Active structural vibration control under limited outputs, nonlinearities and/or uncertainties
At LMSSC, Paris, February 7th 2019, 1 p.m.
Marcelo Areias Trindade
Professor, Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, Brazil
The presentation will focus on two different applications of active structural vibration control in which limited outputs, nonlinearities and/or uncertainties challenge the design for optimal performance. The first application consists on the active control of torsional vibrations in oil well drilling process, which requires opening a borehole in the rock formation as quickly and safely as possible. For that, an actuated rotary table provides torque to a rotating drill-bit through a very slender drillstring. The drill-bit is also subjected to a reaction torque induced by its interaction with the rock formation. Hence, the drillstring may be twisted several turns during drilling process which may cause failure in drill-pipes sections and connections, and, when untwisting, the drill-bit may present much higher angular velocities, leading to potential mechanical failures on the drill-bit. This behavior presents itself as periodic, stable, self-excited and low-frequency oscillations of drilling angular velocity. These may be reduced by using feedback of limited outputs, normally the rotary table angular velocity, combined to properly designed PI control parameters. However, the nonlinear behavior combined to an uncertain bit-rock interaction may undermine the predicted drilling performance. A methodology is presented for evaluating the drilling performance when subjected to uncertainties in the bit-rock interaction. This is done using a stochastic model for the bit-rock interaction model parameters. Using a Monte Carlo simulation, confidence intervals for the stability regions and control parameters are presented and allow one to search for more robust control parameters.
The second application consists on the active control of plate-type structures using output feedback of a limited number of sensors. It is well known that LQR-type full state feedback exhibits significant frequency margins and reduced sensitivity properties, but it requires availability of all state variables to be measured. This problem is not satisfactorily overcome by state observers, since they are sensitive to spillover and their more complex structure can entail time delay. Another alternative to solve this problem is to use only linear combinations of measured signals for feedback, a technique known as optimal static output feedback (OSOF). This method is studied considering additionally sensors locations as optimization variables. Necessary conditions of optimality are presented in order to highlight the dependence of the optimal solution on system initial conditions. A new approach to deal with this dependence, which is based on approaching the performances of OSOF and LQR for any initial condition, is developed and compared to the existing one. The method is tested on a simply supported plate with discrete sensors and on a clamped plate with piezoelectric patches. Results show that with a significantly reduced number of sensors, the OSOF controller has a performance equivalent to LQR. The control system deals well with major problems of non-collocated control, such as sensitivity to control parameters and spillover.