Alfonso Baños

Interconnection of port-Hamiltonian systems and composition of Dirac structures

Port-based network modeling of physical systems leads to a model class of nonlinear systems known as port-Hamiltonian systems. Port-Hamiltonian systems are defined with respect to a geometric structure on the state space, called a Dirac structure. Interconnection of port-Hamiltonian systems results in another port-Hamiltonian system with Dirac structure defined by the composition of the Dirac structures of the subsystems. In this paper the composition of Dirac structures is being studied, both in power variables and in wave variables (scattering) representation. This latter case is shown to correspond to the Redheffer star product of unitary mappings. An equational representation of the composed Dirac structure is derived. Furthermore, the regularity of the composition is being studied. Necessary and sufficient conditions are given for the achievability of a Dirac structure arising from the standard feedback interconnection of a plant port-Hamiltonian system and a controller port-Hamiltonian system, and an explicit description of the class of achievable Casimir functions is derived.

Delay-Independent Stability of Reset Systems

Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma.

Brief paper: Delay-dependent stability of reset systems

This work presents results on the stability of time-delay systems under reset control. The case of delay-dependent stability is addressed, by developing a generalization of previous stability results for reset systems without delay, and also a generalization of the delay-independent case. The stability results are derived by using appropriate Lyapunov-Krasovskii functionals, obtaining LMI (Linear Matrix Inequality) conditions and showing connections with passivity and positive realness. The stability conditions guarantee that the reset action does not destabilize the base LTI (Linear Time Invariant) system. Several interpretations are given for these conditions in terms of impulsive control, which provide insights into the potentials of reset control.

A passivity-based approach to reset control systems stability

The stability of reset control systems has been mainly studied for the feedback interconnection of reset compensators with linear time-invariant systems. This work gives a stability analysis of reset compensators in feedback interconnection with passive nonlinear systems. The results are based on the passivity approach to L2-stability for feedback systems with exogenous inputs, and the fact that a reset compensator will be passive if its base compensator is passive. Several examples of full and partial reset compensations are analyzed, and a detailed case study of an in-line pH control system is given.

Reset Times-Dependent Stability of Reset Control Systems

Reset control systems are a special type of hybrid systems in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the reset instants. In this work, stability of reset control systems is approached by using an equivalent (time-varying) discrete time system, introducing necessary and sufficient stability conditions that explicitly depends on the reset times. These conditions have been simplified for the case in which the linear base control system is stable, resulting in a sufficient condition that only depends on a lower bound of the reset intervals.

Tuning of Fractional PID Controllers by Using QFT

As it is known, a wide range of research activities deal with the application of the quantitative feedback theory (QFT) for the design of different control structures. All these approaches generally use rational controllers. On the other hand, the importance of fractional order controllers is becoming remarkable nowadays, studying aspects such as the analysis, design and synthesis of this kind of controllers. The purpose of this paper is to apply QFT for the tuning of a fractional PID controller (PIlambdaDmu) of the form KP (1 + KIs-lambda + KDsmu ), where lambda, mu are the orders of the fractional integral and derivative, respectively. The objective is to take advantage of the introduction of the fractional orders in the controller and fulfill different design specifications for a set of plants

Delay-Independent Stability of Reset Control Systems

Reset control systems have potential advantages to overcome fundamental limitations of LTI compensation. However, since a reset compensator may destabilize a stable base LTI system, stability needs to be guaranteed in advance for a proper practical application of reset control. This works extends previous stability results of reset control systems to consider the case of LTI plants with time-delays. Stability independent of the delay criteria are developed both by means of LMIs and in the frequency domain by using the KYP Lemma

Bode optimal loop shaping with CRONE compensators

Ideal Bode characteristics give a classical answer to optimal loop design for linear time invariant feedback control systems in the frequency domain. This work recovers eight-parameter Bode optimal loop gains, providing a useful and simple theoretical reference for the best possible loop shaping from a practical point of view. The main result of the paper is to use CRONE compensators to make a good approximation and in addition a way for the synthesis of the Bode optimal loop. For that purpose, a special loop structure based on second and third generation CRONE compensators is used. As a result, simple design relationships will be obtained for tuning the proposed CRONE compensator.

Automatic Loop Shaping in QFT Using CRONE Structures

This work focuses on the problem of automatic loop shaping in quantitative feedback theory (QFT), where the search for an optimum design (a non-convex and nonlinear optimization problem) is traditionally simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator. In relation to previous work, the main idea consists in the study of the use of fractional compensators, which give singular properties to automatically shape the open loop gain function by using a minimum set of parameters. CRONE controllers, in particular CRONE 2 and CRONE 3, are considered as possible candidate structures, being original structures modified for a better approach to the QFT theoretical optimum. CRONE 3 non-minimum-phase zeros are avoided by constraints on the structure parameters.

Design of PI+CI Reset Compensators for second order plants

Reset control is a special kind of nonlinear compensation that has been used to overcome limitations of linear time invariant, LTI, compensation. In recent works by the authors a new type of reset compensator, referred to as PI+CI, has been introduced. It basically consists of adding a Clegg integrator, CI, to a Proportional-Integral, PI, compensator, with the goal of improving the closed loop response by using the nonlinear characteristic of this element. It turns out that by resetting a percentage of the integral term of a PI compensator, a significant improvement can be obtained by considerably reducing overshoot percentage and settling time. This work is devoted to the extension of this previous work by deriving new tuning rules for second order plants with and without delay.