture using a sliding mode observer (SMO). The convergence of the error system in uncertainty-existing circumstances is demonstrated, and the proposed method is developed to estimate components’ performance degradations regardless of modeling uncertainties. Simulations using a nonlinear model of a turbofan engine are presented, in which health monitoring problems are handled by the KF and the SMO, respectively. Results indicate the proposed approach possesses better diagnostic performance compared to the KF-based scheme, and the SMO shows its strong robustness and great potential to be applied to GPHM.