Vibration Annihilation

                A Closed Loop Vibration Control Design Project

Introduction:

Sikorsky Aircraft, headquartered in Stratford, CT, is a leading manufacturer of rotorcraft, namely helicopters. Research is an integral part of the company's continuing success. Sikorsky Aircraft has assigned Pennsylvania State University's Vibration Annihilation team with the task of designing a closed loop vibration control to diminish the undesirable vibrations prevalent in a helicopter's tail boom. Mechanical vibrations have always been a problematic area. Attempts have been made to counteract these excessive and dangerous vibrations.  These tail boom vibrations are caused by turbulent air flowing over the fuselage. These vibrations can affect flight controls and damage several aircraft components. In past semesters senior design groups have tackled this problem. The Fall 2003 team constructed a damped passive vibration absorber and during the following semester the Spring 2004 team expanded upon the problem by designing and testing an open loop vibration control device. It was shown that such a device greatly diminishes resonant vibrations. It is now the goal of Vibration Annihilation to bring the project full circle through the design and implementation of a closed loop vibration control device. Throughout the Fall of 2004 an analysis will be made, prototypes constructed, and designs tested which will address the problem proposed by Sikorsky Aircraft.

Figure 1: 1/3 Scale Mockup of Helicopter Tail boom

Evolution of Design:

The purpose of our senior project is to close the loop on the active vibration absorber. It would be redundant to start from scratch and design our own absorber model, thus our group intends to expand upon the work completed by the Spring 2004 group. Past results had to be reconfirmed before any work could proceed. The analysis of our project was completed by the following different methods:  Simulink testing conducted with varying parameters using Dr. Szefi's code and through laboratory testing using the equipment made available by CSA Engineering and  Dr. Heverly. Throughout the fall semester we used these methods to aid us in our project design. By December 8th, it has been our primary objective to autonomously reduce vibrations in the helicopter tail boom.

LQR Controller:

Our group has focused on two main candidate designs to accomplish our objective. The first control option considered was the Linear Quadratic Regulator (LQR), which is a modern or optimal control technique that utilizes an objective function to optimize a system based on variables that are chosen by the control designer. In this way, data can be directly recorded from the tail boom and input in real time into  MATLAB's LQR algorithm to directly produce an optimal forcing scheme which cancels out the observed vibrations, thus closing the loop. Before we could go forward with this control scheme, a very accurate dynamic system model had to be constructed due to the nature of the LQR. Experimental data was obtained in the laboratory and it was this data which had to be replicated using MATLAB and the model. The first model was a simple rigid beam connected to two different masses as seen in Figure 2. It was found that the model was not adequate enough in modeling the real system (Figure 3).

Figure 2: Modified Tail Boom Model with Offset Actuator.

Figure 3: .  Normalized Acceleration vs. Frequency

After we found that the simple bar element model was not good enough, a FEM (Figure 4) was derived. Using the FEM in MATLAB, a much better match was produced as seen in Figure 5. Since a new dynamic model was derived and found to match up well with the laboratory data, an attempt to implement the LQR was attempted. However, now since a finite element model was being used, the simulink algorithm greatly increased in complexity. This added complexity pushed us towards another method of control.

Figure 4: Finite Element Model

Figure 5: .  Normalized Acceleration vs. Frequency

PD Controller:

The second control algorithm option we looked at was a classical control method known as a proportional derivative (PD) controller. As the output of the tail boom is recorded by the accelerometer, the signal is compared to the desired state (zero velocity) and an error is determined.  It is then processed through the PD controller (Figure 6), where gains can be continually adjusted, resulting in an overall dampening of the tail boom excitation. This method of controlling the system is easier to implement and eventually proved itself in the laboratory.

Figure 6: Simulink schematic of PD controller setup.

Results:

Since the beginning of the semester a great majority of our time and effort has been devoted towards researching viable control options and the running of Simulink simulations of those chosen control designs. If good results could not be produced virtually, the chances of the controller working in the laboratory environment were slim. In the last weeks of November enough simulation work was finalized to warrant a move to the laboratory for experimentation. As expected, a good deal of time was devoted towards honing in on the correct gains.

The project’s goal to decrease the amplitudes of vibrations at the tail boom’s natural frequencies was met, lowering the amplitudes by between thirty and fifty percent.  The response was automatically reduced by the PD controller, eliminating the need for manual tuning, ergo closing the control loop. As seen below, the proportional derivative controller produced a reduction in maximum vibration amplitude in the system compared to no control.  Although the results are not as good as that seen by the Spring 2004 group, it is a closed-loop system that controls the vibrations over a large bandwidth without any human interaction.

Figure 7:  Normalized Acceleration vs. Frequency

As research continues (i.e. Senior Design Phase 4) into controlling the vibration of the helicopter tail boom, improvements could be made to the PD controller to decrease the vibration amplitude.  Although we did not pursue the LQR controller after the model became too complex, we believe that it still has many advantages over the PD controller if it is implemented correctly.  Perhaps if more time was available a more robust system of controlling the tail boom could be devised, such as an absorber that can handle multiple frequencies at once.  As of now we have implemented a system of controlling excitations caused by the simulated white noise. In the end, even though the reductions were not as great as we hoped for, we consider this senior design project to be a success.

We would like to thank the following people for aiding our group throughout the semester:

Bill Welsh, Dr. Ed Smith, Dr. Szefi, Mike Evert & CSA Engineering, Mike Philen, Dr. Eric Mockensturm, Dr. Kulakowski                           

Team Members:

Ian Dux ........................ Chief Engineer (ijd102@psu.edu)

Jeremy Kushner ......... Records (jak407@psu.edu)

Joe Salvey .................  Secretary (jks170@psu.edu)

Andrew Tokarczyk..  Communications (ajt167@psu.edu)

Adam Yoder .............. Web Design  (asy110@psu.edu)