Active Control of Vibration Modes of a Wing Box by Piezoelectric Stack Actuators

Abstract

The paper presents a numerical and experimental study of active control of the coupled bendingtorsion vibration modes of a typical aircraft wing box structure with a tip store, using piezoelectric ceramic stack actuators. Efforts are driven toward design of a control law and its implementation using a suitable data acquisition hardware and software, to determine the efficacy of stack actuators for such control and understand modeling related issues. The design and fabrication of the scaled wing box model, reported in an earlier paper, was such that the first three natural frequencies of an actual wing box and the corresponding mode shapes were replicated closely in the model. In the finite element analysis of the structure, the piezoelectric stack is modeled as a beam element and a thermal analogy concept has been used to simulate the electro-mechanical coupling in the stack actuator. The closed loop model is formulated in state space using experimentally validated modal model for the system characteristics as well as the modal generalized piezoelectric actuation forces. The closed loop implementation is aimed at achieving maximum damping of the three modes of interest. Accelerometers are used for response sensing. To begin with, feedback is taken from one sensor (accelerometer) and only one stack is used for control action. First, simulations and experiments are done using negative velocity feedback for controlling vibration of the structure under harmonic loading. This method results in significant increase in damping of the structure for excitation of the first three modes individually. In some cases, the amplitude of closed loop vibration decreased to 1/5th the value of open loop vibration. However, both, the simulation and experiments, show a significant control spillover to the other two modes, in each case. To avoid spillover, a new method called ‘three gain SISO velocity feedback system’ is designed, wherein, the response signal (obtained from the accelerometer) is split into three components using band-pass filters. Each of these components represent contribution from one of the three modes. These split signals are multiplied by separate gains and combined to form the final control signal. Thus the control spillover problem is partially solved. However, the system becomes unstable much before the complete control power of the stack can be used thereby suggesting that the control method is sub-optimal. The Linear Quadratic Regulator (LQR) method is also tested. A simple choice of coefficients of the Q and R matrices leads to a satisfactory result for vibration control for an impulse input. Simulation and subsequent experiments confirmed that the LQR method can be used to control impulse disturbance effectively. Further studies explore the idea of “minimization of total (kinetic and strain) energy of the structure to arrive at an appropriate Q matrix. The strategy is to establish a suitable weighting configuration for the various elements of the Q matrix depending upon the sensor-actuator combination being used for closed loop control and to validate it using analytical tools like Bode plots, root locus, simulations with SIMULINK and experimental studies. The closed loop damping so obtained shows a substantial improvement over the other techniques studied.