Finite Time Fault Tolerant Control for Robot Manipulators Using Time Delay Estimation and Continuous Nonsingular Fast Terminal Sliding Mode Control
TL;DR: The proposed AFTC scheme possess several advantages such as high precision, strong robustness, no singularity, less chattering, and fast finite-time convergence due to the combined NFTSMC and HOSM control, and requires no prior knowledge of the fault due to TDE-based fault estimation.
Abstract: In this paper, a novel finite time fault tolerant control (FTC) is proposed for uncertain robot manipulators with actuator faults. First, a finite time passive FTC (PFTC) based on a robust nonsingular fast terminal sliding mode control (NFTSMC) is investigated. Be analyzed for addressing the disadvantages of the PFTC, an AFTC are then investigated by combining NFTSMC with a simple fault diagnosis scheme. In this scheme, an online fault estimation algorithm based on time delay estimation (TDE) is proposed to approximate actuator faults. The estimated fault information is used to detect, isolate, and accommodate the effect of the faults in the system. Then, a robust AFTC law is established by combining the obtained fault information and a robust NFTSMC. Finally, a high-order sliding mode (HOSM) control based on super-twisting algorithm is employed to eliminate the chattering. In comparison to the PFTC and other state-of-the-art approaches, the proposed AFTC scheme possess several advantages such as high precision, strong robustness, no singularity, less chattering, and fast finite-time convergence due to the combined NFTSMC and HOSM control, and requires no prior knowledge of the fault due to TDE-based fault estimation. Finally, simulation results are obtained to verify the effectiveness of the proposed strategy.
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TL;DR: Digital Control Of Dynamic Systems This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems with an emphasis on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude.
Abstract: Digital Control Of Dynamic Systems This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Digital Control of Dynamic Systems (3rd Edition): Franklin ... This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Digital Control of Dynamic Systems: Gene F. Franklin ... Digital Control of Dynamic Systems, 2nd Edition. Gene F. Franklin, Stanford University. J. David Powell, Stanford University Digital Control of Dynamic Systems, 2nd Edition Pearson This well-respected work discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. MATLAB statements and problems are thoroughly and carefully integrated throughout the book to offer readers a complete design picture. Digital Control of Dynamic Systems, 3rd Edition ... Digital control of dynamic systems | Gene F. Franklin, J. David Powell, Michael L. Workman | download | B–OK. Download books for free. Find books Digital control of dynamic systems | Gene F. Franklin, J ... Abstract This well-respected work discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic... (PDF) Digital Control of Dynamic Systems Digital Control of Dynamic Systems, Addison.pdf There is document Digital Control of Dynamic Systems, Addison.pdfavailable here for reading and downloading. Use the download button below or simple online reader. The file extension PDFand ranks to the Documentscategory. Digital Control of Dynamic Systems, Addison.pdf Download ... Automatic control is the science that develops techniques to steer, guide, control dynamic systems. These systems are built by humans and must perform a specific task. Examples of such dynamic systems are found in biology, physics, robotics, finance, etc. Digital Control means that the control laws are implemented in a digital device, such as a microcontroller or a microprocessor. Introduction to Digital Control of Dynamic Systems And ... The discussions are clear, nomenclature is not hard to follow and there are plenty of worked examples. The book covers discretization effects and design by emulation (i.e. design of continuous-time control system followed by discretization before implementation) which are not to be found on every book on digital control. Amazon.com: Customer reviews: Digital Control of Dynamic ... Find helpful customer reviews and review ratings for Digital Control of Dynamic Systems (3rd Edition) at Amazon.com. Read honest and unbiased product reviews from our users. Amazon.com: Customer reviews: Digital Control of Dynamic ... 1.1.2 Digital control Digital control systems employ a computer as a fundamental component in the controller. The computer typically receives a measurement of the controlled variable, also often receives the reference input, and produces its output using an algorithm. Introduction to Applied Digital Control From the Back Cover This well-respected, marketleading text discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. Digital Control of Dynamic Systems (3rd Edition) Test Bank `Among the advantages of digital logic for control are the increased flexibility `of the control programs and the decision-making or logic capability of digital `systems, which can be combined with the dynamic control function to meet `other system requirements. `The digital controls studied in this book are for closed-loop (feedback) Every day, eBookDaily adds three new free Kindle books to several different genres, such as Nonfiction, Business & Investing, Mystery & Thriller, Romance, Teens & Young Adult, Children's Books, and others.
902 citations
TL;DR: A novel control methodology for tracking control of robot manipulators based on a novel adaptive backstepping nonsingular fast terminal sliding mode control (ABNFTSMC) is developed and compared with other state-of-the-art controllers.
Abstract: This paper develops a novel control methodology for tracking control of robot manipulators based on a novel adaptive backstepping nonsingular fast terminal sliding mode control (ABNFTSMC). In this approach, a novel backstepping nonsingular fast terminal sliding mode controller (BNFTSMC) is developed based on an integration of integral nonsingular fast terminal sliding mode surface and a backstepping control strategy. The benefits of this approach are that the proposed controller can preserve the merits of the integral nonsingular fast terminal sliding mode control (NFTSMC) in terms of high robustness, fast transient response, and finite-time convergence, as well as backstepping control strategy in terms of globally asymptotic stability based on Lyapunov criterion. However, the major limitation of the proposed BNFTSMC is that its design procedure is dependent on the prior knowledge of the bound value of the disturbance and uncertainties. In order to overcome this limitation, an adaptive technique is employed to approximate the upper bound value; yielding an ABNFTSMC is recommended. The proposed controller is then applied for tracking control of a PUMA560 robot and compared with other state-of-the-art controllers, such as computed torque controller, PID controller, conventional PID-based sliding mode controller, and NFTSMC. The comparison results demonstrate the superior performance of the proposed approach.
273 citations
Cites background or methods from "Finite Time Fault Tolerant Control ..."
...In order to demonstrate the superior performance of the proposed ABNFTSMC controller, we compare it with the state-of-the-art controllers, which have been proposed for improving trajectory tracking performance of robot manipulators such as CTC [6], PID controller [15], [16], conventional PID-SMC [47], and conventional NFTSMC [35], [41], [42]....
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...The model of the fault function is introduced by [10], [42]...
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...Consider the robot dynamics described by [10], [42]...
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...In order to obtain both fast finite-time convergence and singular elimination, nonsingular FTSMC (NFTSMC) has been proposed [35], [41], [42]....
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TL;DR: The improved algorithm has better control performances than the traditional SMC and the power reaching law integral SMC algorithm, such as less chattering, smaller overshoots, and faster response speed.
Abstract: This paper proposes an improved double power reaching law integral SMC algorithm to overcome the chattering, large overshoot, slow response. This improved algorithm has two advantages. Firstly, the designed control law can reach the approaching equilibrium point quickly when it is away from or close to the sliding surface. The chattering and response speed problems can be resolved. Secondly, the proposed algorithm has a good anti-jamming performance, and can maintain a good dynamic quality under the condition of the uncertain external disturbance. Finally, the proposed algorithm is applied to the open-loop unstable magnetic suspension system. Theoretical analysis and Matlab simulation results show that the improved algorithm has better control performances than the traditional SMC and the power reaching law integral SMC algorithm, such as less chattering, smaller overshoots, and faster response speed.
204 citations
TL;DR: This paper investigates the precise and fast trajectory tracking control problem for the free-flying space manipulator, after capturing a space target with uncertain mass, and proves that the estimation error of ASMDO can be stabilized in finite-time, though the bound of the derivative of system uncertainty is unknown.
Abstract: The requirements for the control performances of space manipulators, especially for the stability and accuracy of the attitude control systems of the base spacecrafts, are ever increasing during the space target capturing tasks. However, the system uncertainties caused by parameter variations will degrade the system performances severely. This paper investigates the precise and fast trajectory tracking control problem for the free-flying space manipulator, after capturing a space target with uncertain mass. To compensate the system uncertainty with complex and uncertain dynamics, a novel adaptive sliding mode disturbance observer (ASMDO) is proposed. Then, a composite controller with prescribed transient and steady-state performances is developed. It is proved that the estimation error of ASMDO can be stabilized in finite-time, though the bound of the derivative of system uncertainty is unknown. Meanwhile, the trajectory tracking error can also be stabilized in finite-time and has preassigned maximum overshoot and steady-state error. Finally, numerical simulations and experimental studies are presented to demonstrate the effectiveness of proposed methods.
187 citations
TL;DR: In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes with known or unknown upper bound of the system uncertainty and external disturbances are proposed.
Abstract: In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes.
169 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
"Finite Time Fault Tolerant Control ..." refers methods in this paper
...Due to its inherent robustness to system uncertainties and external disturbances [11], sliding mode observer has been used in the design of fault diagnostic observers [12-15]....
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08 Jul 2003
TL;DR: A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes using the Lyapunov stability theory, and theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained.
Abstract: A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method.
2,040 citations
"Finite Time Fault Tolerant Control ..." refers background or methods in this paper
...When a1 = 1, (11) has the form of FTSM [49], and (11) coincides...
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...In this section, we compare the performance of AFTC based on the uses of the proposed NFTSMC, the NTSMC [the sliding surface is selected as in (10b)] [47] and the FTSMC [the sliding surface is selected as in (11)] [49]....
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...To obtain a finite time convergence, the TSM and NTSM have been developed as follows [47], [49]:...
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...1) The reaching control ure is designed based on a continuous function [49], [57]...
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...To overcome the first disadvantage of the traditional TSM, fast terminal sliding mode (FTSM) control has been developed [48], [49]; however, these approaches still have a singular problem....
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TL;DR: The three-part survey paper aims to give a comprehensive review of real-time fault diagnosis and fault-tolerant control, with particular attention on the results reported in the last decade.
Abstract: With the continuous increase in complexity and expense of industrial systems, there is less tolerance for performance degradation, productivity decrease, and safety hazards, which greatly necessitates to detect and identify any kinds of potential abnormalities and faults as early as possible and implement real-time fault-tolerant operation for minimizing performance degradation and avoiding dangerous situations. During the last four decades, fruitful results have been reported about fault diagnosis and fault-tolerant control methods and their applications in a variety of engineering systems. The three-part survey paper aims to give a comprehensive review of real-time fault diagnosis and fault-tolerant control, with particular attention on the results reported in the last decade. In this paper, fault diagnosis approaches and their applications are comprehensively reviewed from model- and signal-based perspectives, respectively.
2,026 citations
"Finite Time Fault Tolerant Control ..." refers background in this paper
...In literature, the approaches of FTC can be divided into two categories: 1) active and 2) passive [24]....
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TL;DR: In this paper, an order of the maximal differentiation error to the square root of the maximum deviation of the measured input signal from the base signal from Lipschitz's constant of the derivative was proposed.
1,958 citations
"Finite Time Fault Tolerant Control ..." refers methods in this paper
...In this section, we compare the performance of the SOED with BD technique in terms of velocity and acceleration estimation....
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...The parameter of BD is selected as 310L (this value is selected as the sampling time) and the parameters of SOED are all set to 5 ....
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...The velocity estimation using BD and SOED techniques are shown in Fig....
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...The stability and convergence of the STW algorithm can be proved based on the idea of the design of Lyapunov approach [64]–[66] or majorant curves [69]....
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...Through this simulation, five major contributions of this paper are verified: 1) the use of TDE for fault detection, isolation and estimation; 2) the use of SOED method instead of BD method to estimate the velocity and acceleration; 3) the effectiveness of the proposed AFTC compared to the proposed PFTC; 4) the use of STW algorithm defined in (41) to eliminate the chattering compared to the previous developed methods defined in (39) and (40); 5) the use of NFTSMC defined in (12) compared to the use of NTSMC defined in (10b) and FTSMC defined in (11) for the design of finite time FTC....
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TL;DR: This paper presents a global non-singular terminal sliding mode controller for rigid manipulators to enable the elimination of the singularity problem associated with conventional terminal slide mode control.
1,826 citations
"Finite Time Fault Tolerant Control ..." refers background in this paper
...In order to eliminate the singular problem, nonsingular TSMC (NTSMC) [50]–[53] and nonsingular fast TSMC (NFTSMC) [54]–[57] have been proposed....
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...Thus, according to [50], the crossing of trajectories between two boundaries of the vicinity ėi = ξ to ėi = −ξ for si > 0 and from ėi = −ξ to ėi = ξ for si < 0 is executed in finite time, and also the dynamics from the other regions where |ėi| > ξ converges to the boundaries in the finite time....
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...In this section, we compare the performance of the AFTC based on the uses of the proposed NFTSMC, the NTSMC (the sliding surface is selected as in (10b)) [47] and the FTSMC (the sliding surface is selected as in (11)) [49]....
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...However, the FTSMC and NFTSMC have a quite similar convergence but have a faster convergence compared to the NTSMC....
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...In order to eliminate the singular problem, nonsingular TSMC (NTSMC) [50-53] and nonsingular fast terminal sliding mode control (NFTSMC) [54-57] have been proposed....
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