Parameter space optimization towards integrated mechatronic design for uncertain systems with generalized feedback constraints. (July 2019) - Ma, Jun; Chen, Si-Lu; Teo, Chek Sing; Tay, Arthur; Al Mamun, Abdullah; Tan, Kok Kiong
Abstract: There is an increasing trend to apply integrated mechatronic design approaches in precision engineering to synthesize key mechanical and controller parameters simultaneously. However, such technique is yet to be mature, due to the constraints imported by mechanical design and feedback control, as well as the existence of model uncertainties. In this work, we treat the integrated mechatronic design problem as a controller optimization problem with structural constraints. We start from the case when the composite feedback gain matrix (CFGM) has some elements either being zero or with equal or opposite relationships. First, algorithms are proposed to factorize the CFGM. Secondly, the feedback constraints are transformed from the state space to an extended parameter space. In this way, the design problem is reformulated as minimizing the ℋ 2 -norm upper bound of the closed-loop system transmittance from the exogenous disturbance to the regulated variables over the intersection of convex and non-convex domains. Eventually, cutting-plane-based numerical procedures are developed to obtain a global optimal solution, and the closed-loop robust stability is ensured with guaranteed performance. An illustrative example on a flexure-linked biaxial gantry stage is presented to reveal the practical appeal of the proposed approach. This approach is extensively applicable to a class of optimal control problems, such as controller synthesis problem with prescribed sparsity pattern, decentralized control problem with/without structural constraints, etc.