Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems

Sliding mode control (SMC) is a robust and computationally efficient model-based controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. However, the implementation of the conventional continuous-time SMC on digital computers is limited, due to the imprecisions caused by data sampling and quantization, and the chattering phenomena, which results in high frequency oscillations. One effective solution to minimize the effects of data sampling and quantization imprecisions is the use of higher order sliding modes. To this end, in this paper, a new formulation of an adaptive second order discrete sliding mode control (DSMC) is presented for a general class of multi-input multi-output (MIMO) uncertain nonlinear systems. Based on a Lyapunov stability argument and by invoking the new Invariance Principle, not only the asymptotic stability of the controller is guaranteed, but also the adaptation law is derived to remove the uncertainties within the nonlinear plant dynamics. The proposed adaptive tracking controller is designed and tested in real-time for a highly nonlinear control problem in spark ignition combustion engine during transient operating conditions. The simulation and real-time processor-in-the-loop (PIL) test results show that the second order single-input single-output (SISO) DSMC can improve the tracking performances up to 90%, compared to a first order SISO DSMC under sampling and quantization imprecisions, in the presence of modeling uncertainties. Moreover, it is observed that by converting the engine SISO controllers to a MIMO structure, the overall controller performance can be enhanced by 25%, compared to the SISO second order DSMC, because of the dynamics coupling consideration within the MIMO DSMC formulation.Comment: 12 pages, 7 figures, 1 tabl

A Lyapunov approach to Robust and Adaptive Higher Order Sliding Mode

In this paper, we present Lyapunov-based robust and adaptive Higher Order Sliding Mode (HOSM) controllers for nonlinear SISO systems with bounded uncertainty. The proposed controllers can be designed for any arbitrary sliding mode order. The uncertainty bounds are known in the robust control problem whereas they are partially known in the adaptive control problem. Both these problems are formulated as the finite time stabilization of a chain of integrators with bounded uncertainty. The controllers are developed from a class of nonlinear controllers which guarantee finite time stabilization of pure integrator chains. The robust controller establishes ideal HOSM i.e. the sliding variable and its r−1 time derivatives converge exactly to the origin in finite time. The adaptive controller establishes real HOSM, which means that the sliding variable and its r - 1 time derivatives converge to a neighborhood of the origin. Saturation functions are used for gain adaptation, which do not let the states exit the neighborhood after convergence. The effectiveness of these controllers is illustrated through simulations

MIMO First and Second Order Discrete Sliding Mode Controls of Uncertain Linear Systems under Implementation Imprecisions

The performance of a conventional model-based controller significantly depends on the accuracy of the modeled dynamics. The model of a plant's dynamics is subjected to errors in estimating the numerical values of the physical parameters, and variations over operating environment conditions and time. These errors and variations in the parameters of a model are the major sources of uncertainty within the controller structure. Digital implementation of controller software on an actual electronic control unit (ECU) introduces another layer of uncertainty at the controller inputs/outputs. The implementation uncertainties are mostly due to data sampling and quantization via the analog-to-digital conversion (ADC) unit. The failure to address the model and ADC uncertainties during the early stages of a controller design cycle results in a costly and time consuming verification and validation (V&V) process. In this paper, new formulations of the first and second order discrete sliding mode controllers (DSMC) are presented for a general class of uncertain linear systems. The knowledge of the ADC imprecisions is incorporated into the proposed DSMCs via an online ADC uncertainty prediction mechanism to improve the controller robustness characteristics. Moreover, the DSMCs are equipped with adaptation laws to remove two different types of modeling uncertainties (multiplicative and additive) from the parameters of the linear system model. The proposed adaptive DSMCs are evaluated on a DC motor speed control problem in real-time using a processor-in-the-loop (PIL) setup with an actual ECU. The results show that the proposed SISO and MIMO second order DSMCs improve the conventional SISO first order DSMC tracking performance by 69% and 84%, respectively. Moreover, the proposed adaptation mechanism is able to remove the uncertainties in the model by up to 90%.Comment: 10 pages, 11 figures, ASME 2017 Dynamic Systems and Control Conferenc

Discrete Adaptive Second Order Sliding Mode Controller Design with Application to Automotive Control Systems with Model Uncertainties

Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and sensitivity to data sampling imprecisions limit the digital implementation of conventional first order continuous-time SMC. Higher order discrete SMC is an effective solution to reduce the chattering during the controller software implementation, and also overcome imprecisions due to data sampling. In this paper, a new adaptive second order discrete sliding mode control (DSMC) formulation is presented to mitigate data sampling imprecisions and uncertainties within the modeled plant's dynamics. The adaptation mechanism is derived based on a Lyapunov stability argument which guarantees asymptotic stability of the closed-loop system. The proposed controller is designed and tested on a highly nonlinear combustion engine tracking control problem. The simulation test results show that the second order DSMC can improve the tracking performance up to 80% compared to a first order DSMC under sampling and model uncertainties.Comment: 6 pages, 6 figures, 2017 American Control Conferenc

Sliding-mode neuro-controller for uncertain systems

In this paper, a method that allows for the merger of the good features of sliding-mode control and neural network (NN) design is presented. Design is performed by applying an NN to minimize the cost function that is selected to depend on the distance from the sliding-mode manifold, thus providing that the NN controller enforces sliding-mode motion in a closed-loop system. It has been proven that the selected cost function has no local minima in controller parameter space, so under certain conditions, selection of the NN weights guarantees that the global minimum is reached, and then the sliding-mode conditions are satisfied; thus, closed-loop motion is robust against parameter changes and disturbances. For controller design, the system states and the nominal value of the control input matrix are used. The design for both multiple-input-multiple-output and single-input-single-output systems is discussed. Due to the structure of the (M)ADALINE network used in control calculation, the proposed algorithm can also be interpreted as a sliding-mode-based control parameter adaptation scheme. The controller performance is verified by experimental results

Nonlinear and adaptive control

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies

EASILY VERIFIABLE CONTROLLER DESIGN WITH APPLICATION TO AUTOMOTIVE POWERTRAINS

Bridging the gap between designed and implemented model-based controllers is a major challenge in the design cycle of industrial controllers. This gap is mainly created due to (i) digital implementation of controller software that introduces sampling and quantization imprecisions via analog-to-digital conversion (ADC), and (ii) uncertainties in the modeled plant’s dynamics, which directly propagate through the controller structure. The failure to identify and handle these implementation and model uncertainties results in undesirable controller performance and costly iterative loops for completing the controller verification and validation (V&V) process. This PhD dissertation develops a novel theoretical framework to design controllers that are robust to implementation imprecision and uncertainties within the models. The proposed control framework is generic and applicable to a wide range of nonlinear control systems. The final outcome from this study is an uncertainty/imprecisions adaptive, easily verifiable, and robust control theory framework that minimizes V&V iterations in the design of complex nonlinear control systems. The concept of sliding mode controls (SMC) is used in this study as the baseline to construct an easily verifiable model-based controller design framework. SMC is a robust and computationally efficient controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. The SMC structure allows for further modification to improve the controller robustness against implementation imprecisions, and compensate for the uncertainties within the plant model. First, the conventional continuous-time SMC design is improved by: (i) developing a reduced-order controller based on a novel model order reduction technique. The reduced order SMC shows better performance, since it uses a balanced realization form of the plant model and reduces the destructive internal interaction among different states of the system. (ii) developing an uncertainty-adaptive SMC with improved robustness against implementation imprecisions. Second, the continuous-time SMC design is converted to a discrete-time SMC (DSMC). The baseline first order DSMC structure is improved by: (i) inclusion of the ADC imprecisions knowledge via a generic sampling and quantization uncertainty prediction mechanism which enables higher robustness against implementation imprecisions, (ii) deriving the adaptation laws via a Lyapunov stability analysis to overcome uncertainties within the plant model, and (iii) developing a second order adaptive DSMC with predicted ADC imprecisions, which provides faster and more robust performance under modeling and implementation imprecisions, in comparison with the first order DSMC. The developed control theories from this PhD dissertation have been evaluated in real-time for two automotive powertrain case studies, including highly nonlinear combustion engine, and linear DC motor control problems. Moreover, the DSMC with predicted ADC imprecisions is experimentally tested and verified on an electronic air throttle body testbed for model-based position tracking purpose