Hard Constrained LPV Virtual Control with Application to Flutter Suppression of a Smart Airfoil

Hard constrained control problems are popular in practical applications due to physical and power limitations. For instance, the displacement of a linear actuator is finite. A lot of studies have been conducted in this area to deal with certain hard constrained control problems and some are computationally expensive. This paper introduces a novel LPV (linear parameter-varying) virtual control scheme to deal with a class of hard constrained control problems with an application to flutter suppression of a smart airfoil, leading to a state-feedback LPV gain scheduling controller with the guaranteed $${{\cal H}_\infty}$$ performance. The basic idea of LPV virtual control is to add virtual components (such as variable stiffness springs and dampers) near to the hard constraints to prevent actuators from reaching their limits. The LPV virtual controller will be designed based on the model with virtual components and in the implementation stage, these virtual dynamics becomes part of the gain-scheduling controller. The concept is validated by a smart airfoil example. In the smart airfoil example, the virtual varying springs and dampers are placed at both ends of groove to constrain the mass movement. Comparisons studies with conventional LPV hard constrained control, nonlinear control, and regular LPV control without considering hard constraints are conducted to assess the performance of the proposed method and showed advantage over the existing methods. For instance, the control mass $${{\cal L}_2}$$ norm is reduced by 77.5% over the nonlinear control and 35% over the conventional LPV control.