VIBRATION CONTROL OF A SMART STRUCTURE USING PERIODIC OUTPUT FEEDBACK TECHNIQUE

Active vibration control is an important problem in structures. One of the ways to tackle this problem is to make the structure smart, adaptive and self‐controlling. The objective of active vibration control is to reduce the vibration of a system by automatic modification of the system's structural response. This work features the modeling and design of a Periodic Output Feedback (POF) control technique for the vibration control of a smart flexible cantilever beam system for a Single Input Single Output case. A POF controller is designed for the beam by bonding patches of piezoelectric layer as sensor/actuator to the master structure at different locations along the length of the beam. The entire structure is modeled in state space form using the Finite Element Method by dividing the structure into 3, 4, 5 elements, thus giving rise to three types of systems, viz., system 1 (beam divided into 3 finite elements), system 2 (4 finite elements), system 3 (5 finite elements). POF controllers are designed for the above three types of systems for different sensor/actuator locations along the length of the beam by retaining the first two vibratory modes. The smart cantilever beam model is developed using the concept of piezoelectric bonding and Euler‐Bernouli theory principles. The effect of placing the sensor/actuator at various locations along the length of the beam for all the three types of systems considered is observed and the conclusions are drawn for the best performance and for the smallest magnitude of the control input required to control the vibrations of the beam. The tip displacements with the controller is obtained. Performance of the system is also observed by retaining the first 3 vibratory modes and the conclusions are drawn.     

不确定组合时滞系统的鲁棒分散可靠控制

研究一类不确定组合时滞系统的状态反馈鲁棒分散可靠控制问题。系统包含状态时滞,控制输入时滞和参数不确定性。目的是设计分散线性无记忆状态反馈控制器,使得对于任意容许的不确定性以及在每一个子系统中预先指定的执行器子集合内执行器的失效,相应的闭环系统渐近稳定。最后给出一个数值例子验证了本文所给结果的有效性。     

移动质量激励悬臂梁振动主动控制系统

利用压电材料的正逆压电效应,实现了移动质量激励悬臂梁振动主动控制;建立了压电元传感方程和作动方程,进一步将其转化为状态空间模型中的状态方程和输出方程;设计了基于线性二次型最优控制(LQR)策略的振动主动控制器,以TMS320VC33 DSP芯片为核心组建了相应的硬件电路。实验结果表明:采用压电自感作动器可很好地抑制移动质量激励引起的悬臂梁振动。     

Robust fault-tolerant controller design for linear time-invariant systems with actuator failures: an indirect adaptive method

In this paper, indirect adaptive state feedback control schemes are developed to solve the robust faulttolerant control (FTC) design problem of actuator fault and perturbation compensations for linear time-invariant systems. A more general and practical model of actuator faults is presented. While both eventual faults on actuators and perturbations are unknown, the adaptive schemes are addressed to estimate the lower and upper bounds of actuator-stuck faults and perturbations online, as well as to estimate control effectiveness on actuators. Thus, on the basis of the information from adaptive schemes, an adaptive robust state feed-back controller is designed to compensate the effects of faults and perturbations automatically. According to Lyapunov stability theory, it is shown that the robust adaptive closed-loop systems can be ensured to be asymptotically stable under the influence of actuator faults and bounded perturbations. An example is provided to further illustrate the fault compensation effectiveness.     

Robust fault-tolerant controller design for linear time-invariant systems with actuator failures: an indirect adaptive method

In this paper, indirect adaptive state feedback control schemes are developed to solve the robust faulttolerant control (FTC) design problem of actuator fault and perturbation compensations for linear time-invariant systems. A more general and practical model of actuator faults is presented. While both eventual faults on actuators and perturbations are unknown, the adaptive schemes are addressed to estimate the lower and upper bounds of actuator-stuck faults and perturbations online, as well as to estimate control effectiveness on actuators. Thus, on the basis of the information from adaptive schemes, an adaptive robust state feed-back controller is designed to compensate the effects of faults and perturbations automatically. According to Lyapunov stability theory, it is shown that the robust adaptive closed-loop systems can be ensured to be asymptotically stable under the influence of actuator faults and bounded perturbations. An example is provided to further illustrate the fault compensation effectiveness.     

Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies

This paper presents a numerical study concerning the active vibration control of smart piezoelectric beams. A comparison between the classical control strategies, constant gain and amplitude velocity feedback, and optimal control strategies, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller, is performed in order to investigate their effectiveness to suppress vibrations in beams with piezoelectric patches acting as sensors or actuators. A one-dimensional finite element of a three-layered smart beam with two piezoelectric surface layers and metallic core is utilized. A partial layerwise theory, with three discrete layers, and a fully coupled electro-mechanical theory is considered. The finite element model equations of motion and electric charge equilibrium are presented and recast into a state variable representation in terms of the physical modes of the beam. The analyzed case studies concern the vibration reduction of a cantilever aluminum beam with a collocated asymmetric piezoelectric sensor/actuator pair bonded on the surface. The transverse displacement time history, for an initial displacement field and white noise force disturbance, and point receptance at the free end are evaluated with the open- and closed-loop classical and optimal control systems. The case studies allow the comparison of their performances demonstrating some of their advantages and disadvantages.     

Sliding‐mode fault‐tolerant control using the control allocation scheme

This paper is devoted to the design of a novel fault‐tolerant control (FTC) using the combination of a robust sliding‐mode control (SMC) strategy and a control allocation (CA) algorithm, referred to as a CA‐based sliding‐mode FTC (SMFTC). The proposed SMFTC can also be considered a modular‐design control strategy. In this approach, first, a high‐level SMC, designed without detailed knowledge of systems' actuators/effectors, commands a vector of virtual control signals to meet the overall control objectives. Then, a CA algorithm distributes the virtual control efforts among the healthy actuators/effectors using the real‐time information obtained from a fault detection and reconstruction mechanism. As the underlying system is not assumed to have a rank‐deficient input matrix, the control allocator module is visible to the SMC module resulting in an uncertainty. Hence, the virtual control, in this scheme, is designed to be robust against uncertainties emanating from the visibility of the control allocator to the controller and imperfections in the estimated effectiveness gain. The proposed CA‐based SMFTC scheme is a unified FTC, which does not need to reconfigure the control system in the case of actuator fault or failure. Additionally, to cope with actuator saturation limits, a novel redistributed pseudoinverse‐based CA mechanism is proposed. The effectiveness of the proposed schemes is discussed with a numerical example.     

Design and robust optimal control of smart beams with application on vibrations suppression

This paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression. The mechanical modeling of the structure and the subsequent finite element approximation are based on Hamilton's principle and classical engineering theory for bending of beams in connection with simplified modeling of piezoelectric sensors and actuators. Two control schemes LQR and H₂ are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods.     

Retrofit fault‐tolerant tracking control design of an unmanned quadrotor helicopter considering actuator dynamics

This paper presents a retrofit fault‐tolerant tracking control (FTTC) design method with application to an unmanned quadrotor helicopter (UQH). The proposed retrofit fault‐tolerant tracking controller is developed to accommodate loss‐of‐effectiveness faults in the actuators of UQH. First, a state feedback tracking controller acting as the normal controller is designed to guarantee the stability and satisfactory performance of UQH in the absence of actuator faults, while actuator dynamics of UQH are also considered in the controller design. Then, a retrofit control mechanism with integration of an adaptive fault estimator and an adaptive fault compensator is devised against the adverse effects of actuator faults. Next, the proposed retrofit FTTC strategy, which is synthesized by the normal controller and an additional reconfigurable fault compensating mechanism, takes over the control of the faulty UQH to asymptotically stabilize the closed‐loop system with an acceptable performance degradation in the presence of actuator faults. Finally, both numerical simulations and practical experiments are conducted in order to demonstrate the effectiveness of the proposed FTTC methodology on the asymptotic convergence of tracking error for several combinations of loss‐of‐effectiveness faults in actuators.     

Reliable dissipative control for uncertain time‐delayed stochastic systems with Markovian jump switching and multiplicative noise

This paper considers the robust reliable dissipative control problem for a class of hybrid systems, which includes stochastics, Markovian jumping, state time delay, parameter uncertainty, possible actuator failure, multiplicative noises and impulsive effects. We propose a linear feedback memoryless controller and impulsive controller such that the hybrid system is stochastically stable and strictly (Q, S, R) dissipative, which include H_∞ performance as a special case, for all the admissible uncertainties and actuator failures occurring among a prescribed subset of actuators. Based on Itô's differential formula and Lyapunov stability theory, sufficient conditions are obtained in terms of linear matrix inequalities. A numerical example is constructed to show the effectiveness of the controller designed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.     

Robust H-infinity reliable control for a class of nonlinear uncertain neutral delay systems

This paper focuses on the robust H-infinity reliable control for a class of nonlinear neutral delay systems with uncertainties and actuator failures. We design a state feedback controller in terms of linear matrix inequality(LMI) such that the plant satisfies robust H-infinity performance for all adnfissible uncertainties, and actuator failures among a prespecified subset of actuators. An example is also given to illustrate the effectiveness of the proposed approach.     

利用状态反馈增益变化设计广义系统H∞可靠控制器

通过对状态反馈两种增益变化形式的分析,研究广义系统H∞可靠控制器的设计问题.给出基于状态反馈增益变化的广义系统H∞可靠控制器的定义,得到了执行器故障模型.用线性矩阵不等式(LMI)方法,研究两种状态反馈增益变化的广义系统H∞控制器存在的充分条件和设计方法.进而,针对执行器的不同故障情形,用LMI方法给出广义系统存在基于状态反馈增益变化的H∞可靠控制器的充分条件.最后,给出了优化广义系统H∞可靠控制器的设计算法.     

Adaptive actuator failure compensation for multivariable feedback linearizable systems

A feedback linearization‐based adaptive control scheme is developed for multivariable nonlinear systems with redundant actuators subject to uncertain failures. Such an adaptive controller contains a direct adaptive actuator failure compensator to compensate the uncertain actuator failure, a nonlinear feedback to linearize the nonlinear dynamics, and a linear feedback to stabilize the linearized system. The key new design feature is the estimation of both the failure patterns and the failure values, for direct adaptive actuator failure compensation, newly developed for multivariable feedback linearizable nonlinear systems. With direct control signal adaptation, the adaptive failure compensation design ensures closed‐loop stability and asymptotic output tracking in the presence of actuator failure uncertainties. Simulation results from an application to attitude control of a near‐space vehicle dynamic model are presented to verify the desired system performance with adaptive actuator failure compensation. Copyright © 2015 John Wiley & Sons, Ltd.     

An adaptive integral sliding mode FTC scheme for dissimilar redundant actuation system of civil aircraft

ABSTRACT

This paper proposed a new adaptive integral sliding mode FTC scheme to deal with the actuator faults and failure. The scheme combines integral sliding mode control, control allocation scheme and adaptive strategy. The unknown actuator faults are handled by adaptive modulation gain of nonlinear ISMC law. To cope with complete failure, control allocation scheme is integrated with the baseline controller to provide tolerance. The proposed strategy relies on the estimate of actuator effectiveness. Therefore, an adaptive sliding mode observer based fault reconstruction scheme is proposed in this paper. The proposed scheme is implemented on dissimilar redundant actuation system driven by hydraulic and electro-hydraulic actuators. In nominal and faulty conditions, both actuators are contributing to achieving the desired control surface deflection. However, when the actuator failure occurs, the control signals are reallocated to the redundant actuator. The problem of dynamics mismatch is addressed using fractional order controller designed in an inner loop. The comparison with the existing literature is also conducted in the simulation to validate the dominant performance.     

变时滞不确定关联系统的分散鲁棒容错控制

针对一类不确定项具有数值界的变时滞不确定关联系统,运用线性矩阵不等式（LMI）方法对其分散鲁棒容错控制问题进行研究。首先提出以一组LMIs有解作为系统可分散鲁棒容错控制的充分条件,并给出了在此条件下的控制律,它对执行器发生故障时具有完整性;然后求解一个具有LMIs约束的凸优化问题,作为设计具有尽可能小反馈增益的分散鲁棒容错控制律的系统化方法,从而得到更符合实际的满意的分散容错控制律。     

基于风速估计的风力机状态反馈滑模容错控制

针对风力机变桨距执行机构突变故障,提出了基于风速估计的自适应状态反馈滑模容错控制策略.首先,设计了基于自适应状态反馈滑模理论的鲁棒主动容错控制器,并结合全阶补偿器对控制律进行设计;然后,利用基于变速灰狼优化算法的组合径向基函数神经网络实现风速估计,可以改善风速测量精度并提高控制系统可靠性;最后,根据线性矩阵不等式和Lyapunov理论对控制器稳定性进行讨论,并与现有控制策略进行比较.仿真结果表明,在健康/故障的变桨距执行机构条件下,所提容错控制方法均能获得较好的控制效果.     

Adaptive actuator failure compensation for nonlinear MIMO systems with an aircraft control application

A direct adaptive approach is developed for control of a class of multi-input multi-output (MIMO) nonlinear systems in the presence of uncertain failures of redundant actuators. An adaptive failure compensation controller is designed which is capable of accommodating uncertainties in actuator failure time instants, values and patterns. A realistic situation is studied with fixed grouping of actuators and proportional actuation within actuator groups. The adaptive control system is analyzed, to show its desired stability and asymptotic tracking properties in the presence of actuator failure uncertainties. As an application, such an adaptive controller is used for actuator failure compensation of a twin otter aircraft longitudinal model, with design conditions verified and control structure and adaptive laws developed for a nonlinear aircraft dynamic model. The effectiveness of adaptive failure compensation is demonstrated by simulation results.     

数值界不确定性关联大系统分散鲁棒H∞控制

针对一类状态阵,控制输入阵及关联阵中存在数值界不确定性的关联大系统,研究其分散鲁棒H∞状态反馈和输出反馈控制器设计问题.基于有界实引理,推导出了其存在分散鲁棒H∞控制器的充分条件,即一组矩阵不等式有解.利用Schur补引理,通过固定不同变量,提出了一种构建分散控制器的同伦迭代线性矩阵不等式方法.所获得的控制器使闭环大系统鲁棒稳定,并且达到给定的H∞性能指标.最后用数值例子说明了所提的设计方法的有效性.