Fabio Gómez-Estern

This paper presents a novel platform for automated self-paced learning in Computer-Aided Design (CAD) courses within engineering education. The platform fully automates the entire learning cycle, including exercise generation, submission, scheduling, test design, and grading. The central hypothesis posits that complete automation reduces repetitive tasks for instructors, allowing them to dedicate more time to individualized student support. The system also provides key advantages: it generates unique exercises for each student to prevent plagiarism while maintaining comparable complexity; it delivers instantaneous grading and feedback to enhance motivation; and it enables students to work with almost any CAD software, as the evaluation relies on physical properties rather than commercial tools. After several years of successive testing and refinement, the tool can generate and accurately grade frequent activities in large student cohorts, providing abundant data points. Their statistical analysis, via multiple approaches, confirms that the system reliably produces individualized exercises, reduces grading errors, and offers prompt, consistent feedback, thereby supporting a more efficient and engaging learning process.

In this paper, a new control design procedure for a class of power converters based on hybrid dynamical systems theory is presented. The continuous-time dynamics, as voltage and current signals, and discrete-time dynamics, as the on- off state of the switches, are captured with a hybrid model. This model avoids the use of averaged and approximated models and includes the PWM as well as the sample-and-hold mechanism, commonly used in the industry. Then, another simplified hybrid system, whose trajectories match with the original one, is selected to design the controller and to analyse stability properties. Finally, an estimation of the chattering in steady state of the voltage and current signals is provided. The results are validated through simulation and experiments.

In this paper, hybrid dynamical systems theory is applied to the analysis and control of switched converters with Pulse-Width Modulated (PWM) inputs. The system is described by a state-space model with continuous flows and discrete jumps, without averaged equations. The modulation effects are captured in full without using time-dependent signals, by enlarging the state vector to include the PWM waveform generation process. Furthermore, the sample-and-hold mechanism associated with the sampling frequency is also taken into account with this approach. A control law is proposed based on a Lyapunov function candidate. Furthermore, convergence sets and the steady state jitter, inherent to PWM-based controllers, are analyzed estimating limit sets for the augmented state. Consequently, output chattering can be bounded. By using hybrid dynamical system theory, the control designer gains a deeper understanding of the effect of modulation in the closed-loop dynamics, avoiding the problems associated with the use averaged models. Experimental results validate the proposed method.

We consider the challenging problem of creating oscillations in underactuated mechanical systems. Target oscillatory motions of the indirectly actuated degree of freedom of a mechanical system can often be achieved via a straightforward to design feedback transformation. Moreover, the corresponding part of the dynamics can be forced to match a desired second-order system possessing the target periodic solution (Aracil, J., Gordillo, F., and Acosta, J.A. (2002), ‘Stabilization of Oscillations in the Inverted Pendulum’, in Proceedings of the 15th IFAC World Congress, Barcelona, Spain; Canudas-de-Wit, C., Espiau, B., and Urrea, C. (2002), ‘Orbital Stabilisation of Underactuated Mechanical Systems’, in Proceedings of the 15th IFAC World Congress, Barcelona, Spain). Sometimes, it is possible to establish the presence of periodic or bounded motions for the remaining degrees of freedom in the transformed system. However, typically this motion planning procedure leads to an open-loop unstable orbit and by necessity should be followed by a feedback control design. We propose a new approach for synthesis of a (practically) stabilising feedback controller, which ensures convergence of the solutions of the closed-loop system into a narrow tube around the preplanned orbit. The method is illustrated in detail by shaping oscillations in the inverted pendulum on a cart around its upright equilibrium. The complete analysis is based on application of a non-standard higher-order averaging technique assuming sufficiently high frequency of oscillations and is presented for this particular example.