Simultaneous Dynamic Optimization 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.

Simultaneous Dynamic Optimization of Technical Indicators and Mining Sequence in Metal Mines Using Hybrid Coding AADE

Simultaneous Dynamic Optimization of Technical Indicators and Mining Sequence in Metal Mines Using Hybrid Coding AADE

Application of simultaneous dynamic optimization in the productivity of microalgae continuous culture

Microalgae biomass is an up-and-coming option for supplying clean and reliable bio-products and energy for future years. However, its industrial production is not yet accomplished due to its economic unfeasibility. To date, several strategies have been used to improve microalgae productivity. Nonetheless, in most of these strategies, the objective function is minimized by nested procedures that have shown limitations dealing with discontinuities, which is very common in microalgae models. This paper describes the application of simultaneous optimization procedures in GEKKO Python package through the exploration of optimal biomass productivity under continuous operation of the strains Dunaliella tertiolecta and Chlorella vulgaris. The results show the successful implementation with fast convergence times: 7.43s to solve 10800 equations with 900 degrees of freedom in Chlorella vulgaris and 11.45s to solve 6600 equations with 600 degrees of freedom in Dunaliella tertiolecta. Furthermore, in biological terms, simulations show that once an optimal pH>8 level is reached in the Chlorella model, the sensitivity of other variables such as Iin decreases dramatically. Therefore, it is possible to achieve high productivity even without increasing the required light intensity. In addition, in Dunaliella case, the results also infer that larger biomass productivity requires larger input substrate concentration.

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.

Simultaneous dynamic optimization of valves timing and waste gate to improve the load step transient response of a turbocharged spark ignition engine

A result of adding a turbocharger for downsizing of spark ignition engines is slower transient response of the engine in comparison to the naturally aspirated engine. Until recently, it was impossible to use turbocharger in spark ignition engines due to self-ignition problems. However, with the waste gate technology, the turbine speed and hence the boost pressure level are regulated for reduction of self-ignition and increase of torque. In this paper, the engine simulation is done in one-dimensional software GT-POWER and the torque transient response is being focused. For optimization, the coupling between two softwares GT-POWER and MATLAB SIMULINK is used to find an appropriate setting to utilize variable valve timing and waste gate technologies simultaneously during the transient. Variable valve timing in this study refers to opening and closing timings of inlet and exhaust valves. The optimization target is to maximize the torque integral during time interval of the transient. The transient in this paper is the one in which the engine speed is constant and the load increases rapidly and suddenly to a special value (step increase of load). Improved genetic algorithm is used for optimization. With this optimization, the mean improvement percentage in torque integral is about 6.46% for speed 1900 rpm and about 9.33% for speed 2500 rpm. The studied engine is 1.65 L EF7-TC which is a spark ignition engine equipped with turbocharger.

Time-Optimal Maneuver Planning in Automatic Parallel Parking Using a Simultaneous Dynamic Optimization Approach

Autonomous parking has been a widely developed branch of intelligent transportation systems. In autonomous parking, maneuver planning is a crucial procedure that determines how intelligent the entire parking system is. This paper concerns planning time-optimal parallel parking maneuvers in a straightforward, accurate, and purely objective way. A unified dynamic optimization framework is established, which includes the vehicle kinematics, physical restrictions, collision-avoidance constraints, and an optimization objective. Interior-point method (IPM)-based simultaneous dynamic optimization methodology is adopted to solve the formulated dynamic optimization problem numerically. Given that near-feasible solutions have been widely acknowledged to ease optimizing nonlinear programs (NLPs), a critical region-based initialization strategy is proposed to facilitate the offline NLP-solving process, a lookup table-based strategy is proposed to guarantee the on-site planning performance, and a receding-horizon optimization framework is proposed for online maneuver planning. A series of parallel parking cases is tested, and simulation results demonstrate that our proposal is efficient even when the slot length is merely 10.19% larger than the car length. As a unified maneuver planner, our adopted IPM-based simultaneous dynamic optimization method can deal with any user-specified demand provided that it can be explicitly described.

Sensitive phylogenetics ofClematisand its position in Ranunculaceae

Ranunculaceae are a nearly cosmopolitan plant family with the highest diversity in northern temperate regions and with relatively few representatives in the tropics. As a result of their position among the early diverging eudicots and their horticultural value, the family is of great phylogenetic and taxonomic interest. Despite this, many genera remain poorly sampled in phylogenetic studies and taxonomic problems persist. In this study, we aim to clarify the infrageneric relationships of Clematis by greatly improving taxon sampling and including most of the relevant subgeneric and sectional types in a simultaneous dynamic optimization of phenotypic and molecular data. We also investigate how well the available data support the hypothesis of phylogenetic relationships in the family. At the family level, all five currently accepted subfamilies are resolved as monophyletic. Our analyses strongly imply that Anemone s.l. is a grade with respect to the Anemoclema + Clematis clade. This questions the recent sinking of well-established genera, including Hepatica, Knowltonia and Pulsatilla, into Anemone. In Clematis, 12 clades conceptually matching the proposed sectional division of the genus were found. The taxonomic composition of these clades often disagrees with previous classifications. Phylogenetic relationships between the section-level clades remain highly unstable and poorly supported and, although some patterns are emerging, none of the proposed subgenera is in evidence. The traditionally recognized and horticulturally significant section Viorna is both nomenclaturally invalid and phylogenetically unsupported. Several other commonly used sections are likewise unjustified. Our results provide a phylogenetic background for a natural section-level classification of Clematis.

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

Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal.

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.

A hybrid model-based optimal control method for nonlinear systems using simultaneous dynamic optimization strategies

To improve the overall control performance of nonlinear systems, an optimal control method, based on the framework of hybrid systems, is proposed. Firstly, the nonlinear systems are approximated by a number of piecewise affine models which are produced by the nonlinear systems at the specified operating points, then the piecewise affine models are synthesized under the framework of hybrid systems, and an associated optimal control problem, in which decision variables involve not only admissible continuous control but also the scheduling of subsystem modes, is established. Secondly, the optimal control problem is transformed into a MIQP problem by discretization over the whole state space and admissible control space to obtain the numerical optimal solution. For speeding up the algorithm, the simultaneous method on finite elements is used to lower the dimensions of the MIQP problem. Consequently, a hybrid model-based MPC for nonlinear systems is designed, and the adverse effects of model mismatch resulted from simultaneous method is weakened by MPC strategy. Simulations and comparisons with soft-switching method, hard-switching method and MLD method, confirm that a satisfactory performance can be obtained using the presented approach.

Simultaneous mixed-integer dynamic optimization for environmentally benign electroplating

Hoist scheduling, especially cyclic hoist scheduling (CHS), is used to maximize the manufacturing productivity of electroplating processes. Water-reuse network design (WRND) for the electroplating rinsing system targets the optimal water allocation, such that fresh water consumption and wastewater generation are minimized. Currently, there is still a lack of studies on integrating CHS and WRND technologies for electroplating manufacturing. In this paper, a multi-objective mixed-integer dynamic optimization (MIDO) model has been developed to integrate CHS and WRND technologies for simultaneous consideration of productivity and water use efficiency for environmentally benign electroplating. The orthogonal collocation method on finite elements is employed to convert the MIDO problem into a mixed-integer nonlinear programming (MINLP) problem. The efficacy of the methodology is demonstrated by solving a real electroplating example. It demonstrates that the computational methods of production scheduling, process design, and dynamic optimization can be effectively integrated to create economic and environmental win–win situations for the electroplating industry.

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.

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...

Integrated control and process design during optimal polymer grade transition operations

In this work we address the simultaneous process control and design problem of polymerization reactors during dynamic grade transition operation. The problem is cast as a Mixed-Integer Dynamic Optimization (MIDO) formulation and, by using the full discretization approach for solving dynamic optimization problems [Kameswaran, S., & Biegler, L. T. (2006). Simultaneous dynamic optimization strategies: Recent advances and challenges. Computers & Chemical Engineering, 30 (10–12), 1560–1575], is transformed into a Mixed-Integer Nonlinear Program (MINLP). The resulting MINLP is solved using a full space nonconvex optimization formulation [Flores-Tlacuahuac, A., & Biegler, L. T. (2007). Simultaneous Mixed-Integer Dynamic Optimization for integrated design and control. Computers & Chemical Engineering, 31, 588–600]. The control and design formulation has been applied to two polymerization reactors featuring highly nonlinear behavior. In both cases, the proposed MIDO formulation was capable of finding optimal solutions. This amounts to finding optimal steady states, reactor designs, as well as open-loop and closed-loop dynamic optimal trajectories, control structures and controller parameters by specifying either the polymer molecular weight distribution or monomer conversion. Because CPU solution time tends to increase with system complexity, some strategies for lowering CPU time are discussed.

OPTIMAL START-UP AND STEADY-STATE TRANSITION POLICIES IN A PENTENE METATHESIS REACTIVE DISTILLATION COLUMN

The nonlinear analysis and start-up operations of a reactive distillation column were addressed in this paper by approaching the problem as a dynamic optimization problem. A detailed tray by tray model that considers internal tray hydraulics, but ignores vapor dynamics was derived and used for calculations. Several manipulated variables were considered besides the reboiler heat duty. The large scale NLP's generated from the application of the simultaneous dynamic optimization method were successfully solved with the use of Ipopt (an interior point optimizer). It was found that with the use of dynamic optimization large time reductions can be achieved when compared to empirical ramp like changes in the manipulated variables, and, thus, reducing the amount of waste and energy consumption. Overall, when using optimal rather than empirical dynamic operation policies, a one order of magnitude energy and raw material savings where found, which clearly demonstrates that significant economic and environmental advantages can be achieved by approaching the dynamic operation of industrial processes as a formal dynamic optimization problem.

A software environment for simultaneous dynamic optimization

We describe a software environment for dynamic optimization using the simultaneous approach. Over the past few years, there has been significant development in the formulation of simultaneous dynamic optimization problems, using collocation on finite elements, and in the solution of the resulting large-scale nonlinear programming problem, using powerful barrier NLP solvers. Here we describe the background of the simultaneous approach as well as the components that make up the formulation and modeling environment, which we call DynoPC. DynoPC incorporates state-of-the-art NLP and DAE solvers along with a powerful automatic differentiation package. Moreover, it has a number of advanced features including model reduction and moving finite elements. Finally, we describe how DynoPC can be interfaced to other environments using Equation Set Objects (ESO) and the MINLP CAPE-OPEN object. All of these concepts are illustrated with three dynamic optimization examples including a large-scale industrial case study.

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.