Finite-Time Trajectory Tracking of Second-Order Systems Using Acceleration Feedback Only

In this paper, an algebraic approach for the finite-time feedback control problem is provided for second-order systems where only the second-order derivative of the controlled variable is measured. In practice, it means that the acceleration is the only variable that can be used for feedback purposes. This problem appears in many mechanical systems such as positioning systems and force-position controllers in robotic systems and aerospace applications. Based on an algebraic approach, an on-line algebraic estimator is developed in order to estimate in finite time the unmeasured position and velocity variables. The obtained expressions depend solely on iterated integrals of the measured acceleration output and of the control input. The approach is shown to be robust to noisy measurements and it has the advantage to provide on-line finite-time (or non-asymptotic) state estimations. Based on these estimations, a quasi-homogeneous second-order sliding mode tracking control law including estimated position error integrals is designed illustrating the possibilities of finite-time acceleration feedback via algebraic state estimation.

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Smooth second-order nonsingular terminal sliding mode control for reusable launch vehicles

International Journal of Intelligent Computing and Cybernetics ◽

10.1108/ijicc-12-2013-0050 ◽

2014 ◽

Vol 7 (1) ◽

pp. 95-110 ◽

Cited By ~ 10

Author(s):

Shaobo Ni ◽

Jiayuan Shan

Keyword(s):

Finite Time ◽

Sliding Mode ◽

Tracking Error ◽

Second Order ◽

Convergence Time ◽

Control Input ◽

Terminal Sliding Mode ◽

Content Type ◽

Nonsingular Terminal Sliding Mode ◽

Attitude Tracking

Purpose – The purpose of this paper is to present a sliding mode attitude controller for reusable launch vehicle (RLV) which is nonlinear, coupling, and includes uncertain parameters and external disturbances. Design/methodology/approach – A smooth second-order nonsingular terminal sliding mode (NTSM) controller is proposed for RLV in reentry phase. First, a NTSM manifold is proposed for finite-time convergence. Then a smooth second sliding mode controller is designed to establish the sliding mode. An observer is utilized to estimate the lumped disturbance and the estimation result is used for feedforward compensation in the controller. Findings – It is mathematically proved that the proposed sliding mode technique makes the attitude tracking errors converge to zero in finite time and the convergence time is estimated. Simulations are made for RLV through the assumption that aerodynamic parameters and atmospheric density are perturbed. Simulation results demonstrate that the proposed control strategy is effective, leading to promising performance and robustness. Originality/value – By the proposed controller, the second-order sliding mode is established. The attitude tracking error converges to zero in a finite time. Meanwhile, the chattering is alleviated and a smooth control input is obtained.

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Finite time stability of uncertain second order systems using sliding mode control

2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA) ◽

10.1109/sta.2016.7952057 ◽

2016 ◽

Author(s):

Marwa Jouini ◽

Slim Dhahri ◽

Anis Sellami

Keyword(s):

Sliding Mode Control ◽

Finite Time ◽

Sliding Mode ◽

Second Order ◽

Time Stability ◽

Finite Time Stability ◽

Mode Control ◽

Second Order Systems

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Practical finite time vibration suppression of mechatronic systems using proportional–integral–derivative variable structure controls with dead-band nonlinearity

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/09596518211014328 ◽

2021 ◽

pp. 095965182110143

Author(s):

Mohammad Pourmahmood Aghababa ◽

Mehrdad Saif

Keyword(s):

Finite Time ◽

Sliding Mode ◽

Variable Structure ◽

Second Order ◽

Control Input ◽

Stable Equilibrium Point ◽

Proportional Integral Derivative ◽

Mechatronic Systems ◽

Dead Band ◽

Proportional Integral

Vibration is an intrinsic phenomenon in many mechanical and mechatronic applied devices and undesirable vibration can either degrade the performance of the system or lead to unpredictable outputs. The main purpose of this article is to introduce a novel second-order proportional–integral–derivative sliding mode control methodology to suppress the undesirable vibrations of a class of applied dynamical systems with applications to mechatronic and mechanical devices. After designing a nonlinear proportional–integral–derivative terminal sliding manifold, rigorous mathematics are provided to guarantee that the origin is a practical finite time stable equilibrium point. Consequently, two efficient control laws are proposed to ensure the occurrence of the sliding motion with and/or without system unknown parameters. Motivated by situations encountered in practice, unknown lumped uncertainties are also added to the system and their impacts are tackled using adaptive control techniques. Furthermore, a hard nonlinear dead-band function is utilized in the control input and its effects such as lags and delays appeared on the control signals as well as on the system outputs are dealt with by the proposed proportional–integral–derivative variable structure controller. The proposed second-order variable structure controller not only utilizes the simple effective design approach of the proportional–integral–derivative controllers to ensure a reasonable transient performance, but also displays fast convergence properties demonstrated in non-singular terminal sliding modes. Finally, through simulation studies, it is confirmed that the proposed control strategy is effective in vibration attenuation of microelectromechanical resonators.

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Finite-time sliding mode controller for perturbed second-order systems

ISA Transactions ◽

10.1016/j.isatra.2019.05.026 ◽

2019 ◽

Vol 95 ◽

pp. 82-92 ◽

Cited By ~ 6

Author(s):

Roger Miranda-Colorado

Keyword(s):

Finite Time ◽

Sliding Mode ◽

Second Order ◽

Sliding Mode Controller ◽

Second Order Systems

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Second-Order Super-Twisting Sliding Mode Control for Finite-Time Leader-Follower Consensus with Uncertain Nonlinear Multiagent Systems

Mathematical Problems in Engineering ◽

10.1155/2015/292437 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Nan Liu ◽

Rui Ling ◽

Qin Huang ◽

Zheren Zhu

Keyword(s):

Sliding Mode Control ◽

Multiagent Systems ◽

Finite Time ◽

Sliding Mode ◽

Lyapunov Stability Theory ◽

Second Order ◽

Control Input ◽

Control Approach ◽

Mode Control ◽

Consensus Tracking

Consensus tracking problem of the leader-follower multiagent systems is resolved via second-order super-twisting sliding mode control approach. The followers’ states can keep consistent with the leader’s states on sliding surfaces. The proposed approach can ensure the finite-time consensus if the directed graph of the nonlinear system has a directed path under the condition that leader’s control input is unavailable to any followers. It is proved by using the finite-time Lyapunov stability theory. Simulation results verify availability of the proposed approach.

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Fuzzy Finite-time Consensus Control for Nonlinear Second-order Multi-agent Systems with Disturbances by Integral Sliding Mode

2021 7th International Conference on Control, Instrumentation and Automation (ICCIA) ◽

10.1109/iccia52082.2021.9403573 ◽

2021 ◽

Author(s):

Mohammad Javad Mirzaei ◽

Sehraneh Ghaemi ◽

Ehsan Aslmostafa ◽

Mohammad Ali Badamchizadeh ◽

Mahdi Baradarannia

Keyword(s):

Finite Time ◽

Sliding Mode ◽

Second Order ◽

Multi Agent Systems ◽

Consensus Control ◽

Integral Sliding Mode ◽

Agent Systems ◽

Multi Agent

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A New Control Method for Second-Order Multiple Models Control System Based on Global Sliding Mode

Mathematical Problems in Engineering ◽

10.1155/2018/5709162 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Dan-xu Zhang ◽

Yang-wang Fang ◽

Peng-fei Yang ◽

You-li Wu ◽

Tong-xin Liu

Keyword(s):

Control System ◽

Sliding Mode Control ◽

Finite Time ◽

Sliding Mode ◽

Second Order ◽

Multiple Models ◽

Finite Time Convergence ◽

Mode Control ◽

Global Sliding Mode Control ◽

Control Scheme

This paper proposed a finite time convergence global sliding mode control scheme for the second-order multiple models control system. Firstly, the global sliding surface without reaching law for a single model control system is designed and the tracking error finite time convergence and global stability are proved. Secondly, we generalize the above scheme to the second-order multimodel control system and obtain the global sliding mode control law. Then, the convergent and stable performances of the closed-loop control system with multimodel controllers are proved. Finally, a simulation example shows that the proposed control scheme is more effective and useful compared with the traditional sliding mode control scheme.

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Immersion and invariance adaptive finite-time control of air-breathing hypersonic vehicles

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410018785491 ◽

2018 ◽

Vol 233 (7) ◽

pp. 2626-2641 ◽

Cited By ~ 1

Author(s):

Chao Han ◽

Zhen Liu ◽

Jianqiang Yi

Keyword(s):

Control System ◽

Finite Time ◽

Control Method ◽

Sliding Mode ◽

Second Order ◽

Hypersonic Vehicles ◽

Terminal Sliding Mode ◽

Air Breathing ◽

Immersion And Invariance ◽

Time Control

In this paper, a novel adaptive finite-time control of air-breathing hypersonic vehicles is proposed. Based on the immersion and invariance theory, an adaptive finite-time control method for general second-order systems is first derived, using nonsingular terminal sliding mode scheme. Then the method is applied to the control system design of a flexible air-breathing vehicle model, whose dynamics can be decoupled into first-order and second-order subsystems by time-scale separation principle. The main features of this hypersonic vehicle control system lie in the design flexibility of the parameter adaptive laws and the rapid convergence to the equilibrium point. Finally, simulations are conducted, which demonstrate that the control system has the features of fast and accurate tracking to command trajectories and strong robustness to parametric and non-parametric uncertainties.

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