Backstepping PDE Design: A Convex Optimization Approach

Abstract\u2014Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sumof- Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs

State Feedback Nonlinear Control Strategy for Wind Turbine System Driven by Permanent Magnet Synchronous Generator for Maximum Power Extraction and Power Factor Correction

This chapter addresses the problem of controlling the Complete chain of the wind turbine system using the permanent magnet synchronous generator (PMSG) connected with the Distribution network via an AC/DC/AC converters through LCL filter, the control to be applied in different parts of the system, whose objectives are three: (1) adjust the generator speed to track a varying reference signal; (2) the control of the network-side converter must be maintained the current injected into the network in a unit power factor correction (PFC); (3) regulating the DC Link voltage at a constant value. Firstly, the mathematical modeling for all system components studied in d-q frame and its state space equation are established to simplify the proposed control, thereafter a nonlinear backstepping approach is used in this work to achieve the objectives indicated above. The performance of the proposed approach is evaluated based on the various simulations results carried out under Matlab/Simulink/Simpower software

Nonlinear Control of a DC MicroGrid for the Integration of Photovoltaic Panels

New connection constraints for the power network (Grid Codes) require more flexible and reliable systems, with robust solutions to cope with uncertainties and intermittence from renewable energy sources (renewables), such as photovoltaic arrays. The interconnection of such renewables with storage systems through a Direct Current (DC) MicroGrid can fulfill these requirements. A "Plug and Play" approach based on the "System of Systems" philosophy using distributed control methodologies is developed in the present work. This approach allows to interconnect a number of elements to a DC MicroGrid as power sources like photovoltaic arrays, storage systems in different time scales like batteries and supercapacitors, and loads like electric vehicles and the main AC grid. The proposed scheme can easily be scalable to a much larger number of elements.Comment: arXiv admin note: text overlap with arXiv:1607.0848

Nonlinear adaptive controller design to stabilize constant power loads connected-DC microgrid using disturbance accommodation technique

The DC microgrid is comprised of a considerable number of electronically regulated power electronic loads that act as constant power loads (CPLs). These power electronic devices have a high bandwidth regulation capability as well as a high-power conversion efficiency. Specifically, the high bandwidth control for the output of the converter load, when paired with the system’s filtering components, results in negatively damped oscillations. These features, even if needed, may cause system instability and, finally, system failure if not avoided. To achieve effective power flow control in a DC microgrid, it is crucial to eliminate the undesired behaviour of the CPLs. The control objective requires the assessment of the power for uncertain loads, which vary with time. This paper proposes an adaptive controller linked to a cubature Kalman filter(CKF) for a DC microgrid with time-varying non-ideal CPLs. The controller utilises the neuro-fuzzy inference system(ANFIS) to make the design adaptive. The CKF method is used to determine the instantaneous value of time-varying load power. The assessed power is afterward sent to an ANFIS-based controller, which aims to modify the energy storage systems (ESS) injected current adaptively. The suggested controller not only maintains overall stability when the CPLs vary significantly, but it has a rapid dynamic response and accurate tracking across a wide operating range as well. The simulation results demonstrate that the proposed adaptive controller can improve the DC microgrid’s transient response while also increasing the stability margin

Robust Adaptive Stabilization of Nonholonomic Mobile Robots with Bounded Disturbances

The stabilization problem of nonholonomic mobile robots with unknown system parameters and environmental disturbances is investigated in this paper. Considering the dynamic model and the kinematic model of mobile robots, the transverse function approach is adopted to construct an additional control parameter, so that the closed-loop system is not underactuated. Then the adaptive backstepping method and the parameter projection technique are applied to design the controller to stabilize the system. At last, simulation results demonstrate the effectiveness of our proposed controller schemes

Nonlinear backstepping with time delay estimation for six-phase induction machine

In this paper, a robust nonlinear stator currents controller based on a known nonlinear technique is proposed for a six-phase induction machine. First of all, a proportional-integral regulator is used in an outer loop to control the speed. Secondly, the inner loop based on a nonlinear method that combines the nonlinear backstepping control scheme with the time delay estimation consists of controlling the stator currents. The chosen time delay estimation method can approximate the unmeasurable rotor current while the nonlinear backstepping can achieve good tracking performances. The stability analysis of the current closed-loop error dynamics is provided based on a recursive Lyapunov function. Numerical simulations have been conducted to demonstrate the efficiency and the performance of the developed nonlinear control method for the asymmetrical six-phase induction machine.CONACYT – Consejo Nacional de Ciencia y TecnologíaPROCIENCI