Simultaneous Dynamic Optimization Approach Research Articles

Multidisciplinary design optimization of dynamic positioning system for semi-submersible platform

The dynamic positioning system (DPS) is a complex mechatronic system consisting of multiple sub-disciplines. For such highly coupled sub-disciplines and sub-systems within the DPS, the conventional sequential design strategy cannot manage this interaction adequately and explicitly. Achieving the global optimal solution becomes challenging due to the discoordination between the structure and dynamic performance parameters. To address this challenge, a co-design strategy is explored by combining the structure and dynamic performance parameters based on a simultaneous dynamic optimization approach. To minimize the operating cost of the DPS, the radial basis function (RBF) model is extended to the constraint condition. The alpine skiing optimization (ASO) algorithm is applied to solve the multidisciplinary design optimization problem. The results indicate that the co-design strategy not only reduce the operating cost of the DPS but also achieve a smaller rolling response and yaw response.

Multidisciplinary co-design optimization of structural and control parameters for bucket wheel reclaimer

Bucket wheel reclaimer (BWR) is an extremely complex engineering machine that involves multiple disciplines, such as structure, dynamics, and electromechanics. The conventional design strategy, namely, sequential strategy, is structural design followed by control optimization. However, the global optimal solution is difficult to achieve because of the discoordination of structural and control parameters. The co-design strategy is explored to address the aforementioned problem by combining the structural and control system design based on simultaneous dynamic optimization approach. The radial basis function model is applied for the planning of the rotation speed considering the relationships of subsystems to minimize the energy consumption per volume. Co-design strategy is implemented to resolve the optimization problem, and numerical results are compared with those of sequential strategy. The dynamic response of the BWR is also analyzed with different optimization strategies to evaluate the advantages of the strategies. Results indicate that co-design strategy not only can reduce the energy consumption of the BWR but also can achieve a smaller vibration amplitude than the sequential strategy.

Trajectory optimization for lunar soft landing with a Hamiltonian-based adaptive mesh refinement strategy

In this study, the problem of fuel-optimal lunar soft landing trajectory optimization using variable-thrust propulsion is considered. First, the lunar soft landing trajectory optimization problem with three-dimensional kinematics and dynamics model, boundary conditions, and path constraints strictly described is formulated. Then, the formulated trajectory optimization problem is solved by the simultaneous dynamic optimization approach. With bounds imposed on the magnitude of engine thrust, the optimal control solutions typically have a “bang-bang” thrust profile. The general simultaneous dynamic optimization approach has difficulty handling breakpoints in the control profiles. A novel adaptive mesh refinement strategy based on a constant Hamiltonian profile is proposed to address the difficulty of locating breakpoints in the thrust profile. Two cases are simulated. The engine of the first case is throttleable between zero and full thrust. The engine of the second case is throttleable between 10% and 60% of full thrust, and at full thrust. Union property of R-function method is utilized to express the thrust profile of the second case in the trajectory optimization problem. Simulation results show that the enhanced simultaneous dynamic optimization approach with adaptive mesh refinement strategy can effectively capture the breakpoints in the optimal thrust profile and obtain more refined lunar soft landing optimal solutions, compared with the results obtained by the general simultaneous dynamic optimization approach.

Optimization of grade transitions in polyethylene solution polymerization processes

This study considers the development of optimization models for grade transition of polyethylene solution polymerization processes. A detailed mathematical model is developed to capture the dynamics of the solution polymerization process. This includes time delay models for vapor and liquid recycle streams as well as a reduced, yet accurate, vapor‐liquid equilibrium (VLE) model derived from rigorous VLE calculations. Simultaneous dynamic optimization approach is applied to solve the optimization problem to reduce off‐spec production time and transition time. Two optimization formulations, single stage and multistage, are developed to deal with single‐value target and specification bands of product properties, respectively. The results show significant reductions in grade transition time and off‐spec production time. In addition, the multistage formulation designed for problems with specification bands outperforms its single stage counterpart. It minimizes transition time and off‐spec production directly, and leads to higher performance control profiles. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1126–1142, 2016

Co-Design of an Active Suspension Using Simultaneous Dynamic Optimization

Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here, we explore a new technique for combined physical and control system design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinite-dimensional control design problems into finite-dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and fine-grained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to new problem structures and new challenges. Here, we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing co-design methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations. A simultaneous co-design approach was implemented using direct transcription, and numerical results were compared with conventional sequential optimization. The simultaneous optimization approach achieves better performance than sequential design across a range of design studies. The dynamics of the active system were analyzed with varied level of control authority to investigate how dynamic systems should be designed differently when active control is introduced.

Determination of biogeochemical parameters in eutrophication models with simultaneous dynamic optimization approaches

This work addresses a parameter estimation problem in an ecological water quality model through a simultaneous dynamic optimization approach. The model is based on first principles and has a large number of parameters, which must be estimated based on data collected in the water body under study. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem, with a weighted least squares objective function. Main biogeochemical parameters have been obtained, which allow a close representation of the lake dynamics, as it is shown in the numerical results.

Integrated Design and Control Using a Simultaneous Mixed-Integer Dynamic Optimization Approach

In this work, we address the simultaneous design and control of a binary distillation column. The problem is first formulated as a mixed-integer dynamic optimization problem that is then transformed into a mixed-integer nonlinear programming problem using the simultaneous dynamic optimization approach (i.e., full discretization). This formulation is capable of designing the optimal feed tray location, tray sizing, optimal operating steady states, the optimal open-loop trajectory between them, and also the best controller paring and parameters that does the best tracking of the open-loop trajectory. For solving the complex mixed-integer dynamic optimization problem, an optimization decomposition strategy is proposed. The solution strategy is based on solving relaxed versions of the optimization problem and using the results to initialize complex problem versions. The full space problem was solved with the Bonmin solver. Two cases were analyzed, and in both the solver and the proposed decomposition strategy...

Simultaneous mixed-integer dynamic optimization for integrated design and control

We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) program. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimization approach. We also develop three MINLP formulations based on a nonconvex formulation, the conventional Big-M formulation and generalized disjunctive programming (GDP). In addition, we compare the outer approximation and NLP branch and bound algorithms on these formulations. This problem is applied to a system of two series connected continuous stirred tank reactors where a first-order reaction takes place. Our results demonstrate that the simultaneous MIDO approach is able to efficiently address the solution of the integrated design and control problem in a systematic way.

Optimal Operating Policies for the Nitroxide-Mediated Radical Polymerization of Styrene in a Semibatch Reactor

In this work, optimal operating policies for the industrial-level semibatch living free radical polymerization of styrene are proposed. Several operating scenarios are addressed, and one of the most promising ones is identified. The determination of the time-dependent optimal operating policies is posed as a dynamic optimization problem. The simultaneous dynamic optimization approach, involving the full discretization of the states and manipulated variables, was used to solve the resulting optimization problem. Moreover, the optimization problem also involved the determination of design parameters such as the initial holdup, feed stream temperature, and concentrations resulting in a large-scale nonlinear program. The resulting optimal operating conditions lead to a polymer featuring living characteristics matching monomer conversion, molecular-weight distribution, and polydispersity index target values.

Dynamic Optimization of HIPS Open-Loop Unstable Polymerization Reactors

We consider dynamic optimization strategies for grade transitions for high-impact polystyrene reactors. Because our desired operating conditions are at unstable points, we apply a simultaneous dynamic optimization (SDO) approach, where state and control variables in the optimal control problem are discretized and a large-scale nonlinear programming solver is applied. For this purpose, we consider Radau collocation on finite elements and the IPOPT NLP solver. In addition, we describe the stability of the SDO strategy through the presentation of dichotomy properties for boundary-value problems. The resulting SDO approach is then demonstrated on a wide variety of operating scenarios for the high-impact polystyrene (HIPS) reactor, with highly reliable and efficient performance results.