A Minimum-Control-Trajectory-Deviation Time Grid Reconstruction Strategy for Co-Design Approach

Abstract

Optimizing dynamic engineering systems (DESs) is quite challenging due to the increasing pursuit of automation and intelligence in modern industry. However, most of the existing studies generally only focus on plant variables or control variables of DESs, which may fail to explore optimal solutions. In this paper, a novel minimum-control-trajectory-deviation (MCTD) time grid reconstruction strategy is presented for the co-design approach. Three co-design approaches, namely simultaneous, nested, and direct transcription quadratic programming (DTQP) are compared using the MCTD time grid reconstruction strategy. Considering a number of design variables are time-varying in practical dynamic systems, three co-design methods use a special class of numerical analysis methods known as direct transcription (DT) that implies a “discretize-then-optimize” process. Motivated by the inefficiency of the traditional uniform discrete strategy, an MCTD time grid reconstruction strategy is proposed. Combining the presented time grid reconstruction strategy, simultaneous, nested, and DTQP methods are implemented for three test problems. The MCTD time grid reconstruction strategy is verified through a mathematical example, the Van der Pol oscillator, and a machine tool case. All cases have proved the superiority of presented strategy in running cost and solution accuracy.