scholarly journals Discrete-Time Sliding-Mode Control of Uncertain Systems with Time-Varying Delays via Descriptor Approach

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Maode Yan ◽  
Aryan Saadat Mehr ◽  
Yang Shi
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Existence Condition ◽  
Linear Matrix ◽  
Time Varying ◽  
Sliding Surface ◽  
Mode Control ◽  
Descriptor Approach ◽  
Delay Dependent

This paper considers the problem of robust discrete-time sliding-mode control (DT-SMC) design for a class of uncertain linear systems with time-varying delays. By applying a descriptor model transformation and Moon's inequality for bounding cross terms, a delay-dependent sufficient condition for the existence of stable sliding surface is given in terms of linear matrix inequalities (LMIs). Based on this existence condition, the synthesized sliding mode controller can guarantee the sliding-mode reaching condition of the specified discrete-time sliding surface for all admissible uncertainties and time-varying delays. An illustrative example verifies the effectiveness of the proposed method.

Modified Sliding Mode Control for Mismatched Uncertain Systems with Unknown Disturbances

2016 ◽  
Vol 829 ◽  
pp. 123-127
Author(s):  
Van Van Huynh ◽  
Thao Phuong Thi Nguyen
Keyword(s):  
Sliding Mode Control ◽  
Uncertain Systems ◽  
Sliding Mode ◽  
Existence Condition ◽  
Adaptive Sliding Mode Control ◽  
Linear Matrix ◽  
Control Law ◽  
Sliding Surface ◽  
Mode Control ◽  
System States

In this paper, a new sliding mode control law is developed for a class of mismatched uncertain systems with more general exogenous disturbances. First, we derive a new existence condition of linear sliding surface in terms of strict linear matrix inequalities such that the reduce-order sliding mode dynamics is is asymptotically stable. Second, we propose an adaptive sliding mode control law such that the system states reach the sliding surface in finite time and stay on its thereafter. Final, a numerical example is used to demonstrate the efficacy of the proposed method.

Finite-time H∞ sliding mode control of uncertain T-S fuzzy system with time-varying delay based on observer

2021 ◽  
Vol 40 (1) ◽  
pp. 983-999
Author(s):  
Huan Li ◽  
Pengyi Tang ◽  
Yuechao Ma
Keyword(s):  
Sliding Mode Control ◽  
Finite Time ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Time Interval ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Sliding Surface ◽  
State Estimator ◽  
Mode Control

In this paper, a class of observer-based sliding mode controller is designed, and the finite-time H∞ control problem of uncertain T-S fuzzy systems with time-varying is studied. Firstly, an integral-type sliding surface function with time-delay is devised based on the state estimator, and sufficient criteria of finite-time bounded and finite-time H∞ bounded can be obtained for the T-S systems. Moreover, the proposed sliding mode control law is integrated to ensure the dynamics of controlled system into the sliding surface in a finite-time interval. Then, according to the linear matrix inequalities (LMIs), the desired gain matrices of fuzzy sliding mode controller and state estimator are derived. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.

Sliding Mode Control Based on Novel Nonlinear Sliding Surface for a Class of Time-Varying Delay Systems

2014 ◽  
Vol 615 ◽  
pp. 375-381
Author(s):  
Qi Feng Ren ◽  
Cun Che Gao ◽  
Shu Hui Bi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Sliding Surface ◽  
Time Varying Delay ◽  
Mode Control ◽  
Varying Delay

The sliding mode control (SMC) design is discussed for a class of time-varying delay systems which is delay-range-dependent and rate-range-dependent. A novel time-varying nonlinear sliding surface is employed. The choice of nonlinear sliding surface is to change the state matrix of sliding mode system, which can combine the advantages of different conventional linear sliding surfaces. Thus the better transient qualities of system states, i.e., quicker response and smaller overshoot, can be achieved. The sufficient conditions ensuring the asymptotic stability of sliding mode are derived in terms of linear matrix inequalities. The algorithms deciding unknown parameters of the nonlinear sliding surface and the corresponding sliding mode controller are also presented. Finally, A numerical example is given to illustrate the effectiveness of the result here.

Modeling and Robust Discrete-Time Sliding Mode Control Design for a Fluid Power Electrohydraulic Actuator (EHA) System

2009 ◽  
Author(s):  
Yang Lin ◽  
Yang Shi ◽  
Richard Burton
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Existence Condition ◽  
Linear Matrix ◽  
Nonlinear Friction ◽  
Hydraulic Actuator ◽  
Time Dynamic ◽  
Mode Control ◽  
Wide Range

This paper studies the design of a robust discrete-time sliding mode control (DT-SMC) for a high precision electro-hydraulic actuator (EHA) system with nonlinear actuator friction. Nonlinear friction in the hydraulic actuator can greatly influence the performance and accuracy of the hydraulic actuators; however, it is difficult to accurately model nonlinear friction characteristics. In this paper, it is proposed to characterize frictions as an uncertainty in the system matrices. Indeed, the effects of variations of the nonlinear friction coefficients are considered as norm bounded uncertainties that span a bounded region to cover a wide range of real actuator friction. For such a discrete-time dynamic model for the EHA system with system matrices uncertainties and a nonlinear term, a sufficient condition for the existence of stable sliding surfaces is proposed by using the linear matrix inequality (LMI) approach. Based on this existence condition, a discrete-time sliding mode controller is developed such that the reaching motion satisfies the discrete-time sliding mode reaching condition for uncertain systems. Simulation and comparison studies on the EHA system model illustrate the effectiveness of the proposed method. The study is simulation based only as it is important to establish the feasibility and stability of the controller before attempting to apply the controller to a physical system.

scholarly journals New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3811
Author(s):  
Katarzyna Adamiak ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Continuous Time ◽  
Sliding Mode ◽  
Representative Point ◽  
Time Varying ◽  
Sliding Surface ◽  
External Disturbances ◽  
Mode Control ◽  
Switching Type ◽  
Time Systems

This study considers the problem of energetical efficiency in switching type sliding mode control of discrete-time systems. The aim of this work is to reduce the quasi-sliding mode band-width and, as follows, the necessary control input, through an application of a new type of time-varying sliding hyperplane in quasi-sliding mode control of sampled time systems. Although time-varying sliding hyperplanes are well known to provide insensitivity to matched external disturbances and uncertainties of the model in the whole range of motion for continuous-time systems, their application in the discrete-time case has never been studied in detail. Therefore, this paper proposes a sliding surface, which crosses the system’s representative point at the initial step and then shifts in the state space according to the pre-generated demand profile of the sliding variable. Next, a controller for a real perturbed plant is designed so that it drives the system’s representative point to its reference position on the sliding plane in each step. Therefore, the impact of external disturbances on the system’s trajectory is minimized, which leads to a reduction of the necessary control effort. Moreover, thanks to a new reaching law applied in the reference profile generator, the sliding surface shift in each step is strictly limited and a switching type of motion occurs. Finally, under the assumption of boundedness and smoothness of continuous-time disturbance, a compensation scheme is added. It is proved that this control strategy reduces the quasi-sliding mode band-width from O(T) to O(T3) order from the very beginning of the regulation process. Moreover, it is shown that the maximum state variable errors become of O(T3) order as well. These achievements directly reduce the energy consumption in the closed-loop system, which is nowadays one of the crucial factors in control engineering.

scholarly journals Adaptive Neural Network Sliding Mode Control for Nonlinear Singular Fractional Order Systems with Mismatched Uncertainties

2020 ◽  
Vol 4 (4) ◽  
pp. 50
Author(s):  
Xuefeng Zhang ◽  
Wenkai Huang
Keyword(s):  
Neural Network ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Rbf Neural Network ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Sliding Surface ◽  
Mode Control ◽  
Necessary And Sufficient

This paper focuses on the sliding mode control (SMC) problem for a class of uncertain singular fractional order systems (SFOSs). The uncertainties occur in both state and derivative matrices. A radial basis function (RBF) neural network strategy was utilized to estimate the nonlinear terms of SFOSs. Firstly, by expanding the dimension of the SFOS, a novel sliding surface was constructed. A necessary and sufficient condition was given to ensure the admissibility of the SFOS while the system state moves on the sliding surface. The obtained results are linear matrix inequalities (LMIs), which are more general than the existing research. Then, the adaptive control law based on the RBF neural network was organized to guarantee that the SFOS reaches the sliding surface in a finite time. Finally, a simulation example is proposed to verify the validity of the designed procedures.

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

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.

scholarly journals Discrete Sliding Mode Speed Control of Induction Motor Using Time-Varying Switching Line

Electronics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 185 ◽  
Author(s):  
Grzegorz Tarchała ◽  
Teresa Orłowska-Kowalska
Keyword(s):  
Sliding Mode Control ◽  
Induction Motor ◽  
Discrete Time ◽  
Control Method ◽  
Sliding Mode ◽  
Power Converter ◽  
Discrete Version ◽  
Time Varying ◽  
Mode Control ◽  
Switching Line

Sliding mode control (SMC) of electric drives constitutes a very popular control method for nonlinear multivariable and time-varying systems, e.g., induction motor (IM) drives. Nowadays, IM are the most popular electrical machines (EM) applied in many industrial applications as motion control devices, including electrical and hybrid vehicles. Nowadays, the control systems of EM are mostly realized using digital techniques (microprocessors and microcontrollers). Therefore, all control algorithms should be discretized or the whole control system should be designed in the discrete-time domain. This paper deals with a discrete-time sliding mode control (DSMC) for IM drives. The discrete algorithms for sliding mode control of the motor speed and rotor flux are derived in detail and next tested in simulation research. The simulation tests include the discrete nature of the power converter supplying the IM and present excellent performance of the developed control structure. To obtain the rotor speed regulation invariant to external disturbances, like load torque or inertia, especially during the reaching phase of the switching line, the discrete version of a time-varying switching line was introduced. It is shown that the assumed dynamics of the IM flux and speed is achieved and the proposed control algorithm can be realized using commonly available microcontrollers. The paper is illustrated with comprehensive simulation results for 1.5 kW IM drive, which are verified by experimental tests.

Sign in / Sign up

Export Citation Format

Share Document