The design methods that have been traditionally used for controlled mechanical systems suffer from three major drawbacks. First, the design process is generally sequential, with the mechanical design being done first and frozen before the control system design is done. Secondly, the design is usually tuned to improve performance only without worrying about the sensitivity of the system’s performance to small variations in the system parameters. Third, there is a lack of systematic guidance for traversing the design space and arriving at a high quality design. In this work, we propose a design approach that addresses all three of these concerns. This approach first extends the constrained multi-element formulation for multibody systems to include a generic controller model. This gives the basic capability to simulate controlled multibody systems in a general way by numerically solving a set of differential-algebraic equations (DAE’s). A direct differentiation technique is then applied to the unified mathematical model to obtain a set of DAE’s in the sensitivities of the system variables. This is then used to compute the sensitivity of any performance function of interest. The system analysis and sensitivity analysis are then treated as inputs to a suitable nonlinear programming problem (NLP). The NLP serves as a vehicle to unify mechanical system and control criteria in the design process, and to incorporate sensitivity considerations along with performance considerations. The NLP also provides the means for automating the solution process through the use of optimization algorithms. Two representative example, including an industrial problem, are solved using this method. The results clearly show that the methodology is feasible and leads to a vast improvement in the quality of the final design, whatever the design considerations may be.
L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics