Aamer Iqbal Bhatti

Estimation of Gasoline-Engine Parameters Using Higher Order Sliding Mode

Automotive-engine control and fault diagnostics largely depend upon the accuracy of the nonlinear models used. The structure of these nonlinear models is generally agreed upon. However, the model parameters are mostly difficult to obtain. This paper presents the development of second-order sliding-mode technique with real twisting algorithm for estimation of more than one parameter from a single dynamical equation of the nonlinear model. The system under study is a mean-value engine model of a naturally breathing gasoline engine. The parameters estimated are throttle bodys discharge coefficient, load torque, and indicated torque as a function of inlet manifold pressure. The estimated variables are used to compensate for the unmodeled dynamics, modeling inaccuracies, and approximations which arise from the assumptions made for the development of mathematical model of a real-world system. The resulting model is a better description of the actual engine dynamics and gives good agreement to real engine data. The data are acquired from a production model vehicle equipped with an electronic control unit compliant to OBD-II standard. The observer designed is simple enough for implementation, and estimated parameters can also be used for engine-controller design and fault-diagnosis work.

Robust Parameter Estimation of Nonlinear Systems Using Sliding-Mode Differentiator Observer

This paper presents the design, simulation, and experimental results of a new scheme for the robust parameter estimation of uncertain nonlinear dynamic systems. The technique is established on the estimation of robust time derivatives using a variable-structure differentiator observer. A second-order sliding motion is established along designed sliding manifolds to estimate the time derivatives of flat outputs and inputs, leading to better tracking performance of estimates during transients. The parameter convergence and accuracy analysis is rigorously explored systematically for the proposed class of estimators. The proposed method is validated using two case studies; first, the parameters of an uncertain nonlinear system with known, but uncertain nominal parametric values are estimated to demonstrate the convergence, accuracy, and robustness of the scheme; in the second application, the experimental parameter estimation of an onboard-diagnosis-II-compliant automotive vehicle engine is presented. The estimated parameters of the automotive engine are used to tune the theoretical mean value engine model having inaccuracies due to modeling errors and approximation assumptions. The resulting dynamics of the tuned engine model matches exactly with experimental engine data, verifying the accuracy of the estimates.

Estimating SI Engine Efficiencies and Parameters in Second-Order Sliding Modes

Identification and estimation of immeasurable critical parameters/efficiencies of automotive engine provide significant information to monitor its functions and health. This paper proposes a novel estimation scheme for identifying such parameters. Four of the critical parameters discussed are frictional torque, combustion efficiency, volumetric efficiency, and throttle discharge coefficient. These parameters are estimated from a two-state nonlinear inlet manifold pressure and rotational speed dynamics-based engine model. The estimation scheme utilizes a second-order sliding mode observer based on a super twisting algorithm. The estimation is carried out on a production vehicle equipped with an engine control unit compliant to On-Board Diagnostics II standards. The proposed observers are simple enough for implementation. The estimated parameters have vast application in the area of engine modeling, controller design, and fault diagnosis/prognosis.

Hybrid Model of the Gasoline Engine for Misfire Detection

This paper proposes a novel hybrid model for an internal combustion engine, with the power generated due to combustion as the input and the crankshaft speed fluctuations as the output. The individual cylinders of the engine are considered as subsystems for which a nonlinear model, based on the physical principles, is derived. The proposed model is linearized at an operating point, and a switched linear model is formed. The simulation results of the proposed model are validated by matching the results with the experimentally observed data. Using the properties of the validated model, it is shown that the crankshaft speed variations observed in the engine are a Markov process. A novel algorithm that is based on the Markov chain is proposed to detect the misfire in the spark ignition engines. In the ensuing engine rig experiments, an igniter misfire is introduced in the system and is successfully detected. The analysis of the data shows that the engine also has an air leakage in a cylinder (a developing misfire), which is experimentally confirmed later.

Guidance of Air Vehicles: A Sliding Mode Approach

This paper presents a novel nonlinear guidance scheme for ground track control of aerial vehicles. The proposed guidance logic is derived using the sliding mode control technique, and is particularly suited for unmanned aerial vehicle (UAV) applications. The main objective of the guidance algorithm is to control the lateral track error of the vehicle during flight, and to keep it as small as possible. This is achieved by banking the vehicle, that is, by executing roll maneuvers. The guidance scheme must perform well both for small and large lateral track errors, without saturating the roll angle of the vehicle, which serves as the control input for the guidance algorithm. The limitations of a linear sliding surface for lateral guidance are indicated; a nonlinear sliding surface is thereafter proposed which overcomes these limitations, and also meets the criterion of a good helmsman. Stability of the nonlinear surface is proved using Lyapunov theory; control boundedness is also proved to ensure that the controls are not saturated even for large track errors. The proposed guidance law is implemented on the flight control computer of a scaled YAK-54 UAV and flight results for different scenarios (consisting of both small and large errors) are presented and discussed. The flight test results confirm the effectiveness and robustness of the proposed guidance scheme.

A novel anti-windup framework for cascade control systems: an application to underactuated mechanical systems.

This paper describes the anti-windup compensator (AWC) design methodologies for stable and unstable cascade plants with cascade controllers facing actuator saturation. Two novel full-order decoupling AWC architectures, based on equivalence of the overall closed-loop system, are developed to deal with windup effects. The decoupled architectures have been developed, to formulate the AWC synthesis problem, by assuring equivalence of the coupled and the decoupled architectures, instead of using an analogy, for cascade control systems. A comparison of both AWC architectures from application point of view is provided to consolidate their utilities. Mainly, one of the architecture is better in terms of computational complexity for implementation, while the other is suitable for unstable cascade systems. On the basis of the architectures for cascade systems facing stability and performance degradation problems in the event of actuator saturation, the global AWC design methodologies utilizing linear matrix inequalities (LMIs) are developed. These LMIs are synthesized by application of the Lyapunov theory, the global sector condition and the ℒ2 gain reduction of the uncertain decoupled nonlinear component of the decoupled architecture. Further, an LMI-based local AWC design methodology is derived by utilizing a local sector condition by means of a quadratic Lyapunov function to resolve the windup problem for unstable cascade plants under saturation. To demonstrate effectiveness of the proposed AWC schemes, an underactuated mechanical system, the ball-and-beam system, is considered, and details of the simulation and practical implementation results are described.

Extremal Trajectories and Maxwell Strata in Sub-Riemannian Problem on Group of Motions of Pseudo-Euclidean Plane

We consider the sub-Riemannian length minimization problem on the group of motions of pseudo-Euclidean plane that form the special hyperbolic group SH(2). The system comprises of left invariant vector fields with 2-dimensional linear control input and energy cost functional. We apply the Pontryagin maximum principle to obtain the extremal control input and the sub-Riemannian geodesics. A change of coordinates transforms the vertical subsystem of the normal Hamiltonian system into the mathematical pendulum. In suitable elliptic coordinates, the vertical and the horizontal subsystems are integrated such that the resulting extremal trajectories are parametrized by the Jacobi elliptic functions. Qualitative analysis reveals that the projections of normal extremal trajectories on the xy-plane have cusps and inflection points. The vertical subsystem being a generalized pendulum admits reflection symmetries that are used to obtain a characterization of the Maxwell strata.

Robust feedback linearization using higher order sliding mode observer

A novel robust feedback linearization scheme is proposed in this paper based on a modified robust exact differentiator. The states and drift terms in the system are estimated simultaneously by the observer using back injection of the control effort. The estimated drift term is used in the feedback loop to compensate the disturbances and observed states are used for feedback linearization. Finite time convergence of the complete closed-loop system is proved and thus a form of separation principle is satisfied, i.e., the controller and observer can be separately designed. The design is verified through simulations and by experiments on a DC motor rig.

Lateral Control for UAVs using Sliding Mode Technique

Abstract This paper presents sliding mode based lateral control for UAVs using a nonlinear sliding approach. The control is shown to perform well in different flight conditions including straight and turning flight and can recover gracefully from large track errors. Saturation constraints on the control input are met through the nonlinear sliding surface, while maintaining high performance for small track errors. Stability of the nonlinear sliding surface is proved using an appropriate Lyapunov function. The main contribution of this work is to develop a robust lateral control scheme that uses readily available sensor information and keeps the track error as small as possible without violating control constraints. In the proposed scheme the only information used in the control law is the lateral track error and the heading error angle. No information is required about the desired path/mission, which therefore can be changed online during run-time. This scheme is implemented on a high fidelity nonlinear 6-degrees-of-freedom (6-dof) simulation and different scenarios are simulated with large and small track errors in windy and calm conditions. Simulation results illustrate the robustness of the proposed scheme for straight and turning flight, in the presence of disturbances, both for large and small track errors. Furthermore it is shown that the saturation limits of the control input are not exceeded in all cases.

Virtual Sensors for Automotive Engine Sensors Fault Diagnosis in Second-Order Sliding Modes

Automotive engine functions are entirely dependent on installed sensors performance. Any malfunction in the sensors can lead to degraded engine efficiency. This manuscript presents a novel scheme to devise virtual sensors for health monitoring of engine air intake path sensors. The proposed scheme assists in: Sensing of critical immeasurable parameters like Volumetric and Combustion efficiency, development of Virtual Sensor from manifold pressure dynamics for rotational speed and vice versa, Health Monitoring of the manifold pressure and crankshaft sensor. For the suggested scheme, two robust second-order sliding mode observers are employed that require two state mean value engine model based on inlet manifold pressure and rotational speed dynamics. The proposed methodology has the potential of online implementation on any automotive engine after minor tuning. In this paper, the procedure is customized for 1.3 L gasoline engine sensors: Manifold Pressure and Crankshaft sensor. The implementation results demonstrate that all the three mentioned tasks are accomplished efficiently.