Optimal second order sliding mode control for nonlinear uncertain systems

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.     

防抱制动系统参数自适应滑模变结构控制器的研究

首先针对具有参数不确定性的二阶非线性系统提出了自适应滑模变结构的控制算法 ,该算法的基本思想是用自适应策略来估计不确定系统的参数 ,根据估计出的参数值 ,来设计滑模控制器 ,优点是无须事先已知不确定参数的边界 ,并且由于在自适应变结构控制采用了消颤措施 (增加了消颤项 ) ,能削弱常规滑模控制所引起的颤振现象 ,也能提高单纯的自适应控制的鲁棒性能。而后将这一控制策略应用于防抱死制动系统 (ABS)的研究中 ,设计了防抱死制动系统的自适应滑模变结构控制器 ,通过计算机仿真 ,验证了该控制方案在 ABS应用中的可行性和有效性     

Optimal second order sliding mode control for linear uncertain systems

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.     

Finite-time sliding mode controller for perturbed second-order systems

This paper presents a novel finite-time sliding mode controller applied to perturbed second order systems. The proposed scheme employs a disturbance observer that can identify growing in time disturbances. Then, the observer is combined with a sliding mode controller to achieve finite-time stabilization of the second-order system. The convergence of the observer as well as the finite-time stability of the closed-loop system is theoretically demonstrated. Besides, it is also shown that the finite-time convergence properties of a given controller can be enhanced when using a compensation term based on the disturbance observer. The proposed controller is compared with a twisting algorithm and a finite-time sliding mode controller with disturbance estimation. Also, a conventional proportional integral derivative (PID) controller is combined with the proposed disturbance observer in a trajectory tracking task. Numerical simulations indicate that the proposed controller attains finite-time stabilization of the second order system by requiring a less amount of power than that demanded by the other control schemes and without being affected by the peaking phenomenon. Besides, the performance of the PID technique is enhanced by applying the proposed control methodology.     

Precision control of a piezo-actuated micro telemanipulation system

Piezoelectric actuators are widely used in micro manipulation applications. However hysteresis nonlinearity limits accuracy of these actuators. This paper presents a novel approach for utilizing a piezoelectric nano-stage as slave manipulator of a teleoperation system. The Prandtl-Ishlinskii (PI) model is used to model actuator hysteresis in feedforward scheme to cancel out this nonlinearity. To deal with the influence of parametric uncertainties, unmodeled dynamics, and PI identification error a perturbation term is added to the slave model and apply a sliding mode based impedance control with perturbation estimation. The stability of the entire system is guaranteed by Llewellyn’s absolute stability criterion. Performance of the proposed controllers is verified through experiments.     

Compound fault-tolerant attitude control for hypersonic vehicle with reaction control systems in reentry phase

In this paper, a novel compound fault-tolerant attitude control (FTC) scheme is proposed for reentry hypersonic vehicles with aerodynamic surfaces and reaction control systems (RCS) in the presence of parameter uncertainties, external disturbances and aerodynamic surfaces faults. Aerodynamic surfaces work as the primary actuators and RCS serve as auxiliary actuators. When aerodynamic surfaces cannot provide the required attitude control torque due to low dynamic pressure or faults, RCS are activated to assist aerodynamic surfaces to generate the residual torque. A nonlinear disturbance observer-based sliding mode controller is designed to calculate the required attitude control torque which can handle the parametric uncertainties and external disturbances together. The quadratic programming method is applied to obtain the optimal aerodynamic surfaces deflections from the required control torque. An innovative fuzzy rule-based decision-making system is design to solve the RCS control allocation problem, which is conceptually easy to understand and computationally efficiently compared with existing approaches. Based on quantized control theory, the closed-loop control system stability is rigorously analyzed. Simulation results are given to demonstrate the effectiveness and efficiency of developed FTC scheme.     

Nonlinear control of voltage source converters in AC–DC power system

This paper presents the design of a robust nonlinear controller for a parallel AC–DC power system using a Lyapunov function-based sliding mode control (LYPSMC) strategy. The inputs for the proposed control scheme are the DC voltage and reactive power errors at the converter station and the active and reactive power errors at the inverter station of the voltage-source converter-based high voltage direct current transmission (VSC-HVDC) link. The stability and robust tracking of the system parameters are ensured by applying the Lyapunov direct method. Also the gains of the sliding mode control (SMC) are made adaptive using the stability conditions of the Lyapunov function. The proposed control strategy offers invariant stability to a class of systems having modeling uncertainties due to parameter changes and exogenous inputs. Comprehensive computer simulations are carried out to verify the proposed control scheme under several system disturbances like changes in short-circuit ratio, converter parametric changes, and faults on the converter and inverter buses for single generating system connected to the power grid in a single machine infinite-bus AC–DC network and also for a 3-machine two-area power system. Furthermore, a second order super twisting sliding mode control scheme has been presented in this paper that provides a higher degree of nonlinearity than the LYPSMC and damps faster the converter and inverter voltage and power oscillations.     

Adaptive sliding mode control of a piezo-actuated bilateral teleoperated micromanipulation system

Piezoelectric actuators are widely used in micro manipulation applications. However, hysteresis nonlinearity limits the accuracy of these actuators. This paper presents a novel approach for utilizing a piezoelectric nano-stage as the slave manipulator of a teleoperation system based on a sliding mode controller. The Prandtl-Ishlinskii (PI) model is used to model actuator hysteresis in feedforward scheme to cancel out this nonlinearity. The presented approach requires full state and force measurements at both the master and slave sides. Such a system is costly and also difficult to implement. Therefore, sliding mode unknown input observer (UIO) is proposed for full state and force estimations. Furthermore, the effects of uncertainties in the constant parameters on the estimated external forces should be eliminated. So, a robust adaptive controller is proposed and its stability is guaranteed through the Lyapunov criterion. Performance of the proposed control architecture is verified through experiments.     

Sliding mode control with varying boundary layers for an electro-hydraulic position servo system

In this study, a new sliding mode control with varying boundary layers is proposed to improve the tracking performance of a nonlinear electro-hydraulic position servo system, which can be found in many manufacturing devices. The key feature of the proposed control scheme is the use of varying boundary layers instead of fixed boundary layers, which are usually employed in conventional sliding mode control. The validity of the proposed control scheme is verified through practical testing on an experimental electro-hydraulic positioning device. In the cases of step and sinusoidal command inputs, the experimental results strongly suggest that the proposed control scheme is capable of improving the tracking precision without causing any chattering. In addition, the new control scheme seems to be very robust against various set point conditions .     

Real-time regulated sliding mode controller design of multiple manipulator space free-flying robot

The problem of controlling Space Free-flying Robots (SFFRs), which have many degrees of freedom caused by their mechanical manipulators, is challenging because of the strong nonlinearities and their heavy computational burden for the implementation of modelbased control algorithms. In this paper, a chattering avoidance sliding mode controller is developed for SFFR as highly nonlinear-coupled systems. To fulfill stability requirements, robustness properties, and chattering elimination, a regulating routine is proposed to determine the proper positive values for the coefficient of sliding condition. To solve the run-time problem, an explicit direct relationship between the SFFR’s output of actuators (force/torque) and the measurement of distances from the corresponding sliding surfaces is also assumed. To reach perfect performance, the parameters are estimated recursively using the Kalman filter as a parameter estimator. The explicit dynamics of a 14-DOF SFFR is derived using SPACEMAPLE, and the recursive prediction error method (RPEM) is used to parameterize the SFFR model. To alleviate the chattering trend, a multi-input sliding mode control law is proposed and applied to the given SFFR based on the online estimated dynamics to control its orientation and position to catch a moving target. To evaluate the new proposed algorithm in a more complicated condition, only on-off actuators are assumed for controlling the base of SFFR because it is the case in real systems. The obtained results show that the proposed regulated sliding mode controller can significantly reduce the chattering trend. Consequently, energy consumption will be substantially decreased, and running the control algorithm will be within a reasonable time duration.     

A novel adaptive sliding mode control with application to MEMS gyroscope

This paper presents a new adaptive sliding mode controller for MEMS gyroscope; an adaptive tracking controller with a proportional and integral sliding surface is proposed. The adaptive sliding mode control algorithm can estimate the angular velocity and the damping and stiffness coefficients in real time. A proportional and integral sliding surface, instead of a conventional sliding surface is adopted. An adaptive sliding mode controller that incorporates both matched and unmatched uncertainties and disturbances is derived and the stability of the closed-loop system is established. The numerical simulation is presented to verify the effectiveness of the proposed control scheme. It is shown that the proposed adaptive sliding mode control scheme offers several advantages such as the consistent estimation of gyroscope parameters including angular velocity and large robustness to parameter variations and external disturbances.     

Robust adaptive control for a MEMS vibratory gyroscope

This paper presents an adaptive sliding mode controller for a microelectromechanical systems (MEMS) vibratory z-axis gyroscope. The proposed adaptive sliding mode controller can real-time estimate the angular velocity and the damping and stiffness coefficients. The stability of the closed-loop system can be guaranteed with the proposed adaptive sliding mode control strategy. The numerical simulation for MEMS gyroscope is investigated to show the effectiveness of the proposed control scheme. It is shown that the proposed adaptive sliding mode control scheme offers several advantages such as real-time estimation of gyroscope parameters and large robustness to parameter variations and external disturbance.     

虚拟轴机床并联机构的自适应动态滑模运动控制

虚拟轴机床系统模型复杂难以准确建立,高速加工时存在强烈干扰且不确定,难以实际实现高性能控制,为此,提出一种新型自适应动态滑模控制方法,用于虚拟轴机床并联机构运动控制。通过构建新型动态切换函数,设计二阶动态滑模控制,以解决采用常规等效控制设计的滑模控制系统,因忽略执行机构快变动力学特性等而导致控制系统品质降低甚至不稳定的问题,同时避免滑模抖振的出现;引入自适应控制对虚拟轴机床加工时的外界干扰等不确定因素进行在线估计,以克服滑模控制性能需依赖于对未知干扰的先验估计的局限,增强虚拟轴机床克服高速加工时的强烈干扰的能力,进一步提高其控制性能。仿真和试验结果表明,采用自适应动态滑模控制方法,可使虚拟轴机床控制系统具有较好的自适应能力,较强的鲁棒性,良好的动态、稳态品质。     

Continuous higher-order sliding mode control with time-varying gain for a class of uncertain nonlinear systems

This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.     

Output-feedback super-twisting control for line-of-sight angles tracking of non-cooperative target spacecraft

Without the line-of-sight (LOS) angles rate information, this paper investigates the LOS angles tracking problem of non-cooperative target in chaser’s body frame with the external disturbance force and torque via chaser’s control torque. By integrating with the attitude dynamics of the chaser, a novel coupled LOS-based relative motion model is firstly established, which reveals the redundancy relationship between the LOS angles motion with two Degree-of-Freedom (DOF) and three dimensional control torque. More specially, the LOS angles tracking control problem is formulated as an output-feedback control problem of an uncertain nonlinear system with the actuator redundancy. As a stepping-stone, a fourth order high order sliding mode observer (HOSMO) is proposed to estimate the system state and uncertain terms. A combination of modified super twisting algorithm (STA) with nonsingular fast terminal sliding mode (NFTSM) and control allocation is proposed, the main novelty of modified STA is that the NFTSM is introduced to replace the linear sliding mode (LSM), and the original STA cannot be applied directly, a modified STA is proposed, which can guarantee the fast finite-time convergence. Finally, simulations are conducted to show fine performance of the proposed control scheme.     

有限时间不确定性估计的电液伺服跟踪控制技术

在实际工程应用中,参数不确定性是一种非常常见的外部扰动,会对受控系统的动态性能产生消极的影响,而电液伺服系统作为一类常规的机电系统,其控制问题的研究也必然伴随着参数不确定性的问题.首先,介绍了终端滑模观测器来估计电液伺服系统的参数不确定性,相较于其他观测器,其能够实现对系统参数不确定性的快速估计;然后,基于终端滑模观测...     

Adaptive backstepping sliding mode control with fuzzy monitoring strategy for a kind of mechanical system

A novel adaptive backstepping sliding mode control (ABSMC) law with fuzzy monitoring strategy is proposed for the tracking-control of a kind of nonlinear mechanical system. The proposed ABSMC scheme combining the sliding mode control and backstepping technique ensure that the occurrence of the sliding motion in finite-time and the trajectory of tracking-error converge to equilibrium point. To obtain a better perturbation rejection property, an adaptive control law is employed to compensate the lumped perturbation. Furthermore, we introduce fuzzy monitoring strategy to improve adaptive capacity and soften the control signal. The convergence and stability of the proposed control scheme are proved by using Lyaponov′s method. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme.     

Robust tracking control of triaxial angular velocity sensors using adaptive sliding mode approach

This paper presents a robust tracking control strategy using an adaptive sliding mode approach for MEMS triaxial angular sensor device that is able to detect rotation in three orthogonal axes, using a single vibrating mass. An adaptive sliding mode controller with proportional and integral sliding surface is developed and the stability of the closed-loop system can be guaranteed with the proposed adaptive sliding mode control strategy. The proposed adaptive sliding mode controller updates estimates of all stiffness errors, damping, and input rotation parameters in real time, removing the need for any offline calibration stages. To enable all unknown parameter estimates to converge to their true values, the necessary model trajectory is shown to be a three-dimensional Lissajous pattern. The numerical simulation for a MEMS triaxial angular velocity sensor is investigated to verify the effectiveness of the proposed adaptive sliding mode control scheme.     

Sliding mode current control of a NOCULL converter based on hysteresis modulation method in a wide range of operating conditions

This study presents a novel control scheme for voltage regulation of a negative output cascade ultra-lift Luo converter (NOCULLC). Due to the complicated high order model of the converter, its performance is degraded against large load variations, input voltage changes and parametric uncertainties. In order to enhance the converter behavior, a PI compensator and a sliding mode current controller are combined to control the fourth order NOCULLC worked in a wide range of operating conditions. Because of the non-minimum phase structure of the converter, the output voltage of the converter is indirectly regulated by enforcing the input inductor current to track its reference signal. The sliding mode current controller improves the dynamic and static performances of the converter by minimizing the inrush current of the input inductor of the converter and also, the PI controller eliminates the steady state error of the output voltage of the converter. The closed loop system stability is demonstrated by using sliding mode theory. Furthermore, this paper proposes a systematic procedure to compute the gains of the controller based on the stability constraints which guarantees robustness of the developed controller. The experimental results show the robustness and effectiveness of the proposed controller against parametric variations and uncertainties of the converter. Also, a comprehensive comparison of the general aspects of the properties between the developed method and other existed controllers is provided.     

基于级联滑模控制的高精度光电跟踪与捕获

为了进一步提高光电跟踪系统的目标捕获和跟踪性能,提出了一种基于变增益趋近律的级联滑模控制方法。基于反双曲正弦函数和幂次项设计了新型变增益滑模趋近律,在提高滑模面趋近速度的同时抑制滑模抖振现象;基于变增益滑模趋近律设计速度环和位置环滑模控制器构成级联滑模控制,以提高系统的动态响应性能和鲁棒性,提高系统对目标的捕获能力和跟踪精度。最后,以某球形光电跟踪系统的方位轴作为控制对象,进行了传统级联PI控制和级联滑模控制方法的对比分析。实验结果表明,相比于传统级联PI控制,捕获速度为1(°)/s的目标时,级联滑模控制可以将目标捕获时间减小32%;跟踪等效最大速度为4(°)/s和最大加速度为2(°)/s 2的正弦引导信号,可将跟踪误差RMS值减小31%,采用级联滑模控制可有效提高跟踪系统的控制性能。