Stabilization of oscillations through backstepping in high-dimensional systems

This paper introduces a method for obtaining stable and robust self-sustained oscillations in a class of single input nonlinear systems of dimension n ≥ 2. The oscillations are associated to a limit cycle that is produced in a second-order subsystem by means of an appropriate feedback law. Then, the controller is extended to the full system by a backstepping procedure. It is shown that the closed-loop system turns out to be generalized Hamiltonian and that the limit cycle can be thought as born in a Hopf bifurcation after moving a parameter.Ministerio de Ciencia e Innovación (España

Model-based control of slugging: advances and challenges

We review recent advances in the suppression of the slugging phenomenon by model-based control. We focus on three aspects of recent contributions: models, observers and control laws. For each category, we evaluate and compare existing solutions, and propose directions for improvement

Machine Learning Accelerated PDE Backstepping Observers

State estimation is important for a variety of tasks, from forecasting to substituting for unmeasured states in feedback controllers. Performing real-time state estimation for PDEs using provably and rapidly converging observers, such as those based on PDE backstepping, is computationally expensive and in many cases prohibitive. We propose a framework for accelerating PDE observer computations using learning-based approaches that are much faster while maintaining accuracy. In particular, we employ the recently-developed Fourier Neural Operator (FNO) to learn the functional mapping from the initial observer state and boundary measurements to the state estimate. By employing backstepping observer gains for previously-designed observers with particular convergence rate guarantees, we provide numerical experiments that evaluate the increased computational efficiency gained with FNO. We consider the state estimation for three benchmark PDE examples motivated by applications: first, for a reaction-diffusion (parabolic) PDE whose state is estimated with an exponential rate of convergence; second, for a parabolic PDE with exact prescribed-time estimation; and, third, for a pair of coupled first-order hyperbolic PDEs that modeling traffic flow density and velocity. The ML-accelerated observers trained on simulation data sets for these PDEs achieves up to three orders of magnitude improvement in computational speed compared to classical methods. This demonstrates the attractiveness of the ML-accelerated observers for real-time state estimation and control.Comment: Accepted to the 61st IEEE Conference on Decision and Control (CDC), 202

Combined voltage oriented control and direct power control based on backstepping control for four-leg PWM rectifier under unbalanced conditions

The present paper proposes a combined voltage-oriented control and direct power control (VOC-DPC) method associated with the backstepping control technique for a three-phase four-wire grid-connected four-leg rectifier in the synchronous rotating frame without using phase locked loop (PLL) and Parks transformation under balanced and unbalanced load and grid conditions. This control method is proposed in order to remove the drawbacks of the conventional VOC based on the PLL technique .The proposed control method is able to enhance the control performance and dynamic responses of the system when considering slow dynamics and instability issues of the PLL in several cases and can decrease the computational burden due to the absence of PLL and Park transformation. In addition, the performance of the proposed VOC-DPC method is enhanced by using backstepping control (BSC) based on Lyabonov theory for both the input currents and DC-bus voltage loops. As a consequence, constant DC-bus voltage, unit power factor, sinusoidal input currents, and neutral current minimization can be accurately carried out under both DC-bus voltage and load variations. Furthermore, robustness against filter inductance variations can also be achieved. The effectiveness, superiority, and performance of the proposed control method for a four-leg rectifier based on BSC in the dq0-frame are validated by several processor-in-the-loop (PIL) co-simulation tests sing the STM32F407 discovery development board

A Survey of path following control strategies for UAVs focused on quadrotors

The trajectory control problem, defined as making a vehicle follow a pre-established path in space, can be solved by means of trajectory tracking or path following. In the trajectory tracking problem a timed reference position is tracked. The path following approach removes any time dependence of the problem, resulting in many advantages on the control performance and design. An exhaustive review of path following algorithms applied to quadrotor vehicles has been carried out, the most relevant are studied in this paper. Then, four of these algorithms have been implemented and compared in a quadrotor simulation platform: Backstepping and Feedback Linearisation control-oriented algorithms and NLGL and Carrot-Chasing geometric algorithms.Peer ReviewedPostprint (author's final draft

Nonlinear Model-Based Control of Unstable Wells

This paper illustrates the potential of nonlinear model-based control applied for stabilization of unstable flow in oil wells. A simple empirical model is developed that describes the qualitative behavior of the downhole pressure during severe riser slugging. A nonlinear controller is designed by an integrator backstepping approach, and stabilization for open-loop unstable pressure setpoints is demonstrated. The proposed backstepping controller is shown in simulations to perform better than PI and PD controllers for low pressure setpoints, and is in addition easier to tune. Operation at a low pressure setpoint is desirable since it corresponds to a high production flow rate. The simulation results are presented to illustrate the effectiveness of proposed control scheme