Fabio Gómez-Estern

Stabilization of a class of underactuated mechanical systems via total energy shaping

In this paper a system of ODEs and a method for its solution are proposed for passivity-based stabilization of a class of underactuated mechanical systems. This method simplifies the PDEs imposed by the passivity-based control via interconnection and damping assignment (IDA-PBC) technique. For a class of mechanical systems satisfying some mathematical properties the PDEs are reduced to a simple set of nonlinear ODEs. A general solution for these equations in the 2-DOF case is presented, through a new parametrization of the closed loop inertia matrix. Two examples illustrate the method, achieving kinetic and potential energy shaping in a straightforward manner. The simulation analysis in comparison with recent studies highlight the advantages of these techniques.

Differential coding in networked controlled linear systems

This paper investigates the closed-loop properties of the differential coding scheme known as Delta-modulation (A-M) when used in feedback loops within the context of linear systems controlled through some communication network. We propose a new modified scheme of the original form of the Delta-M algorithm which improves the closed-loop properties. The new coding structure explicitly uses information from the system model. Stability properties for both: the continuous-time and the discrete-time version of this new algorithm are assessed. The results shows that the stability domain and the resulting precision of the Delta-M is limited by the position of the unstable poles of the system

Adaptive Delta-modulation Coding for Networked Controlled Systems

This work investigates the closed-loop properties of the differential coding scheme known as delta-modulation (Delta-M) when used in feedback loops within the context of linear systems controlled through some communication network. Our main contribution is to propose and adaptive law for parameter Delta, the resolution of the differential state encoder. The adaptation law is defined exclusively in terms of information available at ends of the communication channel, using only two past samples. With minimal implementation and memory usage, global asymptotic stability of the networked controlled system is achieved for a class of unstable plants.

Stabilization of autonomous oscillations and the Hopf bifurcation in the ball and beam

This paper presents a design method for the stabilization of oscillations in a class of nonlinear systems. The method consists of two steps. In the first one, a second-order generalized Hamiltonian subsystem, which presents stable oscillations, is matched. In the second step, the controller is extended to the full system using backstepping. It is shown that the oscillations emerge through a supercritical Hopf bifurcation. The method proposed was first applied to a second order system. In this paper the method is extended to higher order systems by backstepping. The method is introduced by its application to an underactuated mechanical system: the ball and beam.

Adding automatic evaluation to interactive virtual labs

Automatic evaluation is a challenging field that has been addressed by the academic community in order to reduce the assessment workload. In this work we present a new element for the authoring tool Easy Java Simulations (EJS). This element, which is named automatic evaluation element (AEE), provides automatic evaluation to virtual and remote laboratories built with EJS by using the server application Goodle grading management system (GMS). The integration of both tools entitles a professor to create interactive virtual and remote laboratories and automatically evaluate the work of their students. As a test bed two case studies are presented; a non-linear controller design virtual laboratory used in an advanced control master course and a servomechanism virtual laboratory used in an undergraduate basic control course.

Periodicity of Kalman-based scheduled filters

In this paper, the sensor scheduling problem for estimation is tackled, in which a set of sensors must share a common network to communicate their measurements. It is shown that, under some mild conditions, a Kalman-based scheduled filter results in a periodic selection of the sensors. In those cases, the computational cost and energy consumption can be reduced, as the sensors can await asleep between two consecutive measurements. A suboptimal one-step ahead strategy is thoroughly studied as a possible example of observation scheme.

Generation of autonomous oscillations via output feedback

In this paper, a newly developed method for generating oscillations in arbitrary order nonlinear systems, is redefined as an output feedback controller. In a recent publication, the state feedback orbitally stabilizing controller has been enhanced to provide strict Lyapunov functions for the oscillating behavior. This property is exploited here in order to prove global asymptotic stability of the output feedback controller in systems up to degree four, and global asymptotic stability with limited initial estimation error in higher–order systems. The output feedback controller is then applied to a fourth–order cascade LC network, while the result may be extrapolated to similar circuits with arbitrary number of LC blocks, which may be regarded as discrete approximations of transmission lines.

An optimization approach for modulation in multilevel converters

In the control of power converters, it is well known that the modulation strategy can be used not only for the discretization of averaged control signals, but also for the fulfillment of additional control objectives, such as voltage balance among capacitors or common mode reduction. The resulting number of switches is an important issue since the fulfillment of these additional objectives usually leads to an increase in the number of switches and, thus, in power losses. In this paper, the modulation stage is formulated as an optimization problem in order to minimize the number of switches. The resulting problem is formulated as an linear, mixed-integer programming problem that can be solved offline and the solution can be stored as a look-up table for its use during online operation. The resulting approach is applied to a 3-phase, 5-level diode-clamped converter (DCC) working as rectifier. Simulation results are presented.

Automatic evaluation and data generation for analytical chemistry instrumental analysis exercises

In general, laboratory activities are costly in terms of time, space, and money. As such, the ability to provide realistically simulated laboratory data that enables students to practice data analysis techniques as a complementary activity would be expected to reduce these costs while opening up very interesting possibilities. In the present work, a novel methodology is presented for design of analytical chemistry instrumental analysis exercises that can be automatically personalized for each student and the results evaluated immediately. The proposed system provides each student with a different set of experimental data generated randomly while satisfying a set of constraints, rather than using data obtained from actual laboratory work. This allows the instructor to provide students with a set of practical problems to complement their regular laboratory work along with the corresponding feedback provided by the systems automatic evaluation process. To this end, the Goodle Grading Management System (GMS), an innovative web-based educational tool for automating the collection and assessment of practical exercises for engineering and scientific courses, was developed. The proposed methodology takes full advantage of the Goodle GMS fusion code architecture. The design of a particular exercise is provided ad hoc by the instructor and requires basic Matlab knowledge. The system has been employed with satisfactory results in several university courses. To demonstrate the automatic evaluation process, three exercises are presented in detail. The first exercise involves a linear regression analysis of data and the calculation of the quality parameters of an instrumental analysis method. The second and third exercises address two different comparison tests, a comparison test of the mean and a t-paired test.

Strict Lyapunov functions for generating robust oscillations in nonlinear systems

Abstract This paper deals with the problem of generating stable and robust oscillations in triangular nonlinear systems. The proposed method consists of two steps. First, a globally attractive oscillation is generated in a nominal second-order subsystem. Based on a partition of the state space and solving the Lyapunov equation on each part, a strict Lyapunov function is obtained that ensures exponential convergence to a ring-shaped region containing the target limit cycle. Then, the nominal stabilizing controller and the strict Lyapunov function are extended to arbitrary order systems, via a method in the essence of backstepping. Thanks to the strict Lyapunov functions, a new ability to deal with unmodeled dynamics is acquired, and the original controller is easily extended to quasi-triangular structures.