Decentralized sliding mode control design using overlapping decompositions

This paper discusses overlapping decentralized sliding mode controller design for large-scale continuous-time systems. Design issues, like connective reachability of the sliding manifold and the stability of the sliding mode equations in the expanded and original state spaces are examined. Application of the results to automatic generation control is also discussed briefly.     

Chattering suppression methods in sliding mode control systems

The implementation of sliding mode control is often irritated by high frequency oscillations known as “chattering” in system outputs issued by dynamics from actuators and sensors ignored in system modeling. This paper provides analysis of chattering in such systems with unmodeled based on the Lyapunov theory and the describing function method. It also describes various approaches to reduce chattering including methods based on relay control gain adaptation. And for those systems to which the methods are not applicable, chattering frequency control using hysteresis loop will be provided.     

Decentralized adaptive backstepping stabilization of interconnected systems with dynamic input and output interactions

So far there is still no result available for backstepping based decentralized adaptive stabilization of unknown systems with interactions directly depending on subsystem inputs, even though such interactions commonly exist in practice. In this paper, we provide a solution to this problem by considering both input and output dynamic interactions. To clearly illustrate our approaches, we will start with linear systems and then extend the results to nonlinear systems. Each local controller, designed simply based on the model of each subsystem by using the standard adaptive backstepping technique without any modification, only employs local information to generate control signals. It is shown that the designed decentralized adaptive backstepping controllers can globally stabilize the overall interconnected system asymptotically. The L₂ and L_∞ norms of the system outputs are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.     

Adaptive continuous twisting algorithm

Abstract

In this paper, an adaptive continuous twisting algorithm (ACTA) is presented. For double integrator, ACTA produces a continuous control signal ensuring finite time convergence of the states to zero. Moreover, the control signal generated by ACTA compensates the Lipschitz perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. ACTA also keeps its convergence properties, even in the case that the upper bound of the derivative of the perturbation exists, but it is unknown.     

Sliding mode control of a class of underactuated systems

A sliding mode control approach is proposed to stabilize a class of underactuated systems which are in cascaded form. This class of underactuated systems can represent many real applications after transformations. In the controller design, the sliding surface is designed to stabilize the indirectly controlled modes. Its insensitivity to the model errors, parametric uncertainties and other disturbances and its ability to globally stabilize the system are two advantages of the sliding mode controller.     

无刷直流电机的神经滑模变结构控制

针对工业控制中对无刷直流电机位置控制的高精度要求,研究了滑模变结构控制和神经网络相结合的控制方法.为了消除滑模变结构控制方法中存在的抖振缺点,提出了一种神经滑模控制方法.方法首先设计了一个二阶时变滑模面,使系统的初始状态就在滑模面上,可以增强系统的鲁棒性.然后,通过径向基函数神经网络学习电机的负载、干扰等参数,使滑模控制的切换控制项能随着负载参数的变化而变化,削弱了滑模变结构控制的抖振.对上述方法进行仿真,结果证明了上述方法的有效性,为无刷直流电机优化控制提供了有效手段.     

Quasi-continuous HOSM control for systems with unmatched perturbations

The control of nonlinear systems subject to unmatched perturbations is studied. A new design algorithm is proposed based on the block control and quasi-continuous higher order sliding modes techniques. The proposed method provides for the finite time exact tracking of a smooth desired signal in spite of unmatched perturbations.     

Linear unstable plants with saturating actuators: Robust stabilization by a time varying sliding surface

This paper proposes the use of a time-varying sliding surface for the robust stabilization of linear uncertain SISO plants with saturating actuators. A constructive procedure for its design is also proposed, and stability of the closed loop system is proved in the null controllable region. The proposed technique does not require plant stability, and can manage any bounded disturbance term satisfying the matching condition. Theoretical results have been validated by simulation using the missile roll angle control problem.     

Comments on “Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties”

This note points out that the time complexity of the main multiple-surface sliding control (MSSC) algorithm in Huang and Chen [Huang, A. C. & Chen, Y. C. (2004). Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties. Automatica, 40(11), 1939-1945] is O(2ⁿ). Here, we propose a simplified recursive design MSSC algorithm with time complexity O(n), and, using mathematical induction, we show that this algorithm agrees with this MSSC law.     

一类非线性系统的间接自适应模糊滑模控制

基于启发式知识的模糊控制是一种解决非线性系统控制问题的有效方法。然而其设计缺乏系统性,并且系统的稳定性和鲁棒性难以保证。本文利用滑模控制的概念和Lyapunov综合方法提出一种针对一类非线性系统的间接自适应模糊滑模控制（IAFSMC）方法。仿真研究表明即使在缺少系统先验知识和不确定性干扰的情况下,系统性能也十分理想。     

AN ASYMPTOTIC SECOND‐ORDER SMOOTH SLIDING MODE CONTROL

Presented is a method of smooth sliding mode control design to provide for an asymptotic second‐order sliding mode on the selected sliding surface. The control law is a nonlinear dynamic feedback that in absence of unknown disturbances provides for an asymptotic second‐order sliding mode. Application of the second‐order disturbance observer in a combination with the proposed continuous control law practically gives the second‐order sliding accuracy in presence of unknown disturbances and discrete‐time control update. The piecewise constant control feedback is “smooth” in the sense that its derivative numerically taken at sampling rate does not contain high frequency components. A numerical example is presented.     

Robust synchronization of chaotic systems using slidingmode and feedback control

We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives, while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically, and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms, the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.     

Integrated sliding-mode algorithms in robot tracking applications

An integrated solution based on sliding mode ideas is proposed for robotic trajectory tracking. The proposal includes three sliding-mode algorithms for speed auto-regulation, path conditioning and redundancy resolution in order to fulfill velocity, workspace and C-space constraints, respectively. The proposed method only requires a few program lines and simplifies the robot user interface since it directly deals with the fulfillment of the constraints to find a feasible solution for the robot trajectory tracking in a short computation time. The proposed approach is evaluated in simulation on the freely accessible 6R robot model PUMA-560, for which the main features of the method are illustrated.     

Tracking in a class of nonminimum-phase systems with nonlinear internal dynamics via sliding mode control using method of system center

A method of asymptotic output tracking in a class of causal nonminimum-phase uncertain nonlinear systems is considered. Local asymptotic stability of output tracking-error dynamics are provided for the specified class of systems with the nonlinear hyperbolic at the origin internal dynamics forced by a reference output profile and external disturbances defined by a known linear exosystem. The nonlinear vector field of the internal dynamics is expanded in a power series, obtained at a selected operational point in the internal dynamics state space. The presented technique employs some linear algebraic methods and sliding mode control approach. The solution is a complete constructive algorithm.     

Robust Fuzzy Output Sliding Control without the Requirement of State Measurement

A robust fuzzy output sliding control for nonlinear robotic arms is proposed in this paper. The proposed method not only retains the advantages of the conventional sliding mode control such as robustness against parameter variations and external disturbances, but also uses measurable output signals to define the sliding surface function. A fuzzy controller is developed to modify the control law to avoid state measurement. Control system stability is proved by using the Lyapunov stability theorem. The system robustness is guaranteed. Simulations results demonstrate the validity and effectiveness of the proposed method for uncertain nonlinear robotic arms.