Experimental validation of a geometric method for the design of stable and broadband vibration controllers using a propeller blade test rig Ubaid Ubaid * , Steve Daley † , Simon Pope * , Ilias Zazas † * Automatic Control and Systems Engineering, University of Sheffield, S1 3JD, UK. † Institute of Sound and Vibration Research, University of Southampton, SO17 1BJ, UK. Abstract—A systematic geometric design methodology to gen- erate a stable controller for simultaneous local and remote atten- uation that was previously proposed is experimentally validated on a structure. The local control path transfer function for this experimental system is non-minimum phase due to which the original broadband controller design would yield an unstable controller. Here a modified procedure for systems with local non- minimum phase dynamics is used to generate a stable controller. According to this method, reduction in vibration at local and remote points on a structure can be parameterised in terms of the available design freedom and a controller is realised in terms of the optimal selection of this using the minimum phase counterpart of the local control path transfer function. The modified method results in a controller that is both stable and stabilizing and which achieves the desired vibration attenuation at the local and remote points on the structure. An experimental facility that replicates the vibration transmission through the shaft of a propeller blade rig system is used to demonstrate the method. Vibration for excitation near the first bending mode frequency of the resonating part of this structure is attenuated at the non-resonating part of the system without deteriorating vibration at the resonating end. I. I NTRODUCTION Active control for reduction of vibration at a specific point on a complex interconnected structure can potentially enhance vibration at other points on the structure [1]. A controller design technique to address the vibration attenuation problem at local and remote points on a structure simultaneously using only a single locally placed sensor actuator pair was presented for a discrete frequency excitation case in [2] and later extended for the broadband case [3]. For vibration attenuation over an arbitrary frequency band, controller implementation involves inversion of the local control path transfer function. When the local control path transfer function is non min- imum phase, then the controller itself would be unstable. This problem can be solved using a new design freedom [4] to parameterise reduction in vibration at local and remote points whereby the controller is implemented in terms of the minimum phase counterpart of the local control path transfer function. Additionally, to improve robustness to unmodelled high frequency dynamics, a filter is incorporated into the design freedom selection [5] such that the gain of the closed loop system rolls off at high frequency without deteriorating controller performance in the excitation frequency bandwidth. The aim of this paper is to present experimental verification of this design technique for attenuation of vibration at both local and remote points on a blade rig simultaneously. Trade-offs between stability robustness and disturbance attenuation are also highlighted in terms of the values of the design freedom parameter. II. EXPERIMENTAL SET- UP A schematic diagram of the blade rig is shown in figure 1. The primary excitation signal f p (t) is a common signal fed to the two smaller shakers attached at both ends of the bar which acts as the transient loading force due to rotation of the propeller blades. The vibration at the blade end of the shaft q p (t) is the summation of outputs measured by two accelerometers connected near each of the disturbance shakers. The control input f c (t) is applied to the control shaker attached at the other end of propeller shaft on the thrust block and a local accelerometer on the thrust block measures local vibration levels q c (t). Vibration is transmitted from the blade end along the shaft to the thrust block end and is particularly detrimental at the blade resonant frequency. Due to difficulties in measuring and actuating at the blade end for most applications, it is desired to control both blade vibration and its transmission using sensors and actuators placed at the thrust block only 1 . This blade system can be considered as a two input two output system with the transfer function matrix relating the disturbance and control inputs to the remote and local vibration outputs as  q c (jω) q p (jω)  =  g cc (jω) g cp (jω) g pc (jω) g pp (jω)  f c (jω) f p (jω)  (1) In the next section, a design freedom parameter is introduced which parameterizes reduction in vibration at the thrust block and blade end. A controller implemented in terms of the optimally selected values of this design freedom would achieve the targeted vibration reduction. III. GENERAL ALGORITHM The detailed synthesis of a stable controller using the geo- metric approach is given in [4], [5]. For the system described in (1), the aim is to design a feedback controller k(jω) using as feedback signal only from the thrust block to achieve vibration 1 Note that this general concept is the subject of several BAE Systems patents 369 UKACC International Conference on Control 2012 Cardiff, UK, 3-5 September 2012 978-1-4673-1558-6/12/$31.00 ©2012 IEEE