Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Mohammad Pourmahmood Aghababa
Keyword(s):  
Fractional Derivative ◽  
Sliding Mode ◽  
Variable Structure ◽  
Stability And Convergence ◽  
Control Input ◽  
Fractional Systems ◽  
Sliding Motion ◽  
Efficient Performance ◽  
Sliding Manifold ◽  
Chattering Free

The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.

Sliding Mode Control of a Three Degrees of Freedom Anthropoid Robot by Driving the Controller Parameters to an Equivalent Regime

2000 ◽  
Vol 122 (4) ◽  
pp. 632-640 ◽  
Author(s):  
M. Onder Efe ◽  
Okyay Kaynak ◽  
Xinghuo Yu
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Tracking Error ◽  
Variable Structure ◽  
Mathematical Representation ◽  
Dynamic Complexity ◽  
Variable Structure Systems ◽  
Sliding Motion ◽  
Three Degrees Of Freedom

Noise rejection, handling the difficulties coming from the mathematical representation of the system under investigation and alleviation of structural or unstructural uncertainties constitute prime challenges that are frequently encountered in the practice of systems and control engineering. Designing a controller has primarily the aim of achieving the tracking precision as well as a degree of robustness against the difficulties stated. From this point of view, variable structure systems theory offer well formulated solutions to such ill-posed problems containing uncertainty and imprecision. In this paper, a simple controller structure is discussed. The architecture is known as Adaptive Linear Element (ADALINE) in the framework of neural computing. The parameters of the controller evolve dynamically in time such that a sliding motion is obtained. The inner sliding motion concerns the establishment of a sliding mode in controller parameters, which aims to minimize the error on the controller outputs. The outer sliding motion is designed for the plant. The algorithm discussed drives the error on the output of the controller toward zero learning error level, and the state tracking error vector of the plant is driven toward the origin of the phase space simultaneously. The paper gives the analysis of the equivalence between the two sliding motions and demonstrates the performance of the algorithm on a three degrees of freedom, anthropoid robotic manipulator. In order to clarify the performance of the scheme, together with the dynamic complexity of the plant, the adverse effects of observation noise and nonzero initial conditions are studied. [S0022-0434(00)01704-4]

scholarly journals Chattering-Free Single-Phase Robustness Sliding Mode Controller for Mismatched Uncertain Interconnected Systems with Unknown Time-Varying Delays

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 282 ◽  
Author(s):  
Cong-Trang Nguyen ◽  
Thanh Long Duong ◽  
Minh Quan Duong ◽  
Duc Tung Le
Keyword(s):  
Single Phase ◽  
Sliding Mode ◽  
Variable Structure Control ◽  
Variable Structure ◽  
Sliding Mode Controller ◽  
Time Varying ◽  
Structure Control ◽  
Time Varying Delay ◽  
Chattering Free ◽  
Varying Delay

Variable structure control with sliding mode can provide good control performance and excellent robustness. Unfortunately, the chattering phenomenon investigated due to discontinuous switching gain restricting their applications. In this paper, a chattering free improved variable structure control (IVSC) for a class of mismatched uncertain interconnected systems with an unknown time-varying delay is proposed. A sliding function is first established to eliminate the reaching phase in traditional variable structure control (TVSC). Next, a new reduced-order sliding mode estimator (ROSME) without time-varying delay is constructed to estimate all unmeasurable state variables of plants. Then, based on the Moore-Penrose inverse approach, a decentralized single-phase robustness sliding mode controller (DSPRSMC) is synthesized, which is independent of time delays. A DSPRSMC solves a complex interconnection problem with an unknown time-varying delay term and drives the system’s trajectories onto a switching surface from the initial time instance. Particularly, by applying the well-known Barbalat’s lemma, the chattering phenomenon in control input is alleviated. Moreover, a sufficient condition is established by using an appropriate Lyapunov theory and linear matrix inequality (LMI) method such that a sliding mode dynamics is asymptotically stable from the beginning time. Finally, a developed method is validated by numerical example with computer simulations.

Chattering-free adaptive fast convergent terminal sliding mode controllers for position tracking of robotic manipulators

2015 ◽  
Vol 230 (4) ◽  
pp. 514-526 ◽  
Author(s):  
Shaoming He ◽  
Defu Lin ◽  
Jiang Wang
Keyword(s):  
Sliding Mode ◽  
Robotic Manipulators ◽  
Position Tracking ◽  
Terminal Sliding Mode ◽  
Control Approach ◽  
Nonsingular Terminal Sliding Mode ◽  
Fast Terminal Sliding Mode ◽  
Sliding Manifold ◽  
Chattering Free ◽  
Chattering Elimination

The paper documents a new continuous adaptive fast terminal sliding mode control approach for position tracking of robotic manipulators. Combining linear sliding mode and terminal sliding mode, a fast nonsingular terminal sliding mode manifold is presented. Considering the discontinuous property of the sign function, which is often used in traditional sliding mode controller and will result in high-freqsency chattering in the control channel, the proposed controller adopts the continuous saturation function for chattering elimination. Besides the continuous property, convergence to the origin asymptotically and in finite time can be guaranteed in theory with the proposed controller, which is quite different from traditional boundary layer technique, where only bounded motion around the sliding manifold can be ensured. For asymptotic stability, it is only required that the lumped uncertainty is bounded, but the upper bound may be unknown by virtue of the designed adaptive methodology. The obtained results are applied to the problem of position tracking for robotic manipulators. Detailed simulations with some comparisons under various conditions demonstrate the effectiveness of the proposed method.

scholarly journals Integrated Guidance and Control Method for the Interception of Maneuvering Hypersonic Vehicle Based on High Order Sliding Mode Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Kang Chen ◽  
Bin Fu ◽  
Yuening Ding ◽  
Jie Yan
Keyword(s):  
Fourth Order ◽  
Control Method ◽  
Sliding Mode ◽  
High Order ◽  
Control Input ◽  
Guidance And Control ◽  
Near Space ◽  
Sliding Manifold ◽  
Integrated Guidance And Control ◽  
And Control

This paper focuses on the integrated guidance and control (IGC) method applied in the interception of maneuvering near space hypersonic vehicles using the homogeneous high order sliding mode (HOSM) approach. The IGC model is derived by combining the target-missile relative motion and dynamic equations. Then, a fourth-order sliding mode controller is implemented in the augmented IGC model. To estimate the high order derivatives of the sliding manifold which is required in the HOSM method, an Arbitrary Order Robust Exact Differentiator is presented. At last, the idea of virtual control is introduced to alleviate the chattering of the control input without using any saturation functions which may lead to a loss of the robustness. And the stability of the closed-loop system with presented fourth-order homogeneous HOSM controller is also proved theoretically. Finally, simulation results are provided and analyzed to demonstrate the effectiveness of the proposed method in three typical engagement scenarios.

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

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.

An improved sliding-mode observer-based equivalent-input-disturbance approach for permanent magnet synchronous motor drives with faults in current measurement circuits

2021 ◽  
pp. 014233122110025
Author(s):  
Gang Huang ◽  
Wei Huang ◽  
Zhengtan Li ◽  
Jiajun Li ◽  
Jing He ◽  
...  
Keyword(s):  
Permanent Magnet ◽  
Sliding Mode ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Current Measurement ◽  
Sliding Mode Observer ◽  
Stability And Convergence ◽  
Control Input ◽  
Input Disturbance ◽  
Equivalent Input Disturbance

The reliability of permanent magnet synchronous motor (PMSM) systems is very important in high-precision industrial drives. However, disturbance or sensor fault may cause the performance degradation of the system. This paper presents an improved sliding-mode-observer (SMO)-based equivalent-input-disturbance (EID) approach for the rejection of faults in current measurement circuits of a PMSM drive. A system model, which contains faults in current measurement circuits, is first constructed by using EIDs in control input circuits. Then, an improved SMO is designed to estimate the equivalent-input-faults. The effect of the faults on the system is rejected based on the EID theory. Moreover, the global stability and convergence analysis is also provided. Experiments and comparisons demonstrate the effectiveness of the method.

scholarly journals A Chattering Free Discrete-Time Global Sliding Mode Controller for Optoelectronic Tracking System

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yan Ren ◽  
Zhenghua Liu ◽  
Xiaodong Liu ◽  
Yu Zhang
Keyword(s):  
Discrete Time ◽  
High Frequency ◽  
Sliding Mode ◽  
Tracking System ◽  
Tracking Error ◽  
Switching Function ◽  
Sliding Mode Controller ◽  
Control Input ◽  
Reaching Law ◽  
Chattering Free

Aiming at the uncertainties including parameter variations and external disturbances in optoelectronic tracking system, a discrete-time global sliding mode controller (DGSMC) is proposed. By the design of nonlinear switching function, the initial state of control system is set on the switching surface. An adaptive discrete-time reaching law is introduced to suppress the high-frequency chattering at control input, and a linear extrapolation method is employed to estimate the unknown uncertainties and commands. The global reachability for sliding mode and the chattering-free property are proven by means of mathematical derivation. Numerical simulation presents that the proposed DGSMC scheme not only ensures strong robustness against system uncertainties and small tracking error, but also suppresses the high-frequency chattering at control input effectively, compared with the SMC scheme using conventional discrete-time reaching law.

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