Sliding Mode Control of the Vehicle Speed System Based on LMIs

Due to the nonlinear characteristics of the vehicle speed system, its stability is difficult to control. This paper analyzes the stability and traceability of the vehicle speed system under nonlinear characteristics. A sliding mode control method of the nonlinear system state observation based on linear matrix inequalities (LMIs) is proposed. In the proposed control method, Lyapunov function is used as the control function to track the position and speed of the vehicle speed system in real time. In the design process of the controller, the successive scaling method (SSM) is designed to improve the tracking accuracy. The simulation results demonstrate that the sliding mode control can effectively track the position of the vehicle speed system, which has better stability and traceability for the nonlinear vehicle speed system.

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Nonlinear observer based sliding mode control and oxygen fraction estimation for diesel engine

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217700242 ◽

2017 ◽

Vol 40 (7) ◽

pp. 2227-2239 ◽

Cited By ~ 1

Author(s):

Haoping Wang ◽

Qiankun Qu ◽

Yang Tian

Keyword(s):

Diesel Engine ◽

Sliding Mode Control ◽

Oxygen Concentration ◽

Control Method ◽

Sliding Mode ◽

Observer Design ◽

Nonlinear Observer ◽

Linear Matrix ◽

Model Based ◽

Mode Control

In this paper, a nonlinear observer based sliding mode control (NOSMC) approach for air-path and a model-based observer for oxygen concentration in the diesel engine equipped with a variable geometry turbocharger and exhaust gas recirculation is introduced. We propose a less conservative observer design technique for Lipschitz nonlinear systems using Ricatti equations. The observer gains are obtained by solving the linear matrix inequality (LMI). Then a robust nonlinear control method, sliding mode control is applied for the states of intake and exhaust manifold pressure and compressor mass flow rate for the sake of the minimization of emissions. The proposed NOSMC controller is applied on a mean value model of turbocharged diesel engine. Besides this, a model-based observer is developed to estimate the oxygen concentration in the intake and exhaust manifolds owing to its significance in reducing emissions of diesel engines. The validation and efficiency of the proposed method are demonstrated by AMESim and Matlab/Simulink co-simulation results.

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Robust chattering-free optimal sliding-mode control using recurrent neural networks: An H∞-based approach

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219832953 ◽

2019 ◽

Vol 41 (13) ◽

pp. 3565-3580 ◽

Cited By ~ 3

Author(s):

Hamid Toshani ◽

Mohammad Farrokhi

Keyword(s):

Neural Networks ◽

Sliding Mode Control ◽

Recurrent Neural Networks ◽

Sliding Mode ◽

Linear Matrix ◽

Control Law ◽

Tracking Accuracy ◽

Mode Control ◽

Chattering Free ◽

Feedback Error

In this paper, a robust and chattering-free sliding-mode control strategy using recurrent neural networks (RNNs) and H∞ approach for a class of nonlinear systems with uncertainties is proposed. The dynamic and algebraic models of the RNN are extracted based on the nominal model of the system and formulation of a quadratic programming problem. For tuning the parameters of the sliding surface, the performance index and the switching coefficient, a robust approach based on the H∞ method is developed. To this end, the control law is divided into two parts: (1) the main term, which includes the feedback error and (2) other terms, which include the network states, the reference input and its derivatives and the effects of the uncertainties. The feedback error gain is tuned by solving a linear matrix inequality. The neural optimizer determines the sliding-mode control law without being directly affected by the uncertainties. By applying the proposed method to the continuous-stirred reactor tank and the inverted pendulum problems, the performance of the proposed controller has been evaluated in terms of the tracking accuracy, elimination of the chattering, robustness against the uncertainties and feasibility of the control signals. Moreover, the results are compared with the conventional and twisting sliding-mode control methods.

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Observer-Based Sliding Mode Control for Stabilization of a Dynamic System with Delayed Output Feedback

Mathematical Problems in Engineering ◽

10.1155/2013/537414 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 3

Author(s):

Bo Wang ◽

Peng Shi ◽

Hamid Reza Karimi ◽

Cheng Chew Lim

Keyword(s):

Sliding Mode Control ◽

Output Feedback ◽

Control Method ◽

Sliding Mode ◽

Lyapunov Stability Theory ◽

Delay System ◽

Linear Matrix ◽

Mode Control ◽

Inequality Technique ◽

Integral Sliding Surface

This paper considers the sliding mode control problem for a kind of dynamic delay system. First by utilizing Lyapunov stability theory and a linear matrix inequality technique, an observer based on delayed output feedback is constructed. Then, an integral sliding surface is presented to realize the sliding mode control for the system with the more available stability condition. Finally, some numerical simulations are implemented to demonstrate the validity of the proposed control method.

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Robustness control for nonlinear systems based on homogeneous prescribed sliding mode control

Science & Technology Development Journal - Engineering and Technology ◽

10.32508/stdjet.v4i2.805 ◽

2021 ◽

Vol 4 (2) ◽

pp. 1019-1035

Author(s):

PHU XUAN DO ◽

HUNG QUOC NGUYEN

Keyword(s):

Energy Consumption ◽

Sliding Mode Control ◽

Sliding Mode ◽

Control Function ◽

Linear Matrix ◽

Sliding Surface ◽

Seat Suspension ◽

Mode Control ◽

Input Control ◽

Severe Disturbance

This paper presents a new homogeneous control using dual sliding mode control, and robustness control using linear matrix inequality (LMI) constraints. The controller is applied for the severe disturbance. A sliding surface function, which relates to an exponential function and itself t-norm, is applied to save the energy consumption of the control system. The constraints related LMI are proposed with the matrices and vectors of the systems following the chosen matrices in control the energy for control. Solution of the constraints is also presented with new approach to save the time of calculation. In addition, the proof for the proposed controller is also presented by using the candidate Lyapunov function. In the input control function, the t-norm type is embedded to improve its performance in control disturbance. Besides of the t-norm, the modified sliding surface in the input control is also improve the energy for controlling. The combination of these robustness control elements would bring a new view for the design of control. The advantages of the controller are demonstrated via computer simulation for a seat suspension system. A magneto-rheological fluid seat suspension with its random disturbances is used. To prove the flexibility of the controller, the proposed approach is compared with an existing controller. The compared control has the same structure as shown in the proposed model. However, its design has a disadvantage in control the severe disturbance. The comparison between two controls is a clear view of distinct improvement. The results of simulations show that the controller provides better performance and stability of the system. The stability is also analyzed through the variation of the input control and power spectral density related energy consumption.

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MIMO Fuzzy Sliding Mode Control for Three-Axis Inertially Stabilized Platform

Sensors ◽

10.3390/s19071658 ◽

2019 ◽

Vol 19 (7) ◽

pp. 1658 ◽

Cited By ~ 3

Author(s):

Zhanmin Zhou ◽

Bao Zhang ◽

Dapeng Mao

Keyword(s):

Sliding Mode Control ◽

Control Method ◽

Sliding Mode ◽

Stability And Convergence ◽

Tracking Accuracy ◽

Fuzzy Sliding Mode Control ◽

Mode Control ◽

Fuzzy Sliding Mode ◽

Stabilized Platform ◽

Inertially Stabilized Platform

In this paper, a MIMO (Multi-Input Multi-Output) fuzzy sliding mode control method is proposed for a three-axis inertially stabilized platform. This method is based on the MIMO coupling model of the three-axis inertially stabilized platform in which the dynamic coupling among the three frames, namely the azimuth frame, the pitch frame and the roll frame, is fully considered. Firstly, the dynamic equation of the three-axis inertially stabilized platform is analyzed and its linearized model is obtained. After this, the controller is designed based on the model, during which fuzzy logic is introduced to deal with the frame coupling and the adaptive fuzzy coupling compensation factor is designed to be part of the algorithm. A complete proof of the stability and convergence is also provided in this paper. Finally, the performance of the platform with a MIMO fuzzy sliding mode controller and PI controller is analyzed. The simulation results show that the proposed scheme can guarantee tracking accuracy and effectively suppress the coupling interference between the three frames.

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Sliding Mode Control for Multiagent System with Time-Delay and Uncertainties: An LMI Approach

Mathematical Problems in Engineering ◽

10.1155/2013/805492 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Pengfei Guo ◽

Jie Zhang ◽

Ming Lyu ◽

Yuming Bo

Keyword(s):

Time Delay ◽

Sliding Mode Control ◽

Control Method ◽

Sliding Mode ◽

Linear Matrix ◽

Sliding Surface ◽

Simple Method ◽

Mode Control ◽

Feedback Control Method ◽

System With Time Delay

This paper considers the sliding mode control of multiagent systems (MAS) with time-delay and uncertainties in terms of linear matrix inequality (LMI). By constructing virtual feedback control method, the design of control system is simplified for time-delay independent system without uncertainties. For a class of uncertain systems with single time-delay, the essence of SMC design is analyzed in order to acquire a simple method for designing sliding surface. In terms of multiple timedelay system with uncertainties, a sufficient condition for sliding surface with independent time-delay is acquired, while control law is also designed to ensure the robust stability of closed-loop system. Finally, the effectiveness of conclusion is demonstrated by simulation results.

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Iterative-learning-based sliding mode control design for hypersonic vehicles with wind effects

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219895928 ◽

2020 ◽

Vol 42 (10) ◽

pp. 1769-1781

Author(s):

Jianguo Guo ◽

Yalu Su ◽

Xinming Wang ◽

Jun Zhou

Keyword(s):

Sliding Mode Control ◽

Control Method ◽

Sliding Mode ◽

Lyapunov Stability Theory ◽

Iterative Learning ◽

Attack Angle ◽

Wind Effects ◽

Tracking Accuracy ◽

Mode Control ◽

Flight Vehicles

A new sliding mode control method based on iterative learning is proposed for the longitudinal dynamics of hypersonic flight vehicles in the presence of wind effects. First, the wind effects are taken into the system by introducing the accessional attack angle, and with output-feedback transformation, the effects of the accessional attack angle and aerodynamic uncertainties are all modelled as lumped disturbances. Then, a novel sliding mode control scheme combined with command filtered technique is designed for the velocity subsystem and the altitude subsystem independently, while iterative learning laws are constructed to estimate the unknown disturbances. Furthermore, the stability and learning convergence of the system are rigorously proven via Lyapunov stability theory. By comparison, simulation results demonstrate that the presented strategy can efficiently achieve high tracking accuracy in spite of wind effects.

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Two-sided linear matrix inequality solution of affine input matrix for feasible discrete finite-time sliding mode control of uncertain nonlinear mechanical machines

Journal of Vibration and Control ◽

10.1177/1077546320916637 ◽

2020 ◽

Vol 26 (23-24) ◽

pp. 2243-2260 ◽

Cited By ~ 8

Author(s):

Mohammad Reza Homaeinezhad ◽

Sadeq Yaqubi

Keyword(s):

Sliding Mode Control ◽

Finite Time ◽

Control Method ◽

Sliding Mode ◽

Linear Matrix ◽

Input Matrix ◽

Mode Control ◽

Convex Inequality ◽

Input Gain ◽

Uncertain Input

In this article, a new control method is proposed based on finite-time discrete sliding mode control for uncertain multi-input multi-output systems which are affine to their inputs considering uncertain input multipliers in the case where signs of input gains remain constant over uncertainty spaces. In addition, a method for solving a set of convex control inequalities is introduced. The proposed control strategy is based on merging data obtained from investigation of common candidate Lyapunov functions assigned to various subsystems and their subsequent decoupling based on matrix elementary row operations. Initially, separate sliding functions corresponding to a single degree of freedom are assigned to each subsystem in the overall multi-input multi-output system, which results in obtaining a convex inequality corresponding to input bounds. Stacking the data obtained from various subsystems, the product of the uncertain input gain matrix in input vector is obtained as the middle term in a set of convex inequalities. Subsequently, the convex inequality is solved according to a set of matrix elementary row operations transforming the corresponding input matrix to row echelon form such that the bounds of each input are clearly expressed. Then, based on assigning input bounds proximity factors to each lower bound–upper bound duo, appropriate control inputs are generated. Chattering effects are eliminated as no switching term is included in construction of the control model. Effectiveness of the proposed method is demonstrated using numerical simulations. The implementation of control algorithm using microprocessors is also illustrated, indicating the feasibility of digital application.

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