Fuzzy-logic control of parametrically excited impacting flexible system

Summary In this article, the control of a repetitive impacting elastic link with parametrically excited base in rotational motion is considered. A fuzzy-logic controller is designed and employed to suppress the vibrations resulting after the impact with an external rigid body. The momentum balance method and an empirical coefficient of restitution is used in the collision of the two bodies. The controller is applied successfully to reduce the vibrations of the parametrically excited impacting flexible system. Simulations for several combinations of excitation and rotation parameters are provided. Received 21 April 1997; accepted for publication 12 September 1997     

Non-affine minimum variance controller design by inverse modeling procedure

The minimum variance lower bound (MVLB) represents the best achievable controller capability in the variance sense. Realization of MVLB for nonlinear systems confronts some difficulties. To realize the MVLB, in this paper, a nonlinear non-affine generalized minimum variance controller is designed. The situations in which the model is not in hand, accurate, or invertible are addressed. Moreover, in order to design minimum variance controller for nonlinear structures, inverse of the system is modeled; then, the controller parameters are tuned by a recursive optimization algorithm. The most classical recursive algorithms are gradient-based. In this paper, a relationship between gradient of the controller with that of the system model is derived by inverse lemma. Therefore, the recursive algorithm is free of any need for the gradient of the system model. Finally, an experimental test on four-tank benchmark processes is used to clarify the effectiveness of the proposed control scheme.     

中心刚体-柔性梁系统的最优跟踪控制

对考虑阻尼影响的中心刚体-柔性梁系统的动力特性和主动控制进行研究. 研究 中考虑了3种动力学模型：一次近似耦合模型、一次近似简化模型和线性化模型. 一次近 似模型中同时考虑了柔性梁的轴向变形和横向变形. 若在一次近似耦合模型中忽略轴向变 形的影响,则可得出一次近似简化模型. 线性化模型是对一次近似简化模型的线性化处理. 另外研究中考虑了3种阻尼因素：结构阻尼、风阻、中心刚体轴承处的阻尼. 控制设计采 用最优跟踪控制方法. 给出了从物理测量中提取模态坐标的滤波器方法. 研究结果显 示,一次近似简化模型能够有效地对系统的动力学行为进行描述;阻尼对系统的动力学特 性有着重要影响;当系统大范围运动为低速时,模态滤波器能够较好地提取出控制律所需 的模态坐标,最优跟踪控制方法能够使得系统跟踪所期望的运动轨迹,并且柔性梁的弹性 振动可得到抑制.     

A particle swarm optimization approach for fuzzy sliding mode control for tracking the robot manipulator

In this paper, an optimal fuzzy sliding mode controller is used for tracking the position of robot manipulator, is presented. In the proposed control, initially by using inverse dynamic method, the known sections of a robot manipulator’s dynamic are eliminated. This elimination is done due to reduction over structured and unstructured uncertainties boundaries. In order to overcome against existing uncertainties for the tracking position of a robot manipulator, a classic sliding mode control is designed. The mathematical proof shows the closed-loop system in the presence of this controller has the global asymptotic stability. Then, by applying the rules that are obtained from the design of classic sliding mode control and TS fuzzy model, a fuzzy sliding mode control is designed that is free of undesirable phenomena of chattering. Eventually, by applying the PSO optimization algorithm, the existing membership functions are adjusted in the way that the error tracking robot manipulator position is converged toward zero. In order to illustrate the performance of the proposed controller, a two degree-of-freedom robot manipulator is used as the case study. The simulation results confirm desirable performance of optimal fuzzy sliding mode control.     

Robust optimal attitude control of hexarotor robotic vehicles

Multirotor aerial robotic vehicles attract much attention due to their increased load capacity and high maneuverability. In this paper, a robust optimal attitude controller is proposed for a kind of multirotor helicopters—hexarotors. It consists of a nominal optimal controller and a robust compensator. The nominal controller is designed based on the linear quadratic regulation (LQR) method to achieve desired tracking of the nominal system, and the robust compensator is added to restrain the influence of uncertainties. The key contributions of this work are twofold: firstly, the closed-loop control system is robust against coupling and nonlinear dynamics, parametric uncertainties, and external disturbances; secondly, a decoupled and linear time-invariant control architecture making it ideal for real-time implementation. The attitude tracking errors are proven to be ultimately bounded with specified boundaries. Simulation and experimental results on the hexarotor demonstrate the effectiveness of the proposed attitude control method.     

Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems

The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.     

Attitude control of a rigid spacecraft with one variable-speed control moment gyro

Nonlinear controllability and attitude stabilization are studied for the underactuated nonholonomic dynamics of a rigid spacecraft with one variable-speed control moment gyro(VSCMG), which supplies only two internal torques.Nonlinear controllability theory is used to show that the dynamics are locally controllable from the equilibrium point and thus can be asymptotically stabilized to the equilibrium point via time-invariant piecewise continuous feedback laws or time-periodic continuous feedback laws. Specifically,when the total angular momentum of the spacecraft-VSCMG system is zero, any orientation can be a controllable equilibrium attitude. In this case, the attitude stabilization problem is addressed by designing a kinematic stabilizing law, which is implemented through a nonlinear proportional and derivative controller, using the generalized dynamic inverse(GDI)method. The steady-state instability inherent in the GDI controller is elegantly avoided by appropriately choosing control gains. In order to obtain the command gimbal rate and wheel acceleration from control torques, a simple steering logic is constructed to accommodate the requirements of attitude stabilization and singularity avoidance of the VSCMG. Illustrative numerical examples verify the efcacy of the proposed control strategy.     

Neural-network-based adaptive robust precision motion control of linear motors with asymptotic tracking performance

High precision motion control of permanent magnet linear motors (PMLMs) is limited by undesired nonlinear dynamics, parameter variations, and unstructured uncertainties. To tackle these problems, this paper presents a neural-network-based adaptive robust precision motion control scheme for PMLMs. The presented controller contains a robust feedback controller and an adaptive compensator. The robust controller is designed based on the robust integral of the sign of the error method, and the adaptive compensator consists of a neural network component and a parametric component. Moreover, a composite learning law is designed for the parameter adaption in the compensator to further enhance the control performance. Rigorous stability analysis is provided by using the Lyapunov theory, and asymptotic tracking is theoretically achieved. The effectiveness of the proposed method is verified by comparative simulations and experiments on a PMLM-driven motion stage.

     

Self-tuning fuzzy logic control of a non-linear structural system with ATMD against earthquake

Self-tuning fuzzy logic controllers (STFLC) for the active control of Marmara Kocaeli earthquake excited building structures are studied in this paper. Vibration control using intelligent controllers, such as fuzzy logic has attracted the attention of structural control engineers during the last few years, because fuzzy logic can handle nonlinearities, uncertainties, and heuristic knowledge effectively and easily. The improved seismic control performance can be achieved by converting a simply designed static gain into a real time variable dynamic gain through a self-tuning mechanism. Self-tuning fuzzy logic controller is designed to reduce the story-drift of each floor. The simulated system has a nine-degree-of-freedom, which is modeled using nonlinear behavior of the base-structure interaction. Modeled system was simulated against the ground motion of the Marmara Kocaeli earthquake (M _w=7.4) in Turkey on 17 August, 1999. At the end of the study, the time history of the story displacements, accelerations, ATMD displacements, control voltage, and frequency responses of the both uncontrolled and controlled cases are presented. The robustness of the controller has been checked through the uncertainty in stiffness of the structure. Performance of the designed STFLC has been demonstrated for the different disturbance using ground motion of the Kobe earthquake. Simulations of an earthquake excited nine story structure are performed to prove the validity of proposed control strategy.     

Impact of an elastic rod on a deformable barrier: analytical and numerical investigations on models of a valve and a rod-shaped stamping tool

The longitudinal motion of an elastic rod is studied for the case that the rod is suddenly elastically fixed at one end and is hit by a mass at its other end. This configuration represents real settings e.g. as a valve impacts an elastic valve-seat or as a stamping device used in forging is hit by a large mass. The solution of the problem is formulated in the Laplace transformation space. The inverse transformation into the time domain is performed by engaging the so-called Laguerre polynomial technique. This method allows to calculate exact solutions for finite times from a finite number of series elements. Rigorous mathematical proofs not established up to now are given with respect to the convergence of the series encountered and the validity of exchanging the order of inversion of the Laplace transformation and summation of the established series. For comparison also a numerical solution of the problem is presented. An analysis of the energy transfer between rod, impacting mass and elastic barrier elucidates the marked influence of the deformability of the elastic barrier on the stress state in the rod.     

两柔性梁碰撞振动类型的实验研究

基于对两弹性部件碰撞振动的理论及数值研究,设计了两柔性梁碰撞实验来研究碰撞振动类型．在实验中观察到亚谐、超谐、概周期、混沌等多种碰撞振动类型．此外,发现系统存在类似“频率锁定”性质的碰撞振动,以及同时存在性质相异的碰撞行为,如谐碰撞与混沌振动共存现象     

Self-tuning fuzzy logic control of crane structures against earthquake induced vibration

Self-tuning fuzzy logic controllers (STFLC) for the active control of Marmara Kocaeli Earthquake excited crane structures are studied in this paper. Vibration control using intelligent controllers, such as fuzzy logic has attracted the attention of structural control engineers during the last few years, because fuzzy logic can handle, uncertainties and heuristic knowledge and even non-linearities effectively and easily. The improved seismic control performance can be achieved by converting a simply designed static gain into a real time variable dynamic gain through a self-tuning mechanism. A self-tuning fuzzy logic controller is designed to reduce the vibrations of the crane structure. The simulated system has a five degrees-of-freedom and modeled system was simulated against the ground motion of the Marmara Kocaeli Earthquake (M _w =7.4) in Turkey on August 17, 1999. At the end of the study, the time history of the crane bridge and portal legs displacements, accelerations, and frequency responses of the both uncontrolled and controlled cases are presented. Additionally, the performance of the designed STFLC is also compared with a PD controller. Simulations of an earthquake excited bridge and portal legs are performed to prove the validity of proposed control strategy.     

TRAJECTORY TRACKING CONTROL AND VIBRATION SUPPRESSION OF SPACE-BASED ROBOT WITH ELASTIC FOUNDATION

讨论了基座存在弹性情况下,载体位置无控、姿态受控的漂浮基空间机械臂惯性空间轨迹跟踪控制及基座弹性振动主动抑制问题。由系统位置几何关系及动量守恒关系,建立了系统运动Jacobi 关系;之后利用拉格朗日方法并结合系统动量守恒关系建立了系统动力学方程。基于奇异摄动理论的两种时间尺度假设,将该方程分解为描写系统刚性运动的慢变子系统与描写系统弹性振动的快变子系统。对慢变子系统设计了基于计算力矩法的轨迹跟踪控制器;对于快变子系统则设计了线性二次最优控制方案。数值仿真证实了提出的控制方法的有效性。     

Model-free chaos control based on AHGSA for a vibro-impact system

For a vibro-impact system with clearance, the model-free chaos control method based on adaptive hybrid gravitational search algorithm (or AHGSA algorithm for short) is proposed. Nonparametric time-varying dynamic linear model based on pseudo-partial-derivative is established using input/output data of the controlled system, and on this basis, the optimal controller is designed according to the quadratic performance index, and the controller parameters is optimized using AHGSA algorithm. By combining the artificial bee colony search operator and chaos optimization strategy, gravitational search algorithm (or GSA algorithm for short) is improved from three aspects (i.e., population initialization, velocity and position update, gravity coefficient adjustment) to achieve a balance between the global detection ability and the local development ability. AHGSA algorithm has good optimization accuracy and efficiency: The arbitrariness is avoided in controller parameters selection, and the quality of the chaos control is ensured as well. In simulation experiment, the model-free controller optimized is used to control the chaotic motion of a single-degree-of-freedom vibro-impact system with clearance to verify the validity and feasibility of the proposed chaos control method. The simulation results show that the control effect is good, and the proposed chaos control method has the following advantages: the proposed chaos control method does not depend on the precise model of the controlled system, and the controller is easy to be designed and implemented.     

A switching fractional calculus-based controller for normal non-linear dynamical systems

In this paper, a fractional calculus-based terminal sliding mode controller is introduced for finite-time control of non-autonomous non-linear dynamical systems in the canonical form. A fractional terminal switching manifold which is appropriate for canonical integer-order systems is firstly designed. Then some conditions are provided to avoid the inherent singularities of the conventional terminal sliding manifolds. A non-smooth Lyapunov function is adopted to prove the finite time stability and convergence of the sliding mode dynamics. Afterward, based on the sliding mode control theory, an equivalent control and a discontinuous control law are designed to guarantee the occurrence of the sliding motion in finite time. The proposed control scheme uses only one control input to stabilize the system. The proposed controller is also robust against system uncertainties and external disturbances. Two illustrative examples show the effectiveness and applicability of the proposed fractional finite-time control strategy. It is worth noting that the proposed sliding mode controller can be applied for control and stabilization of a large class of non-autonomous non-linear uncertain canonical systems.     

Dynamic model based nonlinear tracking control of a planar parallel manipulator

Based on the dynamic model, a novel nonlinear tracking controller is developed to overcome the nonlinear dynamics and friction of a planar parallel manipulator. The dynamic model is formulated in the active joint space, and the active joint friction is described with the Coulomb + viscous friction model. A nonlinear tracking controller is designed to eliminate the tracking error by using the power function. The nonlinear tracking controller is proven to guarantee asymptotic convergence to zero of both the tracking error and error rate with the Barbalat’s lemma. The trajectory tracking experiment of the proposed controller is implemented on an actual five-bar planar parallel manipulator both at the low-speed and high-speed motion. Moreover, the control performances of the proposed controller are compared with the results of the augmented PD (APD) controller.     

Open-plus-closed-loop control for chaotic motion of 3D rigid pendulum

An open-plus-closed-loop （OPCL） control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitationM force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler＇s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts： the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.     

ROBUST CONTROL OF VORTEX-INDUCED VIBRATION OF A RIGID CYLINDER SUPPORTED BY AN ELASTIC BEAM USING μ -SYNTHESIS

For lightweight and flexible structures, it is important to suppress the vibrations induced by interactions between fluid and structures. This paper presents the robust control of the vortex-induced vibration of a rigid circular cylinder supported by an elastic cantilever beam in which the fluid force is considered as an external excitation on the structure. For the problems considered here, the excitation frequency is assumed to be equal to the natural frequency of the structure or the “lock-in” frequency. The natural frequencies of this analytical model are calculated by using the modal analysis method and then modal coordinates are introduced to obtain the state equations of the structural system. A pair of piezoelectric devices fixed under the base plate, on which the elastic beam is clamped, were used as actuators. A robust controller satisfying the nominal performance and robust performance is designed using μ -synthesis theory based on the structured singular value. Simulation and experiment were carried out with the designed controller and the effectiveness of the robust control strategy was verified by both experimental and simulation results.     

Adaptive inverse control of variable speed wind turbine

The efficiency and reliability of wind power has been shown to be depending on the applied control strategy of the wind turbine. In this paper, an adaptive control strategy is proposed for variable speed wind turbine (VSWT), producing energy limitation above rated wind speed. In the proposed control strategy, the process is modeled using a neural networks based identifier, providing the sensitivity information of the process to the control input. Another neural networks is employed as an inverse model controller established via inverse system method. These two neural networks are off-line learned firstly and are on-line updated using the back propagation algorithm. Simulation results have shown the effectiveness of the proposed adaptive control strategy.