OPTIMAL CONTROL METHOD WITH TIME DELAY IN CONTROL

Optimal control method for active vibration control of linear time-delay systems is investigated in this paper. In terms of two cases that time delay is integer and non-integer times of sampling period, motion equation with time delay is transformed as standard discrete forms which contain no time delay by using zero order holder respectively. Discrete quadratic function is used as objective function in design of controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Because the controller is deduced directly from time-delay differential equation, system stability can be guaranteed easily, thus this method is generally applicable to ordinary control systems. The performance of the control method proposed and system stability when using this method are all demonstrated by numerical simulation results. Simulation results demonstrate that the presented method is a viable and attractive control strategy for applications to active vibration control. Instability in responses occurs possibly if the systems with time delay are controlled using controller designed in case of no time delay.     

Active control of high-frequency vibration: Optimisation using the hybrid modelling method

This work presents active control of high-frequency vibration using skyhook dampers. The choice of the damper gain and its optimal location is crucial for the effective implementation of active vibration control. In vibration control, certain sensor/actuator locations are preferable for reducing structural vibration while using minimum control effort. In order to perform optimisation on a general built-up structure to control vibration, it is necessary to have a good modelling technique to predict the performance of the controller. The present work exploits the hybrid modelling approach, which combines the finite element method (FEM) and statistical energy analysis (SEA) to provide efficient response predictions at medium to high frequencies. The hybrid method is implemented here for a general network of plates, coupled via springs, to allow study of a variety of generic control design problems. By combining the hybrid method with numerical optimisation using a genetic algorithm, optimal skyhook damper gains and locations are obtained. The optimal controller gain and location found from the hybrid method are compared with results from a deterministic modelling method. Good agreement between the results is observed, whereas results from the hybrid method are found in a significantly reduced amount of time.     

Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities

Nonlinearities in aircraft mechanisms are inevitable, especially in the control system. It is necessary to investigate the effects of them on the dynamic response and control performance of aeroelastic system. In this paper, based on the state-dependent Riccati equation method, a state feedback suboptimal control law is derived for aeroelastic response and flutter suppression of a three degree-of-freedom typical airfoil section. With the control law designed, nonlinear effects of freeplay in the control surface and time delay between the control input and actuator are investigated by numerical approach. A cubic nonlinearity in pitch degree is adopted to prevent the aeroelastic responses from divergence when the flow velocity exceeds the critical flutter speed. For the system with a freeplay, the responses of both open- and closed-loop systems are determined with Runge-Kutta algorithm in conjunction with Henon’s method. This method is used to locate the switching points accurately and efficiently as the system moves from one subdomain into another. The simulation results show that the freeplay leads to a forward phase response and a slight increase of flutter speed of the closed-loop system. The effect of freeplay on the aeroelastic response decreases as the flow velocity increases. The time delay between the control input and actuator may impair control performance and cause high-frequency motion and quasi-periodic vibration.     

Optimal tracking control with zero steady-state error for time-delay systems with sinusoidal disturbances

The problem of optimal tracking control with zero steady-state error for linear time-delay systems with sinusoidal disturbances is considered. Based on the internal model principle, a disturbance compensator is constructed such that the system with external sinusoidal disturbances is transformed into an augmented system without disturbances. By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance. The obtained optimal tracking control law with zero steady-state error consists of accurate linear state feedback terms and a time-delay compensating term, which is an infinite sum of an adjoint vector series. The accurate linear terms can be obtained by solving a Riccati matrix equation and a Sylvester equation, respectively. The compensation term can be approximately obtained through a recursive algorithm. A numerical simulation shows that the algorithm is effective and easily implemented, and the designed tracking controller is robust with respect to the sinusoidal disturbances.     

An efficient method for the solution of Riccati equation in structural control implementation

An efficient method for the solution of the Riccati equation in structural control implementation is presented in this paper. Through order reduction and appropriate selection of weighting functions, the solution time for the Riccati equation is dramatically reduced as no iteration is involved in the solution process. This achievement is very useful and sometimes critical in the structural control as the solution process of the Riccati equation is the most time-consuming part of any optimal control problem. It requires an inordinate amount of processing time when applied to large optimal control problems. As is well known, any time delay in structural control will cause unsynchronized application of the control forces and this can not only reduce the effectiveness of a structural active control system, but may also cause instability in the control system. The proposed method is easy to implement and high in efficiency and can significantly reduce the time delay in structural control implementation.     

Modified independent modal space control of m.d.o.f. systems

The performance of the independent modal space control (IMSC) algorithm for structural vibration control is examined in this paper. Both the theoretical analysis and numerical simulation show that, for a multi-degree-of-freedom system, the modal control forces may increase the contributions of the vibration of higher modes (uncontrolled modes) to the system response if the IMSC algorithm is used to design a structural control system. Therefore, the responses of the controlled structure may be underestimated if the effects of control forces on the higher modes are not considered in the response analysis. A new control algorithm—modified independent modal space control (MIMSC) algorithm is proposed in this paper for eliminating the effect of modal control force on the uncontrolled modes. Numerical example shows that the structural responses can be effectively reduced when control system design is carried out based on the proposed algorithm. By comparing the simulated results obtained by the IMSC and MIMSC algorithms, it is found that, in order to achieve the same control objective, the proposed algorithm is more effective than IMSC since the modal control forces do not have any effect on the uncontrolled modes. In order to verify the effectiveness of the proposed algorithm, a practical example—active control design of UCLA Math-Science Building is presented and discussed.     

Actuator saturation control of uncertain structures with input time delay

This paper presents a robust saturation control approach for active vibration attenuation of building structures involving parameter uncertainties and input time delay. The parameter uncertainties are described in both polytopic and norm-bounded forms and represent the variations of floor masses, stiffnesses and damping coefficients. The input time delay can be time-varying within a known bound. In terms of the feasibility of certain delay-dependent linear matrix inequalities (LMIs), a state feedback controller can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties, actuator saturation, and input time delay. The effectiveness of the proposed approach is investigated by numerical simulations on the vibration control of a three-storey building structure subject to seismic excitation. It is validated that the designed robust saturation controller can effectively suppress the structural vibration and keep the system stability when there are parameter uncertainties and input time delay.     

Dynamic behavior of time-delayed acceleration feedback controller for active vibration control of flexible structures

This paper addresses the design problem of the controller with time-delayed acceleration feedback. On the basis of the reduction method and output state-derivative feedback, a time-delayed acceleration feedback controller is proposed. Stability boundaries of the closed-loop system are determined by using Hurwitz stability criteria. Due to the introduction of time delay into the controller with acceleration feedback, the proposed controller has the feature of not only changing the mass property but also altering the damping property of the controlled system in the sense of equivalent structural modification. With this feature, the closed-loop system has a greater logarithmic decrement than the uncontrolled one, and in turn, the control behavior can be improved. In this connection, the time delay in the acceleration feedback control is a positive factor when satisfying some given conditions and it could be actively utilized. On the ground of the analysis, the developed controller is implemented on a cantilever beam for different controller gain–delay combinations, and the control performance is evaluated with the comparison to that of pure acceleration feedback controller. Simulation and experimental results verify the ability of the controller to attenuate the vibration resulting from the dominant mode.     

基于时延补偿机理的网络化输出反馈控制器设计

本文考虑前向和反馈通道均存在网络时延的网络化控制系统,提出了一种新的动态输出反馈控制器的设计方法.针对状态可测和不可测两种情况,整个设计过程采用不同的时延补偿机理,来主动地消除网络时延的影响.同时,讨论了闭环网络化控制系统的稳定性.最后的仿真实例表明了该方法的有效性.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

基于飞行器网络控制系统的多速率控制器设计

为了减少网络环境中的时延和数据包丢失对飞行器网络控制器系统的影响,设计了一种具有多速率的保性能控制器设计方法;多速率是指在具有多通道数据传输的系统中,各通道所需控制输入的频率不完全相同;在存在时延和丢包的情况下,利用增广技术对飞行器控制系统在整个循环周期内建立离散模型,此时为了使多速率控制方法更加有效,先基于此模型在控制器输入端构造一个预测器,根据预测器的输出为整个系统设计一个具有多控制速率的动态输出反馈控制器;然后给出并证明保性能控制器的存在条件和求解方法;最后通过某飞行器网络控制系统的数值算例验证了所提方法的有效性。     

Adaptive fuzzy sliding mode control of smart structures

Smart structures are usually designed with a stimulus-response mechanism to mimic the autoregulatory process of living systems. In this work, in order to simulate this natural and self-adjustable behavior, an adaptive fuzzy sliding mode controller is applied to a shape memory two-bar truss. This structural system exhibits both constitutive and geometrical nonlinearities presenting the snap-through behavior and chaotic dynamics. On this basis, a variable structure controller is employed for vibration suppression in the chaotic smart truss. The control scheme is primarily based on sliding mode methodology and enhanced by an adaptive fuzzy inference system to cope with modeling inaccuracies and external disturbances. The robustness of this approach against both structured and unstructured uncertainties enables the adoption of simple constitutive models for control purposes. The overall control system performance is evaluated by means of numerical simulations, promoting vibration reduction and avoiding snap-through behavior.     

复杂高阶对象的预测PID控制

针对复杂高阶对象提出了一种基于数值最优模型降阶方法,并基于这种降阶模型设计了预测PID控制器,将此控制器应用于原始模型能够得到很好地控制效果。数值最优模型降阶算法使高阶对象能近似为一阶加时滞对象或二阶加时滞对象,通过模型阶跃响应和Bode图对比,降阶模型曲线很好地逼近原始模型曲线。预测PID对大时滞对象有着很好地控制效果,模型降阶使得预测PID很好地控制复杂高阶对象,且其结构简单,可调参数少的特点。     

A novel method to obtain a real-time control force strategy using genetic algorithms for dynamic systems subjected to external arbitrary excitations

The paper deals with a discrete differential dynamic programming type of problem. It is an optimal control problem where an external disturbance is controlled over the time horizon by a control force constituted with the well-known convolution approach. The paper presents a simple and novel idea to achieve an optimally controlled response when a linear system is subjected to an arbitrary external disturbance. The proposed approach uses the convolution concept and states that if a control method can be established to restore a unit external disturbance, then the convolution integral can be applied to generate an overall control strategy to control the system when it is subjected to an arbitrary external disturbance. In spite of its simplicity, such a strategy has not been encountered in the literature. The only requirement for this method to be useful is to obtain an optimal control strategy to suppress the vibration of the system when it is subjected to unit response disturbance. To accomplish this, a method from classical optimal control theory such as linear quadratic regulator (LQR) that involves solving the Riccati equation of the associated system can be used. However, genetic algorithm (GA) can be adopted as an alternative way to obtain an optimal control strategy against impulse input. As any arbitrary excitation can be divided into impulses, the convolution concept will constitute the overall optimal control strategy for any arbitrary excitation with simply shifting, scaling and summation (or integration) of the GA-optimized control strategy for each impulse of the arbitrary excitation. The proposed method can be used for real time control applications. Once the control strategy for the impulse disturbance is established, the results can then be used at each time step when online control is performed. Computer simulations were carried out to control the response of a quarter-vehicle active suspension system using the proposed method. The obtained results were compared to those of linear quadratic regulator (LQR) and passive suspension applications. The overall results demonstrated the effectiveness of the proposed method for active suspension systems, especially in suppressing the vehicle body displacement when compared to both the LQR based and passive systems. Furthermore, such a control system proves to be simpler requiring less information to process, which is crucial for real-time applications.     

一种基于并行化方法的自适应光学闭环预测控制器

自适应光学系统的性能受限于伺服系统的延迟误差和波前传感器的光电子噪声。提出了一种多模型单变量预测模型,该模型采用基于Levenberg-Marquardt学习算法的前馈型神经网络。利用计算机多核处理器,设计了一个具有并行处理能力的预测控制器,来实现对自适应光学闭环控制电压的预测,以消除延迟误差的影响。通过数值仿真实验,研究了预测控制器对控制电压和远场斯特雷尔比的影响,与未采用预测控制器的系统进行了比较,并对预测算法的并行性能进行了分析。实验结果表明,使用并行化方法的预测控制器可以有效缩短系统的预测时间,提高预测算法的加速比,与经典比例积分(PI)控制算法相比可以更有效地降低系统由于伺服延迟引起的误差,远场的斯特雷尔比有明显地提高。     

A multi-input multi-output adaptive feed-forward controller for vibration alleviation on a large blended wing body airliner

Turbulent atmosphere, gusts, and manoeuvres significantly excite aircraft rigid body motions and structural vibrations, which leads to reduced ride comfort and increased structural loads. In particular BWB (Blended Wing Body) aircraft configurations, while promising a significant fuel efficiency improvement compared to wing-tube configurations, exhibit severe sensitivity to gusts. In general, a flexible aircraft represents a lightly damped structure involving a large variety of uncertainties due to fuel mass variations during flight, control system nonlinearities, aerodynamic nonlinearities, and structural nonlinearities, to name just a few. Especially at the beginning of flight testing of a newly developed aircraft type, plant models generally require a lot of verification and adjustment based on obtained flight test data, before they can be used reliably for control law design. Adaptive control already is a well-established method for many active noise and vibration control problems, and thus is proposed here for application to the problem of gust load alleviation. However, safety requirements are significantly higher for gust load alleviation systems than for most noise and vibration control systems. This paper proposes a MIMO (Multi-Input Multi-Output) adaptive feed-forward controller for the alleviation of turbulence-induced rigid body motions and structural vibrations on aircraft. The major contribution to the research field of active noise and vibration control is the presentation of a detailed stability analysis of the MIMO adaptive algorithm in order to support potential certification of this method for a safety-critical application. Finally, the proposed MIMO adaptive feed-forward vibration controller is applied to a longitudinal flight dynamics model of a large flexible BWB airliner in order to verify the derived vibration controller on a challenging control problem.     

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.     

Vibration control by recursive time-delayed acceleration feedback

This paper presents a theoretical basis of time-delayed acceleration feedback control of linear and nonlinear vibrations of mechanical oscillators. The control signal is synthesized by an infinite, weighted sum of the acceleration of the vibrating system measured at equal time intervals in the past. The proposed method is shown to have controlled linear resonant vibrations, low-frequency non-resonant vibrations, primary and 1/3 subharmonic resonances of a forced Duffing oscillator. The concept of an equivalent damping and natural frequency of the system is also introduced. It is shown that a large amount of damping can be produced by appropriately selecting the control parameters. For some combinations of the control parameters, the effective damping factor of the system is shown to be inversely related to the time-delay in the small delay limit. Selection of the optimum control parameters for controlling the forced and free vibrations is discussed. It is shown that forced vibration is best controlled by unity recursive gain and smaller values of the time-delay parameter. However, the transient response can be optimally controlled by suitably selecting the time delay depending upon the gain. The delay values for the optimal forced response may be different from that required for the optimum transient response. When both are important, a suboptimal choice of the delay parameters with unity recursive gain is recommended.     

一类非线性不确定系统的高阶积分自适应滑模控制

针对一类非线性不确定系统的滑模控制,结合有限时间收敛理论、高阶积分滑模理论与自适应控制理论,提出了一种高阶积分自适应滑模控制方法,改善了传统积分滑模存在的抖振问题。该方法通过对有限时间收敛反馈量的选取和高阶积分滑模面的设计,不但确保了系统状态误差在有限时间内的收敛性,而且还保证了系统具备对不确定性干扰的抑制能力。同时,采用自适应方法估计滑模控制的趋近速率,使得无须已知不确定项的边界范围。仿真结果验证了所提方法的有效性。     

A modeling technique for active control design studies with application to spacecraft microvibrations

Microvibrations, at frequencies between 1 and 1000 Hz, generated by on board equipment, can propagate throughout a spacecraft structure and affect the performance of sensitive payloads. To investigate strategies to reduce these dynamic disturbances by means of active control systems, realistic yet simple structural models are necessary to represent the dynamics of the electromechanical system. In this paper a modeling technique which meets this requirement is presented, and the resulting mathematical model is used to develop some initial results on active control strategies. Attention is focused on a mass loaded panel subjected to point excitation sources, the objective being to minimize the displacement at an arbitrary output location. Piezoelectric patches acting as sensors and actuators are employed. The equations of motion are derived by using Lagrange's equation with vibration mode shapes as the Ritz functions. The number of sensors/actuators and their location is variable. The set of equations obtained is then transformed into state variables and some initial controller design studies are undertaken. These are based on standard linear systems optimal control theory where the resulting controller is implemented by a state observer. It is demonstrated that the proposed modeling technique is a feasible realistic basis for in-depth controller design/evaluation studies.