P. Scott Harvey

Optimal performance of constrained control systems

This paper presents a method to compute optimal open-loop trajectories for systems subject to state and control inequality constraints in which the cost function is quadratic and the state dynamics are linear. For the case in which inequality constraints are decentralized with respect to the controls, optimal Lagrange multipliers enforcing the inequality constraints may be found at any time through Pontryagin’s minimum principle. In so doing, the set of differential algebraic Euler–Lagrange equations is transformed into a nonlinear two-point boundary-value problem for states and costates whose solution meets the necessary conditions for optimality. The optimal performance of inequality constrained control systems is calculable, allowing for comparison to previous, sub-optimal solutions. The method is applied to the control of damping forces in a vibration isolation system subjected to constraints imposed by the physical implementation of a particular controllable damper. An outcome of this study is the best performance achievable given a particular objective, isolation system, and semi-active damper constraints.

Experimental Evaluation of Multi-functional Nonlinear Floor Isolation Systems

Acceleration-sensitive equipment housed inside of buildings is susceptible to damage from strong floor motions of the primary structure produced by earthquakes. Floor isolation systems (FISs) represent an effective strategy to protect such equipment from these motions by decoupling the equipment from the primary structure. However, even the most effective isolation systems are incapable of protecting equipment from building collapse in the event of strong ground shaking. This study experimentally explores the use of a novel multi-functional FIS capable of mitigating both equipment accelerations and facility drifts by passively adapting to achieve desired building-system performance. For low intensity disturbances, the system functions like a traditional isolation system, but for high intensity events, impacts in the isolation system act to increase the coupling between the primary structure and the FIS, pumping energy like a vibro-impact absorber. A scale experimental model, consisting of a three-story frame and an isolated mass, is used to demonstrate and evaluate the design methodology via shake table tests. The dynamic properties of the experimental model are identified, and the isolator’s displacement capacity and the disturbance frequency and amplitude provide the parametric variation. The performance of the multi-functional FIS was established and is described in this study.