Discrete-Time Fast Terminal Sliding Mode Control for Permanent Magnet Linear Motor
TL;DR: Rigorous analysis is provided to demonstrate that the fast terminal SMC law can offer a higher accuracy than the traditional linear SMClaw and show the advantages of the present discrete-time fast terminalSMC approach over some existing approaches, such as discrete- time linear sliding mode control approach and the PID control method.
Abstract: The main objective of this paper is to solve the position tracking control problem for the permanent magnet linear motor by using the discrete-time fast terminal sliding mode control (SMC) method. Specifically, based on Euler's discretization technique, the approximate discrete-time model is first obtained and analyzed. Then, by introducing a new type of discrete-time fast terminal sliding surface, an improved discrete-time fast SMC method is developed and an equivalent-control-based fast terminal SMC law is subsequently designed. Rigorous analysis is provided to demonstrate that the fast terminal SMC law can offer a higher accuracy than the traditional linear SMC law. Numerical simulations and experimental results are finally performed to demonstrate the effectiveness of the proposed approach and show the advantages of the present discrete-time fast terminal SMC approach over some existing approaches, such as discrete-time linear sliding mode control approach and the PID control method.
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TL;DR: A new approach to the design of nonlinear disturbance observers (DOBs) for a class of non linear systems described by input–output differential equations is presented, with the most important feature that only measurement of the output variable is required, rather than the state variables.
Abstract: A new approach to the design of nonlinear disturbance observers (DOBs) for a class of nonlinear systems described by input–output differential equations is presented in this paper. In contrast with established forms of nonlinear DOBs, the most important feature of this new type of DOB is that only measurement of the output variable is required, rather than the state variables. An inverse simulation model is first constructed based on knowledge of the structure and parameters of a conventional model of the system. The disturbance can then be estimated by comparing the output of the inverse model and the input of the original nonlinear system. Mathematical analysis demonstrates the convergence of this new form of nonlinear DOB. The approach has been applied to disturbance estimation for a linear system and a new form of linear DOB has been developed. The differences between the proposed linear DOB and the conventional form of frequency-domain DOB are discussed through a numerical example. Finally, the nonlinear DOB design method is illustrated through an application involving a simulation of a jacketed continuous stirred tank reactor system.
174 citations
Cites background from "Discrete-Time Fast Terminal Sliding..."
...However, such methods can present difficulties in terms of estimation of the disturbances or may tend to overestimate their upper bounds [3], [4]....
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TL;DR: The ATSMRL is presented with the aim of reducing the input control efforts, which can dynamically adopt all positive aspects in terms of the finite time convergence, high tracking precision, and reduction of the chattering in the control input of the system.
Abstract: In order to enhance the speed control performance of the permanent magnet synchronous motor (PMSM) with internal and external disturbances, a new adaptive terminal sliding mode reaching law (ATSMRL) is proposed with continuous fast terminal sliding mode control (CFTSMC). Firstly, the ATSMRL is presented with the aim of reducing the input control efforts, which can dynamically adopt all positive aspects in terms of the finite time convergence, high tracking precision, and reduction of the chattering in the control input of the system. Secondly, an extended sliding mode disturbance observer (ESMDO) is designed to estimate the total disturbances of the system, and then the estimated disturbance has been brought for the feed-forward compensation technique, which would enhance the disturbance rejection ability of the system. Afterwards, the close loop stability is validated by the Lyapunov function. Finally the comprehensive numerical and experimental analyses have been carried out to demonstrate the superiority of the ATSMRL method than those of conventional exponential sliding mode reaching law (ESMRL) and terminal sliding mode reaching law (TSMRL).
150 citations
Cites background from "Discrete-Time Fast Terminal Sliding..."
...The nonlinear algorithms include robust control [3], fuzzy control [4], sliding mode control (SMC) [5], disturbance rejection control [6], predictive control [7], [8], terminal sliding mode control (TSMC) [9]–[15], and so on....
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TL;DR: The inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies, and a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived.
Abstract: The present draft investigates the finite-time stabilization of T–S fuzzy semi-Markov switching systems by using a coupling memory sampled-data control approach. The main study concerned is how to effectively design the sampled-data control such that closed-loop T–S fuzzy semi-Markov switching systems is finite-time boundedness. By utilizing a Bernoulli distributed sequence, a more general coupling memory fuzzy sampled-data control strategy that involving time delay effect is derived. By virtue of fuzzy-basis-dependent membership functions, an asynchronous approach is proposed for T–S fuzzy semi-Markov switching system. Moreover, the inverted pendulum model is presented to demonstrate the feasibility and validity of the proposed strategies.
108 citations
TL;DR: Experiments demonstrate the superior property of stronger robustness and fewer chattering effects of the proposed method compared to existing disturbance observers and adaptive recursive terminal sliding mode (ARTSM) controller.
104 citations
TL;DR: This paper investigates the global asymptotical stabilization using sampled-data output feedback for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin.
96 citations
References
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Book•
01 Feb 1992
TL;DR: The theory and practical application of Lyapunov's Theorem, a method for the Study of Non-linear High-Gain Systems, are studied.
Abstract: I. Mathematical Tools.- 1 Scope of the Theory of Sliding Modes.- 1 Shaping the Problem.- 2 Formalization of Sliding Mode Description.- 3 Sliding Modes in Control Systems.- 2 Mathematical Description of Motions on Discontinuity Boundaries.- 1 Regularization Problem.- 2 Equivalent Control Method.- 3 Regularization of Systems Linear with Respect to Control.- 4 Physical Meaning of the Equivalent Control.- 5 Stochastic Regularization.- 3 The Uniqueness Problems.- 1 Examples of Discontinuous Systems with Ambiguous Sliding Equations.- 1.1 Systems with Scalar Control.- 1.2 Systems Nonlinear with Respect to Vector-Valued Control.- 1.3 Example of Ambiguity in a System Linear with Respect to Control ..- 2 Minimal Convex Sets.- 3 Ambiguity in Systems Linear with Respect to Control.- 4 Stability of Sliding Modes.- 1 Problem Statement, Definitions, Necessary Conditions for Stability ..- 2 An Analog of Lyapunov's Theorem to Determine the Sliding Mode Domain.- 3 Piecewise Smooth Lyapunov Functions.- 4 Quadratic Forms Method.- 5 Systems with a Vector-Valued Control Hierarchy.- 6 The Finiteness of Lyapunov Functions in Discontinuous Dynamic Systems.- 5 Singularly Perturbed Discontinuous Systems.- 1 Separation of Motions in Singularly Perturbed Systems.- 2 Problem Statement for Systems with Discontinuous control.- 3 Sliding Modes in Singularly Perturbed Discontinuous Control Systems.- II. Design.- 6 Decoupling in Systems with Discontinuous Controls.- 1 Problem Statement.- 2 Invariant Transformations.- 3 Design Procedure.- 4 Reduction of the Control System Equations to a Regular Form.- 4.1 Single-Input Systems.- 4.2 Multiple-Input Systems.- 7 Eigenvalue Allocation.- 1 Controllability of Stationary Linear Systems.- 2 Canonical Controllability Form.- 3 Eigenvalue Allocation in Linear Systems. Stabilizability.- 4 Design of Discontinuity Surfaces.- 5 Stability of Sliding Modes.- 6 Estimation of Convergence to Sliding Manifold.- 8 Systems with Scalar Control.- 1 Design of Locally Stable Sliding Modes.- 2 Conditions of Sliding Mode Stability "in the Large".- 3 Design Procedure: An Example.- 4 Systems in the Canonical Form.- 9 Dynamic Optimization.- 1 Problem Statement.- 2 Observability, Detectability.- 3 Optimal Control in Linear Systems with Quadratic Criterion.- 4 Optimal Sliding Modes.- 5 Parametric Optimization.- 6 Optimization in Time-Varying Systems.- 10 Control of Linear Plants in the Presence of Disturbances.- 1 Problem Statement.- 2 Sliding Mode Invariance Conditions.- 3 Combined Systems.- 4 Invariant Systems Without Disturbance Measurements.- 5 Eigenvalue Allocation in Invariant System with Non-measurable Disturbances.- 11 Systems with High Gains and Discontinuous Controls.- 1 Decoupled Motion Systems.- 2 Linear Time-Invariant Systems.- 3 Equivalent Control Method for the Study of Non-linear High-Gain Systems.- 4 Concluding Remarks.- 12 Control of Distributed-Parameter Plants.- 1 Systems with Mobile Control.- 2 Design Based on the Lyapunov Method.- 3 Modal Control.- 4 Design of Distributed Control of Multi-Variable Heat Processes.- 13 Control Under Uncertainty Conditions.- 1 Design of Adaptive Systems with Reference Model.- 2 Identification with Piecewise-Continuous Dynamic Models.- 3 Method of Self-Optimization.- 14 State Observation and Filtering.- 1 The Luenberger Observer.- 2 Observer with Discontinuous Parameters.- 3 Sliding Modes in Systems with Asymptotic Observers.- 4 Quasi-Optimal Adaptive Filtering.- 15 Sliding Modes in Problems of Mathematical Programming.- 1 Problem Statement.- 2 Motion Equations and Necessary Existence Conditions for Sliding Mode.- 3 Gradient Procedures for Piecewise Smooth Function.- 4 Conditions for Penalty Function Existence. Convergence of Gradient Procedure.- 5 Design of Piecewise Smooth Penalty Function.- 6 Linearly Independent Constraints.- III. Applications.- 16 Manipulator Control System.- 1 Model of Robot Arm.- 2 Problem Statement.- 3 Design of Control.- 4 Design of Control System for a Two-joint Manipulator.- 5 Manipulator Simulation.- 6 Path Control.- 7 Conclusions.- 17 Sliding Modes in Control of Electric Motors.- 1 Problem Statement.- 2 Control of d. c. Motor.- 3 Control of Induction Motor.- 4 Control of Synchronous Motor.- 18 Examples.- 1 Electric Drives for Metal-cutting Machine Tools.- 2 Vehicle Control.- 3 Process Control.- 4 Other Applications.- References.
5,422 citations
"Discrete-Time Fast Terminal Sliding..." refers methods in this paper
...Motivated by the fact that the sliding mode control (SMC) method has been successfully applied in practice due to its distinguished features, such as easy implementation, strong robustness to parameter uncertainties and external disturbances [12]–[14], a control strategy for PMLM was designed in [15] based on SMC method and a proportional-integral-based equivalent disturbance observer....
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TL;DR: This paper presents a treatment of discrete variable structure control systems, and a recently introduced "reaching law approach" is conveniently used to develop the control law for robust control.
Abstract: This paper presents a treatment of discrete variable structure control systems. The purpose is to lay a foundation upon which design of such type of systems can be made properly. Phenomena of switching, reaching, and quasi-sliding mode are investigated thoroughly. Terms pertaining to discrete variable structure control are defined. A method of quasi-sliding mode design is given. The inherently existing quasi-sliding mode band is analyzed. A recently introduced "reaching law approach" is conveniently used to develop the control law for robust control. Comments are given regarding chattering. The design technique is illustrated by a simulated system. >
1,428 citations
"Discrete-Time Fast Terminal Sliding..." refers methods in this paper
...For example, the reaching-law-based discrete-time SMC laws were designed in [25] and [26] and the equivalent-control-based discrete-time SMC laws were studied in [27] and [28]....
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TL;DR: A robust MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators are developed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed.
Abstract: In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero. >
853 citations
"Discrete-Time Fast Terminal Sliding..." refers methods in this paper
...To improve the dynamic response of closed-loop system, the terminal SMC (TSMC) method was introduced in [17]–[20], which can ensure the finite-time convergence during the sliding mode stage....
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TL;DR: A fast terminal dynamics is proposed and used in the design of the sliding-mode control for single-input single-output nonlinear dynamical systems.
Abstract: A fast terminal dynamics is proposed and used in the design of the sliding-mode control for single-input single-output nonlinear dynamical systems. The inherent dynamic properties of the fast terminal sliding modes are explored and conditions to ensure its applicability for control designs are obtained.
677 citations
"Discrete-Time Fast Terminal Sliding..." refers background or methods in this paper
...The rigorous theoretical analysis about this issue for continuous-time FTSMC has been given in [23]....
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...To handle the shortcoming that the TSMC has a slower convergence rate than the linear sliding mode controller (LSMC) when the system state is far away from the equilibrium, the fast terminal SMC (FTSMC) method was proposed in [23] and [24]....
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TL;DR: In this article, a terminal sliding mode control design scheme for uncertain dynamic systems in the pure-feedback form is presented, which employs a recursive procedure which utilizes a set of switching manifolds to realize finite time convergence.
487 citations