Observer Design for Interconnected Systems and Implementation via Differential-Algebraic Equations

A new approach to the design of observers of nonlinear dynamical systems is presented. Generally, linear or nonlinear control systems are expressed as explicit systems of differential equations and solved either analytically or numerically. If numerically, they are implemented using standard ordinary differential equation (ODE) solvers. In this thesis, a system is decomposed and modeled as an interconnection between two observer subsystems, particularly, as canonical DAE observers. In general, control design engineers may be faced with a formidable problem of solving this system analytically or in obtaining closed-form solutions. To attest to the complexity and complications in treating a system of interconnected DAE observer systems, a scaled-down version of a publication on “Small-Gain Theorem” is included in the appendix for the reader’s perusal. (A brief introduction to “Small-Gain Theorem” can be found in Chapter 4). The premise of this thesis is to demonstrate that, where the design of an observer plays a major role involving output feedback, there may be advantages in formulating a control system as a differential-algebraic equation (DAE), especially in the case of interconnected subsystems. An implicit system of interconnected DAE observers is considered and shown implementable using an existing DAE solver, whose resolution allows one the capability of computing input and output bounds. This is based on fixed or variable timesteps within the operating interval of each subsystem to ensure input-output stability (IOS) and the observability property of the interconnected observer system. The observer design method is based on the extended linearization approach. The basic background is provided for the design process of an interconnected observer system using DAE. Note, the application of the new approach has not been considered previously for the case of an interconnected DAE observer system

Numerical solutions for DAEs using Legendre wavelets

In this paper, a method for solving singular differential algebraic equations combining Legendre wavelets with a collocation technique is presented. Numerical examples show that the method is easy to implement and yields very accurate results.Facultad de Ingenierí

Numerical solutions for DAEs using Legendre wavelets

In this paper, a method for solving singular differential algebraic equations combining Legendre wavelets with a collocation technique is presented. Numerical examples show that the method is easy to implement and yields very accurate results.Facultad de Ingenierí

How AD Can Help Solve Differential-Algebraic Equations

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical solution. This is often done with the help of a computer algebra system. We show in two significant cases that it can be done efficiently by pure algorithmic differentiation. The first is the Dummy Derivatives method, here we give a mainly theoretical description, with tutorial examples. The second is the solution of a mechanical system directly from its Lagrangian formulation. Here we outline the theory and show several non-trivial examples of using the "Lagrangian facility" of the Nedialkov-Pryce initial-value solver DAETS, namely: a spring-mass-multipendulum system, a prescribed-trajectory control problem, and long-time integration of a model of the outer planets of the solar system, taken from the DETEST testing package for ODE solvers

Numerical Simulation Approach for a Dynamically Operated Sorption-Enhanced Water-Gas Shift Reactor

A dynamically operated sorption-enhanced water–gas shift reactor is modelled to leverage its performance by means of model-based process design. This reactor shall provide CO₂-free synthesis gas for e-fuel production from pure CO. The nonlinear model equations describing simultaneous adsorption and reaction are solved with three numerical approaches in MATLAB: a built-in solver for partial differential equations, a semi-discretization method in combination with an ordinary differential equation solver, and an advanced graphic implementation of the latter method in Simulink. The novel implementation in Simulink offers various advantages for dynamic simulations and is expanded to a process model with six reaction chambers. The continuous conditions in the reaction chambers and the discrete states of the valves, which enable switching between reactive adsorption and regeneration, lead to a hybrid system. Controlling the discrete states in a finite-state machine in Stateflow enables automated switching between reactive adsorption and regeneration depending on predefined conditions, such as a time span or a concentration threshold in the product gas. The established chemical reactor simulation approach features unique possibilities in terms of simulation-driven development of operating procedures for intensified reactor operation. In a base case simulation, the sorbent usage for serial operation with adjusted switching times is increased by almost 15%

Non-linear model predictive energy management strategies for stand-alone DC microgrids

Due to substantial generation and demand fluctuations in stand-alone green micro-grids, energy management strategies (EMSs) are becoming essential for the power sharing purpose and regulating the microgrids voltage. The classical EMSs track the maximum power points (MPPs) of wind and PV branches independently and rely on batteries, as slack terminals, to absorb any possible excess energy. However, in order to protect batteries from being overcharged by realizing the constant current-constant voltage (IU) charging regime as well as to consider the wind turbine operational constraints, more flexible multivariable and non-linear strategies, equipped with a power curtailment feature, are necessary to control microgrids. This dissertation work comprises developing an EMS that dynamically optimises the operation of stand-alone dc microgrids, consisting of wind, photovoltaic (PV), and battery branches, and coordinately manage all energy flows in order to achieve four control objectives: i) regulating dc bus voltage level of microgrids; ii) proportional power sharing between generators as a local droop control realization; iii) charging batteries as close to IU regime as possible; and iv) tracking MPPs of wind and PV branches during their normal operations. Non-linear model predictive control (NMPC) strategies are inherently multivariable and handle constraints and delays. In this thesis, the above mentioned EMS is developed as a NMPC strategy to extract the optimal control signals, which are duty cycles of three DC-DC converters and pitch angle of a wind turbine. Due to bimodal operation and discontinuous differential states of batteries, microgrids belong to the class of hybrid dynamical systems of non-Filippov type. This dissertation work involves a mathematical approximation of stand-alone dc microgrids as complementarity systems (CSs) of Filippov type. The proposed model is used to develop NMPC strategies and to simulate microgrids using Modelica. As part of the modelling efforts, this dissertation work also proposes a novel algorithm to identify an accurate equivalent electrical circuit of PV modules using both standard test condition (STC) and nominal operating cell temperature (NOCT) information provided by manufacturers. Moreover, two separate stochastic models are presented for hourly wind speed and solar irradiance levels

Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter

This paper investigates the state estimation of a high-fidelity spatially resolved thermal- electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1 % in less than 200 s despite a 30 % error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.Comment: Submitted to the Journal of Power Source

Numerical solutions for DAEs using Legendre wavelets

In this paper, a method for solving singular differential algebraic equations combining Legendre wavelets with a collocation technique is presented. Numerical examples show that the method is easy to implement and yields very accurate results.Facultad de Ingenierí