An output feedback sliding mode control strategy for MIMO systems of arbitrary relative degree

This paper develops an output feedback sliding mode controller for multi‐input multi‐output (MIMO) systems of any relative degree. A minimal set of outputs and output derivatives are identified to determine an augmented system which is relative degree 1, and a robust sliding mode differentiator is presented as the means to construct the extended output signal. It is shown that the transmission zeroes of the original plant appear directly in the reduced order sliding mode dynamics relating to the augmented system. A super twisting control algorithm is shown to provide robust control performance. Simulation results for a rationalized helicopter model taken from the literature are used to demonstrate the attraction of the approach. Copyright © 2010 John Wiley & Sons, Ltd.     

SLIDING MODES, Δ‐MODULATORS,AND GENERALIZED PROPORTIONAL INTEGRAL CONTROL OF LINEAR SYSTEMS

In this article, we attempt a reapproachment between sliding mode control of linear systems and classical control through the possibilities of evading state measurements and circumventing the use of asymptotic state observers in the sliding surface synthesis. This is shown to be possible thanks to the use of integral state reconstructors combined with iterated integral output error compensation. The proposed scheme is also robust with respect to unmatched perturbation inputs. A connection between sliding modes and classical analog Δ‐modulators, and their natural generalization, is also brought to attention as a tool for the realization of integral reconstructor based sliding mode control schemes.     

Dynamic output feedback integral sliding mode control design for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm for linear MIMO systems with mismatched parameter uncertainties along with disturbances and matched nonlinear perturbations. Once the system is in the sliding mode, the proposed output‐dependent integral sliding surface can robustly stabilize the closed‐loop system and obtain the desired system performance. Two types of mismatched disturbances are considered and their effects on the sliding mode are explored. By introducing an additional dynamics into the controller design, the developed control law can guarantee that the system globally reaches and is maintained on the sliding surface in finite time. Finally, the feasibility of the proposed method is illustrated by numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Sliding mode control of DC‐to‐DC power converters using integral reconstructors

A sliding mode feedback controller, based on integral reconstructors is developed for the regulation of the ‘boost’ DC‐to‐DC power converter circuit conduction in continuous conduction mode. The feedback control scheme uses only output capacitor voltage measurements, as well as knowledge of the available input signal, represented by the switch positions. The robustness of the feedback scheme is tested with abusively large, unmodelled, sudden load resistance variations. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust Fault‐Tolerant Control of Launch Vehicle Via GPI Observer and Integral Sliding Mode Control

A robust fault‐tolerant attitude control scheme is proposed for a launch vehicle (LV) in the presence of unknown external disturbances, mismodeling dynamics, actuator faults, and actuator's constraints. The input‐output representation is employed to describe the rotational dynamics of LV rendering three independently decoupled second order single‐input‐single‐output (SISO) systems. In the differential algebraic framework, general proportional integral (GPI) observers are used for the estimations of the states and of the generalized disturbances, which include internal perturbations, external disturbances, and unknown actuator failures. In order to avoid the defects of the conventional sliding surface, a new nonlinear integral sliding manifold is introduced for the robust fault‐tolerant sliding mode controller design. The stability of the GPI observer and that of the closed‐loop system are guaranteed by Lyapunov's indirect and direct methods, respectively. The convincing numerical simulation results demonstrate the proposed control scheme is with high attitude tracking performance in the presence of various disturbances, actuator faults, and actuator constraints.     

Disturbance observer–based adaptive boundary layer sliding mode controller for a type of nonlinear multiple‐input multiple‐output system

In this paper, a disturbance observer–based adaptive boundary layer sliding mode controller (ABLSMC) is proposed to compensate external disturbance and system uncertainty for a class of output coupled multiple‐input multiple‐output (MIMO) nonlinear systems. To show the effectiveness of the proposed ABLMSC, a traditional adaptive sliding mode controller (ASMC) is also designed. The stability of the closed‐loop system is examined by using the Lyapunov stability approach. The proposed control approach is implemented for a class of nonlinear output coupled MIMO systems. For real‐time validation, a coupled tank system is considered for study. Finally, simulation and real‐time results show that the proposed ABLMSC gives better performance such as reduced chattering and energy efficiency than that of the ASMC and some reported works in the literature.     

A sliding mode controller for a model of flow separation in boundary layers

In this paper, we propose a sliding mode controller for a MIMO model of flow separation in boundary layers. The model consists in a bilinear system with constant delays in both the state and the input. The main motivation to consider such a class of systems is that it has shown to be suitable for input‐output modeling and control design of some turbulent flow control systems. Stability and robustness properties of the control scheme are studied by means of Volterra equations theory, which provides easily verifiable stability conditions.     

基于积分滑动流形的高阶滑模控制器设计

滑模变结构控制方法因其易实现,鲁棒性强等优点广泛应用于实际控制系统中,讨论了具有积分滑动流形的高阶滑模控制器的设计方法.通过设计含积分滑动流形的高阶滑模面,使系统状态在一阶乃至高阶滑模面上均能达到滑动模态.同时利用高阶滑模面为状态变量设计新的状态空间系统,将原先促使系统状态接近并停留在滑模面上的控制目标,拓展为使高阶滑模状态变量趋近于零的控制目标,并结合最优控制方法来设计等效控制量,利用积分流形设计切换控制的切换面,通过严格证明来证实控制器设计的稳定性.在仿真验证部分采用了一阶倒立摆模型,通过比较常规趋近律滑模控制方法和本文方法的仿真结果,可以得出本文方法在减小系统控制量抖振方面的重要作用和优异效果.     

Robust output tracking of constrained perturbed linear systems via model predictive sliding mode control

A robustifying strategy for constrained linear multivariable systems is proposed. A combination of tracking model predictive control with output integral sliding mode techniques is used to completely reject bounded matched perturbations. It can be guaranteed that all constraints on inputs, states, and outputs are satisfied although only output information is used. Finally, real‐world experiments with an unstable plant are presented in order to demonstrate the validity and the effectiveness of the proposed approach.     

Discrete time output feedback sliding mode control for nonlinear MIMO system: a stepper motor case

This article, presents discrete sliding mode control algorithm using multirate output feedback for control of stepper motor. The algorithm developed by the authors uses past output samples and past control inputs. When all the states of the system are neither physical variable nor available for measurement, multirate output feedback can be used. The stepper motor is known to be a differentially flat system. The dynamics of the stepper motor are highly nonlinear, hence feedback linearization based on endogenous feedback has been used. The linear model is obtained and multirate output feedback-based discrete sliding mode control has been designed. The discrete sliding mode control with multirate output feedback has been applied for regulator as well as tracking case for the motor. The proposed algorithm uses only two outputs. It is essentially shown that first output needs to be sampled only once and second output must be sampled at least thrice in every τ sampling interval in order to achieve acceptable performance. The system parameter variation has been considered and the results obtained are found to be satisfactory. Thus, it has been shown that discrete sliding mode control algorithm using multirate output feed back can be extended to a class of nonlinear MIMO system.     

High‐order sliding mode control design based on adaptive terminal sliding mode

High‐order sliding mode control techniques are proposed for uncertain nonlinear SISO systems with bounded uncertainties based on two different terminal sliding mode approaches. The tracking error of the output converges to zero in finite time by designing a terminal sliding mode controller. In addition, the adaptive control method is employed to identify bounded uncertainties for eliminating the requirement of boundaries needed in the conventional design. The controllers are derived using Lyapunov theory, so the stability of the closed‐loop system is guaranteed. In the first technique, the developed procedure removes the reaching phase of sliding mode and realizes global robustness. The proposed algorithms ensure establishment of high‐order sliding mode. An illustrative example of a car control demonstrates effectiveness of the presented designs. Copyright © 2011 John Wiley & Sons, Ltd.     

不确定输入时滞系统的滑模输出反馈控制

研究了在状态不可测,并且状态参数和控制输入矩阵同时存在不确定性的情况下,不确定输入时滞系统的滑模控制问题.为了有效克服不确定性和时滞对系统稳定性的影响,在状态估计空间选择了一种积分型的切换函数,设计了一种基于状态观测器的滑模控制器,并证明了所设计切换面的可达性.通过李亚普诺夫理论,给出了闭环系统渐近稳定的充分条件.数值仿真验证了算法的有效性.     

A nonlinear sliding surface to improve performance of a discrete-time input-delay system

A sliding mode controller is proposed for an uncertain input-delay system to enhance performance. A nonlinear sliding surface is proposed to achieve better transient response for general uncertain discrete SISO linear systems with input delay. Both matched and unmatched perturbations are considered and ultimate boundedness of motion is proved. The step tracking problem is analysed. The proposed surface increases the damping ratio of the transformed system (delay free) as the output moves nearer to the setpoint. To simplify the surface design, a linear matrix inequality based tuning procedure is proposed. The control law is designed based on an equivalent control approach which guarantees one step reaching. The scheme is able to achieve low overshoot and low settling time simultaneously which is not possible with a linear sliding surface. Simulation results verify the effectiveness of the proposed nonlinear surface over different linear surfaces.     

A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control (DTSMC) technique is proposed for a class of single-input and single-output (SISO) uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.     

A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control （DTSMC） technique is proposed for a class of single-input and single-output （SISO） uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.     

On a new adaptive sliding mode control for MIMO nonlinear systems with uncertainties of unknown bounds

This paper proposes a new approach of adaptive sliding mode controller designs for multiple‐input multiple‐output nonlinear systems with uncertainties of unknown bounds and limited available inputs. The goal is to obtain robust, smooth, and fast transient performance for real sliding mode control so that the phenomena of the slow response and the gain overestimation in most adaptive sliding mode controller designs can be greatly improved. We introduce an Integral/Exponential adaptation law with boundary‐layer targeting the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously speeding up the system response to the uncertainties. The gain is further reduced when the system state is in the boundary layer. The simulation and experimental results demonstrate the proposed design. Copyright © 2016 John Wiley & Sons, Ltd.     

SISO线性系统的滑模变结构状态范数控制

在线性系统滑模控制理论的基础上,给出了对于一般SLSO线性系统状态范数控制的形式,提出了状态范数的控制器结构。基于李亚普诺夫稳定性理论证明了状态范数控制系统的闭环稳定性。然后分别针对状态范数控制器与趋近率控制和单位向量控制进行了数值仿真的分析与比较,结果说明状态范数控制综合了趋近率控制和单位向量控制各自的优点,控制信号抖振更小,闭环系统稳态性能有了一定改进。     

Output feedback integral sliding mode controller of time‐delay systems with mismatch disturbances

For uncertain time‐delay systems with mismatch disturbances, this paper presented an integral sliding mode control algorithm using output information only. An integral sliding surface is comprised of output signals and an auxiliary full‐order compensator. The designed output feedback sliding mode controller can locally satisfy the reaching and sliding condition and maintain the system on the sliding surface from the initial moment. Since the system is in the sliding mode and two specific algebraic Riccati inequalities are established, the proposed algorithm can guarantee the stability of the closed‐loop system and satisfy the property of disturbance attenuation. Moreover, the design parameters of the controller and compensator can be simultaneously determined by solutions to two algebraic Riccati inequalities. Finally, a numerical example illustrates the applicability of the proposed scheme. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

Integral sliding mode control for Euler‐Lagrange systems with input saturation

This paper investigates the robust control for the Euler‐Lagrange (EL) system with input saturation by using the integral sliding mode control and adaptive control. An integral sliding mode surface that is suitable for solving the problem of the input constraint is given based on the saturation function. By using the integral sliding mode surface, two robust antisaturation controllers are designed for the EL system with external disturbances. The first controller can deal with the external disturbances with known bounds, whereas the second one can compensate the external disturbances with unknown bounds by using the adaptive control. Finally, the effectiveness of the proposed controllers is demonstrated by strict theoretical analysis and numerical simulations.