A Computation-Efficient Framework for the Integrated Design of Structural and Control Systems

This paper proposes a new integrated design method to simultaneously optimize the coupled structural parameters and controllers of mechanical systems by combining decentralized control techniques and Riccati-based control theories. The proposed integrated design method aims at minimizing the closed-loop H₂ norm from the disturbance to the system cost. In this paper, the integrated design problems have been formulated in the cases of full state-feedback controllers and full order output-feedback controllers. We extend the current linear time invariant (LTI) control system to a more general framework suitable for the needs of integrated design, where the structural design is treated as a passive control optimization tackled by decentralized control techniques with static output feedback, while the active controller is optimized by solving modified Riccati equations. By using this dual-loop control system framework, the original integrated design problem is transferred to a constrained structural design problem with some additional Riccati-equation based constraints simultaneously integrating the controller synthesis. This reduces the independent design variables from the structural design parameters and the parameters of the controller to the structural design parameters only. As a result, the optimization efficiency is significantly improved. Then the constrained structural design problem is reformed as an unconstrained optimization problem by introducing Lagrange multipliers and a Lagrange function. The corresponding optimal conditions for the integrated design are also derived, which can be efficiently solved by gradient-based optimization algorithms. Later, two design examples, an active–passive vehicle suspension system and an active–passive tuned mass damper (TMD) system, are presented. The improvement of the overall system performance is also presented in comparison with conventional design methods.