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 new LMI-based robust Sliding Mode Control for the uncertain discrete-time systems

© 2014 IEEE. In this paper, a new approach for designing a robust Discrete-time Sliding Mode Control (DSMC) is proposed for the uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the linear sliding functions which are linear to the state. The LMI approach proposed in this paper is designed to deal with uncertain systems (matched and unmatched). It is wellknown that the finite sampling rate for the discrete-time systems leads to this fact that state move within a bound around the predetermined sliding surface referred to as quasi-sliding mode band. In this paper, this matter will be discussed in a new point of view and an innovative method will be used to obtain the ultimate bound on the system state

Review of sliding mode control application in autonomous underwater vehicles

973-984This paper presents a review of sliding mode control for autonomous underwater vehicles (AUVs). The AUVs are used under water operating in the presence of uncertainties (due to hydrodynamics coefficients) and external disturbances (due to water currents, waves, etc.). Sliding mode controller is one of the nonlinear robust controllers which is robust towards uncertainties, parameter variations and external disturbances. The evolution of sliding mode control in motion control studies of autonomous underwater vehicles is summarized throughout for the last three decades. The performance of the controller is examined based on the chattering reduction, accuracy (steady state error reduction), and robustness against perturbation. The review on sliding mode control for AUVs provides insights for readers to design new techniques and algorithms, to enhance the existing family of sliding mode control strategies into a new one or to merge and re-supervise the control techniques with other control strategies, in which, the aim is to obtain good controller design for AUVs in terms of great performance, stability and robustness

Variable-parameter double-power reaching law sliding mode control method

To solve the problem of the slow convergence rate of the reaching law and the chattering problems in the dynamic response in the sliding mode control, an improved double-power sliding mode reaching law is proposed. The reaching law is adjusted by changing the magnitude of the power terms adaptively at different stages of the system approach process, and the convergence speed of the dynamic response process is greatly improved. Its existence, accessibility and stability are proven by theory. The simulation results show that the improved double-power reaching law is faster than the double-power reaching law and the fast power reaching law. When there is uncertainty in the system, the system state and its derivatives can rapidly converge to the neighbor-hood of the equilibrium zeros. In the presence of time-varying perturbations of the two-order system, the sliding mode control system based on the improved double-power sliding mode reaching law has higher tracking precision of the given signal and differential signal and effectively reduces the high-frequency chattering phenomenon of the control input signal

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

Discrete‐Time Sliding Mode Control with Outputs of Relative Degree More than One

This work deals with sliding mode control of discrete‐time systems where the outputs are defined or chosen to be of relative degrees more than one. The analysis brings forward important advancements in the direction of discrete‐time sliding mode control, such as improved robustness and performance of the system. It is proved that the ultimate band about the sliding surface could be greatly reduced by the choice of higher relative degree outputs, thus increasing the robustness of the system. Moreover, finite‐time stability in absence of uncertainties is proved for such a choice of higher relative degree output. In presence of uncertainties, the system states become finite time ultimately bounded in nature. The work presents in some detail the case with relative degree two outputs, deducing switching and non‐switching reaching laws for the same, while for arbitrary relative degree outputs, it shows a general formalisation of a control structure specific for a certain type of linear systems

Robust output-feedback discrete-time sliding mode control utilizing disturbance observer

© 2015 IEEE. This paper is devoted to the problem of designing a robust dynamic output-feedback discrete-time sliding mode controller (ODSMC) for uncertain discrete-time systems. The basic idea behind this scheme comes from the fact that output feedback discrete-time sliding mode control (ODSMC), unlike its continuous-time counterpart, does not require to exploit a discontinuous term including the sliding function. Therefore, it is not a vital requirement that the sliding function is expressed in terms of the system outputs only. Furthermore, our observer-based discrete-time sliding mode controller (DSMC) leads to a considerably larger region of applicability. Besides, with the assumption of dealing with slow exogenous disturbances, a methodology is developed which aims to reduce the thickness of the boundary layer around the sliding surface. Moreover, the boundedness of the obtained closed-loop system is analyzed and the bound on the underlying system state is derived

Perspectives on the simulation of micro gas and nano liquid flows

Micro- and nano-scale fluid systems can behave very differently from their macro-scale counterparts. Remarkably, there is no sufficiently accurate, computationally efficient, and — most importantly — generally agreed fluid dynamic model that encapsulates all of this important behaviour. The only thing that researchers can agree on is that the conventional Navier-Stokes fluid equations are unable to capture the unique complexity of these often locally non-thermodynamic-equilibrium flows. Here, we outline recent work on developing and exploring new models for these flows, highlighting, in particular, slip flow as a quintessential non-equilibrium (or sub-continuum) phenomenon. We describe the successes and failures of various hydrodynamic and molecular models in capturing the non-equilibrium flow physics in current test applications in micro and nano engineering, including the aerodynamic drag of a sphere in a rarefied gas, and the flow of water along carbon nanotubes

Robust Position-based Visual Servoing of Industrial Robots

Recently, the researchers have tried to use dynamic pose correction methods to improve the accuracy of industrial robots. The application of dynamic path tracking aims at adjusting the end-effector’s pose by using a photogrammetry sensor and eye-to-hand PBVS scheme. In this study, the research aims to enhance the accuracy of industrial robot by designing a chattering-free digital sliding mode controller integrated with a novel adaptive robust Kalman filter (ARKF) validated on Puma 560 model on simulation. This study includes Gaussian noise generation, pose estimation, design of adaptive robust Kalman filter, and design of chattering-free sliding mode controller. The designed control strategy has been validated and compared with other control strategies in Matlab 2018a Simulink on a 64bits PC computer. The main contributions of the research work are summarized as follows. First, the noise removal in the pose estimation is carried out by the novel ARKF. The proposed ARKF deals with experimental noise generated from photogrammetry observation sensor C-track 780. It exploits the advantages of adaptive estimation method for states noise covariance (Q), least square identification for measurement noise covariance (R) and a robust mechanism for state variables error covariance (P). The Gaussian noise generation is based on the collected data from the C-track when the robot is in a stationary status. A novel method for estimating covariance matrix R considering both effects of the velocity and pose is suggested. Next, a robust PBVS approach for industrial robots based on fast discrete sliding mode controller (FDSMC) and ARKF is proposed. The FDSMC takes advantage of a nonlinear reaching law which results in faster and more accurate trajectory tracking compared to standard DSMC. Substituting the switching function with a continuous nonlinear reaching law leads to a continuous output and thus eliminating the chattering. Additionally, the sliding surface dynamics is considered to be a nonlinear one, which results in increasing the convergence speed and accuracy. Finally, the analysis techniques related to various types of sliding mode controller have been used for comparison. Also, the kinematic and dynamic models with revolutionary joints for Puma 560 are built for simulation validation. Based on the computed indicators results, it is proven that after tuning the parameters of designed controller, the chattering-free FDSMC integrated with ARKF can essentially reduce the effect of uncertainties on robot dynamic model and improve the tracking accuracy of the 6 degree-of-freedom (DOF) robot

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area