Newton-Raphson Solution of Nonlinear Delay-Free Loop Filter Networks

For their numerical properties and speed of convergence, Newton-Raphson methods are frequently used to compute nonlinear audio electronic circuit models in the digital domain. These methods are traditionally employed regardless of preliminary considerations about their applicability, primarily because of a lack of flexible mathematical tools making the convergence analysis an easy task. We define the basin delimiter, a tool that can be applied to the case when the nonlinear circuit is modeled by a delay-free loop network. This tool is derived from a known convergence theorem providing a sufficient condition for quadratic speed of convergence of the method. After substituting the nonlinear characteristics with equivalent linear filters that compute Newton-Raphson on the existing network, through the basin delimiter, we figure out constraints guaranteeing quadratic convergence speed in the diode clipper. Further application to a ring modulator circuit does not lead to comparably useful constraints for quadratic convergence; however, also in this circuit, the basin delimiter has a magnitude roughly proportional to the number of iterations needed by the solver to find a solution. Together, such case studies foster refinement and generalization of this tool as a speed predictor, with potential application to the design of virtual analogue systems for real-time digital audio effects

Extended Fixed-Point Methods for the Computation of Virtual Analog Models

A family of iterative root-finding methods for nonlinear discrete-time systems of equations is presented, with a formulation that puts it in between the Fixed-Point (FP) and Newton-Raphson (NR) methods. Applicability of this family is allowed, provided that the Jacobian matrix of the nonlinear system has a spectral radius less than one. By varying the order of a matrix geometric sum that approximates the inverse Jacobian matrix, root-finding at any iteration can be steered toward the FP or conversely toward the NR method, becoming identical to either of them if the order is equal to zero or infinitely large, respectively. Since the methods in this family do not need the solution of a linear system at each iteration as required by NR, their computational cost makes them palatable for the online digital implementation of nonlinear models. As an example of application, a Virtual Analog model of the voltage-controlled filter onboard a popular music synthesizer is tested, showing that for some orders of the aforementioned geometric sum the proposed methods perform better than FP and NR in terms of computational cost, while exhibiting the same accuracy

Nonlinear Modeling of Power Electronics-based Power Systems for Control Design and Harmonic Studies

The massive integration of power electronics devices in the modern electric grid marked a turning point in the concept of stability, power quality and control in power systems. The evolution of the grid toward a converter-dominated network motivates a deep renovation of the classical power system theory developed for machine-dominated networks. The high degree of controllability of power electronics converters, furthermore, paves the way to the investigation of advanced control strategies to enhance the grid stability, resiliency and sustainability. This doctoral dissertation explores four cardinal topics in the field of power electronics-based power systems: dynamic modeling, stability analysis, converters control, and power quality with particular focus on harmonic distortion. In all four research areas, a particular attention is given to the implications of the nonlinearity of the converter models on the power system

Novel Internet of Vehicles Approaches for Smart Cities

Smart cities are the domain where many electronic devices and sensors transmit data via the Internet of Vehicles concept. The purpose of deploying many sensors in cities is to provide an intelligent environment and a good quality of life. However, different challenges still appear in smart cities such as vehicular traffic congestion, air pollution, and wireless channel communication aspects. Therefore, in order to address these challenges, this thesis develops approaches for vehicular routing, wireless channel congestion alleviation, and traffic estimation. A new traffic congestion avoidance approach has been developed in this thesis based on the simulated annealing and TOPSIS cost function. This approach utilizes data such as the traffic average travel speed from the Internet of Vehicles. Simulation results show that the developed approach improves the traffic performance for the Sheffield the scenario in the presence of congestion by an overall average of 19.22% in terms of travel time, fuel consumption and CO2 emissions as compared to other algorithms. In contrast, transmitting a large amount of data among the sensors leads to a wireless channel congestion problem. This affects the accuracy of transmitted information due to the packets loss and delays time. This thesis proposes two approaches based on a non-cooperative game theory to alleviate the channel congestion problem. Therefore, the congestion control problem is formulated as a non-cooperative game. A proof of the existence of a unique Nash equilibrium is given. The performance of the proposed approaches is evaluated on the highway and urban testing scenarios. This thesis also addresses the problem of missing data when sensors are not available or when the Internet of Vehicles connection fails to provide measurements in smart cities. Two approaches based on l1 norm minimization and a relevance vector machine type optimization are proposed. The performance of the developed approaches has been tested involving simulated and real data scenarios

Parameter Identification of Nonlinear System on Combustion Engine Based MVEM using PEM

In four-stroke engine injection system, often called spark ignition (SI) engine, the air-fuel ratio (AFR) is taken from the measurement of lambda sensor in the exhaust. This sensor does not directly describe how much AFR in the combustion chamber due to the large transport delay. Therefore, the lambda sensor is used only as a feedback in AFR control "correction", not as the "main" control. The purpose of this research is to identify the parameters of the non-linear system in SI engines to produce AFR estimator. The AFR estimator is expected to be used as a feedback of the main "AFR" control system. The process of identifying the parameters using the Gauss-Newton method, due to its rapid computation to Achieve convergence, is based on prediction error minimization (PEM). The models of AFR estimator is an open-loop system without a universal exhaust gas oxygen (UEGO) sensors as feedback, called a virtual AFR sensor. The high price of UEGO sensors makes the virtual AFR sensor can be a practical solution to be applied in AFR control. The model in this research is based on the mean value engine models (MVEM) with some modifications. The research dataset was taken from a Hyundai Verna 2002 with the additional UEGO type of lambda sensors. The throttle opening angle (input) is played by stepping on the gas pedal and the signal to the injector (input) is set to a certain quantity to produce the AFR (output) value read by the UEGO sensor. This research produces an open loop estimator model or AFR virtual sensors with normalized root mean square error (NRMSE) = 0.06831 = 6.831%

U-model based adaptive internal model control for tracking of nonlinear dynamic plants

We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs using a special-purpose calculus and an SMT encoding. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large class of examples

Non-iterative simulation methods for virtual analog modelling

The simulation of nonlinear components is central to virtual analog simulation. In audio effects, circuits often include devices such as diodes and transistors, mostly operating in a strongly nonlinear regime. Mathematical models are in the form of systems of nonlinear ordinary differential equations (ODEs), and traditional integrators, such as the trapezoid and midpoint methods, can be employed as solvers. These methods are fully implicit and require the solution of a nonlinear algebraic system at each time step, introducing further complications regarding the existence and uniqueness of the solution, as well as the choice of halting conditions for the iterative root finder. On the other hand, fast explicit methods such as Forward Euler, are prone to unstable behaviour at standard audio sample rates. For these reasons, in this work, a family of linearly-implicit schemes is presented. These schemes take the form of a perturbation expansion, making the construction of higher-order schemes possible. Compared with classic implicit designs, the proposed methods have the advantage of efficiency, since the update is computed in a single iteration. Furthermore, the existence and uniqueness of the update are proven by simple inspection of the update matrix. Compared to classic explicit designs, the proposed schemes display stable behaviour at standard audio sample rates. In the case of a single scalar ODE, sufficient conditions for numerical stability can be derived, imposing constraints on the choice of the sampling rate. Several theoretical results are provided, as well as numerical examples for typical stiff equations used in virtual analog modelling

Opto-VLSI processing for reconfigurable optical devices

The implementation of Wavelength Division Multiplexing system (WDM) optical fibre transmission systems has the potential to realise this high capacity data rate exceeding 10 Tb/s. The ability to reconfigure optical networks is a desirable attribute for future metro applications where light paths can be set up or taken down dynamically as required in the network. The use of microelectronics in conjunction with photonics enables intelligence to be added to the high-speed capability of photonics, thus realising reconfigurable optical devices which can revolutionise optical telecommunications and many more application areas. In this thesis, we investigate and demonstrate the capability of Opto-VLSI processors to realise a reconfigurable WDM optical device of many functions, namely, optical multiband filtering, optical notch filtering, and reconfigurable-Optical-Add-Drop Multiplexing (ROADM). We review the potential technologies available for tunable WDM components, and discuss their advantages and disadvantages. We also develop a simple yet effective algorithm that optimises the performance of Opto-VLSI processors, and demonstrate experimentally the multi-function WDM devices employing Opto-VLSI processors. Finally, the feasibility of Opto-VLSI-based WDM devices in meeting the stringent requirements of the optical communications industry is discussed

Efficient simulation of acoustic physical models with nonlinear dissipation

One long-term goal of physics-based sound synthesis and audio effect modeling has been to open the door to models without a counterpart in the real world. Less explored has been the fine-grained adjustment of the constituent physical laws that underpin such models. In this paper, the introduction of a nonlinear damping law into a plate reverberation model is explored, through the use of four different functions, transferred from the setting of virtual-analog electronics. First, a case study of an oscillator with nonlinear damping is investigated. Results are compared against linear dissipation, illustrating differing spectral characteristics. To solve the systems, a recently proposed numerical solver is employed, that entirely avoids the use of iterative routines such as Newton-Raphson for solving nonlinearities, thus allowing very efficient numerical solution. This scheme is then used to simulate a plate reverbation unit, and tests are run, to investigate spectral variations induced by nonlinear damping. Finally, a musical case is presented that includes frequency-dependent damping coefficients