Multivariable Isoperformance Methodology for Precision Opto-Mechanical Systems

Abstract

Precision opto-mechanical systems, such as space telescopes, combine structures, optics and controls in order to meet stringent pointing and phasing requirements. In this context a novel approach to the design of complex, multi-disciplinary systems is presented in the form of a multivariable isoperformance methodology. The isoperformance approach first finds a point design within a given topology, which meets the performance requirements with sufficient margins. The performance outputs are then treated as equality constraints and the nonuniqueness of the design space is exploited by trading key disturbance, plant, optics and controls parameters with respect to each other.Three algorithms (branch-and-bound, tangential front following and vector spline approximation) are developed for the bivariate and multivariable problem. The challenges of large order models are addressed by presenting a fast diagonal Lyapunov solver, apriori error bounds for model reduction as well as a governing sensitivity equation for similarity transformed state space realizations. Specific applications developed with this technique are error budgeting and multiobjective design optimization. The goal of the multiobjective design optimization is to achieve a design which is pareto optimal, such that multiple competing objectives can be satisfied within the performance invariant set. Thus, situations are avoided where very costly and hard-to-meet requirements are levied onto one subsystem, while other subsystems hold substantial margins.An experimental validation is carried out on the DOLCE laboratory testbed. The testbed allows verification of the predictive capability of the isoperformance technique on models of increasing fidelity. A comparison with experimental results, trading excitation amplitude and payload mass, is demonstrated. The predicted performance contours match the experimental data very well at low excitation levels, typical of the disturbance environment on precision opto-mechanical systems. The relevance of isoperformance to space systems engineering is demonstrated with a comprehensive NEXUS spacecraft dynamics and controls analysis. It is suggested that isoperformance is a useful concept in other fields of engineering science such as crack growth calculations in structures. The isoperformance approach enhances the understanding of complex opto-mechanical systems beyond the local neighborhood of a particular point design. Sharon-Leah Brown provided encouragement and professional financial management.

2.1.1 Isoperformance: Analysis and Design of Complex Systems with Known or Desired Outcomes

“…It is the combination of these settings that enables satisfactory system performance. While the details of the model are available elsewhere [de Weck and Miller, 2002], we can see that performance is most sensitive to a subset of these variables (Table II). Isoperformance analysis was performed on this problem and several hundred potential designs that would all meet the performance requirement were identified.…”

“…Both of these can be simulated using a computer model. Details of the model are presented in de Weck and Miller [2002]. The simulation results for J z,2 are for an initial design x O and are shown in Figure 9.…”

“…The interested reader is referred to de Weck and Miller [2002] for details on these algorithms. Nevertheless, the second algorithm, gradient-based contour following, Select x iso * * ∈ X iso * ⊆ X iso ⊆ R n , according to non-quantified objectives/criteria and stakeholder consensus.…”

“…Hence, isoperformance solutions can be obtained from the nullspace of the system Jacobian matrix. Figure 6 shows for a sample problem (de Weck and Miller, [2002]) in three dimensions how the algorithm finds isoperformance surfaces by following performance-invariant directions in the nullspace.…”

“…In de Weck and Miller [2002], the following three algorithms have been developed: -Branch-and-Bound Design Space Exploration -Gradient-based Contour Following -Progressive Vector Spline Approximation…”