Biologically inspired approaches for reduced order control of distributed elastic systems.

Abstract

The control of distributed systems by multiple piezoelectric actuators has shown much promise. However for higher modal densities, many actuators are required and the order of the controller (i.e., number of channels) becomes large, leading to implementation problems and performance degradation. In this paper, a control approach, which was largely inspired by biological systems, is analytically investigated so as to reduce the order of the main controller. The inspiration for the system was derived from biological muscle control, where one main signal from the brain is sent to a large area of muscle tissue, but is processed locally by cell action into multiple subsequent signals for individual muscle cell elongation or contraction. In the present study, the system to be controlled consists of a simply supported beam excited by a harmonic point force disturbance. Control is attempted by multiple piezoelectric actuators attached to the beam surface. One actuator is chosen as the master actuator and is under direction of the main controller. The other (slave) actuators derive their control inputs by localized learning rules related to the behavior of their neighbor actuators. The master actuator uses linear quadratic optimal control theory while very simple local learning rules are employed to minimize beam vibrational energy density. The results presented demonstrate that the use of the multiple slave actuators in conjunction with the main channel of control significantly enhances control performance over the single actuator case, particularly for off resonance cases, by reducing control spillover. [Work supported by NASA Langley and ONR.]