Advances in Control Theory and Applications

Frontmatter

Modeling and Control of Autonomous Helicopters

Abstract

This chapter presents an overview on the modeling and model-based control of autonomous helicopters. Firstly it introduces some of the platforms and control architectures that has been developed in the last 15 years. Later, the Chapter considers the modeling of the helicopter and the identification techniques. Then, it overviews different linear and non-linear model-based control approaches. This section also includes experiments on the control of the helicopter vertical motion that illustrate the presented techniques and point out the interest of nonlinear analysis methods to study the dynamic behavior of the helicopter. Finally, the Chapter presents open research lines coming from two challenging applications: the autonomous landing in oscillating platforms and the lifting and transporting of a single load with several helicopters.

Manuel Béjar, Anibal Ollero, Federico Cuesta

Efficient Quantization in the Average Consensus Problem

Abstract

In the average consensus a set of linear systems has to be driven to the same final state which corresponds to the average of their initial states. This mathematical problem can be seen as the simplest example of coordination task and in fact it can be used to model both the control of multiple autonomous vehicles which all have to be driven to the centroid of the initial positions, and to model the decentralized estimation of a quantity from multiple measure coming from distributed sensors. In general we can expect that the performance of a consensus strategy will be strongly related to the amount of information the agents exchange each other. This contribution presents a consensus strategy in which the exchanged data are symbols and not real numbers. This is based on a logarithmic quantizer based state estimator. The stability of this technique is then analyzed.

Ruggero Carli, Sandro Zampieri

Human-Robot Interaction Control Using Force and Vision

Abstract

The extension of application domains of robotics from factories to human environments leads to implementing proper strategies for close interaction between people and robots. In order to avoid dangerous collision, force and vision based control can be used, while tracking human motion during such interaction.

Agostino De Santis, Vincenzo Lippiello, Bruno Siciliano, Luigi Villani

A Dissipation Inequality for the Minimum Phase Property of Nonlinear Control Systems

Abstract

The minimum phase property is an important notion in systems and control theory. In this paper, a characterization of the minimum phase property of nonlinear control systems in terms of a dissipation inequality is derived. It is shown that this dissipation inequality is equivalent to the classical definition of the minimum phase property in the sense of Byrnes and Isidori, if the control system is affine in the input and the so-called input-output normal form exists.

Christian Ebenbauer, Frank Allgöwer

Input Disturbance Suppression for Port-Hamiltonian Systems: An Internal Model Approach

Abstract

In this paper an internal model based approach to periodic input disturbance suppression for port-Hamiltonian systems is presented; more specifically, an adaptive solution able to deal with unknown periodic signal belonging to a given class is introduced.

After an introductive section, the adaptive internal model design procedure is presented in order to solve the input disturbance problem. This theoretical machinery is specialized for the energy-based port-Hamiltonian framework in order to prove the global asymptotical stability of the solution.

Finally, in order to clearly point out the effectiveness of the presented design procedure a tracking problem is solved for a robotic manipulator affected by torque ripples.

Luca Gentili, Andrea Paoli, Claudio Bonivento

A Systems Theory View of Petri Nets

Abstract

Petri nets are a family of powerful discrete event models whose interest has grown, within the automatic control community, in parallel with the development of the theory of discrete event systems. In this tutorial paper our goal is that of giving a flavor, by means of simple examples, of the features that make Petri nets a good model for systems theory and of pointing out at a few open areas for research. We focus on Place/Transitions nets, the simplest Petri net model. In particular we compare Petri nets with automata, and show that the former model has several advantages over the latter, not only because it is more general but also because it offers a better structure that has been used for developing computationally efficient algorithms for analysis and synthesis.

Alessandro Giua, Carla Seatzu

Wireless Sensing with Power Constraints

Abstract

We introduce two conceptual models for wireless sensing and control with power-limited sensors and controllers. The limited battery power of the wireless device is captured in the models by imposing hard constraints on either the number of available transmissions the device can make, or on the number of cycles it can stay awake. Such hard constraints can be viewed as a measurement budget, under which estimation or control policies will have to be developed over a given decision horizon. Among the two representative models studied here, the first one is one of optimal scheduling of a finite measurement budget for a Gauss-Markov process over an observation horizon. The second one is an optimal estimation problem where the number of transmissions the wireless sensor can make is limited to a number, M, which is less than the observation horizon, N. It is shown that both problems can be solved by employing dynamic-programming type arguments, and their solutions have a threshold characterization.

Orhan C. Imer, Tamer Başar

The Important State Coordinates of a Nonlinear System

Abstract

We offer an alternative way of evaluating the relative importance of the state coordinates of a nonlinear control system. Our approach is based on making changes of state coordinates to bring the controllability and observability functions into input normal form. These changes of coordinates are done degree by degree and the resulting normal form is unique through terms of degree seven.

Arthur J. Krener

On Decentralized and Distributed Control of Partially-Observed Discrete Event Systems

Abstract

This paper surveys recent work of the author with several collaborators, principally Feng Lin, Weilin Wang, and Tae-Sic Yoo; they are kindly acknowledged. Decentralized control of discrete event systems, where local controllers cannot explicitly communicate in real-time, is considered in the first part of the paper. Then the problem of real-time communication among a set of local discrete-event controllers (or diagnosers) is discussed. The writing is descriptive and is meant to inform the reader about important conceptual issues and some recently-completed or on-going research efforts.

Stéphane Lafortune

A Unifying Approach to the Design of Nonlinear Output Regulators

Abstract

The goal of this paper is to propose a unique vision able to frame a number of results recently proposed in literature to tackle problems of output regulation for nonlinear systems. This is achieved by introducing the so-called asymptotic internal model property as the crucial property which, if fulfilled, leads to the design of the regulator for a fairly general class of nonlinear systems satisfying a proper minimum-phase condition. It is shown that recent frameworks based upon the use of nonlinear high-gain and adaptive observer techniques for the regulator design can be cast in this setting. A recently proposed technique for output regulation without immersion is also framed in these terms.

Lorenzo Marconi, Alberto Isidori

Controller Design Through Random Sampling: An Example

Abstract

In this chapter, we present the scenario approach, an innovative technology for solving convex optimization problems with an infinite number of constraints. This technology relies on random sampling of constraints, and provides a powerful means for solving a variety of design problems in systems and control. Specifically, the virtues of this approach are here illustrated by focusing on optimal control design in presence of input saturation constraints.

Maria Prandini, Marco C. Campi, Simone Garatti

Digital Control of High Performance Power Supplies for a Synchrotron Light Source

Abstract

Design and control of Power Supplies (PSs) feeding the magnets of a Synchrotron Light Source have to match severe specifications; high accuracy in the range of ppm in output current tracking is required for the correct operation of the magnets, while a Power Factor (PF) close to the unit is demanded at the input section due to the high power involved.

In this paper an advanced control strategy is presented for a particular kind of Quadrupole Magnet Power Supply, where variable output current has to be imposed. The case of the “switch-mode” multilevel power converter for booster quadrupole magnets of the DIAMOND synchrotron radiation facility under construction at the Harwell Chilton Science Campus, Didcot, has been considered.

High accuracy in the tracking of the desired output current reference is reached by means of a digital internal model-based controller. A multivariable controller is adopted in order to ensure current balancing between the stages of the multilevel converter.

Front-end topology selection, proper dimensioning and control design are exploited to guarantee high power factor and low harmonic distortion of the input currents, and to avoid low-frequency components related to the quadrupole magnets’ oscillating currents. For this purpose, confined oscillatory behavior imposed to the voltage of the DC-link capacitors plays a key role.

Simulations and experimental validations are reported that confirm the expected results.

Carlo Rossi, Andrea Tilli, Manuel Toniato

Distributed PCHD-Systems, from the Lumped to the Distributed Parameter Case

Abstract

The Hamiltonian approach has turned out to be an effective tool for modeling, system analysis and controller design in the lumped parameter case. There exist also several extensions to the distributed parameter case. This contribution presents a class of extended distributed parameter Hamiltonian systems, which preserves some useful properties of the well known class of Port Controlled Hamiltonian systems with Dissipation. In addition, special ports are introduced to take the boundary conditions into account. Finally, an introductory example and the example of a piezoelectric structure, a problem with two physical domains, show, how one can use the presented approach for modeling and design.

Kurt Schlacher

Observability and the Design of Fault Tolerant Estimation Using Structural Analysis

Abstract

This chapter presents a structural analysis approach for the design of fault tolerant estimation algorithms. The general fault tolerance problem setting is first given, and structural analysis is presented in the component based modeling frame. An original condition for structural observability is developed, which is constructive, since it allows to identify those Data Flow Diagrams by which unknown variables can be estimated, both in healthy and in faulty conditions. The link with two basic dependability concepts, namely critical faults and reliability is shown.

Marcel Staroswiecki

Robust Hybrid Control Systems: An Overview of Some Recent Results

Abstract

This paper gives an overview of a framework for analyzing hybrid dynamical systems. The emphasis is on modeling assumptions that guarantee robustness. These conditions lead to a general invariance principle and to results on the existence of smooth Lyapunov functions (converse theorems) for hybrid systems. In turn, the stability analysis tools motivate novel hybrid control algorithms for nonlinear systems.

Andrew R. Teel

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