A biologically inspired controller for sound and vibration applications

A biologically Inspired control approach for reducing vibrations in and radiated sound power from distributed elastic systems has been experimentally verified for narrowband excitation. The control paradigm approximates natural biological systems for initiating movement, in that a low number of signals are sent from an advanced, centralized controller (analogous to the brain) and are then distributed by local rules and actions to multiple actuators (analogous to muscle fiber). The controller was applied to attenuate vibrations in a beam and radiated sound power from a plate. Experimental investigations of two different local learning rules were carried out including controller convergence considerations and a comparison with the standard MlMO Filtered-X LMS feedforward control approach. In general the results have demonstrated that the biological control approach has the potential to control multi-modal response in distributed elastic systems using an array of many actuators with a reduced order main controller. Performance was comparable with the Filtered-X LMS approach. Thus significant reductlons in control system computational complexity have been realized by this approach. J. Introduction Recent work has demonstrated the potentlal of active control of distributed elastic systems using multiple, independent actuators and sensors. In work concerned with the control of sound radiation from vibrating panels, the importance of number of channels of control and optimization of the transducer position and shape has been demonstrated1. However these investigations were carried out for a fixed frequency and it is apparent that for good control over a bandwidth of frequencies, the control actuators and sensors need to be adaptive in shape. At first sight this problem could be solved using an overall transducer broken up into many individual small elements each connected by an individual control channel. In this situation the control transducer would effectively reoptimize its configuration for different conditions by adaptively weighting each transducer segment. Meirovitch and orris^ have demonstrated the advantage of such an approach by considering fully distributed control in reducing control spillover. The disadvantage of this approach is that, for systems with a high modal density, 'Ph.D. Candidate, Dept. of Mechanical Engineering "Professor, Dept. of Mechanical Engineering, Associate Fellow. AIM. Copyright 63 American Institute of Aeronautics and the number of actuators and sensors required becomes extremely large. A high number of control channels has a number of problems mainly associated with memory requirements and computational time in the hardware systems used to implement the control. In additlon, colllnearity of transducer transfer functions causes stability problems in systems with a high number of transducers. A new approach of controlling distributed elastic systems is presented. The approach is inspired by the action of biological natural systems where a low number of main signals are transmitted from the brain to a large area of muscle tissue to activate many independent segments of muscle. The signals then stimulate local action which is governed by, for example, chemical interaction of locally connected nerves, etc., resulting in multiple subsequent signals for individual muscle cell elongation or contraction. Put simply, a signal is sent from a central complex processor (the brain) and then is broken into multiple signals by local simplified control rules (muscle cells, etc.13. This paper details an experimental implementation of such a process, which has been previously studied in a limited analytical investigation4. A distributed elastic system is harmonically excited and controlled by multiple control inputs. In the biologically inspired (BIO) control approach, one control input is chosen as the "master" and is under direction of the main, centralized advanced controller. The other "slave" inputs derive their control laws by localized, simple learning rules related to the behavior of their neighbor actuators and are independent of the main controller direct signal, as seen in Figure 1. In the following sections, the control algorithm is outlined for the "master" control input and the local learning approaches, the "phase variation" and "optimal distribution* methods. The experimental investigation is discussed including performance metrics, experimental Figure 1. Biological control approach Astronautics, Inc., 1994. All rights reserved. 474 control path. Also, note the addition of the slave control paths, H2 to Hp, along with gains 7.2 to yp, where P is the total number of control paths. In this case, the phase variation algorithm is defined as follows. The master control voltage is applied to the neighbor slave actuator (i.e., the actuator immediately alongside). The slave control voltage is varied in-phase (y =+I), out-of-phase (y=-1) or turned off (y=O) while the cost function, J, is observed for each change. The gain (y) that results In the lowest cost function Is kept and the process Is then applied to the next slave control path until all slave control paths are progressively tested. Note that the sequence of activating the slave paths can be varied. By this method, a distributed actuator with a generalized function that drives a response similar to the uncontrolled vibration distribution with low control spillover is constructed. Note that the previous process is suboptimal as are many biological systems. However, it is believed that good control performance will still be obtained. 3 ~ p t i m a i D l s t r ~ b m . . . The optimal distribution local learning rule was solved a priori and was developed from adaptive feedforward control theory. Essentially, the measured or calculated control path transfer functions between the actuators and sensors are used to calculate the theoretical optimal gains. These gains are then scaled relative to the master actuator which calibrates the slave gains with respect to the master actuator. The weights of the adaptive filter of the master channel can then be adapted to minimize the cost function, and simuRaneously the slave control signals will be derived by proportion. The Implementation of the optimal distribution into the control system is shown in Figure 4. The control signal fed to the master control input (w) is operated on by the optimal complex gains (y2..yp) and fed to the slave transfer functions (H2..Hp). Upon application of the optimal distribution to control of total beam out-of-plane vibrational energy density, an interesting phenomenon became apparent. As can be seen in Figure 5, the optimal distribution approximates the static moment distribution in a slmply supported beam when a point force is applied. This observation lead to the development of the moment distribution method, described below. Another Important observation was that the optimal distribution is independent of frequency. , . ent O~str~bution The optimal distribution was seen to approximate the static moment distribution in a simply supported beam when a point force was applied. Therefore, a local rule was developed based on the internal beam moment, which is zero at the boundary and linear to the maximum moment, which is at the position of the point force. The moment distribution was derived from the position of the control input relative to the point force, defined as: Figure 4. Optimal distribution control system schematic simply supported beam point force I piezoelectric I actuator