Optimum placement of actuators in structural and control design using Stackelberg games

Actuator placement has a significant impact on the dynamic response of actively controlled structures. Misplaced actuators and sensors often lead to controllability and observability problems, and the desired system performance may not be achieved with any choice of control law. This paper addresses the design of actively controlled structures wherein both the actuator placement and controller design aspects are addressed simultaneously. It is assumed that a hierarchical structure exists between the actuator placement and controller design objective functions with the actuator placement problem considered as being more important. The resulting multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the two levels (leader and follower). The optimization problem has mixed discrete-continuous variables with discrete variables corresponding to actuator placement and continuous variables associated with the controller design problem. The solution approach includes a blend of genetic algorithms and sequential quadratic programming techniques and is applied to the design of a flexible truss structure. The proposed approach successfully designed an optimum controller while minimizing the weight of the structure and simultaneously maximizing the energy dissipated by the controller to bring the structure to its equilibrium position when subjected to an external disturbance.