Combining state estimator and disturbance observer in discrete‐time sliding mode controller design

In response to a multiple input/multiple output discrete‐time linear system with mismatched disturbances, an algorithm capable of performing estimated system states and unknown disturbances is proposed first, and then followed with the design of the controller. Attributed to the fact that both system states and disturbances can be estimated simultaneously with our proposed method, the estimation error is constrained at less than O(T) as the disturbance between the two sampling points is insignificant. In addition, the estimated system states and disturbances are then to be used in the controller when implementing our algorithm in a non‐minimum phase system (with respect to the relation between the output and the disturbance). The tracking error is constrained in a small bounded region and the system stability is guaranteed. Finally, a numerical example is presented to demonstrate the applicability of the proposed control scheme. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Chattering-free sliding mode control-based disturbance observer for MEMS gyroscope system

Microsystem Technologies - This paper proposes a novel disturbance observer (DOB) based on the free-chattering sliding-mode control (SMC) to compensate the changing of the disturbance and uncertain...     

Fast terminal sliding mode tracking control of hypersonic vehicles based on non-homogeneous disturbance observer

The tracking control problem of hypersonic vehicles is studied and analyzed in this paper using terminal sliding mode control method (TSMC) and non-homogeneous disturbance observer(NHDO) considering parametric uncertainty and external disturbances. Non-singular terminal sliding mode controller is provided based on NHDO. The key idea is that the NHDO is adopted to estimate the aerodynamic uncertainties and external disturbances simultaneously, which can enhance the robustness of the system and lower the gain of the switch controller. Rigorous stability analysis for the closed-loop system is given via Lyapunov stability theory, which proves that the system states are always bounded even during the estimation process when the estimation error is not zero. The sliding manifold can be reached in finite time and the tracking errors can converge to zero asymptotically. Numerical simulations are conducted with the longitudinal nonlinear dynamic model of hypersonic vehicles to verify the effectiveness and robustness of the designed controller.     

Adaptive sliding mode controller design based on T-S fuzzy system models

An adaptive sliding mode control (ASMC) technique based on T-S fuzzy system models is proposed in this paper for a class of perturbed nonlinear MIMO dynamic systems in order to solve tracking problems. A T-S fuzzy model is firstly formed by utilizing fuzzy theorem to amalgamate a set of linearized dynamic equations. The adaptive sliding mode controller is then designed based on this fuzzy model with perturbations. The proposed control scheme can drive the dynamics of controlled system into a designated sliding surface in finite time, and guarantee the property of asymptotical stability. It is also shown that the information of upper bound of modeling errors as well as perturbations, except the information of upper bound of input uncertainty, is not required when using the proposed controller.     

Linear extended state observer based sliding mode disturbance decoupling control for nonlinear multivariable systems with uncertainty

In this paper, the sliding mode dynamic disturbance decoupling tracking control method based on the linear extended state observer (LESO) is proposed for a class of square multivariable nonlinear uncertain system. The model plant contains the known linear dynamics, the unknown nonlinear dynamics and the internal and external disturbances, and the various input-output pairs are interacted. The system states are not available for measurement. An improved LESO is developed. The leading feature which is different from the typical ESO lies in that its extended state does not contain the known linear dynamics. The improved LESO can guarantee the error variables to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. So this ball radius can be arbitrarily as small as desired by tuning design parameters. And we give a simple method by which the gain parameters of LESO can be computed easily. This estimation to the total disturbance of the original system is introduced into the sliding mode control design to complete disturbance rejection and decoupling. Rigorous stability analysis shows that the system output can track the desired signal closely. Finally, a class of mass–spring–damper system is taken to make the numerical simulation analysis to illustrate the effectiveness of the proposed control method.     

On the robust fault detection via a sliding mode disturbance observer

This paper deals with robust fault detection for non-linear systems. This problem is usually solved by designing an observable subsystem which is only affected by the fault and not by the control and disturbance inputs. However, such a subsystem may not exist so that the so-called fundamental problem of residual generation (FPRG) is not solvable. The aim of the present paper is to design a fault detection filter when the conditions for the existence of a solution to the non-linear FPRG are not satisfied. Our approach is made in a geometric context. Under some decoupling assumptions, the design of sliding mode observers allows us to reconstruct the disturbance inputs and then to generate an effective residual. An illustrative example is given throughout the paper.     

基于跟踪微分器的离散滑模控制器

利用跟踪微分器设计了一种新的离散滑模控制器,可以从不连续的指令信号中合理提取连续信号及微分信号,且不需要利用线性外推的方法预测指令信号下一时刻的值及其微分．与基于趋近律的离散滑模控制器进行的对比仿真表明,所设计的控制器在保持传统滑模控制固有强鲁棒性的同时,控制器的输出几乎不存在抖振现象,而且在跟踪不连续的指令信号时,系统表现出良好的动态品质．     

An adaptive fuzzy controller based on sliding mode for robotmanipulators

This paper considers adaptive fuzzy control of robotic manipulators based on sliding mode. It is first shown that an adaptive fuzzy system with the system representative point (RP, or as is often termed, a switching function in variable structure control (VSC) theory) and its derivative as inputs, can approximate the robot nonlinear dynamics in the neighborhood of the switching hyperplane. Then a new method for designing an adaptive fuzzy control system based on sliding mode is proposed for the trajectory tracking control of a robot with unknown nonlinear dynamics. The system stability and tracking error convergence are also proved by Lyapunov techniques.     

Discrete-time track following controller design using a state-space disturbance observer

This paper presents a method to design a discrete-time track following controller using a state-space disturbance observer. To improve sensitivity, an add-on state-space disturbance observer is introduced to a LQG/LTR track following controller, which does not affect the observer and state feedback poles thereby preserving the separation principle. Therefore disturbance observer design is possible to shape the sensitivity without affecting the stability of the LQG/LTR track following controller. The proposed disturbance observer is designed in state-space without disturbance model such as plant's inverse dynamics, periodic signal generator, and Q filter. Simulation and experimental results verify the effectiveness of the proposed design method using a disturbance observer.     

Second-order sliding mode control with backstepping for aeroelastic systems based on finite-time technique

In this paper, a backstepping second-order sliding mode control scheme (BSOSMC) is proposed for suppressing both flutter and limit cycle oscillation in the aeroelastic system. The proposed control scheme combining the sliding mode control and backstepping technique, which obtain the properties of fast response and improve the control accuracy. To obtain a better disturbance rejection property, we employ compensated control term. The compensated control term provides the complete compensation of the uncertainty and disturbance, and it relax the requirement of the bound of uncertainty and disturbance. The convergence and stability of the proposed control scheme are proved by using Lyapunov’s method. Finally, the simulation results demonstrate the effectiveness of the proposed control scheme.     

Output integral sliding mode control based on algebraic hierarchical observer

The problem of the realization of integral sliding mode controllers based only on output information is discussed. The implementation of an output integral sliding mode controller ensures insensitivity of the state trajectory with respect to the matched uncertainties from the initial time moment. In the case when the number of inputs is more than or equal to the number of outputs, the closed loop system, describing the output integral sliding mode dynamics, is shown to lose observability. For the case when the number of inputs is less than the number of outputs, a hierarchical sliding mode observer is proposed. The realization of the proposed observer requires a filtration to obtain the equivalent output injections. Assigning the first order low-pass filter parameter small enough (during this filter realization), the convergence time and the observation error can be made arbitrarily small. The results obtained are illustrated by simulations.     

Sliding mode control for an aerodynamic missile based on backstepping design

In order to solve the mismatched uncertainties of a class of nonlinear systems,a control method of sliding mode control (SMC) based on the backstepping design is proposed. It introduces SMC in to the last step of backstepping design to modify the backstepping algorithm. This combination not only enables the generalization of the backstepping design to be applied to more general nonlinear systems, but also makes the SMC method become effective in solving the mismatched uncertainties. The SMC based on the backstepping design is applied to the flight control system design of an aerodynamic missile. The control system is researched through simulation. The simulation results show the effectiveness of the proposed control method.     

四旋翼双环滑模姿态控制系统设计与仿真

针对四旋翼姿态角难以快速跟踪实际控制指令,传统线性化方法稳定性能不佳、用简单滑模控制存在控制律难以实现等问题,提出了一种基于双环滑模控制系统的设计方案。通过建立四旋翼的姿态动力学模型推导出姿态角和角速度的控制律方程。最后,基于实验室搭建的四旋翼硬件实验平台对该方案进行MATLAB仿真分析,并与常规PID控制方法和反步法进行了比较。结果表明该方法有效可行,跟踪姿态角更加快速、精确。     

Decentralized sliding mode adaptive controller design based on fuzzy neural networks for interconnected uncertain nonlinear systems

A new type controller, fuzzy neural networks sliding mode controller (FNNSMC), is developed for a class of large-scale systems with unknown bounds of high-order interconnections and disturbances. Although sliding mode control is simple and insensitive to uncertainties and disturbances, there are two main problems in the sliding mode controller (SMC): control input chattering and the assumption of known bounds of uncertainties and disturbances. The FNNSMC, which incorporates the fuzzy neural networks (FNNs) and the SMC, can eliminate the chattering by using the continuous output of the FNN to replace the "discontinuous" sign term in the SMC. The bounds of uncertainties and disturbances are also not required in the FNNSMC design. Two examples are presented to support the validity of the new controller. The simulation results show that the FNNSMC is more robust than the SMC.     

Enhanced backstepping sliding mode controller for motion tracking of a nonlinear 2-DOF piezo-actuated micromanipulation system

Microsystem Technologies - In this paper a robust backstepping sliding mode controller is developed for tracking control of 2-DOF piezo-actuated micromanipulation system. The control approach is...     

The neural sliding mode controller design of fan-plate system

This paper proposed a sliding mode angle control with neural network estimator design for a fan-plate system. The neural network estimator is based on radial basis function and it estimates the unknown lumped bounded uncertainty of parameter variations and external disturbances in real-time. The abilities of anti-disturbance and anti-chattering are better than conventional sliding mode controller and adaptive sliding mode controller. The Lyapunov stability theorem is employed to ensure the stability of the proposed controller. The convergence and signal tracking properties are better than the conventional sliding mode controller. Finally, we employed the experiment to validate the proposed method is feasible.     

基于滑模观测器的永磁同步电机变结构鲁棒控制

提出一种由一个变结构控制器和一个滑模观测器组成的控制系统,用于永磁同步电机的无传感器鲁棒控制.首先利用Lyapunov稳定性原理分析得到观测器的收敛条件及自适应率,并证明了其稳定性,然后以转速误差为参量建立滑模面,构造出变结构速度控制器,推导出自适应速度控制律,并得到速度控制的参考电流和参考电压.该方案的控制性能不依赖于电机参数和干扰变化,具有较强的鲁棒性.仿真结果验证了该方案的有效性与正确性.