Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Sachit Rao ◽  
Vadim Utkin ◽  
Martin Buss
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Engineering Systems ◽  
Sliding Modes ◽  
Algebraic Equations ◽  
Electric Networks ◽  
Electrical Systems ◽  
Mode Control

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventional simulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter.

Combined DAE and Sliding Mode Control Methods for Simulation of Constrained Mechanical Systems

2000 ◽  
Vol 122 (4) ◽  
pp. 691-698 ◽  
Author(s):  
M. D. Compere ◽  
R. G. Longoria
Keyword(s):  
Sliding Mode Control ◽  
Numerical Method ◽  
Hybrid Method ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Stabilization Method ◽  
Mode Control ◽  
Hybrid Numerical Method

In dynamic analysis of constrained multibody systems (MBS), the computer simulation problem essentially reduces to finding a numerical solution to higher-index differential-algebraic equations (DAE). This paper presents a hybrid method composed of multi-input multi-output (MIMO), nonlinear, variable-structure control (VSC) theory and post-stabilization from DAE solution theory for the computer solution of constrained MBS equations. The primary contributions of this paper are: (1) explicit transformation of constrained MBS DAE into a general nonlinear MIMO control problem in canonical form; (2) development of a hybrid numerical method that incorporates benefits of both Sliding Mode Control (SMC) and DAE stabilization methods for the solution of index-2 or index-3 MBS DAE; (3) development of an acceleration-level stabilization method that draws from SMC’s boundary layer dynamics and the DAE literature’s post-stabilization; and (4) presentation of the hybrid numerical method as one way to eliminate chattering commonly found in simulation of SMC systems. The hybrid method presented can be used to simulate constrained MBS systems with either holonomic, nonholonomic, or both types of constraints. In addition, the initial conditions (ICs) may either be consistent or inconsistent. In this paper, MIMO SMC is used to find the control law that will provide two guarantees. First, if the constraints are initially not satisfied (i.e., for inconsistent ICs) the constraints will be driven to satisfaction within finite time using SMC’s stabilization method, urobust,i=−ηisgnsi. Second, once the constraints have been satisfied, the control law, ueq and hybrid stabilization techniques guarantee surface attractiveness and satisfaction for all time. For inconsistent ICs, Hermite-Birkhoff interpolants accurately locate when each surface reaches zero, indicating the transition time from SMC’s stabilization method to those in the DAE literature. [S0022-0434(00)02404-7]

scholarly journals A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1134
Author(s):  
Yongpeng Tai ◽  
Ning Chen ◽  
Lijin Wang ◽  
Zaiyong Feng ◽  
Jun Xu
Keyword(s):  
Fractional Calculus ◽  
Sliding Mode Control ◽  
Numerical Method ◽  
Present Method ◽  
Sliding Mode ◽  
Constitutive Relations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Mode Control ◽  
Fractional Differential

Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and the fractional calculus definition of Grünwald–Letnikov. The algebraic equation is considered as the sliding mode surface. The validity of the present method is verified by comparing with an example with exact solutions. The accuracy and efficiency of the present method are studied. It is found that the present method has very high accuracy and low time consumption. The effect of violation corrections on the accuracy is investigated for different time steps.

scholarly journals Synchronization of Synchronous Reluctance Motors Using the Discrete Sliding Mode Control Technique

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Salahuddin Abdul Rahman ◽  
Mohamed Zribi ◽  
Nejib Smaoui
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Control Technique ◽  
Mode Control ◽  
Synchronous Reluctance Motor ◽  
Control Scheme ◽  
Bounded Disturbances ◽  
Simulation Results

The synchronous reluctance motor (SynRM) drive system is known to exhibit chaotic behavior under specified conditions. In this paper, the discrete-time sliding mode control (DSMC) technique is used to synchronize two SynRMs starting from different sets of initial conditions. The mixed variable speed reaching law is adopted in the design of the controller scheme. The parameters of the designed control scheme are tuned using a genetic algorithm (GA). Simulation results are presented to demonstrate the effectiveness of the proposed controller. In addition, the performance of the proposed control scheme is studied through simulations when bounded disturbances and mismatches between the parameters of the systems and those of the control scheme exist. The simulation results show that the designed control scheme is robust to bounded external disturbances and to mismatches in the parameters of the systems.

New fixed-time sliding mode control for a mismatched second-order system

2020 ◽  
pp. 014233122095230
Author(s):  
Guo Jianguo ◽  
Yang Shengjiang
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Nonlinear Function ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Time Stability ◽  
Mode Control ◽  
Mismatched Uncertainties

A fixed-time sliding mode control (FTSMC) method is proposed for a second-order system with mismatched uncertainties in this paper. A new sliding mode, which is insensitive to the mismatched disturbance, is present to eliminate the effect of mismatched uncertainties by adopting the differentiable nonlinear function, and to obtain the fixed time stability independent of initial conditions by using the fraction-order function. In order to improve the performance of control system, the extended disturbance-observer-based fixed-time sliding mode control (EDO-FTSMC) approach is investigated to obtain the fixed-time stability subject to the mismatched uncertainties. Finally, the performance of the proposed control method is illustrated to compare other control approaches with numerical simulation results and application examples.

A Novel Fuzzy Sliding Mode Control Scheme for Nonlinear Systems with Bounded Inputs

2002 ◽  
Vol 8 (7) ◽  
pp. 945-965 ◽  
Author(s):  
Juhng-Perng Su ◽  
Chi-Ying Liang
Keyword(s):  
Sliding Mode Control ◽  
Fuzzy Controller ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Variable Structure ◽  
Single Frequency ◽  
Bench Mark ◽  
Mode Control ◽  
Variable Structure System ◽  
Control Scheme

In this paper, we investigated the design of robust controllers for a class of nonlinear uncertain systems with bounded inputs, which have not yet been thoroughly discussed. Based on the variable structure system theory, we developed a novel stable sliding mode control scheme for this class of systems. A key feature of this control scheme is the introduction of a new generalized error as a complement to the conventional generalized error to form a meaningful error measure so that a new sliding mode controller incorporated with a two-input one-output fuzzy controller can be constructed to improve the reaching behavior of the system during the reaching phase as well as the tracking precision while in the boundary layer. The nonlinear bench mark problem, TORA, was used as an example to demonstrate the effectiveness of the design. Simulation results showed that, as compared with various available controllers in literature, much better responses to any initial conditions and to single-frequency sinusoidal disturbances can be obtained.

scholarly journals Active Sliding Mode Control Antisynchronization of Chaotic Systems with Uncertainties and External Disturbances

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Wafaa Jawaada ◽  
M. S. M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Sliding Mode Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
External Disturbances ◽  
Mode Control ◽  
Active Sliding Mode Control

The antisynchronization behavior of chaotic systems with parametric uncertainties and external disturbances is explored by using robust active sliding mode control method. The sufficient conditions for achieving robust antisynchronization of two identical chaotic systems with different initial conditions and two different chaotic systems with terms of uncertainties and external disturbances are derived based on the Lyapunov stability theory. Analysis and numerical simulations are shown for validation purposes.

scholarly journals Control of Chaos in a Single Machine Infinite Bus Power System Using the Discrete Sliding Mode Control Technique

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Mohamed Zribi ◽  
Muthana T. Alrifai ◽  
Nejib Smaoui
Keyword(s):  
Sliding Mode Control ◽  
Power System ◽  
Discrete Time ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Control Technique ◽  
Reaching Law ◽  
Mode Control ◽  
Control Scheme ◽  
Simulation Results

Under certain conditions, power systems may exhibit chaotic behaviors which are harmful and undesirable. In this paper, the discrete time sliding mode control technique is used to control a chaotic power system. The objective of the control is to eliminate the chaotic oscillations and to bring order to the power system. Two discrete time sliding mode control (DSMC) schemes are proposed for a fourth order discrete time chaotic power system. The first DSMC control scheme is based on the well-known exponential reaching law. The second DSMC control scheme is based on the recently developed double power reaching law. It is shown that the states of the controlled system converge to their desired values. Simulation results are presented for different values of the gains of the controllers as well as for different initial conditions. These results indicate that both control schemes work well. However, the simulation results show that the second control scheme gave better results since it was able to greatly reduce the chattering problem.

scholarly journals Sliding Mode Control for Chaotic Oscillations in SMIB Power System

2021 ◽  
Vol 9 (7) ◽  
pp. 4027-4037
Author(s):  
Tandel Zankhana
Keyword(s):  
Sliding Mode Control ◽  
Power Systems ◽  
Power System ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Chaotic Oscillation ◽  
Voltage Collapse ◽  
Chaotic Oscillations ◽  
Mode Control ◽  
Matlab Programming

Abstract: Power systems may revelation the harmful and undesirable chaotic phenomenon in certain conditions. This project describes the control of a chaotic oscillation in power system. Chaos may lead the power system to voltage instability and voltage collapse when voltage stability conditions are broken. Chaotic oscillations are very sensitive to parameter and initial conditions of power system. Many controllers are projected in practical to suppress the chaos and avoid voltage collapse. In this thesis, a Conventional Sliding Mode Control is applied for removal of chaotic oscillations. The aim of the controller is to remove the chaotic oscillations and bring the order to the nonlinear system. It is also shown that the proposed controller assurances the system state convergence to their desired ethics. To demonstrate the effectiveness of the projected controller, MATLAB Programming is done. Keywords: Chaotic oscillations, SMIB, Conventional Sliding Mode Control

scholarly journals A Compound Fuzzy Disturbance Observer Based on Sliding Modes and Its Application on Flight Simulator

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yunjie Wu ◽  
Youmin Liu ◽  
Dapeng Tian
Keyword(s):  
Sliding Mode Control ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
Frequency Component ◽  
High Frequency Component ◽  
Flight Simulator ◽  
Sliding Modes ◽  
Disturbance Estimation ◽  
Mode Control ◽  
Fuzzy Disturbance Observer

A compound fuzzy disturbance observer based on sliding modes is developed, and its application on flight simulator is presented. Fuzzy disturbance observer (FDO) is an effective method in nonlinear control. However, traditional FDO is confined to monitor dynamic disturbance, and the frequency bandwidth of the system is restricted. Sliding mode control (SMC) compensates the high-frequency component of disturbance while it is limited by the chattering phenomenon. The proposed method uses the sliding mode technique to deal with the uncompensated dynamic equivalent disturbance. The switching gain of sliding mode control designed according to the error of disturbance estimation is a small value. Therefore, the proposal also helps to decrease the chattering. The validity of the proposal method is confirmed by experiments on flight simulator.

Switching Plane Design for the Sliding Mode Control of Systems with Elastic Input Constraints

2005 ◽  
Vol 219 (6) ◽  
pp. 393-403 ◽  
Author(s):  
A Bartoszewicz ◽  
A Nowacka
Keyword(s):  
Sliding Mode Control ◽  
Input Signal ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Initial Time ◽  
Control Input ◽  
Time Varying ◽  
Input Constraints ◽  
Mode Control ◽  
Elastic Constraint

In this paper a new sliding mode control algorithm for the third-order non-linear, time-varying, uncertain system subject to unknown disturbance is proposed. Since the conventional input constraints expressed by inequalities are often impractical, in this paper the situation is considered where the input signal is subject to elastic constraint. It is assumed that the threshold value of the system input signal is known and exceeding this value is undesirable but possible if justified by essential improvement of the system performance. The proposed algorithm employs a time-varying switching plane. At the initial time the plane passes through the point determined by the system initial conditions in the error state space and afterwards moves with a constant velocity to the origin of the space. The plane is designed in such a way that fast error convergence is achieved using limited control input. By this means, the reaching phase is eliminated, insensitivity of the system to external disturbance is ensured from the very beginning of the control action, and fast, monotonic error convergence to zero is achieved. Moreover, it is demonstrated that the conventional input constraint expressed by an inequality is a limit case of the elastic constraint considered in the paper.

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