The design of physical (plant) and control aspects of a dynamic system have traditionally been treated as two separate problems, often solved in sequence. Optimizing plant and control design disciplines separately results in sub-optimal system designs that do not capitalize on the synergistic coupling between these disciplines. This coupling is inherent in most actively controlled dynamic systems, including wind turbines. In this case structural and control design both affect energy production and loads on the turbine. This article presents an integrated approach to achieve system-optimal wind turbine designs using codesign, a design methodology that accounts directly for the synergistic coupling between physical and control system design. A case study, based on multidisciplinary simulation, is presented here that demonstrates a promising increase (up to 8%) in annualized wind turbine energy production compared to the results of a conventional sequential design strategy. The case study also revealed specific synergistic mechanisms that enable performance improvements, which are accessible via co-design but not sequential design.

Optimization of nonlinear (or linear state-dependent) dynamic systems often requires system simulation. In many cases the associated state derivative evaluations are computationally expensive, resulting in simulations that are significantly slower than real-time. This makes the use of optimization techniques in the design of such systems impractical. Optimization of these systems is particularly challenging in cases where control and physical systems are designed simultaneously. In this article, an efficient two-loop method, based on surrogate modeling, is proposed for solving dynamic system design problems with computationally expensive derivative functions. A surrogate model is constructed for only the derivative function instead of the complete system analysis, as is the case in previous studies. This approach addresses the most expensive element of system analysis (i.e., the derivative function), while limiting surrogate model complexity. Simulation is performed based on the surrogate derivative functions, preserving the nature of the dynamic system, and improving estimation accuracy. The inner loop solves the system optimization problem for a given derivative function surrogate model, and the outer loop updates the surrogate model based on optimization results. This solution approach presents unique challenges. For example, the surrogate model approximates derivative functions that depend on both design and state variables. As a result, the method must not only ensure accuracy of the surrogate model near the optimal design point in the design space, but also the accuracy of the model in the state space near the state trajectory that corresponds to the optimal design. This method is demonstrated using two simple design examples, followed by a wind turbine design problem. In the last example, system dynamics are modeled using a linear state-dependent model where updating the system matrix based on state and design variable changes is computationally expensive.

Anand P. Deshmukh 1t , Daniel R. Herber 2t , and James T. Allison 3t Ahstract-Here we propose a novel framework for the comb i ned plant and controller arch i tecture des i gn based on a set of systematic studies that culminate in an optimal plant architecture and associated realizable control law. This framework bridges the inherent gap between open-loop opt i mal trajectories provided by particular co-design studies and practically implementable control laws. This is accomplished through a step-by-step process where a series of optimization problems are solved that provide important system insights such as maximum system performance limits, controller architecture, actuator selection, etc. at appropriate design phases. Each optimization problem thus informs subsequent formulations.This methodology is applied to semi-active suspension design.

Optimization of dynamic systems often requires system simulation. Several important classes of dynamic system models have computationally expensive time derivative functions, resulting in simulations that are significantly slower than real time. This makes design optimization based on these models impractical. An efficient two-loop method, based on surrogate modeling, is presented here for solving dynamic system design problems with computationally expensive derivative functions. A surrogate model is constructed for only the derivative function instead of the simulation response. Simulation is performed based on the computationally inexpensive surrogate derivative function; this strategy preserves the nature of the dynamic system, and improves computational efficiency and accuracy compared to conventional surrogate modeling. The inner-loop optimization problem is solved for a given derivative function surrogate model (DFSM), and the outer loop updates the surrogate model based on optimization results. One unique challenge of this strategy is to ensure surrogate model accuracy in two regions: near the optimal point in the design space, and near the state trajectory in the state space corresponding to the optimal design. The initial evidence of method effectiveness is demonstrated first using two simple design examples, followed by a more detailed wind turbine codesign problem that accounts for aeroelastic effects and simultaneously optimizes physical and control system design. In the last example, a linear state-dependent model is used that requires computationally expensive matrix updates when either state or design variables change. Results indicate an order-of-magnitude reduction in function evaluations when compared to conventional surrogate modeling. The DFSM method is expected to be beneficial only for problems where derivative function evaluation expense, and not large problem dimension, is the primary contributor to solution expense (a restricted but important problem class). The initial studies presented here revealed opportunities for potential further method improvement and deeper investigation.