Scalable distributed optimal control of vibrating modular structures

Abstract

Summary A scalable optimal control method for structural vibration mitigation is studied. The method relies on a structure's partitioning that leads to a set of dynamically interconnected subsystems. Each subsystem is operated with an individual subcontroller that collects the local state information and collaborates with the neighboring subcontrollers to estimate a short time prediction of the interconnecting forces defining the subsystem's boundary conditions. Using the extended model that represents the subsystem's dynamics together with the evolution of its boundary conditions, each subcontroller computes the control decision based on the solution to a finite‐time horizon optimal control problem. In order to cope with the changes in the boundary conditions, the optimal solution is computed repetitively according to the receding horizon scheme. The method is validated numerically for a cantilever structure equipped with actively controlled electromagnetic actuators and subjected to a variety of initial condition scenarios. The performance of the designed controller is tested by comparisons to the centralized and isolated decentralized controllers. The introduced system partitioning and distributed controller allow performing parallel computing which makes the method fully scalable and applicable to large‐scale structures. The computational complexity of the designed distributed control is studied for different settings in the modeling of the subsystem's boundary conditions.

Decentralized semi‐active structural vibration control based on optimal system modelling

“…The PAR's low performance in mitigating the higher modes is a consequence of the lack of coordination between the subcontrollers. A similar observation has already been made for a decentralized active controller for a cantilever beam structure in Pisarski et al 14 It has been validated that the isolated subcontrollers that operate on a local state‐feedback law can be successfully implemented for mitigating the first vibration mode, where the simplest yet effective policy is to generate for each actuator the forces in the directions that are opposite to the local deflections and/or velocities. This uncoordinated policy applied to a larger structure subjected to higher vibration modes may lead to antagonistic operations of the actuators, and as a result, an extended duration of large vibration amplitudes.…”

“…However, for the construction of the decentralized control functions, they relied on the instantaneous optimal control scheme 13 . The concept of the isolated subsystems was also employed in Pisarski et al 14 for an active cantilever structure, where the authors suggested using an autoregressive model for the estimation of the coupling forces. The control functions were designed based on repetitive solution to the linear‐quadratic regulator problem.…”

Semi‐active modal control of structures with lockable joints: general methodology and applications

“…Finally, the third class of feedback architectures (distributed) attempts to increase the overall control system performance by allowing the decentralized controllers to communicate locally. An interesting example of such an approach has been proposed in Pisarski et al, 17 where a scalable optimal control methodology was used for mitigation of structural vibration. The proposed method has been validated numerically for a cantilever structure equipped with actively controlled electromagnetic actuators and subjected to a variety of initial condition scenarios.…”