Experimental evaluation of evolutionary predictive input shaping applied to a flexible structure

Abstract

This work reports the results of an experimental study, which has been carried out to evaluate the applicability of nonlinear Model Predictive Control for the reduction of vibrations in flexible structures. Reference was made to a clamped flexible beam on the tip of which a controlled pendulum is attached. The control strategy consists of two stages: in the first one a PD controller is employed to ensure the accurate tracking of the pendulum position with respect to a reference shaped signal; in the second one the shaped trajectory is generated by a model based predictive controller. For the online nonlinear constrained optimization a new Evolutionary Algorithm is proposed. The results of some experiments are reported, comparing the performance of a pure feedforward scheme with others that employ either a continuous or an intermittent output feedback strategy. I. INTRODUCITONFor the class of mechanical systems like disk drivers, flexible robots and servo-controlled positioning systems, the unwanted motion induced vibrations could cause excessive settling time and poor tracking accuracy. The design of effective control systems dedicated to vibration reduction has always been an active field of research and many feedback and feedforward control schemes have been proposed. Recognizing that in many applications a great part of the vibration energy is not produced by unexpected disturbances, but rather, directly generated by actuators induced motion [l], many advantages can be obtained by a feedforward control scheme that conveniently shapes the input command. The advantages of feedforward schemes lie on the intrinsic predictive action performed by the controller; in this way, the effects of undesired actions are removed before entering in the control loop; this aspect is very important in the field of vibration control. Model based feedforward controllers can be designed to implement an inverse model based control scheme with the aim of canceling the known dynamics of the open or closed loop system[2]; in this way, in absence of unmodeled dynamics and disturbances, a perfect tracking without residual vibrations of any trajectory could be obtained. The drawback of this approach is the difficulty of designing general model inversion algorithms and the lack of robustness. The problem of generating robust input trajectories, which guarantee good performance despite of uncertainties in the natural frequencies and damping ratios for flexible linear systems, can be overcome using the impulse shaping approach introduced 0-78034736-7/01/$10.00 0 2001 IEEE by Singer [3], where the command input, convolved with a convenient sequence of impulses, causes the system to move but not to excite the elastic modes of vibration. The impulse shaping approach has been recently extended to linear time varying systems by Cho et al. 141.Another kind of predictive action can be obtained by applying Model Predictive Control (MPC) techniques [5]. MPC has often been applied in process control, where a model is used to predict the future behavior...