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

Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

Switching frequency regulation in sliding mode control by a hysteresis band controller

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksFixing the switching frequency is a key issue in sliding mode control implementations. This paper presents a hysteresis band controller capable of setting a constant value for the steady-state switching frequency of a sliding mode controller in regulation and tracking tasks. The proposed architecture relies on a piecewise linear modeling of the switching function behavior within the hysteresis band, and consists of a discrete-time integral-type controller that modifies the amplitude of the hysteresis band of the comparator in accordance with the error between the desired and the actually measured switching period. For tracking purposes, an additional feedforward action is introduced to compensate the time variation of the switching function derivatives at either sides of the switching hyperplane in the steady state. Stability proofs are provided, and a design criterion for the control parameters to guarantee closed-loop stability is subsequently derived. Numerical simulations and experimental results validate the proposal.Accepted versio

Analysis and Design of Hybrid Control Systems

Different aspects of hybrid control systems are treated: analysis, simulation, design and implementation. A systematic methodology using extended Lyapunov theory for design of hybrid systems is developed. The methodology is based on conventional control designs in separate regions together with a switching strategy. Dynamics are not well defined if the control design methods lead to fast mode switching. The dynamics depend on the salient features of the implementation of the mode switches. A theorem for the stability of second order switching together with the resulting dynamics is derived. The dynamics on an intersection of two sliding sets are defined for two relays working on different time scales. The current simulation packages have problems modeling and simulating hybrid systems. It is shown how fast mode switches can be found before or during simulation. The necessary analysis work is a very small overhead for a modern simulation tool. To get some experience from practical problems with hybrid control the switching strategy is implemented in two different software environments. In one of them a time-optimal controller is added to an existing PID controller on a commercial control system. Successful experiments with this hybrid controller shows the practical use of the method

A Novel Fuzzy Logic Based Adaptive Supertwisting Sliding Mode Control Algorithm for Dynamic Uncertain Systems

This paper presents a novel fuzzy logic based Adaptive Super-twisting Sliding Mode Controller for the control of dynamic uncertain systems. The proposed controller combines the advantages of Second order Sliding Mode Control, Fuzzy Logic Control and Adaptive Control. The reaching conditions, stability and robustness of the system with the proposed controller are guaranteed. In addition, the proposed controller is well suited for simple design and implementation. The effectiveness of the proposed controller over the first order Sliding Mode Fuzzy Logic controller is illustrated by Matlab based simulations performed on a DC-DC Buck converter. Based on this comparison, the proposed controller is shown to obtain the desired transient response without causing chattering and error under steady-state conditions. The proposed controller is able to give robust performance in terms of rejection to input voltage variations and load variations.Comment: 14 page

Comparison of first- and second-order sliding-mode controllers for a dc-dc dual active bridge

This paper compares four sliding-mode control strategies for a dual active bridge. The proposed control algorithms define different switching functions resulting in first-and second-order controllers, and using both discontinuous and continuous sliding-mode algorithms. The paper details the design stage and includes simulation and experimental tests to better compare the performance for each control scheme.Peer ReviewedPostprint (published version

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

Variable structure control in natural frame for three-phase grid-connected inverters with LCL filter

This paper presents a variable structure control in natural frame for a three-phase voltage source inverter. The proposed control method is based on modifying the converter model in natural reference frame, preserving the low frequency state space variables dynamics. Using this model in a Kalman filter, the system state-space variables are estimated allowing to design three robust current sliding-mode controllers in natural frame. The main closed-loop features of the proposed method are: 1) robustness against grid inductance variations because the proposed model is independent of the grid inductance, 2) the power losses are reduced since physical damping resistors are avoided, and 3) the control bandwidth can be increased due to the combination of a variable hysteresis controller with a Kalman filter. To complete the control scheme, a theoretical stability analysis is developed. Finally, selected experimental results validate the proposed control strategy and permit illustrating all its appealing features.Postprint (author's final draft

Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight

Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms