Robust stability—degree assignment and its applications to the control of flexible structures

A new method of robust controller synthesis is introduced which is an extension of robust stabilization to robust stability-degree assignment. This method guarantees a lower bound of stability degree for all uncertainties within a prescribed magnitude band. The method is applied to the control of four types of flexible structures, namely, colocated beam, non-colocated beam, beam with moving base and large scale satellite model. Excellent performances have been obtained experimentally with respect to the response speed and the robustness.     

A self-organizing fuzzy logic controller for the active control of flexible structures using piezoelectric actuators

This paper proposes an on-line self-organizing fuzzy logic controller (FLC) design applied to the control of vibrations in flexible structures containing distributed piezoelectric actuator patches. In this methodology, the fuzzy rules are generated using the history of input/output (I/O) pairs without using any plant model. The generated rules are stored in the fuzzy rule space and updated on-line by a self-organizing procedure. The validity of the proposed fuzzy logic control has been demonstrated experimentally in a steel cantilever test beam and a set of experimental tests are made in the system to verify the efficiency of the on-line self-organizing fuzzy controller.     

Robust H∞ control design for systems with structured parameter uncertainty

In a recent paper a unification of the H₂ (LQG) and H_∞ control-design problems was obtained in terms of modified algebraic Riccati equations. In the present paper these results are extended to guarantee robust H₂ and H_∞ performance in the presence of structured real-valued parameter variiations (ΔA, ΔB, ΔC) in the state space model. For design flexibility the paper considers two distinct types of uncertainty bounds for both full- and reduced-order dynamic compensation. An important special case of these results generates H₂/H_∞ controller designs with guaranteed gain margins.     

Robust stabilization for multivariable systems with constrained control: Frequency domain approach

In this paper, robust stabilization conditions based on theH ^∞-norm are derived for multivariable feedback systems under perturbations and constrained control. The parametrized controller of Youlaet al. is employed to treat this problem. In addition, a necessary and sufficient condition is derived for the solvability of the synthesis problem for a controller which achieves robust stability. Finally, a design procedure is proposed for selecting the parameters of the robust controller, and an illustrative example is given.     

Robust control of a hydraulically driven flexible arm

A new robust controller is proposed to regulate both flexural vibrations and rigid body motion of a hydraulically driven flexible ann. The controller combines backsteppmg control and sliding mode to arrive at a controller capable of dealing with a nonlinear system with uncertainties. The sliding mode technique is used to achieve an asymptotic joint angle and vibration regulation in the presence of payload uncertainty by providing a virtual torque input at the joint while the backstepping technique is used to regtthte the spool position of a hydraulic valve to provide the required torque. It is shown that there is no chatter in the hydraulic valve, which results in smoother operation of the system.     

Controller design for flexible structure vibration suppression with robustness to contacts

Model-based feedback control of vibration in flexible structures can be complicated by the possibility that interaction with an external body occurs. If not accounted for, instability or poor performance may result. In this paper, a method is proposed for achieving robust vibration control of flexible structures under contact. The method uses robust linear state feedback, coupled with a state estimation scheme utilizing contact force measurement. Uncertain contact characteristics are modelled by a sector-bounded non-linear function, such that state feedback gains can be synthesized using a matrix inequality formulation of the Popov stability criterion. A separation theorem is used to establish a robust H₂ cost bound for the closed loop system. Experimental results from a multi-mode flexible structure testbed confirm that vibration attenuation and stability can be maintained over a broad range of contact characteristics, in terms of compliance and clearance.     

Continuous bounded controllers for active control of structures

This paper considers nonlinear controller under bounded capacity of the actuators. The controller is first derived based on bang-bang type controllers. In order to avoid high-speed switching effect, a continuous function is used to replace signum function in bang-bang controller. Although a variety of continuous and bounded functions are available, a hyperbolic tangent is chosen as the candidate of the controller. The proposed control law is then applied to three- and six-storey buildings utilising active bracing systems. Different earthquake excitations with various intensities are used in the simulation to show the potential benefit of the proposed control law. Numerical results show that in contrast to bang-bang type controllers that utilise maximum capacity of the actuator, the proposed controller is adaptive in the sense that the maximum capacity of the actuator is utilised when only needed. In addition, the proposed controller can avoid the high-speed switching effects presence in the bang-bang controllers if the weighting variables are chosen appropriately.     

具有非线性扰动的广义系统的鲁棒H∞控制

研究具有非线性结构扰动广义系统的鲁棒H∞控制和鲁棒H∞保性能控制问题,该不确定性为时间和状态的函数.且满足Lipschitz条件.目的是分别设计系统的鲁棒H∞控制器和鲁棒H∞保性能控制器.应用线性矩阵不等式方法,分别给出了系统的鲁棒H∞控制器和鲁棒H∞保性能控制器存在的充分条件.当这些条件可解时,分别给出了鲁棒H∞控制器和鲁棒H∞保性能控制器的表达式.最后通过一个仿真算例说明了所给出方法的应用.     

Robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances

This brief paper deals with the problem of robust exponential stabilization of a class of dynamic systems subject to time-varying delays, external disturbances and control saturation. A linear memoryless state feedback controller is synthesized to guarantee that there is a domain of admissible initial conditions from which all solutions of the class of systems considered converge exponentially to a ball with a prespecified convergence rate. The problem is formulated as a two-step optimization problem with matrix inequality constraints to enlarge the size of the ball of admissible initial conditions.     

Active vibration control of flexible structures using delayed position feedback

The paper discusses the use of a simple position control system approach to improve the performance of lightly damped dynamic systems. This approach uses a delayed position feedback signal to actively control the vibrations of flexible structures. A complete analysis of the stability of a single-link flexible manipulator under time delay control is presented and critical values of time delay for a given controller gain have been determined. The paper also presents a short comparison between the delayed feedback signal control and the linear quadratic regulator.     

Robust nonlinear control of systems with input unmodeled dynamics

We consider systems with unmodeled dynamics appearing at the input, and present a redesign that preserves global asymptotic stability. The admissible unmodeled dynamics are relative degree zero and minimum phase. The redesign is illustrated on an analytical example.     

Design of remotely located and multi-loop vibration controllers using a sequential loop closing approach

In some applications, vibration control objectives may require reduction of levels at locations where control system components cannot be sited due to space or environmental considerations. Control actuators and error sensors for such a scenario will need to be placed at appropriate locations which are potentially remote from the points where ultimate attenuation is desired. The performance of the closed loop system, therefore, cannot be assessed simply by the measurement obtained at this local error sensor. The control design objective has to take into account the vibration levels at the remote locations as well. A design methodology was recently proposed that tackles such problems using a single-loop feedback control architecture. The work in this paper describes an extension of this control design procedure to enable the systematic design of multiple decentralised control loops. The approach is based upon sequential loop closing and conditions are provided that ensure that closed loop stability is maintained even in the event of failure in some control loops. The design procedure is illustrated through its application to a laboratory scale slab floor that replicates the problems associated with human induced vibration in large open-plan office buildings. The experimental results demonstrate the efficacy of the approach and significant suppression of the dominant low frequency modes in the floor is achieved using two independent acceleration feedback control loops.     

Adaptive input shaping for maneuvering flexible structures

In the control of flexible structures many methods are used to reduce residual vibration due to the excitation of flexible modes. Input shaping, a feed-forward method, typically convolves the input with a sequence of impulses that are independent of the system maneuver. While reducing the residual vibration, input shaping extends the duration of the maneuver command by the length of the input shaper. This paper explores the idea of adaptive input shaping which allows a fast input shaper to be used while providing robustness to parameter uncertainty by tuning the shaper to the flexible mode frequency. The adaptive input shaping method presented can adapt between maneuvers or during maneuvers. Analysis yields a large range of convergence that is verified by simulation and shows this method to be less complex than other adaptive approaches.     

Position/vibration control of two-degree-of-freedom arms having one flexible link with artificial pneumatic muscle actuators

A manipulator with a light and thus flexible link would be advantageous over a rigid link in the sense that it is physically safer when it comes into contact with its environment than a manipulator with a rigid and thus heavy link, even though it is harder for a flexible link manipulator to be robustly controlled. On the other hand, if an actuator can deliver enough force while maintaining proper compliance, it would be advantageous for the sake of safety. An artificial pneumatic muscle-type actuator is an adequate choice in this case. In this work, position control problem of a two-degree-of-freedom arm system having a flexible second link with artificial pneumatic muscle-type actuators is addressed. A composite controller design method is proposed in the framework of the singular perturbation method. Various robust control schemes are designed in order to meet with payload variation, parameter uncertainty, unmodeled vibration mode, actuator dynamics both in the slow and the fast subsystems.     

Intelligent fault-tolerant system of vibration control for flexible structures

This paper describes an intelligent fault-tolerant control method for vibration control of flexible structures. We consider a case where the fault phenomena of the control system for flexible structures can be treated as a change of system parameters. Therefore, the adaptive control method can be applied to a vibration control system for flexible structures with a fault. In this paper, a neural network (NN) adaptive control system is used to compensate for the change in the parameters of a plant with a fault. When the characteristics of the plant and of a nominal model have been agreed by a NN adaptive control system, the control method designed for the nominal model, such as decoupling feedback control or linearizing feedback control, can be used even if the change in the system parameters has been caused by a fault. To confirm the effectiveness of the proposed fault-tolerant control method, the simulational results from a 5-link robotic arm are shown at the end of the paper. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity

This brief proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of parametric uncertainty, external disturbances and control input nonlinearity/dead-zone. The designed controller based on adaptive variable structure output feedback control satisfies the global reaching condition of sliding mode and ensures that the system state globally converges to the sliding mode. A modified version of the proposed control law is also designed for adapting the unknown upper bounds of the lumped uncertainties and perturbations. The stability of the system under the modified control law is established. Numerical simulations show that the precise attitude pointing and vibration suppression can be accomplished using the derived robust or adaptive controller.     

Non-parametric modelling of a rectangular flexible plate structure

This research investigates the performance of dynamic modelling using non-parametric techniques for identification of a flexible structure system for development of active vibration control. In this paper, the implementation details are described and the experimental studies conducted in this research are analysed. The input-output data of the system were first acquired through the experimental studies using National Instruments (NI) data acquisition system. A sinusoidal force was applied to excite the flexible plate and the dynamic response of the system was then investigated. Non-parametric modelling of the system were developed using several artificial intelligent methodologies namely Adaptive Elman Neural Networks (ENN), Backpropagation Multi-layer Perceptron Neural Networks (MLPNN) and Adaptive Neuro-Fuzzy Inference System (ANFIS). The performance of all these methodologies were compared and discussed. Finally, validation and verification of the obtained model was conducted using One Step Ahead (OSA) prediction, mean squared error (MSE) and correlation tests. The prediction ability of the model was further observed with unseen data. The results verified that the MLPNN converge to an optimum solution faster and the dynamic model obtained described the flexible plate structure very well. The non-parametric models of the flexible plate structure thus developed and validated will be used as the representation of the transfer function of the system in subsequent investigations for the development of active vibration control strategies for vibration suppression in flexible structures.     

Grasping impact force control of a flexible robotic gripper using a piezoelectric actuator

This paper presents robust force tracking control of a flexible beam during a grasping operation using a piezoceramic actuator. Equations describing the motion of the gripper in conditions of contact and noncontact are derived based on the cantilever beam. In this study, contact force is regulated, in addition to the impact force generated at the instant of contact, based on variable structure model reference adaptive control theory using only force measurements. For the derivation of the control law, it is assumed that parameters of the beam and the stiffness of the object are unknown. Computer simulations show the effectiveness the controller. This work was presented, in part, at the Fourth International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–22, 1999     

Vibration control of a flexible aerial refuelling hose with input saturation

In this study, we consider a boundary control problem of a flexible aerial refuelling hose in the presence of input saturation. To provide an accurate and concise representation of the hose's behaviour, the flexible hose is modelled as a distributed parameter system described by partial differential equations (PDEs). By using the backstepping method, a boundary control scheme is proposed based on the original PDEs to regulate the hose's vibration. An auxiliary system based on a smooth hyperbolic function and a Nussbaum function is designed to handle the effect of the input saturation. Then based on Lyapunov's direct method, the state of the system is proven to converge to a small neighbourhood of zero by appropriately choosing design parameters. Finally, the results are illustrated using numerical simulations for control performance verification.