Nonlinear Dynamic Optimization Research Articles

Multi-objective optimized operation of integrated energy system with hydrogen storage

In this paper, an integrated energy system (IES) consisting of wind turbine unit, photovoltaic cell unit, electrolytic hydrogen unit, fuel cell unit, and hydrogen storage unit is proposed, and the construction of multi objectives for day-ahead power dispatching of the IES considering both operation and environment cost is discussed. By adopting piecewise linearization method, the optimization variables are divided into 24 periods, and the day-ahead power dispatching optimization problem is transformed into a 24-h piecewise optimization problem. On the basis, a complete non-linear mixed integer dynamic scheduling optimization model is established. An improved non-dominated sorting genetic algorithm (NSGA-II) is applied to solving the model. In optimization process, an interactive strategy is adopted to solve the coordination between discretization of variables and restriction of switching times of electrolyzer. Optimization results show that, compared with the single objective of minimizing operating costs, the multi-objective optimization scheme can reduce carbon emissions by 3.5% with 2.8% increase of operating cost. Compared with the single objective of minimizing environmental, the multi-objective optimization scheme can reduce operating cost carbon by 5.12% with 2.6% increase of environmental cost.

A Two-Stage Method for Parameter Identification of a Nonlinear System in a Microbial Batch Process

This paper deals with the parameter identification of a microbial batch process of glycerol to 1,3-propanediol (1,3-PD). We first present a parameter identification model for the excess kinetics of a microbial batch process of glycerol to 1,3-PD. This model is a nonlinear dynamic optimization problem that minimizes the sum of the least-square and slope errors of biomass, glycerol, 1,3-PD, acetic acid, and ethanol. Then, a two-stage method is proposed to efficiently solve the presented dynamic optimization problem. In this method, two nonlinear programming problems are required to be solved by a genetic algorithm. To calculate the slope of the experimental concentration data, an integral equation of the first kind is solved by using the Tikhonov regularization. The proposed two-stage method could not only optimally identify the model parameters of the biological process, but could also yield a smaller error between the measured and computed concentrations than the single-stage method could, with a decrease of about 52.79%. A comparative study showed that the proposed two-stage method could obtain better identification results than the single-stage method could.

Integrated Design and Control of Various Hydrogen Production Flowsheet Configurations via Membrane Based Methane Steam Reforming.

This work focuses on the development and implementation of an integrated process design and control framework for a membrane-based hydrogen production system based on low temperature methane steam reforming. Several alternative flowsheet configurations consisted of either integrated membrane reactor modules or successive reactor and membrane separation modules are designed and assessed by considering economic and controller dynamic performance criteria simultaneously. The design problem is expressed as a non-linear dynamic optimization problem incorporating a nonlinear dynamic model for the process system and a linear model predictive controller aiming to maintain the process targets despite the effect of disturbances. The large dimensionality of the disturbance space is effectively addressed by focusing on disturbances along the direction that causes the maximum process variability revealed by the analysis of local sensitivity information for the process system. Design results from a multi-objective optimization study, where only the annualized equipment and operational costs are minimized, are used as reference case in order to evaluate the proposed design framework. Optimization results demonstrate the controller’s ability to track the imposed setpoint changes and alleviate the effects of multiple simultaneous disturbances. Also, significant economic improvements are observed by the implementation of the integrated design and control framework compared to the traditional design methodology, where process and controller design are performed sequentially.

Frontal-Sagittal Dynamic Coupling in the Optimal Design of a Passive Bipedal Walker

The parametric design of passive bipedal walkers (PBWs) has been addressed by considering its dynamics in sagittal plane only. Nevertheless, with the aim of obtaining a complete parametric description, frontal plane dynamics must also be involved. Hence, in order to obtain a synergetic design of a PBW that simultaneously couples operating requirements of both planes, a concurrent design problem is proposed. The concurrent design approach is established as a nonlinear discontinuous dynamic optimization problem with mixed design variables and is solved by using four variants of differential evolution (DE) algorithm. The reduction in differences among Poincare mapping values related to consecutive gait cycles is proposed as the performance function, where its minimization must induce the convergence toward a limit cycle in PBW frontal and sagittal planes. A comparative analysis between the proposed concurrent design and a sequential design process is carried out for a particular case study: the PBW with single joint and curved feet. The simulation results show the advantages of the obtained concurrent design solutions to provide stable gait cycles in both PBW planes. In addition, the statistical analysis of the applied DE variants indicates that DE/best/1/bin promotes an efficient tradeoff between exploration and exploitation of solutions in the objective space. For the particular problem, this results in a high design reconfigurability, mainly associated with the material assignment diversity provided by the optimizer.

Dynamic Optimization of High-Altitude Solar Aircraft Trajectories Under Station-Keeping Constraints

This paper demonstrates the use of nonlinear dynamic optimization to calculate energy-optimal trajectories for a high-altitude, solar-powered unmanned aerial vehicle (UAV). The objective is to maximize the total energy in the system while staying within a 3 km mission radius and meeting other system constraints. Solar energy capture is modeled using the vehicle orientation and solar position, and energy is stored both in batteries and in potential energy through elevation gain. Energy capture is maximized by optimally adjusting the angle of the aircraft surface relative to the sun. The UAV flight and energy system dynamics are optimized over a 24 h period at an 8 s time resolution using nonlinear model predictive control. Results of the simulated flights are presented for all four seasons, showing an 8.2% increase in end-of-day battery energy for the most limiting flight condition of the winter solstice.

Toward Fast Dynamic Optimization: An Indirect Algorithm That Uses Parsimonious Input Parameterization

Dynamic optimization plays an important role toward improving the operation of chemical systems, such as batch and semibatch processes. The preferred strategy to solve constrained nonlinear dynamic optimization problems is to use a so-called direct approach. Nevertheless, based on the problem at hand and the solution algorithm used, direct approaches may lead to large computational times. Indirect approaches based on Pontryagin’s Minimum Principle (PMP) represent an efficient alternative for the optimization of batch and semibatch processes. This paper details the combination of an indirect solution scheme together with a parsimonious input parametrization. The idea is to parametrize the sensitivity-seeking inputs in a parsimonious way so as to decrease the computational load of constrained nonlinear dynamic optimization problems. In addition, this article discusses structural differences between direct and indirect approaches. The proposed method is tested on both a batch binary distillation column with ...

Study on Nonlinear Dynamic Optimization of Bridge Type Pneumatic Energy Saving Circuit

Study on Nonlinear Dynamic Optimization of Bridge Type Pneumatic Energy Saving Circuit

A design methodology for structural and control systems of a prosthetic leg

A design methodology is proposed to optimize a prosthetic leg considering the structural and control aspects. Previous studies mainly focused on each of a structural design problem or a control problem. The structural design variables of a prosthetic leg are determined in a structural design problem while the trajectory tracking based on the human gait cycle is found to be a control problem. The two problems have been separately solved. However, they should be simultaneously considered to obtain a better design. Then the problem would be nonlinear dynamic response optimization of structural and control systems. An optimization method was recently developed for a linear system of structural and control design problems using the equivalent static loads (ESLs). In this study, a design methodology for the prosthetic leg is presented by expanding the equivalent static loads method (ESLM) to nonlinear dynamic systems. A simple example is solved to validate the proposed methodology, and then a prosthetic leg is optimized to reduce the weight and energy consumption.

Structural Optimization for Roof Crush Test Using an Enforced Displacement Method

A roof crush test has been utilized to reduce passengers’ injuries from a vehicle rollover. The Federal Motor Vehicle Safety Standards (FMVSS) 216 and the Insurance Institute for Highway Safety (IIHS) perform actual vehicle tests and evaluate the vehicle’s ratings. Nonlinear dynamic response structural optimization can be employed not only for achievement of a high rating but also minimization of the weight. However, the technique needs a huge computation time and cost because many nonlinear dynamic response analyses are required in the time domain. A novel method is proposed for nonlinear dynamic response structural optimization regarding the roof crush test. The process of the proposed method repeats the analysis domain and the design domain until the convergence criteria are satisfied. In the analysis domain, the roof crush test is simulated using a high fidelity model of nonlinear dynamic finite element analysis. In the design domain, a low fidelity model of linear static response structural optimization is utilized with enforced displacements that come from the analysis domain. Correction factors are employed to compensate the differences between a nonlinear dynamic analysis response and a linear static analysis response with enforced displacement. A full-scale vehicle problem is optimized with a constraint on the rigid wall force from the analysis in the design domain.

Energy efficiency control of pneumatic actuator systems through nonlinear dynamic optimization

Abstract As one of the most widely used power sources in the engineering field, compressed air is especially common in industrial applications. In a traditional pneumatic circuit, a three-position five-way valve is used to control the air inlet and exhaust with a single pressure, which has low efficiency. This paper proposed a novel bridge-type circuit with variable pressure control using four on-off valves to improve the energy efficiency of compressed air for pneumatic actuators. The key idea of the method was to use air expansion energy to do work. Reducing the volume of consumed air was the goal, and a numerical method was presented to calculate the optimal on-off time sequence of the four valves using nonlinear dynamic optimization. The sequence was obtained based on the combination of a finite element polynomial configuration method and a reduced space sequential quadratic programming algorithm. Then, experimental validation was conducted to illustrate the energy efficiency, including pneumatic cylinder motion test under different conditions. Compared with the traditional circuit, the experimental results show that the bridge-type circuit put forward by this paper can significantly improve the energy efficiency of pneumatic driving systems by 50–70%. Additionally, the bridge-type circuit allows the piston to move smoothly to the end of the stroke, which can take the place of the function of cushion component and speed control valve of the traditional circuit.

MULTIPERIOD CREDIBILITIC MEAN SEMI-ABSOLUTE DEVIATION PORTFOLIO SELECTION

In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- absolute deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with the return rate on a risky asset by its credibilitic expected value and semi- absolute deviation. Since the proposed model is a nonlinear dynamic optimization problem with path dependence, we design a novel forward dynamic programming method to solve it. Finally, we provide a numerical example to demonstrate the performance of the designed algorithm and the application of the proposed model.

Nonlinear dynamic optimization of CEPC booster lattice

In September 2012, Chinese scientists proposed a circular electron positron collider (CEPC) at 240 GeV center of mass for Higgs studies. The CEPC booster (CEPCB) provides 120 GeV electron and positron beams to the CEPC collider. The phase-shift-optimizing method is proposed and used in the CEPC booster design. We also explain the physics picture of this method, and then some numerical results are listed to confirm our idea. With the phase-shift-optimizing method, the dynamic aperture increases in varying degrees, especially for off-momentum particles. In this paper, we find out the key point of CEPC booster lattice design. Using phase-shift-optimizing method, a CEPC booster lattice design with good dynamic aperture is given.

A Moving Horizon Estimation Algorithm Based on Carleman Approximation: Design and Stability Analysis

The moving horizon estimation (MHE) method is an optimization-based technique to estimate the unmeasurable state variables of a nonlinear dynamic system with noise in transition and measurement. One of the advantages of MHE over extended Kalman filter, the alternative approach in this area, is that it considers the physical constraints in its formulation. However, to offer this feature, MHE needs to solve a constrained nonlinear dynamic optimization problem which slows down the estimation process. In this paper, we introduce and employ the Carleman approximation method in the MHE design to accelerate the solution of the optimization problem. The Carleman method approximates the nonlinear system with a polynomial system at a desired accuracy level and recasts it in a bilinear form. By making this approximation, the Karush–Kuhn–Tucker (KKT) matrix required to solve the optimization problem becomes analytically available. Additionally, we perform a stability analysis for the proposed MHE design. As a result ...

A Constrained Optimization Approach to Integrated Active Fault Detection and Control

In this paper, a novel approach is proposed to formulate and solve the problem of active fault detection and control for multi-model discrete-time systems. The main objectives are to design an optimal fixed-order controller for stabilizing the healthy and faulty models by minimizing a well-defined quadratic performance index, meanwhile synthesizing a test signal for active fault detection in the presence of bounded energy uncertainty. To do this, an optimal solution is proposed to obtain the trade-off between the optimal fixed-order stabilizing controller signal and optimal test signal for active fault detection. These objectives could be achieved by solving a finite-dimensional constrained optimization problem. The dynamic nonlinear optimization problem is solved by two constructive recursive solution algorithms which are finally applied to a numerical example. Simulation results show the effectiveness of the proposed algorithms.

Conceptual design of a pre-booster ring for FCC e+e- injector

The FCC-e+e- injector complex needs to produce and to transport a high-intensity e+/e- beam at a fast repetition rate of about 0.1 Hz for topping up the collider at its collision energy. A basic parameter set exists for all the collider energies, assuming a 10 GeV linac operating with a large number of bunches being accumulated in the existing SPS, which serves as pre-accelerator and damping ring before the bunches are transferred to the high-energy booster. The purpose of this study is to provide the conceptual design of an alternative accelerator ring, replacing the SPS in the present scheme. This ring will have injection energy of 6 GeV and extraction energy of 20 GeV. In this study, the basic parameters of the ring are established, including the optics design and layout. Preliminary consideration for non-linear dynamics optimization and the impact of intra beam scattering are also presented.

力学モデルによる大域的最適化手法 : 非線形ダイナミクスと非線形最適化(「システム制御理論の新領域特集号」)

力学モデルによる大域的最適化手法 : 非線形ダイナミクスと非線形最適化(「システム制御理論の新領域特集号」)

Multidisciplinary design optimization of the flapping wing system for forward flight

The success of a flapping wing air vehicle flight is strongly related to the flapping motion and wing structure. Various disciplines should be considered for analysis and design of the flapping wing system. A design process for a flapping wing system is defined by using multidisciplinary design optimization. Unsteady aeroelastic analysis is employed as the system analysis. From the results of the aeroelastic analysis, the deformation of the wing is transmitted to the fluid discipline and the dynamic pressure is conveyed to the structural discipline. In the fluid discipline, a kinematic optimization problem is solved to maximize the time-averaged thrust coefficient and the propulsive efficiency simultaneously. In the structural discipline, nonlinear dynamic topology optimization is performed to find the distribution of reinforcement by using the equivalent static loads method for nonlinear static response structural optimization. The defined design process is applied to a flapping wing air vehicle model and the flapping wing air vehicle model is fabricated based on the optimization results.

Optimal energy management strategy for self-reconfigurable batteries

This paper proposes a novel energy management strategy for multi-cell high voltage batteries where the current through each cell can be controlled, called self-reconfigurable batteries. An optimized control strategy further enhances the energy efficiency gained by the hardware architecture of those batteries. Currently, achieving cell equalization by using the active balancing circuits is considered as the best way to optimize the energy efficiency of the battery pack. This study demonstrates that optimizing the energy efficiency of self-reconfigurable batteries is no more strongly correlated to the cell balancing. According to the features of this novel battery architecture, the energy management strategy is formulated as nonlinear dynamic optimization problem. To solve this optimal control, an optimization algorithm that generates the optimal discharge policy for a given driving cycle is developed based on dynamic programming and code vectorization. The simulation results show that the designed energy management strategy maximizes the system efficiency across the battery lifetime over conventional approaches. Furthermore, the present energy management strategy can be implemented online due to the reduced complexity of the optimization algorithm.

Off-line PID control tuning for a planar parallel robot using DE variants

Optimization methods have shown to be a very important approach for control engineers. They emulate the decision-making ability of a human expert to tune the control gains for a process or system with the formulation and solution of a mathematical optimization problem. In such formulation, evolutionary algorithms (EAs) have been widely used to obtain the control gains. Nevertheless a bad selection of the control gains through the optimization process can result in instability of the closed-loop control system such that the convergence and diversity in the EAs can be compromised. In this paper the PID control tuning for a planar parallel robot with a five-bar mechanism to follow a highly nonlinear trajectory is stated as an off-line nonlinear dynamic optimization problem (OLNLDOP). In order to promote individuals with a stable behavior in the closed-loop control system, a dynamic constraint and a method to handle such constraint is proposed into the OLNLDOP and into eight different variants of the differential evolution algorithm, respectively. Comparative analysis shows that the proposal finds suitable solutions for the OLNLDOP with a better convergence time. Laboratory testing with the optimum PID control gains on a real prototype validates the tuning optimization method.

Non-linear dynamic response structural optimization for frontal-impact and side-impact crash tests

Vehicle crash optimization is a representative non-linear dynamic response structural optimization that utilizes highly non-linear vehicle crash analysis in the time domain. In the automobile industries, crash optimization is employed to enhance the crashworthiness characteristics. The equivalent-static-loads method has been developed for such non-linear dynamic response structural optimization. The equivalent static loads are the static loads that generate the same displacement field in linear static analysis as those of non-linear dynamic analysis at a certain time step, and the equivalent static loads are imposed as external loads in linear static structural optimization. In this research, the conventional equivalent-static-loads method is expanded to the crash management system with regard to the frontal-impact test and a full-scale vehicle for a side-impact crash test. Crash analysis frequently considers unsupported systems which do not have boundary conditions and where adjacent structures do not penetrate owing to contact. Since the equivalent-static-loads method uses linear static response structural optimization, boundary conditions are required, and the impenetrability condition cannot be directly considered. To overcome the difficulties, a problem without boundary conditions is solved by using the inertia relief method. Thus, relative displacements with respect to a certain reference point are used in linear static response optimization. The impenetrability condition in non-linear analysis is transformed to the impenetrability constraints in linear static response optimization.