scholarly journals Adaptive Discrete Second-Order Sliding Mode Control With Application to Nonlinear Automotive Systems

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Mohammad Reza Amini ◽  
Mahdi Shahbakhti ◽  
Selina Pan
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Real Time ◽  
Sliding Mode ◽  
Second Order ◽  
Operating Conditions ◽  
Data Sampling ◽  
Mode Control ◽  
Modeling Uncertainties ◽  
Highly Nonlinear

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 controller (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 (SI) 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.

A Nonlinear Sliding Surface in Sliding Mode Control to Reduce Vibrations of a Three-Link Flexible Manipulator

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Francesco Ripamonti ◽  
Lorenzo Orsini ◽  
Ferruccio Resta
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Operating Conditions ◽  
Nonlinear Observer ◽  
Flexible Manipulator ◽  
Engineering Practice ◽  
Sliding Surface ◽  
Mode Control ◽  
Highly Nonlinear

Many mechanical systems often show nonlinear behavior related to particular operating conditions or to the nonlinear characteristic of the elements (springs, dampers, etc.) making up the system. In these cases, common engineering practice is to linearize the equation of motion around a particular operating point and to design a linear controller. Although this approach is simple, its main disadvantage is that stability properties and validity of the controller are only local. For these reasons, over the last decades, nonlinear control techniques have been investigated more and more in order to improve control performance. In particular, in this paper, sliding mode control (SMC) technique, which is based on the model of the system (model-based), is considered because of its easy implementation, especially on simple mechanical systems, and the considerable robustness of the controller even under significant model uncertainties. This technique is analyzed numerically with respect to the pendulum system to better understand the influence of the control action on the system dynamics. A nonlinear sliding surface is also considered, recalling the terminal sliding mode (TSM) control already analyzed in the scientific literature. This sliding surface is characterized for the numerical system, and then it is applied experimentally in order to control a highly nonlinear system, consisting of a three-link flexible manipulator. For this system, a nonlinear modal model is developed, and a nonlinear observer is designed. Finally, results of experimental tests on the manipulator are reported, in order to compare the performances of the linear embedded control and the sliding mode controllers with the linear and nonlinear sliding surface.

scholarly journals Novel Nonsingular Fast Terminal Sliding Mode Control for a Class of Second-Order Uncertain Nonlinear Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Huihui Pan ◽  
Guangming Zhang
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Second Order ◽  
Terminal Sliding Mode Control ◽  
Uncertain Nonlinear Systems ◽  
Terminal Sliding Mode ◽  
Mode Control ◽  
Fast Terminal Sliding Mode

This paper presents a novel nonsingular fast terminal sliding mode control scheme for a class of second-order uncertain nonlinear systems. First, a novel nonsingular fast terminal sliding mode manifold (NNFTSM) with adaptive coefficients is put forward, and a novel double power reaching law (NDP) with dynamic exponential power terms is presented. Afterwards, a novel nonsingular fast terminal sliding mode (NNFTSMNDP) controller is designed by employing NNFTSM and NDP, which can improve the convergence rate and the robustness of the system. Due to the existence of external disturbances and parameter uncertainties, the system states under controller NNFTSMNDP cannot converge to the equilibrium but only to the neighborhood of the equilibrium in finite time. Considering the unsatisfying performance of controller NNFTSMNDP, an adaptive disturbance observer (ADO) is employed to estimate the lumped disturbance that is compensated in the controller in real-time. A novel composite controller is presented by combining the NNFTSMNDP method with the ADO technique. The finite-time stability of the closed-loop system under the proposed control method is proven by virtue of the Lyapunov stability theory. Both simulation results and theoretical analysis illustrate that the proposed method shows excellent control performance in the existence of disturbances and uncertainties.

scholarly journals Continuous Prescribed-Time Sliding Mode Control with A Prescribed-Time ESO for Second-Order Nonlinear Systems with Mismatched Disturbance

2021 ◽  
Author(s):  
Xiaozhe Ju ◽  
Feng Wang ◽  
Yingzi Guan ◽  
Shihao Xu
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Practical Applications ◽  
Mode Control ◽  
System States ◽  
Mismatched Disturbances

Abstract This paper aims to settle the continuous prescribed-time stabilization problem of second-order nonlinear systems with mismatched disturbances. A continuous prescribed-time sliding mode control (CPTSMC) method with a prescribed-time extended state observer (PTESO) is proposed. The PTESO can precisely estimate the unknown states and disturbances, with its upper bound for the settling time (UBST) prescribed by only one parameter more tightly than existing finite-time or fixed-time ESOs. Furthermore, as a common concern for ESOs, the peaking value problem is well addressed. Then, a novel prescribed-time convergent form with little conservatism and simple tuning procedures is designed, and the internal mechanism in acquiring higher transient performance is explicitly researched. By using the estimated states and disturbances, the CPTSMC makes system states converge in a chattering-alleviated manner following the novel prescribed-time form. In addition to proving that the UBST of the whole system is tightly prescribed by only one design parameter, we show the continuity of the CPTSMC and the boundedness of all system signals, which are vital for practical applications. Ultimately, numerical simulations on the second-order system and a DC motor servo verify the efficiency of the proposed control system.

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