Determining the physical limits on semi-active control performance: A tutorial

Control forces in semi-active control systems are constrained by the dynamics of actuators that regulate energy transmission through variable damping and/or stiffness mechanisms. The potential benefit of developing and implementing new semi-active control devices and applications can be determined by optimizing the controlled performance subject to the constraints of the dynamics of the system being controlled (given by the state equations), the constraints associated with the dynamics of the semi-active device, and the expected external forcing. Performance optimization of semi-active control systems is a constrained two-point boundary value problem. This paper shows how this constrained problem can be transformed into an unconstrained problem and how to easily solve the related unconstrained problem with Matlab. The method is illustrated on the performance optimization of a simple semi-active tuned-mass-damper for a structure subjected to ground accelerations. Several possible extensions of this method and application are described in detail.