The objective of this study is to demonstrate that sliding mode observers can eliminate observation spillover in the vibration control of flexible structures. It is common to build a state feedback controller and a state estimator based on the mathematical model of the system with a finite number of vibration modes, but this may cause control and observation spillover due to the residual (uncontrolled) modes. This paper deals with the elimination of observation spillover using a sliding mode observer. The performance of a sliding mode observer is compared with that of a conventional Kalman filter to demonstrate robustness and disturbance decoupling characteristics. Simulation and experimental results using the sliding mode observer are presented for active vibration control of a cantilever beam.

Reduction of Observation Spillover in Vibration Suppression Using a Sliding Mode Observer

A method of sliding mode control (SMC) is proposed for the control of flexible, nonlinear, and structural systems. The method departs from standard sliding mode control by dispensing with generalized accelerations during the control law design. Global, asymptotic stability of rigid body motion is maintained if knowledge on the bounds of the neglected terms exists. Furthermore, this method provides damping for the measured flexible body modes. This paper investigates an augmented SMC technique for slewing flexible manipulators. A conventional sliding surface uses a first order system including a combination of error and error rate terms. The augmented sliding surface includes an enhanced term that helps to reject flexible degrees-of-freedom. The algorithms are theoretically developed and experimentally tested on a slewing single flexible link robot. The test apparatus is instrumented with a strain gauge at the root and an accelerometer attached at the tip. A DC motor and encoder are used to servo the link from an initial position to a final position. A standard cubic polynomial is employed to generate the reference trajectories. The augmented SMC algorithm showed improved performance by reducing the flexible link tip oscillations.

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Augmented Sliding Mode Control for Flexible Link Manipulators

A new optimal sliding mode (OSM) controller is developed for a linear stochastic system and applied to the Middeck Active Control Experiment (MACE) which represents the control structure interaction problem for a precision spacecraft. The OSM controller minimizes the expected value of a quadratic objective function consisting of only states with the constraints that estimated states always remain on the intersection of sliding hyperplanes This controller is designed for two subsets of MACE problems: a single input, single output gimbal inertial pointing problem and a three input, three output torque wheel attitude control problem. Using numerical simulations, performance of the OSM controller is compared to that of the classical LQG controller. The OSM controllers are digitally implemented on the Development Model of MACE. The experimental results are shown to be in good agreement with theoretical results.

Optimal sliding-mode control of a flexible spacecraft under stochastic disturbances

A robust nonlinear observer, utilizing the sliding mode concept, is developed for the dynamic positioning of ships. The observer provides the estimates of linear velocities of the ship and bias from the slowly varying environmental loads. It also filters out wave frequency motion to avoid wear of actuators and excessive fuel consumption. Especially, the observer structure with a saturation function makes the proposed observer robust against neglected nonlinearties, disturbances and uncertainties. A direct adaptive neural network controller is developed for a model of an underwater vehicle. Radial basis neural network and multilayer neural network are used in the closed-loop to approximate the nonlinear vehicle dynamics. No prior off-line training phase and no explicit knowledge of the structure of the plant are required, and this scheme exploits the advantages of both neural network control and adaptive control. A control law and a stable on-line adaptive law are derived using the Lyapunov theory, and the convergence of the tracking error to zero and the boundedness of signals are guaranteed. Comparison of the results with different neural network architectures is made, and performance of the controller is demonstrated by computer simulations. The sliding mode observer is used to eliminate observation spillovers in the vibration control of flexible structures. It is common to build a state feedback controller and a state estimator based on the mathematical model of the system with a finite number of vibration modes, but this may cause control and observation spillover due to the residual (uncontrolled) modes. The performance of a sliding mode observer is compared with that of a conventional Kalman filter in order to demonstrate robustness and disturbance decoupling characteristics. Simulation and experimental results using the sliding mode observer are presented for the active vibration control of a cantilever beam using smart materials. Acknowledgments It is my great pleasure to thank the many people who enabled me to perform this work. First, I am extremetly grateful to my advisor, Professor Daniel J. Inman, for his outstanding guidance, support and patience throughout the course of this research. His enthusiasm, dedication and the dazzling sense of humor has been invaluable source of inspiration and motivation for me during the last five years. His support made my stay at VT a very rich experience. I also would like to thank my committe member, Prof. for all the knowledge they shared with me through coursework, evaluation steps and discussions. I also would …

Nonlinear Control and Robust Observer Design for Marine Vehicles

An innovative magnetically levitated system design is presented in this paper. The proof mass, used as the seismic detection components for gyroscopes, is levitated by the presented micro-coil actuator so that the concerns that mechanical fatigue, asymmetry and mis-alignments, which are inevitably present in the traditional mechanical springs design, can be ruled out. In addition, the limited range of dual-axis motion of the proof mass is completely relaxed and therefore the resolution and sensitivity of the gyroscope can be greatly upgraded. That is, the proof mass can be much at higher frequencies and the stroke of the sense-mode motion can be more enlarged, in comparison with the conventional design (i.e., mechanical springs). In addition, self-sensing technique is employed to replace the gap sensors which provide the feedback signal for position regulation of the proof mass, for the sake of cost-down for mass production. A sliding mode control strategy is included to account for the effects of nonlinearity of the maglev system dynamics and hysteresis uncertainty of the micro-coil actuator. The proposed controller is verified by computer simulations and experiments to illustrate its superior capability to stabilize the inherently unstable maglev system and ensure fast response for the lateral position regulation of the seismic proof mass.

Magnetic actuator design for single-axis micro-gyroscopes

The sliding mode control algorithm is developed for the coupled modal space control of a flexible structure when the bounds on the system parameters' errors are known. An explicit method to construct the desired sliding hyperplanes for the coupled modal sliding mode control is formulated. A boundary layer is used around each sliding hyperplane to eliminate the chattering phenomenon. Three types of steady-state solutions for the closed-loop system inside the boundary layers are found: the zero solution (origin of the state space), the constant nonzero solution, and the limit cycle. The amplitudes, phase angles, and the frequency of the limit cycle have been estimated by the describing function approach. The modal displacements corresponding to the constant nonzero solution have been obtained analytically. The stability of the zero solution has been examined by the linearized system analysis. Using a flexible tetrahedral truss structure, numerical examples are presented to verify the theoretical analyses.

C. K. Kao

Papers

Coupled modal sliding mode control of vibration in flexible structures

Coupled modal sliding mode control of vibration in flexible structures