Alexey Pavlov

Straight Line Path Following for Formations of Underactuated Marine Surface Vessels

The problem of formation control and path following for underactuated 3-degrees-of-freedom (3-DOF) marine surface vessels is considered. The proposed decentralized controller makes the vessels asymptotically constitute a desired formation that follows a given straight line path with a given forward speed profile. The controller consists of a cross-track control law, based on line-of-sight guidance, and a nonlinear synchronization control law. The closed-loop dynamics of both the cross-track errors and the synchronization errors are analyzed in detail using nonlinear cascaded systems theory and the overall cascaded system is shown to be both uniformly globally asymptotically stable and uniformly globally exponentially stable under mild assumptions. The proposed control strategy is validated in experiments in both calm water and in waves using a scale model vessel.

Integral LOS control for path following of underactuated marine surface vessels in the presence of constant ocean currents

In this paper, we consider the development of a control strategy for path following of underactuated marine surface vessels in the presence of ocean currents. The proposed control strategy is based on a modified Line-of-Sight (LOS) guidance law with integral action and a pair of adaptive feedback controllers. Traditional LOS guidance has several nice properties and is widely used in practice for path following of marine vehicles. However, it has the drawback of being susceptible to environmental disturbances. In this work, we propose a modified LOS guidance law with integral action for counteracting environmental disturbances. Paired with a set of adaptive feedback controllers, we show that this approach guarantees global asymptotic path following of straight-line paths in the presence constant and irrotational ocean currents.

Uniform Output Regulation of Nonlinear Systems

The problem of asymptotic regulation of the output of a dynamical system plays a central role in control theory. An important variant of this problem is the output regulation problem, which can be used in such areas as set-point control, tracking reference signals and rejecting disturbances generated by an external system, controlled synchronization of dynamical systems, and observer design for autonomous systems. This book is one of the first systematic studies on the nonlinear output regulation problem that embraces both the local and global solvability analysis, covering such aspects as solvability conditions, controller design, and practical implementation issues. The book opens with the development of the mathematical apparatus of convergent systems—very useful for studying nonlinear control systems—laying the foundation for most of the results presented in the work. The study then proceeds to a new problem statement—the so-called uniform output regulation problem. A comprehensive solvability analysis of this problem is provided in the next part of the work. Based on the solvability analysis, constructive controller design methods for the global uniform output regulation problem are presented for various classes of nonlinear systems. In an attempt to bridge the gap between theory and practice, the authors conclude with a presentation of an experimental case study. The experiment—one of the first in the field of nonlinear output regulation—deals with control of a translational oscillator with a rotational actuator, illustrating the applicability of the nonlinear output regulation theory in experiments and raising a number of questions to be addressed in future research. The scope of questions addressed in the book, the uniformity of their treatment, the novelty of the proposed approach, and the obtained results make this volume unique with respect to other works on the problem of nonlinear output regulation. In addition to being an excellent reference for the uniform output regulation problem, the book has a tutorial value on convergent systems. The work will be of interest to control engineers, theorists, and students, and may be used as a textbook for a graduate course on nonlinear control.

Frequency Response Functions for Nonlinear Convergent Systems

Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency response functions for convergent systems give rise to nonlinear Bode plots, which serve as a graphical tool for performance analysis of nonlinear convergent systems in the frequency domain. The results are illustrated with an example.

Modeling and Control of Heave-Induced Pressure Fluctuations in Managed Pressure Drilling

Managed pressure drilling is an advanced pressure control method which is intended to meet increasingly high demands in drilling operations in the oil and gas industry. In this method, the circulating drilling fluid, which takes cuttings out of the well, is released at the surface through a controlled choke. This choke is used for active control of the fluid pressure in the well. The corresponding automatic control system keeps the pressure at the bottom of the well at a specified set-point despite various disturbances. One of such disturbances, vertical motion of the drill string, causes severe pressure fluctuations which need to be actively attenuated. In this paper we present two different disturbance rejection strategies based on discretized partial differential equations for the well hydraulic system. The performance of the controllers is shown through simulations both under idealized conditions as well as by simulations on a high fidelity drilling simulator.

On convergence properties of piecewise affine systems

In this paper convergence properties of piecewise affine (PWA) systems are studied. In general, a system is called convergent if all its solutions converge to some bounded globally asymptotically stable steady-state solution. The notions of exponential, uniform and quadratic convergence are introduced and studied. It is shown that for non-linear systems with discontinuous right-hand sides, quadratic convergence, i.e., convergence with a quadratic Lyapunov function, implies exponential convergence. For PWA systems with continuous right-hand sides it is shown that quadratic convergence is equivalent to the existence of a common quadratic Lyapunov function for the linear parts of the system dynamics in every mode. For discontinuous bimodal PWA systems it is proved that quadratic convergence is equivalent to the requirements that the system has some special structure and that certain passivity-like condition is satisfied. For a general multimodal PWA system these conditions become sufficient for quadratic convergence. An example illustrating the application of the obtained results to a mechanical system with a one-sided restoring characteristic, which is equivalent to an electric circuit with a switching capacitor, is provided. The obtained results facilitate bifurcation analysis of PWA systems excited by periodic inputs, substantiate numerical methods for computing the corresponding periodic responses and help in controller design for PWA systems.

Brief paper: Tracking and synchronisation for a class of PWA systems

In this paper, the tracking problem for a class of discontinuous piecewise affine (PWA) systems is addressed. We propose an observer-based output-feedback control design, consisting of a feedforward, a piecewise affine feedback law and a model-based observer, solving the tracking problem. These synthesis results can also be employed to tackle the master-slave synchronisation problem for PWA systems. It is shown that for certain classes of PWA systems the design is characterised in terms of linear matrix inequalities. The results are illustrated by application to mechanical systems with discontinuous friction characteristics.

Drilling seeking automatic control solutions

Abstract This paper addresses control challenges within drilling for the oil and gas industry. Drilling has not been modernized as much as other industries and there is still a great potential for automatic control. Heavy machinery is used to handle pipes and other equipment topside and in and out of the hole. These machines can be controlled remotely with a joystick. Very advanced tools are being used downhole several km away from the rig and these are often controlled remotely. Mud pulse telemetry with low bandwidth is used to communicate with downhole equipment. Drilling involves certain risks and mistakes may have disastrous consequences both for people and economically, e.g. a blow-out. Safety is therefore always the most important issue, and new solutions must be robust and fault tolerant. Extensive testing is required before being used in an actual drilling operation. Managed pressure drilling is a relative new method for drilling challenging wells with narrow margins requiring precise pressure control. Nonlinear model based control solutions and observers have been developed for this technology. This is addressed in this paper together with experimental results. In addition an overview of some other interesting challenges is given.

Convergent piecewise affine systems: analysis and design Part II: discontinuous case

In this paper convergence properties of piecewise affine (PWA) systems with discontinuous right-hand sides are studied. It is shown that for discontinuous PWA systems existence of a common quadratic Lyapunov function is not sufficient for convergence. For discontinuous bimodal PWA systems necessary and sufficient conditions for quadratic convergence, i.e. convergence with a quadratic Lyapunov function, are derived.

Performance of convergence-based variable-gain control of optical storage drives

In this paper, a method for the performance assessment of a variable-gain control design for optical storage drives is proposed. The variable-gain strategy is used to overcome well-known linear control design trade-offs between low-frequency tracking properties and high-frequency noise sensitivity. A convergence-based control design is proposed that guarantees stability of the closed-loop system and a unique bounded steady-state response for any bounded disturbance. These favourable properties, guaranteed by virtue of convergence, allow for a unique performance evaluation of the control system. Moreover, technical conditions for convergence are derived for the variable-gain controlled system and a quantitative performance measure, taking into account both low-frequency tracking properties and high-frequency measurement noise sensitivity, is proposed. The convergence conditions together with the performance measure jointly constitute a design tool for tuning the parameters of the variable-gain controller. The resulting design is shown to outperform linear control designs.