Active control design for acoustic radiation using mixed-norm optimization

Abstract

The interpretation of system norms is important in the design of optimal control laws. The infinity-norm allows for stability analysis even when the design model contains errors or uncertainties. H∞ robust control design makes use of this property. In many physical situations the two-norm can be related to system energy and is a more meaningful measure of performance. This is the basis of control designs such as LQR/LQG. Traditionally, optimal control laws are designed with respect to one of these norms. New methods in solving linear matrix inequalities (LMIs), however, make it possible to directly solve optimization problems whose cost functions involve a mixture of norms. In this work linear matrix inequalities are used to design controllers which suppress acoustic radiation from a driven plate. Specifically, a rectangular aluminum plate is instrumented with four piezoelectric sensoriactuators which provide both sensing and actuation. A laser Doppler velocimeter is used to measure velocity of the plate over a grid of points. Radiation filters predict far field acoustic power from the velocity measurements and are used for the design of optimal control laws. Both experimental and simulated results are presented which show the benefit of mixed norm control design made possible using LMIs.

Robust active sound radiation control of a piezo-laminated composite circular plate of arbitrary thickness based on the exact 3D elasticity model

“…Subsequent use of expansions (3b), (17), and (19), in the surface conditions (18), after using the classical orthogonality relation in cylindrical coordinates, and with some tedious manipulations, leads to…”

“…Here, it should be noted that, as H 2 and H 1 control methodologies are standard tools in the control community, there is not a vital need for detailed re-description of this mathematically intensive subject, where the interested reader is referred to the literatures. [13][14][15][16][17][18][19][20][21][77][78][79][80][81][82][83] Figure 2(a) shows the standard configuration of the multi-objective H 2 =H 1 robust output feedback controller where P s ð Þ is the generalized plant comprising the arrangement of all dynamics required for design and synthesis of the generalized controller K s ð Þ based on the measurable error signal e, while w denotes the exogenous input vector to the generalized plant (e.g. reference signal, r, disturbances, d, noise, n, etc., see Figure 2(b)).…”

“…It is also of applied benefit for structural acoustics engineers interested in improvement of low-frequency sound radiation characteristics of thick piezo-composite smart circular plates in the face of uncertainties. 15,19,[41][42] These elements are of realistic concern in advancement of intelligent micro-electromechanical systems, 43,44 for which precise movement control is essential. It can readily be combined with the classical passive control methods 1,2,45,46 and/or expediently be augmented with multiple pairs of electroded piezoelectric actuator/sensor segments in a multi-input multi-output (MIMO) active control framework [47][48][49] to effectively deal with the medium-and high-frequency acoustic radiation problems.…”

“…16,17 As a further step, the H 2 and H 1 control objectives can be unified in a single (mixed) time-frequency domain design framework, in order to simultaneously optimize system performance and enforce robustness constraints. 18,19 Synthesis of such multi-objective controllers can expediently be achieved by employment of the linear matrix inequalities (LMIs) 18,20 that provide algebraic representations of various control specifications and allow computationally efficient and systematic design of robust controllers by reducing the controller design into a standard convex optimization problem. Furthermore, application of extra robust regional pole placement constraints can cause ample satisfaction of both the stability robustness and the temporal performance requirements.…”