Maximal Modal Force Rule for Optimal Placement of Point Piezoelectric Actuators for Plates

Optimal placement of actuators on intelligent structures is an important part of intelligent structure designs. The optimal collocation of actuators includes placement collocation and number collocation. It decides stability, controllability and control efficiency of structural control systems. With the development of control technology, the optimal collocation of actuators in structures is more and more important. Although optimal collocation of actuators can be determined by experience in some cases, experience is useless for complicated structures. So optimal collocation of actuators must be realized by optimal theory. Based on modal control theory, the Maximal Modal Force Rule is put forward for intelligent flexible plates bonded point piezoelectric actuators on their surface in this paper. The rule points out that point piezoelectric actuators should be bonded on the places of maximal modal strains of every order mode to produce maximal modal control forces. The formulae for independent modal space control and coupling modal space control are derived. The results of computer emulating of a plate show that the rule is right and effective.