Sliding mode and shaped input vibration control of flexible systems

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the vibration reduction problem is investigated for a flexible spacecraft during attitude maneuvering. A new control strategy is proposed, which integrates both the command input shaping and the sliding mode output feedback control (SMOFC) techniques. Specifically, the input shaper is designed for the reference model and implemented outside of the feedback loop in order to achieve the exact elimination of the residual vibration by modifying the existing command. The feedback controller, on the other hand, is designed based on the SMOFC such that the closed-loop system behaves like the reference model with input shaper, where the residual vibrations are eliminated in the presence of parametric uncertainties and external disturbances. An attractive feature of this SMOFC algorithm is that the parametric uncertainties or external disturbances of the system do not need to satisfy the so-called matching conditions or invariance conditions provided that certain bounds are known. In addition, a smoothed hyperbolic tangent function is introduced to eliminate the chattering phenomenon. Compared with the conventional methods, the proposed scheme guarantees not only the stability of the closed-loop system, but also the good performance as well as the robustness. Simulation results for the spacecraft model show that the precise attitudes control and vibration suppression are successfully achieved

Numerical Aspects and Performances of Trajectory Planning Methods of Flexible Axes

Adequate Path Planning design is an important stage for controlling flexible axes because it may allow to cancel vibrations induced by oscillating modes. Among bang-bang profiles which are linked to optimal control, jerk assignment (acceleration derivative) and input shapers have been investigated. Theoretical results show the performance and robustness with respect to natural frequency mismatch. Practical validations on a real robot arm show the relevance of the jerk algorithm which is more robust with the same productivity performances as input shaping techniques

Input shaping-based control schemes for a three dimensional gantry crane

The motion induced sway of oscillatory systems such as gantry cranes may decrease the efficiency of production lines. In this thesis, modelling and development of input shaping-based control schemes for a three dimensional (3D) lab-scaled gantry crane are proposed. Several input shaping schemes are investigated in open and closed-loop systems. The controller performances are investigated in terms of trolley position and sway responses of the 3D crane. Firstly, a new distributed Delay Zero Vibration (DZV) shaper is implemented and compared with Zero Vibration (ZV) shaper and Zero Vibration Derivative (ZVD) shaper. Simulation and experimental results show that all the shapers are able to reduce payload sway significantly while maintaining desired position response specifications. Robustness tests with ±20% error in natural frequency show that DZV shaper exhibits asymmetric robustness behaviour as compared to ZV and ZVD shapers. Secondly, as analytical technique could only provide good performance for linear systems, meta-heuristic based input shaper is proposed to reduce sway of a gantry crane which is a nonlinear system. The results show that designing meta-heuristic-based input shapers provides 30% to 50% improvement as compared to the analytical-based shapers. Subsequently, a particle swarm optimization based optimal performance control scheme is developed in closed-loop system. Simulation and experimental results demonstrate that the controller gives zero overshoot with 60% and 20% improvements in settling time and integrated absolute error value of position response respectively, as compared to a specific designed PID-PID anti swing controller for the lab-scaled gantry crane. It is found that crane control with changing cable length is still a problem to be solved. An adaptive input shaping control scheme that can adapt to variation of cable’s length is developed. Simulation with real crane dimensions and experimental results verify that the controller provides 50% reduction in payload sway for different operational commands with hoisting as compared to the average travel length approach

Design and optimization of input shapers for liquid slosh suppression

The need for fast maneuvering and accurate positioning of flexible structures poses a control challenge. The flexibility inherent in these lightly damped systems creates large residual vibrations in response to fast disturbances. Several control approaches have been proposed to tackle this class of problems, of which the input shaping technique seems quite appealing. While input shaping has been widely investigated to attenuate residual vibrations in flexible structures, less attention was granted to expand its viability in further applications. It is therefore the aim of this work to develop a methodology for applying input shaping techniques to suppress sloshing effects in open moving containers to facilitate safe and fast point-to-point movements. The liquid behavior is modeled using finite element analysis. The input shaper parameters are optimized to find the commands that would result in minimum residual vibration. Other objectives, such as improved robustness and motion constraints such as deflection limiting are also included in the optimization scheme. Numerical results are verified on an experimental setup consisting of a small motor-driven water tank that is precisely guided to undergo rectilinear motion, while measuring both the tank motion and free surface displacement of the water. The results obtained suggest that input shaping is an effective method for suppressing residual liquid vibrations

Model reference control for ultra-high precision positioning systems

Due to the increasing demands of high-density semiconductors, molecular biology, optoelectronics, and MEMS/NEMS in the past decades, control of ultra-high precision positioning using piezoelectricity has become an important area because of its high displacement resolution, wide bandwidth, low power consumption, and potential low cost. However, the relatively small displacement range limits its application. This work proposed a practical ultra-high precision piezoelectric positioning system with a complementary high displacement range actuation technology. Solenoids are low cost, high speed electromagnetic actuators which are commonly used in on-off mode only because of the inherent high nonlinear force-stroke characteristics and unipolar forces (push/pull) generated by the magnetic fields. In this work, an integrated positioning system based on a monolithic piezoelectric positioner and a set of push-pull dual solenoid actuators is designed for high speed and high precision positioning applications. The overall resolution can be sub-nanometer while the moving range is in millimeters, a three order of magnitude increase from using piezoelectric positioner alone. The dynamic models of the dual solenoid actuator and piezoelectric nanopositioner are derived. The main challenge of designing such positioning systems is to maintain the accuracy and stability in the presence of un-modeled dynamics, plant variations, and parasitic nonlinearities, specifically in this work, the friction and forcestroke nonlinearities of the dual solenoid actuator, and the friction, hysteresis and coupling effects of piezoelectric actuator, which are impossible to be modeled accurately and even time-varying. A model reference design approach is presented to attenuate linear as well as nonlinear uncertainties, with a fixed order controller augmenting a reference model that embeds the nominal dynamics of the plant. To improve transient characteristics, a Variable Model Reference Zero Vibration (VMRZV) control is also proposed to stabilize the system and attenuate the adverse effect of parasitic nonlinearities of micro-/nano- positioning actuators and command-induced vibrations. The speed of the ultra-high precision system with VMRZV control can also be quantitatively adjusted by systematically varying the reference model. This novel control method improves the robustness and performance significantly. Preliminary experimental data on dual solenoid system confirm the feasibility of the proposed method

An adaptive neuro-fuzzy controller for vibration suppression of a flexible structure in aerial refueling

Air-to-air refueling (AAR) has been commonly used in military jet applications. Recently, civilian applications of AAR have been garnering increased attention due to the high cost of air travel, which is largely dictated by the cost of jet fuel. There are two types of AAR approaches: probe-drogue and flying boom systems. This work explores the probe-drogue AAR system in commercial applications. Typical AAR applications deploy a drogue connected to a long flexible hose behind a moving aircraft tanker. The drogue is connected to a probe in a receiver aircraft before initiating fuel transfer and is retracted back into the tanker when the fuel transfer is completed. In order to ensure a safe and efficient refueling operation sophisticated systems need to be developed to accommodate the turbulences encountered, particularly in respect to vibration reduction of the flexible hose and drogue. The objective of this work is to develop a probe-drogue system for helicopter AAR applications. The first project is to make a preliminary design of a new AAR system for helicopter refuelling from a modified AT-802 tanker aircraft. [...