Unmatched uncertainties compensation based on high‐order sliding mode observation

The problem of compensation of the effects of unmatched uncertainties ∕ perturbations is considered. High‐order sliding mode observers are employed for exact state and uncertainties ∕ perturbations reconstruction. A sliding mode control design is proposed ensuring theoretically exact compensation of the uncertainties ∕ perturbations for the corresponding unmatched states based on the identified perturbation values. An inverted pendulum simulation example is considered illustrating the feasibility of the proposed approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Integral Sliding‐Mode Observation and Control for Switched Uncertain Linear Time Invariant Systems: a Robustifying Strategy

A robustifying methodology for switched systems with matched and unmatched uncertainties/perturbations and autonomous location transitions is presented. We avail of such methodology to design a control strategy based on integral sliding modes, thereby ensuring theoretically exact compensation of the matched uncertainties/perturbations and the minimization of the effects of the unmatched ones. An output integral sliding‐mode control technique, based on a switched algebraic hierarchical observer is also proposed. This approach allows the theoretically exact compensation of the matched uncertainties/perturbations right after the first moment. The proposed approach is illustrated via numerical simulations.     

带有非匹配扰动的连铸结晶器振动位移系统自适应反步滑模控制

针对伺服电机驱动的连铸结晶器振动位移系统中存在非匹配的参数不确定性、干扰等问题,提出一种基于非线性扩张状态观测器(ESO)的自适应反步滑模控制方法.首先,基于双曲正切函数和高增益构造ESO对系统中的非匹配扰动进行估计.然后,利用反步法将非匹配扰动视为匹配扰动进行处理, 并在每一步设计自适应积分滑模控制器,以消除非匹配扰动对系统的影响.另外,在反步设计的后两步引入了积分滑模滤波器用于估计前一步虚拟控制律的导数.理论分析表明,所设计的ESO能够保证估计误差收敛到原点附近的小邻域内;所设计的控制器能够保证闭环系统所有信号有界,并且,通过选取适当的参数能够保证系统状态可渐近收敛到原点.最后,通过仿真结果验证了所提出方法的有效性.     

Alternative identification of wheeled mobile robots with skidding and slipping

This paper proposes the new identification of dynamics for Type(2,0) wheeled mobile robots(WMRs) in the presence of wheel skidding and slipping. This paper presents dynamics models that explicitly relate perturbations to the vehicle skidding and slipping. They cause parameter uncertainties, input-additive, matched and unmatched perturbations of WMRs. To solve the problem, this paper determines the new identification of dynamics for WMRs with skidding and slipping. The proposed dynamics lay a base for the deployments of various control design techniques to overcome the addressed perturbations. Finally, this paper verifies the tracking performance of the proposed feedback linearization controller for simulation results.     

Dynamic sliding mode control design using attracting ellipsoid method

A methodology for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations is proposed. It is considered that the control signal is applied through a first-order low-pass filter. The technique is based on the existence of an attracting (invariant) ellipsoid such that the convergence to a quasi-minimal region of the origin using the suboptimal control signal is guaranteed. The design procedure is given in terms of the solution of a set of Matrix Inequalities. A benchmark example illustrating the design is given.     

Active Disturbance Rejection Control of a Magnetic Suspension System

This paper proposes a novel output feedback control scheme for robust stabilization and tracking tasks in a magnetic suspension system. Active disturbance rejection control, differential flatness and on‐line asymptotic disturbance estimation are properly used for the proposed control synthesis. The controlled system is subjected to a wide spectrum of unknown significant matched and unmatched disturbances due to external forces and voltages, parametric uncertainties, control and state‐dependent perturbations and possibly input unmodeled dynamics. The effectiveness and robustness of the proposed active disturbance control scheme is verified by computer simulations for the robust tracking of a rest‐to‐rest reference position trajectory specified to firstly stabilize the suspended mass at a desired vertical position and next transfer it to another equilibrium position for both continuous and switched control voltage signals.     

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.     

Modeling and Analysis of Skidding and Slipping in Wheeled Mobile Robots: Control Design Perspective

This paper aims to give a general and unifying presentation on modeling of wheel mobile robots (WMRs) in the presence of wheel skidding and slipping from the perspective of control design. We present kinematic models that explicitly relate perturbations to the vehicle skidding and slipping. Four configurations of mobile robots are considered, and perturbations due to skidding and slipping are categorically classified as input-additive, input multiplicative, and/or matched/unmatched perturbations. Furthermore, we relate the WMR's maneuverability with the vehicle controllability that provides a measure on the WMR ability to track a trajectory in the presence of wheel skidding and slipping. These classifications and formulations lay a base for the deployments of various control design techniques to overcome the addressed perturbations.     

Adaptive robust fault-tolerant control for linear MIMO systems with unmatched uncertainties

In this paper, two novel fault-tolerant control design approaches are proposed for linear MIMO systems with actuator additive faults, multiplicative faults and unmatched uncertainties. For time-varying multiplicative and additive faults, new adaptive laws and additive compensation functions are proposed. A set of conditions is developed such that the unmatched uncertainties are compensated by actuators in control. On the other hand, for unmatched uncertainties with their projection in unmatched space being not zero, based on a (vector) relative degree condition, additive functions are designed to compensate for the uncertainties from output channels in the presence of actuator faults. The developed fault-tolerant control schemes are applied to two aircraft systems to demonstrate the efficiency of the proposed approaches.     

A parameter-varying filtered PID strategy for air–fuel ratio control of spark ignition engines

In this paper, a new synthesis method is presented to control air–fuel ratio (AFR) in spark ignition engines to maximize the fuel economy while minimizing exhaust emissions. The major challenge in the control of AFR is the time-varying delay in the control loop which restricts the application of conventional control techniques. In this paper, the time-varying delay in the system dynamics is first approximated by Padé approximation to render the system dynamics into non-minimum phase characteristics with time-varying parameters. Application of parameter-varying dynamic compensators is invoked to retrieve unstable internal dynamics. The associated error dynamics is then utilized to construct a filtered PID controller combined with a parameter-varying dynamic compensator to track the desired AFR command using the feedback from the universal exhaust gas oxygen sensor. The proposed method achieves desired dynamic properties independent of the matched disturbances. It also accommodates the unmatched perturbations due to the dynamic compensator features. The results of applying the proposed method to experimental numerical data demonstrate the closed-loop system stability and performance against time-varying delay, canister purge disturbances and measurement noise for both port fuel injection engines and lean-burn engines.     

非匹配不确定系统的终端滑模分解控制

针对非匹配多变量模型不确定系统,提出了一种终端滑模分解控制方法.通过状态变换和去耦合处理将系统转换为块能控标准型,它由匹配扰动的值域空间子系统和稳定的非匹配扰动的零动态子系统组成.提出了特殊的终端滑模超曲面,采用滑模控制策略,使值域空间子系统的状态在有限时间内收敛至平衡点,随后非匹配扰动的零动态子系统渐近收敛至平衡点附近的邻域内,且建立了该邻域的范围与系统的非匹配不确定性范围之间的数学关系,并用于系统的设计与分析.所提方法对于维数较高的非匹配不确定系统的控制具有较大的意义,可简化设计,实现递阶控制.仿真实     

Block approach to analysis and design of the invariant nonlinear tracking systems

Consideration was given to the nonlinear multiple-input multiple-output systems under the action of unmatched exogenous perturbations. For the general systems where the conditions for bounded problem of autonomous control are not met, formalized were the organization principles and existence conditions for the affine block input–output form underlying the block design of the basic law of open-plus-closed-loop control providing invariance of the output variables with respect to the exogenous perturbations. The constructions are augmented by the derivatives of the exogenous and control actions, but in distinction from the existing approaches their generating dynamic models are not included. To realize the basic law of control, used is an observer of the mixed phase and exogenous variables based on a virtual system with respect to the tracking errors with closed local links. An original decomposition procedure to design correcting observer actions was presented as a linear saturation functions estimating the mixed variables with the desired precision.     

Nonlinear H ∞ control of a Quadrotor (UAV), using high order sliding mode disturbance estimator

A nonlinear H _∞ output feedback controller is proposed and coupled to a high-order sliding mode estimator to regulate an UAV in the presence of the unmatched perturbations. The plant to be controlled is a Quadrotor helicopter described by nonlinear dynamics with plant uncertainties due to the variations of inertia moments and payload operation. A robust state estimation is considered under model uncertainties as well as external/measurement disturbances. Performance issues of the controller are illustrated in a simulation study made for an UAV prototype.     

Analysis and design of integral sliding manifolds for systems with unmatched perturbations

The robustness properties of integral sliding-mode controllers are studied. This note shows how to select the projection matrix in such a way that the euclidean norm of the resulting perturbation is minimal. It is also shown that when the minimum is attained, the resulting perturbation is not amplified. This selection is particularly useful if integral sliding-mode control is to be combined with other methods to further robustify against unmatched perturbations. H/sub /spl infin// is taken as a special case. Simulations support the general analysis and show the effectiveness of this particular combination.     

Adaptive dynamic surface control for integrated missile guidance and autopilot

Integrated guidance and control for homing missiles utilizing adaptive dynamic surface control approach is considered based on the three channels independence design idea. A time-varying integrated guidance and control model with unmatched uncertainties is first formulated for the pitch channel, and an adaptive dynamic surface control algorithm is further developed to deal with these unmatched uncertainties. It is proved that the proposed feedback controller can ensure not only the accuracy of target interception, but also the stability of the missile dynamics. Then, the same control approach is further applied to the control design of the yaw and roll channels. The 6-degree-of-freedom (6-DOF) nonlinear missile simulation results demonstrate the feasibility and advantage of the proposed integrated guidance and control design scheme.     

带有非线性不确定奇异系统的积分滑模控制

针对一类含有非线性不确定的奇异系统, 提出了一种面向性能的鲁棒控制器. 控制器由3部分组成: 积分滑模控制、附加的非线性控制及复合非线性反馈控制. 积分滑模控制可将匹配不确定完全抵消并使系统轨迹进入理想滑模; 附加的非线性控制用来抑制理想滑动模态上非匹配不确定对系统稳定性和性能的影响; 复合非线性反馈控制则保证闭环系统输出按性能要求渐近地跟踪参考输入信号. 最后通过算例说明所提算法的有效性.     

非匹配不确定离散系统的无抖振积分滑模控制

针对一类非匹配不确定离散系统, 设计一种无抖振离散积分滑模控制器. 为了抑制非匹配不确定性对系统的影响, 采用线性矩阵不等式方法设计一种新型的切换函数和对应的滑模控制律, 并证明了闭环系统的Lyapunov 稳定性. 同时, 引入饱和函数设计控制器, 使系统状态在积分滑模面的某个小邻域内做准滑模运动, 并通过合理选择饱和函数的边界层厚度, 使控制信号不含任何抖振. 理论分析和数值仿真验证了所提出方法的有效性.

     

Discrete sliding mode control of systems with unmatched uncertainty using multirate output feedback

Systems with uncertainties and disturbances are common in practice. In some cases, these disturbances are unmatched. Moreover, in most cases the entire state information is also not available for control purpose. This note proposes a control algorithm for achieving quasi-sliding mode in discrete-time linear time-invariant (LTI) systems with bounded unmatched uncertainties. A multirate output feedback based strategy is used for this purpose. The proposed algorithm is illustrated through an example.     

Robust adaptive control of nonlinearly parametrized multivariable systems with unmatched disturbances

A new robust adaptive control scheme is developed for nonlinearly parametrized multivariable systems in the presence of parameter uncertainties and unmatched disturbances. The developed control scheme employs a new integrated framework of a functional bounding technique for handling nonlinearly parametrized system dynamics, an adaptive parameter estimation algorithm for dealing with parameter uncertainties, a nonlinear feedback controller structure for stabilization of interconnected system states, and a robust adaptive control design for accommodating unmatched disturbances. It is proved that such a new robust adaptive control scheme is capable of ensuring the global boundedness and mean convergence of all closed‐loop system signals. A complete simulation study on an air vehicle system with nonlinear parametrization in the presence of an unmatched wind disturbance is conducted, and its results verify the effectiveness of the proposed robust adaptive control scheme.     

Functional observer-based sliding mode controller design for discrete-time stochastic LTI systems with unmatched uncertainty

Discrete-time sliding mode control is one of the most prominent robust control technique to stabilise systems. However, the assumption of full state feedback being available is seldom satisfied in practice. This paper presents the functional observer-based sliding mode controller (SMC) design for discrete-time stochastic systems with unmatched uncertainty. A disturbance-dependent sliding function method is proposed such that the effect of unmatched uncertainty of the system is minimised. Furthermore, SMC is calculated using the functional observer method. Finally, a simulation example is given to show the effectiveness of the proposed method.