Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Optimization techniques in respiratory control system models

One of the most complex physiological systems whose modeling is still an open study is the respiratory control system where different models have been proposed based on the criterion of minimizing the work of breathing (WOB). The aim of this study is twofold: to compare two known models of the respiratory control system which set the breathing pattern based on quantifying the respiratory work; and to assess the influence of using direct-search or evolutionary optimization algorithms on adjustment of model parameters. This study was carried out using experimental data from a group of healthy volunteers under CO2 incremental inhalation, which were used to adjust the model parameters and to evaluate how much the equations of WOB follow a real breathing pattern. This breathing pattern was characterized by the following variables: tidal volume, inspiratory and expiratory time duration and total minute ventilation. Different optimization algorithms were considered to determine the most appropriate model from physiological viewpoint. Algorithms were used for a double optimization: firstly, to minimize the WOB and secondly to adjust model parameters. The performance of optimization algorithms was also evaluated in terms of convergence rate, solution accuracy and precision. Results showed strong differences in the performance of optimization algorithms according to constraints and topological features of the function to be optimized. In breathing pattern optimization, the sequential quadratic programming technique (SQP) showed the best performance and convergence speed when respiratory work was low. In addition, SQP allowed to implement multiple non-linear constraints through mathematical expressions in the easiest way. Regarding parameter adjustment of the model to experimental data, the evolutionary strategy with covariance matrix and adaptation (CMA-ES) provided the best quality solutions with fast convergence and the best accuracy and precision in both models. CMAES reached the best adjustment because of its good performance on noise and multi-peaked fitness functions. Although one of the studied models has been much more commonly used to simulate respiratory response to CO2 inhalation, results showed that an alternative model has a more appropriate cost function to minimize WOB from a physiological viewpoint according to experimental data.Postprint (author's final draft

Methods of system identification, parameter estimation and optimisation applied to problems of modelling and control in engineering and physiology

Mathematical and computer-based models provide the foundation of most methods of engineering design. They are recognised as being especially important in the development of integrated dynamic systems, such as “control-configured” aircraft or in complex robotics applications. These models usually involve combinations of linear or nonlinear ordinary differential equations or difference equations, partial differential equations and algebraic equations. In some cases models may be based on differential algebraic equations. Dynamic models are also important in many other fields of research, including physiology where the highly integrated nature of biological control systems is starting to be more fully understood. Although many models may be developed using physical, chemical, or biological principles in the initial stages, the use of experimentation is important for checking the significance of underlying assumptions or simplifications and also for estimating appropriate sets of parameters. This experimental approach to modelling is also of central importance in establishing the suitability, or otherwise, of a given model for an intended application – the so-called “model validation” problem. System identification, which is the broad term used to describe the processes of experimental modelling, is generally considered to be a mature field and classical methods of identification involve linear discrete-time models within a stochastic framework. The aspects of the research described in this thesis that relate to applications of identification, parameter estimation and optimisation techniques for model development and model validation mainly involve nonlinear continuous time models Experimentally-based models of this kind have been used very successfully in the course of the research described in this thesis very in two areas of physiological research and in a number of different engineering applications. In terms of optimisation problems, the design, experimental tuning and performance evaluation of nonlinear control systems has much in common with the use of optimisation techniques within the model development process and it is therefore helpful to consider these two areas together. The work described in the thesis is strongly applications oriented. Many similarities have been found in applying modelling and control techniques to problems arising in fields that appear very different. For example, the areas of neurophysiology, respiratory gas exchange processes, electro-optic sensor systems, helicopter flight-control, hydro-electric power generation and surface ship or underwater vehicles appear to have little in common. However, closer examination shows that they have many similarities in terms of the types of problem that are presented, both in modelling and in system design. In addition to nonlinear behaviour; most models of these systems involve significant uncertainties or require important simplifications if the model is to be used in a real-time application such as automatic control. One recurring theme, that is important both in the modelling work described and for control applications, is the additional insight that can be gained through the dual use of time-domain and frequency-domain information. One example of this is the importance of coherence information in establishing the existence of linear or nonlinear relationships between variables and this has proved to be valuable in the experimental investigation of neuromuscular systems and in the identification of helicopter models from flight test data. Frequency-domain techniques have also proved useful for the reduction of high-order multi-input multi-output models. Another important theme that has appeared both within the modelling applications and in research on nonlinear control system design methods, relates to the problems of optimisation in cases where the associated response surface has many local optima. Finding the global optimum in practical applications presents major difficulties and much emphasis has been placed on evolutionary methods of optimisation (both genetic algorithms and genetic programming) in providing usable methods for optimisation in design and in complex nonlinear modelling applications that do not involve real-time problems. Another topic, considered both in the context of system modelling and control, is parameter sensitivity analysis and it has been found that insight gained from sensitivity information can be of value not only in the development of system models (e.g. through investigation of model robustness and the design of appropriate test inputs), but also in feedback system design and in controller tuning. A technique has been developed based on sensitivity analysis for the semi-automatic tuning of cascade and feedback controllers for multi-input multi-output feedback control systems. This tuning technique has been applied successfully to several problems. Inverse systems also receive significant attention in the thesis. These systems have provided a basis for theoretical research in the control systems field over the past two decades and some significant applications have been reported, despite the inherent difficulties in the mathematical methods needed for the nonlinear case. Inverse simulation methods, developed initially by others for use in handling-qualities studies for fixed-wing aircraft and helicopters, are shown in the thesis to provide some important potential benefits in control applications compared with classical methods of inversion. New developments in terms of methodology are presented in terms of a novel sensitivity based approach to inverse simulation that has advantages in terms of numerical accuracy and a new search-based optimisation technique based on the Nelder-Mead algorithm that can handle inverse simulation problems involving hard nonlinearities. Engineering applications of inverse simulation are presented, some of which involve helicopter flight control applications while others are concerned with feed-forward controllers for ship steering systems. The methods of search-based optimisation show some important advantages over conventional gradient-based methods, especially in cases where saturation and other nonlinearities are significant. The final discussion section takes the form of a critical evaluation of results obtained using the chosen methods of system identification, parameter estimation and optimisation for the modelling and control applications considered. Areas of success are highlighted and situations are identified where currently available techniques have important limitations. The benefits of an inter-disciplinary and applications-oriented approach to problems of modelling and control are also discussed and the value in terms of cross-fertilisation of ideas resulting from involvement in a wide range of applications is emphasised. Areas for further research are discussed

Meta-heuristic algorithms in car engine design: a literature survey

Meta-heuristic algorithms are often inspired by natural phenomena, including the evolution of species in Darwinian natural selection theory, ant behaviors in biology, flock behaviors of some birds, and annealing in metallurgy. Due to their great potential in solving difficult optimization problems, meta-heuristic algorithms have found their way into automobile engine design. There are different optimization problems arising in different areas of car engine management including calibration, control system, fault diagnosis, and modeling. In this paper we review the state-of-the-art applications of different meta-heuristic algorithms in engine management systems. The review covers a wide range of research, including the application of meta-heuristic algorithms in engine calibration, optimizing engine control systems, engine fault diagnosis, and optimizing different parts of engines and modeling. The meta-heuristic algorithms reviewed in this paper include evolutionary algorithms, evolution strategy, evolutionary programming, genetic programming, differential evolution, estimation of distribution algorithm, ant colony optimization, particle swarm optimization, memetic algorithms, and artificial immune system

Numerical Non-Linear Modelling Algorithm Using Radial Kernels on Local Mesh Support

Estimation problems are frequent in several fields such as engineering, economics, and physics, etc. Linear and non-linear regression are powerful techniques based on optimizing an error defined over a dataset. Although they have a strong theoretical background, the need of supposing an analytical expression sometimes makes them impractical. Consequently, a group of other approaches and methodologies are available, from neural networks to random forest, etc. This work presents a new methodology to increase the number of available numerical techniques and corresponds to a natural evolution of the previous algorithms for regression based on finite elements developed by the authors improving the computational behavior and allowing the study of problems with a greater number of points. It possesses an interesting characteristic: Its direct and clear geometrical meaning. The modelling problem is presented from the point of view of the statistical analysis of the data noise considered as a random field. The goodness of fit of the generated models has been tested and compared with some other methodologies validating the results with some experimental campaigns obtained from bibliography in the engineering field, showing good approximation. In addition, a small variation on the data estimation algorithm allows studying overfitting in a model, that it is a problematic fact when numerical methods are used to model experimental values.This research has been partially funded by the Spanish Ministry of Science, Innovation and Universities, grant number RTI2018-101148-B-I00

디젤 엔진의 성능과 배기 최적화를 위한 연소 디자인 연구

학위논문(박사) -- 서울대학교대학원 : 공과대학 기계공학부, 2021.8. 이광호.최근 내연기관 성능향상을 위한 연구는 연비, 배출량, 소음, 진동 등의 측면에 초점이 맞춰지고 있다. 연비는 지구온난화에 영향을 준 이산화탄소 배출 감소와 관련이 있다. 또한, 디젤 연소로 인한 질소산화물과 그을음 배출은 인간의 건강에 해로우며 생명까지도 위협한다. 배기 가스의 유해성은 많은 나라들의 정부들로 하여금 차량 배출 규제를 엄격하게 만들도록 동기를 부여하고 있다. 최근에는 실험실의 인증치와 도로의 실제 배출량 수준 간의 차이를 고려해 Real-driving emissions 규제가 시행됐다. 소음 공해는 또한 인간과 공중 보건 문제의 관점에서 중요한 주제이다. 엔진에서 발생하는 연소 소음은 엔진 변수 및 연소 특성에 의해 영향을 받는 실린더 압력 배출에 따라 달라진다. 적절한 분사 전략 또는 연소 형태는 원하는 연소 소음 수준을 만족하도록 최적화할 수 있다. 엔진 개발 과정 중에 연비, 배기 배출물 및 소음의 각 성능을 최적화하기 위한 많은 노력과 시간이 소모된다. 최적의 성능을 얻으려면 연소 및 엔진 작동 변수를 최적화하기 위해 많은 실험이 필요하다. 실험 없이 엔진 성능을 최적화하기 위해 전산유체역학 시뮬레이션을 수행하려면 높은 계산 비용이 필요하다. 따라서, 계산 비용이 낮은 0-D 연소 최적화 방법론을 개발하는 것이 중요하다. 이전 연구들에 의한 0-D 연소 최적화 방법은 분사 전략 또는 엔진 변수를 최적화했다. 결과로 도출되는 연소는 기존 연소 형상의 범위 내에 있으며 연소 형상의 다양성 측면에서 실험적으로 변수를 최적화하는 방법과 다를 바 없다. 본 연구에서는 원하는 성능을 입력으로, 최적 연소 및 연소 변수를 출력으로 도출되는 연소 디자인 방법론을 개발하였다. 첫 번째 단계로 엔진 실험을 수행하여 베이스 조건, EGR 스윙, 흡기 온도 및 냉각수 온도 스윙 조건에서의 연비 및 배기 배출의 기본 성능을 평가하였다. 이 결과는 연소 디자인에 활용되는 0-D soot 모델 수립과 최적화 과정에서 초기 조건으로 사용되었다. Soot 생성 모델은 lift-off length에서 당량비를 계산하는 단순화된 스프레이 모델을 기반으로 했다. Lift-off length에서의 당량비는 그을음 형성 모델의 주요 요인 중 하나로 사용되었다. 연소 디자인 과정에서 IMEP는 연비를 대변하는 인자로 사용되었다. 연소 소음 평가에는 연소 소음 지수가 사용되었다. NOx 배출량 예측에는 이전 연구로부터 개발된 0-D NOx 모델이 적용되었다. 연소 디자인 방법론에서, 실린더 내 압력 계산에 필요한 변수는 흡기 압력, 람다 및 질량 연소율이었다. 질량 연소율은 기존에 널리 사용되는 위베 함수와 연소상에 대한 새로운 접근법으로 다항식 함수를 사용하여 결정되었다. 실린더 내 공기의 질량과 EGR율은 초기 조건으로 결정된 흡기 압력, 온도, 람다 및 화학 반응 방정식으로 계산되었다. 연소 중의 기체 조성비는 polytropic 지수 및 여러 열역학적 변수의 계산을 위해 계산되었다. 실린더 내 압력은 polytropic 과정과 열 발생률으로 계산되었다. 최적화 과정에서 연소 디자인 방법에 사용된 최적화 알고리즘은 제한된 비선형 다변량 함수(Interior-point 기법)와 입자 군집 최적화의 최소값이었다. 경계 조건과 제약 조건은 최적화 과정의 효율적인 iteration을 위해 결정되었다. 최적화를 위한 목적 함수의 기본 형태는 입력으로 사용된 원하는 성능을 가지는 특정한 연소를 찾을 수 있게 했다. 목표 성능을 최대화하는 다양한 디자인 목적에 따라 목표 함수는 변형되어 사용되었다. 연소 디자인의 결과는 다양한 운전 영역에서 MFB와 목적 함수에 따라 연구되었다. WLTP 운전 영역에서 정상 상태 연소들을 디자인하여 연소 디자인 방법론을 WLTP에 적용하였다. 적용 결과, WLTP 중 연료 소모량은 4.7% 감소되었다. NOx와 soot 배출은 각각 44.7%와 60.7%의 감소율을 보였다. 본 연구에서는 원하는 성능의 연소를 도출하는 0-D 연소 시뮬레이션 및 최적화 방법을 제공하였다. 이 연구는 원하는 성능 혹은 최적화된 성능을 가지는 연소상을 열역학적인 조건들과 함께 제시할 수 있어 이를 바탕으로 기존의 연구 방법과 다른 목표 연소를 구현하기 위한 엔진과 연소 전략 개발 방향을 제시할 수 있다.Recently, the researches for improving the performance of the internal combustion engines have been focused on the respect of thermal efficiency, emissions, noise and vibration. The thermal efficiency is related with decreasing carbon dioxide (CO2) emission that has affected global warming. Also, nitrogen oxides (NOx) and soot emissions from diesel combustion are harmful for human. The harmfulness of exhaust gases has motivated governments of many countries to make vehicle emission regulations stringent. Recently, real-driving emissions (RDE) regulation was enforced, considering the discrepancy between the certified values in laboratory and the actual emission levels on the road. Noise pollution is also important in the perspective of human and public health problem. The combustion noise from the engine depends on the cylinder pressure excitation, which is affected by the engine parameters and combustion characteristics. Proper injection strategies or combustion shape can be optimized to meet the desired combustion noise level. The engine development process takes a lot of effort and time to optimize each performance of thermal efficiency, emissions and noise. To achieve desired optimal performance, many trials and errors and experiments are required to optimize combustion and engine operating parameters. As an optimization tool, computational fluid dynamics (CFD) simulation needs substantial calculation cost. Thus, it is important to develop 0-D combustion optimization methodology that has low calculation cost. Previously studied 0-D combustion optimization methods have been optimized the injection strategy or engine parameters. The resulting combustion comes out of a narrow range and it is similar to the methodology of optimizing variables experimentally in terms of diversity of combustion. In this study, the combustion design methodology was developed that used the desired performance as input and derived combustion and combustion parameters as outputs in a diesel engine. The thermal efficiency, noise and emissions were needed to be calculated by 0-D combustion simulation for the combustion optimization. As a one of emission models, the 0-D soot model was developed through cooperative research with Youngbok Lee. The engine test that evaluated the soot emission by EGR rate, intake and coolant temperature was conducted to develop the 0-D soot model and acquire initial conditions for combustion design. The soot formation model was based on the simplified spray model to calculate the equivalence ratio at lift-off length. The equivalence ratio at the lift-off length was used as a one of the main factor for the soot formation model. In the combustion design process, IMEP represented the thermal efficiency. For the combustion noise evaluation, the combustion noise index was used. The 0-D NOx model from previous research was applied to estimate NOx emission. In the combustion design methodology, the initial parameters for constructing in-cylinder pressure were intake pressure, lambda and the mass faction burned. The MFB was determined by using Wiebe function and polynomial function as new approach to combustion phase. The mass of in-cylinder air and EGR rate were calculated from intake pressure, temperature, lambda, that were determined as initial conditions, and the chemical reaction equation. Compression and expansion strokes were assumed as polytropic process. The gas compositions during the combustion were calculated for calculation of polytropic index and other thermodynamic parameters. The in-cylinder pressure was calculated by the heat release rate and polytropic process with the estimated polytropic index. In the optimization process, the optimization algorithms used in the combustion design method were a minimum of constrained nonlinear multivariable function (interior-point) and particle swarm optimization. MATLAB was used as the optimization tool. The boundary conditions and constraints were determined for efficient iteration in optimization process. The base form of objective function for optimization allowed to find specific combustion of desired performance that was used as input. The objective functions for various design concepts were used in maximizing target performance. The results of combustion design were investigated by objective function and MFB function type at various operation point. The combustion design method was applied to WLTP by designing the steady points in WLTP operation region. The fuel consumption during WLTP decreased by 4.6% compared to experimental result The NOx and soot emissions could be reduced by 44.7% and 60.7%. In this study, the 0-D combustion simulation and optimization method that derived the combustion of desired performance were provided. This research can contribute to provide combustion shape with desired or optimized performance in combination with thermodynamic conditions, suggesting the development process different from existing research methods of engine and combustion strategies for target combustion.Chapter 1. Introduction 1 1.1 Background 1 1.2 Literature Review 8 1.2.1 Combustion noise model 8 1.2.2 NOx emission model 11 1.2.3 Soot emission model 13 1.2.4 Combustion optimization 18 1.3 Research Objectives and Contributions 28 1.4 Structure of the Thesis 29 Chapter 2. Experimental Apparatus 31 2.1 Experimental Setup 31 2.1.1 Test engine 31 2.1.2 Test cell and data acquisition systems 31 2.1.3 Emission measurement systems 32 2.1.4 Engine operating conditions 34 Chapter 3. Semi-physical 0-D Soot Model 46 3.1 Simplified Spray Model 46 3.1.1 Spray model description 46 3.1.2 Liquid length calculation 48 3.1.3 Laminar flame speed model 50 3.1.4 The equivalence ratio at the lift-off length 53 3.2 Semi-physical 0-D Soot Model 64 3.2.1 Soot formation model 64 3.2.2 Soot oxidation model 65 3.2.3 The model validation 68 Chapter 4. Other Models for Thermal Efficiency, Noise and NOx Emission 74 4.1 Thermal Efficiency 74 4.2 Noise – Combustion Noise Index (CNI) 74 4.3 The NOx Estimation Model 78 Chapter 5. Combustion Design Methodology 81 5.1 Concept of Combustion Design Method 81 5.2 Process of Constructing Combustion Pressure 86 5.2.1 Mass fraction burned and heat release rate 86 5.2.2 Calculation of in-cylinder air flow and EGR rate 95 5.2.3 Gas composition during the combustion process 102 5.2.4 Polytropic index and constructing cylinder pressure 103 5.2.5 Calculation of the fuel injection timing 107 5.3 Optimization Methodology 113 5.3.1 Optimization algorithms 113 5.3.2 Boundary conditions and constraints 116 5.3.3 Determination of the objective function 121 Chapter 6. Results of Combustion Design 131 6.1 Results from Base Objective Function 131 6.1.1 Low load: 1500 rpm, BMEP 4 bar 131 6.1.2 High load: 2000 rpm, BMEP 8 bar 136 6.2 Results by various design concept 141 6.3 Results Using Polynomial Function as MFB 148 6.4 Application of Combustion Design to WLTP 153 6.4.1 Combustion design at steady points in WLTP operating area 153 6.4.2 Results of an application to WLTP 164 Chapter 7. Conclusions 169 Bibliography 174 국 문 초 록 193박