Adaptive Fuzzy Control for Stochastic Nonlinear Systems via Sliding Mode Method

In this paper, an adaptive fuzzy controller is designed for a nonlinear stochastic system to track the given reference via the sliding mode method. The nonlinear stochastic system is modeled by a deterministic nonlinear system with white noise obtained from the derivative of a Wiener process, which eventually generates an Itô differential equation. Compared with existing results, the main advantage is that information of the nonlinear functions is not required. Under the designed controller with the proposed update laws, the tracking error trajectories converge to an arbitrary small region around zero in the mean square norm. Simulations to show the efficiency of the proposed controller are provided.     

Reliable Sliding-Mode Control for Markovian Jumping Systems Subject to Partial Actuator Degradation

In this work, a novel robust sliding-mode control (SMC) method has been provided for uncertain stochastic Markovian jumping systems subject to actuator degradation, such that the closed-loop system is globally asymptotically stable (with probability one). In the design of switching functions, a set of specified matrices are employed such that the connections among sliding surfaces corresponding to each mode are established. Then, a sliding-mode controller is synthesized to ensure the reachability of the specified switching surface despite actuator degradation and uncertainties. Finally, the simulation results illustrate the proposed method and the effectiveness.     

Frequency-domain characterization of sliding mode control of an inverter used in DSTATCOM application

In this paper, the commonly used switching schemes for sliding mode control of power converters is analyzed and designed in the frequency domain. Particular application of a distribution static compensator (DSTATCOM) in voltage control mode is investigated in a power distribution system. Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters. Magnitude conditions of carrier signals are developed for robust switching of the inverter under carrier-based modulation scheme of sliding mode control. The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter. The load bus voltage of an unbalanced three-phase nonstiff radial distribution system is controlled using the proposed carrier-based design. The results are validated using PSCAD/EMTDC simulation studies and through a scaled laboratory model of DSTATCOM that is developed for experimental verification.     

新型终端滑模在光电稳定平台中的应用

为了提高光电伺服稳定平台的跟踪精度,针对系统中干扰的影响提出一种新型终端滑模控制算法。首先,提出一种新型终端滑模干扰观测器的设计方法,实现对系统中干扰的快速估计和实时补偿。其次,设计新型终端滑模控制器来提高系统的跟踪精度,结合有限时间收敛和自适应控制的思想,对切换增益进行在线调整,有效地抑制了滑模控制中的抖振问题,使系统状态能够在有限时间内快速地收敛到所设计的滑模面上,并对未估计干扰进行精细化补偿。最后利用Lyapunov理论证明控制系统的稳定性。实验结果表明:该控制策略保证了光电跟踪系统视轴对运动目标的跟踪精度,在0.05 Hz时误差小于0.002,在2 Hz时误差小于0.034,增强了系统的鲁棒性。     

基于滑模变结构控制的数字化软开关电源

基于滑模变结构控制技术,采用FLEX10KAFPGA（EPF10K30AQC208）数字控制芯片研制开发了容量为180W的有源箝位正激软开关电源;并且详细分析了该电源的控制时序及滑模变结构的数字化控制方案,最后给出了系统的实验结果。从实验结果可以看出滑模变结构控制鲁棒性强,系统的稳定性能好,动态响应速度快,而且主回路的开关管实现了零电压软开关。     

Adaptive Fuzzy Sliding Mode Control Algorithm for a Non-Affine Nonlinear System

This paper concerns the design of robust controller for a nonlinear system that can be represented or approximated in a non-affine form. The control algorithm is based on sliding mode control that incorporates a fuzzy tuning technique, and it superposes equivalent control, switching control, and fuzzy control. An equivalent control law is firstly designed based on a nominal system model that was obtained by using curve fitting techniques under MATLAB. Switching control is then added to guarantee that the state reaches the sliding surface in the presence of parameter and disturbance uncertainties. Also, fuzzy tuning schemes, which can be supported by learning techniques derived from neural networks, are employed to improve control performance and to reduce chattering in the sliding mode. To verify the performance of this controller, an experimental platform of a pneumatically actuated top-guided single-seated control valve, which belongs to a classical complex nonlinear system, was constructed. Also, the experimental results show that high performance and attenuated chatter are achieved and thus verify the validity of the proposed control approach to dynamic systems characterized by severe uncertainties.     

Boost变换器的滑模变结构控制方法研究

本文提出了一种Boost变换器的滑模变结构控制方法。这种方法基于Boost变换器的开关模型。在控制器中引入滞环环节，使系统可以获得固定的开关频率，并分析了开关频率与滞环宽度的关系，给出了控制器参数的渊节方法。所设计的控制器响应速度快，对负载变化和电压波动鲁棒性强，易于实现。     

Discrete-time quasi-sliding-mode control strategies

In this paper, discrete-time quasi-sliding-mode control systems are considered. A new definition describing the quasi-sliding mode as a motion of the system, such that its state always remains in a certain band around the sliding hyperplane, is introduced. Then, two novel reaching laws satisfying conditions of the definition are proposed and applied to the design of appropriate linear control strategies which drive the state of the controlled system to a band around the sliding hyperplane. Consequently, the undesirable chattering and high-frequency switching between different values of the control signal are avoided. The strategies, when compared with previously published results, guarantee better robustness, faster error convergence, and improved steady-state accuracy of the system. Furthermore, better performance of the system is achieved using essentially reduced control effort     

MPC of Switching in a Boost Converter Using a Hybrid State Model With a Sliding Mode Observer

In this paper, a model of a dc–dc (boost) converter is first expressed as a hybrid/switched/variable-structure system state model for the purpose of applying recently developed hybrid optimal control theory to control switching in a boost converter. Switching control is achieved by forming the embedded form of the hybrid state model, which enables the derivation of a control that solves for the switching function that minimizes a user-defined performance index. This approach eliminates the need to form average-value models and provides flexibility to balance competing objectives through appropriate weighting of individual terms in the performance index. Since, in practical situations, both the source voltage and the load resistance vary with time in unknown and unmeasurable ways, we introduce a sliding mode observer based on an enlarged state model which allows implicit estimation of the unknown variables. The combined optimal switching control and sliding mode observer are applied to a boost converter in which several nonidealities and losses are represented. The results of time-domain simulation and hardware experiments are used to validate and compare the response of the hybrid optimal control–sliding mode observer to that of a traditional current-mode control strategy.      

Adaptive incremental sliding mode control for a robot manipulator

An adaptive incremental sliding mode control (AISMC) scheme for a robot manipulator is presented in this paper. Firstly, an incremental backstepping (IBS) controller is designed using time-delay estimation (TDE) to reduce dependence on the mathematical model. After substituting IBS controller into the nonlinear system, a linear system w.r.t. tracking errors is obtained while TDE error is the disturbance. Then, the AISMC scheme, including a nominal controller and an SMC, is developed for the resulted linear system to improve control performance. According to the equivalent control method, the SMC in the AISMC scheme is to handle TDE error. To receive optimal control performance at the sliding manifold, an LQR controller is selected as the nominal controller. The SMC is designed based on positive semi-definite barrier function (PSDBF) since it prevents switching gains from being over/under-estimated, and two practical problems are addressed in this paper: A new PSDBF is designed and conservative (large) setting bounds affecting tracking precision and/or system stability are avoided; An improved PSDBF based SMC is developed where the PSDBF and an adaptive parameter are used simultaneously to regulate switching gains, and the system is still stable when sliding variable occasionally exceeds the predefined vicinity. Moreover, finite-time convergence property of the sliding variable is strictly analyzed. Finally, real-time experiments are conducted to verify the effectiveness of the proposed control method.     

Design of multivariable variable structure system for nonlinear time-varying systems using nonlinear switching surfaces

Using nonlinear switching surfaces, a multivariable variable structure system (VSS) for nonlinear time-varying systems in the presence of disturbances and parameter variations is proposed. In the previous sliding mode control, the switching surfaces are linear functions and therefore the speed of response is relatively low. To overcome this problem, the proposed method improves the speed of response and good transient response is thus obtained. An example has shown its effectiveness in controlling nonlinear time-varying systems.<>     

Sliding Mode Control for Linear Systems with Time-Varying Input and State Delays

This paper deals with a sliding mode control for linear systems with input and state time-varying delays. Two different time delays are considered for the sliding mode control of a continuous linear system. Delay-dependent sufficient conditions are given for the existence of sliding manifolds in terms of linear matrix inequalities. A reaching motion controller is also proposed for such systems by means of both reaching law and inequality approach. An inverted pendulum system is utilized to illustrate the effectiveness of the developed techniques.     

车式移动机器人轨迹跟踪控制方法

针对车式移动机器人轨迹跟踪这一典型控制任务,本文提出一种滑模轨迹跟踪控制方法.该方法采用PI型滑模面设计等效控制律,利用变速函数代替符号函数获得切换控制率,并运用Lyapunov理论证明系统的稳定性.仿真结果表明该方法不但能使机器人有效跟踪任意参考轨迹,而且能减小在控制中的抖振现象,即使在外界干扰影响的情况下,也具有良好的控制品质.     

Technical note Sliding mode control for a class of hydraulic position servo

The present paper discusses a sliding mode control method suitable for controlling a hydraulic position servo with a flexible load. Due to the requirements of the control system, the reference model is designed for the case of a flexible load. The core of sliding mode control is switching surfaces which are specially defined for the system according to the mathematical model and control goal. A novel algorithm is developed, and the simulated and experimental results of the control system are shown. The results show the extremely good robustness of the proposed method.     

Passivity-based fractional-order integral sliding-mode control design for uncertain fractional-order nonlinear systems

This paper concerns with the problem of designing a passivity-based fractional-order (FO) integral sliding mode controller for uncertain FO nonlinear systems. Utilizing the FO calculus, it is showed that the state trajectories of the closed-loop system reach the FO switching manifold in finite time. The control law ensures the asymptotical stability on the sliding surface. A parameter adjustment scheme for FO integral sliding surface is proposed by using the linear matrix inequality (LMI) approach. The proposed controller can be applied to different systems such as chaotic systems. Finally, simulation results are provided to show the effectiveness of the proposed method controlling chaos in FO Chua circuit and FO Van-der-Pol oscillator.     

Dithered Sliding-Mode Control for Switched Systems

Dithering is proposed as a technique for the regulation of the boundary layer for switched systems under sliding-mode control. It is proved that dithering maintains the state of the system close to the ideal sliding manifold and that state error and practical stability depend on the dither amplitude, period, and shape, all by preserving the natural switching mode of the system. Experiments on a dc/dc buck power converter confirm the theoretical results.     

Sliding mode control with closed-loop filtering architecture for a class of nonlinear systems

It is well known by equivalent control theory, that in the sliding mode a low-pass filter, working as an average operator, can capture the desired control fairly well from the switching control signals. However, directly adding the filtered signals in parallel with the switching control does not warrant any improvement in the control system performance. In this work, we make clear the underlying reason why the sliding mode control (SMC) system does not function properly with such a simple closed-loop filtering structure. The correct way of incorporating the closed-loop filtering into SMC requires a second low-pass filter, which works concurrently with the first low pass filter to scale down the gain of the switching control. The SMC system with the new closed-loop filtering is able to realize the acquisition of equivalent control or estimate the disturbance, effectively reduce the switching gain to the minimum level, and as a result to eliminate chattering. Complementary to existing SMC, the proposed control system can easily incorporate feed-forward control into the closed-loop for bounded system perturbations. In addition, the frequency-domain knowledge can be easily used to construct the two filters.     

DC/DC开关变换器滑模变结构控制的新方案

本文在滑模等价控制的基础上,考虑实际控制中的非理想切换条件,提出了一种适合PWM型DC/DC开关变换器的滑模变结构控制算法简单的新方案.该控制算法依开关工作周期,动态地对滑模误差进行修正,从而动态地补偿控制量的大小,将有利于近似地保证系统沿着切换面运动,并可以减少系统稳态误差,达到削弱乃至消除高频抖动的目的.以Boost变换器为例的仿真结果表明,本文的控制方案可以减少系统超调,缩短过渡过程时间,改善系统的动态品质,并有效地解决滑模控制中的高频抖动问题.     

An Efficient Switching Frequency Limitation Process Applied to a High Dynamic Voltage Supply

This paper presents the analysis and design of a simple and effective switching frequency limitation process with sliding mode synthesis. The control scheme is based on self-oscillating phenomenon which naturally appears in relay feedback systems. Thanks to an analytical study, it shows that the maximum switching frequency of a sliding mode structure can always be limited by adding a simple second order filter in the feedback loop. To illustrate the implementation and the validity of this process, it is applied to a high dynamic voltage supply with a bandwidth of 2000 Hz and with a maximum switching frequency of 15 kHz. According to the experimental results, the switching frequency limitation process shows similar robustness properties to those of sliding mode control when the load and voltage supply change.