A technique to develop simplified and linearised models of complex dynamic supply chain systems

There is a need to identify and categorise different types of nonlinearities that commonly appear in supply chain dynamics models, as well as establishing suitable methods for linearising and analysing each type of nonlinearity. In this paper simplification methods to reduce model complexity and to assist in gaining system dynamics insights are suggested. Hence, an outcome is the development of more accurate simplified linear representations of complex nonlinear supply chain models.  We use the highly cited Forrester production-distribution model as a benchmark supply chain system to study nonlinear control structures and apply appropriate analytical control theory methods. We then compare performances of the linearised model with numerical solutions of the original nonlinear model and with other previous research on the same model.  Findings suggest that more accurate linear approximations can be found. These simplified and linearised models enhance the understanding of the system dynamics and transient responses, especially for inventory and shipment responses.  A systematic method is provided for the rigorous analysis and design of nonlinear supply chain dynamics models, especially when overly simplistic linear relationship assumptions are not possible or appropriate. This is a precursor to robust control system optimisation

Establishing a framework for the effective design of resilient supply chains with inherent non-linearities

Purpose of this paper: Previous control theory research on supply chain dynamics has predominantly taken a linear perspective of the real world, whereas nonlinearities have usually been studied via a simulation approach. Nonlinearities can naturally occur in supply chains through the existence of physical and economic constraints, for example, capacity limitations. Since the ability to flex capacity is an important aspect of supply chain resilience, there is a need to rigorously study such nonlinearities. Hence, the purpose of this paper is to propose a framework for the dynamic design of supply chains so that they are resilient to nonlinear system structures

Towards an Automated Tool Chain for MPC in Multi-zone Buildings

Heating Ventilation and Air Conditioning (HVAC) represents a large fraction of the world’s primary energy demand. Novel control strategies such as Model Predictive Control (MPC) aim to reduce energy use, while also improving occupant comfort. For MPC to be a viable alternative to classical Rule Based Control (RBC), it should be able to incorporate multiple emission and production systems, multiple zones, and aspects such as thermal comfort and indoor air quality (IAQ). Identifying grey-box or black-box MPC controller models for hybrid energy systems in multi-zone buildings has proven to be difficult. White-box models use physical knowledge of the system and take into account the desired dynamics. This approach however requires a substantial time investment since every building requires a custom model. The goal of this paper is to describe on-going work aiming at an automated methodology for setting up MPC controllers for buildings using white-box models. For this methodology, firstly, a detailed ‘emulator’ model of the building needs to be developed. Secondly this emulator is linearised to obtain a state space formulation of the building system and thirdly the emulator is used to generate MPC input data such as disturbances. Fourthly, a custom MPC tool uses this information to compute optimal control set points. These steps are elaborated below. The first step of the methodology is to the IDEAS library in Modelica to set up a detailed building envelope model. Modelica is an object-oriented equation based language that allows assembling complex systems by combining component models from open source libraries such as IDEAS. The second step is to linearise the building model. The IDEAS library is parametrized such that non-linearities such as convection correlations and radiation can be linearised around a well-chosen working point. Hydraulic connections from the HVAC are simplified and converted into heat flow rates. The HVAC is therefore simplified such that their the heat flow rate set points can be optimized. Disturbances such as the ambient temperature are also model inputs. The state space model resulting from the linearisation, although linear, accurately predicts the temperatures of the building’s zones. In the third step the emulator model is used to compute and store time series data for all state space model inputs such as ambient and radiative temperatures, solar incidence on glazing and internal gains from occupants. In step four the highly accurate state space model (step two) and corresponding input data (step three) files are used to set up the MPC problem. This MPC optimizes the remaining inputs from the state space model, subject to constraints and using a cost function that are passed to the optimization problem using augmented rows of the state space matrices. The state space matrices are pre-processed using CasADi such that a computationally efficient linear program is generated. This methodology is demonstrated on a medium size office building with 32 zones and hybrid emission and production systems. Results and performance are discussed. The strong points are the applicability to hybrid energy systems in multi-zone buildings, allowing the evaluation of thermal comfort and IAQ in different zones.

Designing supply chains resilient to nonlinear system dynamics

Purpose: To propose an analytical framework for the design of supply chains that are resilient to nonlinear system dynamics. For this purpose, it is necessary to establish clearly elucidated performance criteria that encapsulate the attributes of resilience. Moreover, by reviewing the literature in nonlinear control engineering, this work provides a systematic procedure for the analysis of the impact of nonlinear control structures on systems behaviour. Design/method/approach: The Forrester and APIOBPCS models are used as benchmark supply chain systems. Simpli�cation and nonlinear control theory techniques, such as low order modelling, small perturbation theory and describing functions, are applied for the mathematical analysis of the models. System dynamics simulations are also undertaken for cross-checking results and experimentation. Findings: Optimum solutions for resilience yield increased production on-costs. Inventory redundancy has been identi�ed as a resilience building strategy but there is a maximum resilience level that can be achieved. A methodological contribution has also been provided. By using nonlinear control theory more accurate linear approximations were found for reproducing nonlinear models, enhancing the understanding of the system dynamics and actual transient responses. Research limitations/implications: This research is limited to the dynamics of single-echelon supply chain systems and focus has been given on the analysis of individual nonlinearities. Practical Implications: Since that the resilience performance trades-o� with production, inventory and transportation on-costs, companies may consider to adjust the control parameters to the resilience `mode' only when needed. Moreover, if companies want to invest in additional capacity in order to become more resilient, manufacturing processes should be prioritised. Originality/value: This research developed a framework to quantitatively assess supply chain resilience. Moreover, due consideration of capacity constraint has been given by conducting in-depth analyses of systems nonlinearities

Multi-period whole system optimisation of an integrated carbon dioxide capture, transportation and storage supply chain

Carbon dioxide capture and storage (CCS) is an essential part of the portfolio of technologies to achieve climate mitigation targets. Cost efficient and large scale deployment of CCS necessitates that all three elements of the supply chain (capture, transportation and storage) are coordinated and planned in an optimum manner both spatially and across time. However, there is relatively little experience in combining CO2 capture, transport and storage into a fully integrated CCS system and the existing research and system planning tools are limited. In particular, earlier research has focused on one component of the chain or they are deterministic steady-state supply chain optimisation models. The very few multi-period models are unable to simultaneously make design and operational decisions for the three components of the chain. The major contribution of this thesis is the development for the first time of a multi-period spatially explicit least cost optimization model of an integrated CO2 capture, transportation and storage infrastructure under both a deterministic and a stochastic modelling framework. The model can be used to design an optimum CCS system and model its long term evolution subject to realistic constraints and uncertainties. The model and its different variations are validated through a number of case studies analysing the evolution of the CCS system in the UK. These case studies indicate that significant cost savings can be achieved through a multi-period and integrated system planning approach. Moreover, the stochastic formulation of the model allows analysing the impact of a number of uncertainties, such as carbon pricing or plant decommissioning schedule, on the evolution of the CSS system. In conclusion, the model and the results presented in this thesis can be used for system planning purposes as well as for policy analysis and commercial appraisal of individual elements of the CCS network.Open Acces

Small-signal modelling of maximum power point tracking for photovoltaic systems

In grid connected photovoltaic (PV) generation systems, inverters are used to convert the generated DC voltage to an AC voltage. An additional dc-dc converter is usually connected between the PV source and the inverter for Maximum Power Point Tracking (MPPT). An iterative MPPT algorithm searches for the optimum operating point of PV cells to maximise the output power under various atmospheric conditions. It is desirable to be able to represent the dynamics of the changing PV power yield within stability studies of the AC network. Unfortunately MPPT algorithms tend to be nonlinear and/or time-varying and cannot be easily combined with linear models of other system elements. In this work a new MPPT technique is developed in order to enable linear analysis of the PV system over reasonable time scales. The new MPPT method is based on interpolation and an emulated-load control technique. Numerical analysis and simulations are employed to develop and refine the MPPT. The small-signal modelling of the MPPT technique exploits the fact that the emulated-load control technique can be linearised and that short periods of interpolation can be neglected. A small-signal PV system model for variable irradiation conditions was developed. The PV system includes a PV module, a dc-dc boost converter, the proposed controller and a variety of possible loads. The new model was verified by component-level time-domain simulations. Be cause measured signals in PV systems contain noise, it is important to assess the impact of that noise on the MPPT and design an algorithm that operates effectively in pr esence of noise. For performance assessment of the new MPPT techniques, the efficiencies of various MPPT techniques in presence of noise were compared. This comparison showed superiority of the interpolation MPPT and led to conclusions about effective use of existing MPPT methods. The new MPPT method was also experimentally tested.Open Acces

Delivery time dynamics in an assemble-to-order inventory and order based production control system

System dynamics play a critical role in influencing supply chain performance. However, the dynamic property of the assemble-to-order (ATO) system remain unexplored. Based on control theory, the inventory and order based production control system (IOBPCS) family, can be utilized as a base framework for assessing system dynamics. However, the underlying assumption in traditional IOBPCS-based analytical studies is that the system is linear and the delivery time to end customers is negligible or backlog is used as a surrogate indicator. Our aim is to incorporate customer delivery lead-time variance as the third assessment measure alongside capacity availability and inventory variance as part of the so-called ‘performance triangle’– capacity at the supplier, the customer order decoupling point (CODP) inventory and the delivery lead-time. Using the ‘performance triangle’ and adopting non-linear control engineering techniques, we assess the dynamic behaviour of an ATO system in the electronics sector. We benchmark the ATO system dynamics model against the IOBPCS family. We exploit frequency response analysis to ensure a robust system design by considering three measures of the ‘performance triangle’. The findings suggest delivery LT variance can be minimised by maintaining the ATO system as a true Push-Pull hybrid state with sufficient CODP stock, although increased operational cost driven by bullwhip and CODP variance need to be considered. However, if the hybrid ATO system 'switches' to the pure Push state, the mean and variance of delivery LT can be significantly increased

Real-time receding horizon optimisation of gas pipeline networks

Real-time optimisation of gas pipelines in transient conditions is considered to be a challenging problem. Many pipeline systems are, however, only mildly non-linear. It is shown, that even the shutdown event of a compressor station can be described using a linear model. A dynamic, receding horizon optimisation problem is defined, where the free response prediction of the pipeline is obtained from a pipeline simulator and the optimal values of the decision variables are obtained solving a Quadratic Programming (QP) problem set up by using linear models, linearised constraints and quadratic approximations of the cost function, which is the energy consumption of the compressor stations (CSs). The problem is extended with discrete decision variables, the shutdown/start-up commands of CSs. A Mixed Logical Dynamical (MLD) system is defined, but the resulting Mixed Integer QP problem is shown to be very high-dimensional. Instead, a series of QP problems, each containing linear constraints modelling the shut down state of CSs, results in an optimisation problem with considerably smaller dimension. The receding horizon optimisation is tested in a simulation environment and comparison with data from the Finnish natural gas pipeline shows that 5 to 8 % savings in compressor energy consumption can be achieved using optimisation. A new idea, maximisation of energy consumption, is used to calculate maximal energy savings potential of the pipeline. A new result is that step response models used in conjunction with MLD systems do not produce the same model change behaviour than state space models.reviewe