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.

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.

Sliding Mode Control for Wheeled Inverted Pendulum

2014 ◽  
Vol 971-973 ◽  
pp. 714-717 ◽  
Author(s):  
Xiang Shi ◽  
Zhe Xu ◽  
Qing Yi He ◽  
Ka Tian
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
High Performance ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Experimental Results ◽  
Control Law ◽  
Collaborative Simulation ◽  
Mode Control ◽  
Wheeled Inverted Pendulum

To control wheeled inverted pendulum is a good way to test all kinds of theories of control. The control law is designed, and it based on the collaborative simulation of MATLAB and ADAMS is used to control wheeled inverted pendulum. Then, with own design of hardware and software of control system, sliding mode control is used to wheeled inverted pendulum, and the experimental results of it indicate short adjusting time, the small overshoot and high performance.

Conditional integrator sliding mode control of an unmanned quadrotor helicopter

2021 ◽  
pp. 095965182110498
Author(s):  
Yohan Díaz-Méndez ◽  
Leandro Diniz de Jesus ◽  
Marcelo Santiago de Sousa ◽  
Sebastião Simões Cunha ◽  
Alexandre Brandão Ramos
Keyword(s):  
Sliding Mode Control ◽  
Transient Response ◽  
Tracking Control ◽  
Position Control ◽  
Sliding Mode ◽  
Control Technique ◽  
Control Law ◽  
Control Problems ◽  
Control Activity ◽  
Mode Control

Sliding mode control (SMC) is a widely used control law for quadrotor regulation and tracking control problems. The purpose of this article is to solve the tracking problem of quadrotors using a relatively novel nonlinear control law based on SMC that makes use of a conditional integrator. It is demonstrated by a motivation example that the proposed control law can improve the transient response and chattering shortcomings of the previous approaches of similar SMC based controllers. The adopted Newton–Euler model of quadrotor dynamics and controller design is treated separately in two subsystems: attitude and position control loops. The stability of the control technique is demonstrated by Lyapunov’s analysis and the effectiveness and performance of the proposed method are compared with a similar integral law, also based on SMC, and validated by tracking control problems using numerical simulations. Simulations were developed in the presence of external disturbances in order to evaluate the controller robustness. The effectiveness of the proposed controller was verified by performance indexes, demonstrating less accumulated tracking errors and control activity and improvement in the transient response and disturbance rejection when compared to a conventional integrator sliding mode controller.

scholarly journals On Chattering-Free Dynamic Sliding Mode Controller Design

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Jeang-Lin Chang
Keyword(s):  
Sliding Mode Control ◽  
Controller Design ◽  
Sliding Mode ◽  
Control Law ◽  
Mode Control ◽  
Chattering Free ◽  
Dynamic Sliding Mode Control ◽  
System States ◽  
Dynamic Sliding Mode ◽  
Free Dynamic

For a class of linear MIMO uncertain systems, a dynamic sliding mode control algorithm that avoids the chattering problem is proposed in this paper. Without using any differentiator, we develop a modified asymptotically stable second-order sliding mode control law in which the proposed controller can guarantee the finite time convergence to the sliding mode and can show that the system states asymptotically approach to zero. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.

Integration of Multibody System Dynamics With Sliding Mode Control Using FPGA Technique for Trajectory Tracking Problems

2018 ◽  
Author(s):  
Ayman A. Nada ◽  
Abdullateef H. Bashiri
Keyword(s):  
Sliding Mode Control ◽  
Mobile Robot ◽  
Control Systems ◽  
Trajectory Tracking ◽  
Sliding Mode ◽  
Integrated Control ◽  
Equations Of Motion ◽  
Multiple Input Multiple Output ◽  
Control Law ◽  
Mode Control

Trajectory tracking robotic systems require complex control procedures that occupy less space and need less energy. For these reasons, the development of computerized and integrated control systems is crucial. Recently, developing reconfigurable Field Programmable Gate Arrays (FPGAs) give a prominence of the complete robotic control systems. Furthermore, it has been found in the literature that the model-based control methods are most efficient and cost-effective. This model must interpret how multiple moving parts interact with each other and with their environment. On the other hand, MultiBody Dynamic (MBD) approach is considered to solve these difficulties to attain the models accurately. However, the obtained equations of motion do not match the well-developed forms of control theory. In this paper, the MBD model of a mobile robot is established; and the equations of motion are reshaped into their control canonical form. Additionally, the Sliding Mode Control (SMC) theory is used to design the control law. The constraints’ manifold, which is available in the equations of the MBD system, are imposed systematically as the switching surface. SMC is applied because of its ability to address multiple-input/multiple-output nonlinear systems without resorting any approximations. Eventually, the experimental verification of the proposed algorithm is carried out using DaNI mobile robot in which, a Reconfigurable Input/Output (RIO) board is used to reorient the control design, so that can fit the required trajectory. The control law is implemented using LabVIEW software and NI-sbRIO-9631 with acceptable performance. It is obvious that the integration of MBD/SMC/FPGA can be used successfully to develop embedded systems for the applications of trajectory tracking robotics.

scholarly journals Robust Fuzzy Sliding Mode Controller for Discrete Nonlinear Systems

2008 ◽  
Vol 3 (1) ◽  
pp. 6 ◽  
Author(s):  
Hafedh Abid ◽  
Mohamed Chtourou ◽  
Ahmed Toumi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Fuzzy Model ◽  
Uncertain System ◽  
Control Technique ◽  
Control Law ◽  
Mode Control ◽  
Equivalent Control ◽  
Fuzzy Sliding Mode ◽  
Discrete Nonlinear Systems

In this work we are interested to discrete robust fuzzy sliding mode control. The discrete SISO nonlinear uncertain system is presented by the Takgi- Sugeno type fuzzy model state. We recall the principle of the sliding mode control theory then we combine the fuzzy systems with the sliding mode control technique to compute at each sampling time the control law. The control law comports two terms: equivalent control law and switching control law which has a high frequency. The uncertainty is replaced by its upper bound. Inverted pendulum and mass spring dumper are used to check performance of the proposed fuzzy robust sliding mode control scheme.

Design Robust Nonlinear Controllers for Autonomous Underwater Vehicles with Comparison of Simulated and At-sea Test Data

2002 ◽  
Vol 8 (2) ◽  
pp. 189-217 ◽  
Author(s):  
Feijun Song ◽  
Edgar An ◽  
Samuel M. Smith
Keyword(s):  
Sliding Mode Control ◽  
Test Data ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sliding Mode ◽  
Autonomous Underwater Vehicles ◽  
Simulation Software ◽  
Control Law ◽  
Mode Control ◽  
Highly Nonlinear

Successful controller development involves three distinct stages, namely, control law design, code debugging and field test. For Autonomous Underwater Vehicle (AUV) applications, the first two stages require special strategies. Since the dynamics of an AUV is highly nonlinear, and the environment that an AUV operates in is noisy with external disturbance that cannot be neglected, a robust control law must be considered in the first stage. The control law design is even more difficult when optimal criteria are also involved. In the second stage, since the software architecture on an AUV is very complicated, debugging the controllers alone without all the software routines running together often can not reveal subtle faults in the controller code. Thorough debugging needs at-sea test, which is costly. Therefore, a platform that can help designers debug and evaluate controller performance before any at-sea experiment is highly desirable. Recently, a 6 Degree of Freedom (DOF) AUV simulation toolbox was developed for the Ocean Explorer (OEX) series AUVs developed at Florida Atlantic University. The simulation toolbox is an ideal platform for controller in-lab debugging and evaluation. This paper first presents a novel robust controller design methodology, named the Sliding Mode Fuzzy Controller (SMFC). It combines sliding mode control and fuzzy logic control to create a robust, easy on-line tunable controller structure. A formal proof of the robustness of the proposed nonlinear sliding mode control is also given. A pitch and a heading controller have been designed with the presented structure and the controller code was tested on the simulation software package as well as at sea. The simulated and at-sea test data are compared. The whole controller design procedure described in this paper clearly demonstrates the advantage of using the simulation toolbox to debug and test the controller in-lab. Moreover, the pitch and heading controller have been used in the real system for more than 2 years, and have also been successfully ported to other types of vehicles without any major modification on the controller parameters. The similarity of the controller performances on different vehicles further demonstrates the robustness of the proposed Sliding Mode Fuzzy Controller. The main contribution of this paper is to provide useful insights into the design and implementation of the proposed control architecture, and its application in AUV control.

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