Suppressing Aeroelastic Vibrations via Stability Region Maximization and Numerical Continuation Techniques Max Demenkov * Mikhail Goman ** * Faculty of Computing Sciences and Engineering, De Montfort University, Queens bld. 2.14, The Gateway, Leicester LE1 9BH, UK (e-mail: demenkov@dmu.ac.uk) ** Faculty of Computing Sciences and Engineering, De Montfort University, Gateway bld. 6.56, The Gateway, Leicester LE1 9BH, UK (e-mail: mgoman@dmu.ac.uk) Abstract: An active flutter suppression using linear sub-optimal control scheme is investigated for a 2dof airfoil system with nonlinear torsional stiffness and limited deflection amplitude of its single actuator. The suppression of limit cycle oscillations in the nonlinear closed-loop system is achieved through maximization of the stability region of its linearized system. The critical value of the control input amplitude is determined via numerical continuation of the closed-loop limit cycle. At this value, the cycle experiences saddle-node bifurcation and disappears, satisfying the necessary condition for the global stability in the closed-loop system. Keywords: Active vibration control, nonlinear systems, control input constraints, stability regions, bifurcation analysis 1. INTRODUCTION Active flutter suppression approach has been studied in many papers to prevent catastrophic structural failures due to excessive vibrations in aeroelastic systems. It is expected that a designed feedback stabilizes an unstable aeroelastic system with nonlinear torsional and/or bending stiffness around nominal zero-pitch, zero-plunge equilib- rium and delays the onset of the limit cycle oscillations (LCO). The limited control power of aerodynamic surfaces can be, however, insufficient to suppress these oscillations globally. It is well known that the origin of a closed-loop nonlinear system can be asymptotically stable only in some bounded region in the state-space (called stability region, or region of attraction ). Nonlinear systems may posses many differ- ent attractors (such as stable limit cycles) with their own stability regions. The closed-loop system performance can degrade, for example, because of the small stability region of the origin in the presence of LCO. In this case, it is natural to create a feedback that maximizes the stability region of the origin as much as possible in order to delay flutter onset in an aeroelastic system. This approach to the flutter suppression problem was considered in Goman and Demenkov [2004] and Applebaum and Ben-Asher [2007]. In these two papers, aeroelastic systems were represented by linear systems with constrained control inputs and the influence of nonlinear stiffness on the closed-loop system performance was not studied. Due to the nonlinear nature of aeroelastic systems, it is theoretically possible that with maximization of the closed-loop stability region, the closed-loop limit cycle will Fig. 1. Stability region maximization for the limit cycle elimination. disappear. In this case, its stability region will merge with the region of attraction of the origin, resulting in globally stable closed-loop system (see Fig. 1). In this paper we investigate this scenario using a math- ematical model of the aeroelastic apparatus developed in Texas A&M University. In (Ko et al. [1997, 1998], Kurdila et al. [2001], Platanitis and Strganac [2004]) (see also references therein) different approaches were used for con- trolling the apparatus with amplitude constrained trailing edge actuator. In Platanitis and Strganac [2004] the lead-