Joaquín Cervera

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.

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

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.

Network-Based Reset Control Systems With Time-Varying Delays

Reset compensators have shown to have advantages over linear and time-invariant compensators, especially when used in control loops with time delays. In this work, the potentials of reset control in networked control systems are investigated. Specifically, stability conditions are developed for the case in which network-induced delays are time-varying. To this end, it is shown how a network-based reset control system may be represented as a discrete-time reset control system. In addition, both state-dependent and time-dependent discrete-time reset compensators are analyzed. Finally, a case study is developed and simulation results are discussed, showing the superior performance of reset compensation.

Discrete-time reset control applied to networked control systems

Reset compensators have shown to have advantages over LTI compensators, specially when used in control loops with time-delays. In this work, it is is investigated for the first time the potentials of reset control in networked control systems. To this end, it will be defined a discrete time reset control system, and conditions for stability of a networked reset control system will be given.

AUTOMATIC LOOP SHAPING IN QFT BY USING CRONE STRUCTURES

Abstract This work focus on the problem of automatic loop shaping in QFT, where traditionally the search of an optimum design, a non convex and nonlinear optimization problem, is simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator. However, 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. (Modified) CRONE controllers are considered as possible candidate structures.

On composition of Dirac structures and its implications for control by interconnection

Network modeling of complex physical systems leads to a class of nonlinear systems, called Port-Controlled Hamiltonian Systems (PCH systems). These systems are geometrically defined by a state space manifold of energy variables, a power-conserving interconnection formalized as a Dirac structure, together with the total stored energy and a resistive structure. Basic features of these systems include their compositionality properties (a power-conserving interconnection of PCH systems is again a PCH system), and their stability and stabilizability properties exploiting the energy function and the Casimir functions. In the present paper we further elaborate on the compositionality properties of Dirac structures by providing an explicit parametrization of all achievable closed-loop Dirac structures in terms of their constituent parts. Amongst others this opens up the way to a complete characterization of the class of PCH systems which are stabilizable by interconnection with a PCH controller.

Nonlinear nonconvex optimization by evolutionary algorithms applied to robust control.

This work focuses on the problem of automatic loop shaping in the context of robust control. More specifically in the framework given by Quantitative Feedback Theory (QFT), traditionally the search of an optimum design, a non convex and nonlinear optimization problem, is simplified by linearizing and/or convexifying the problem. In this work, the authors propose a suboptimal solution using a fixed structure in the compensator and evolutionary optimization. The main idea in relation to previous work consists of the study of the use of fractional compensators, which give singular properties to automatically shape the open loop gain function with a minimum set of parameters, which is crucial for the success of evolutionary algorithms. Additional heuristics are proposed in order to guide evolutionary process towards close to optimum solutions, focusing on local optima avoidance.

Design of networked periodic reset control systems

The aim of this work is to develop tunnig rules for networked reset control systems with periodic reset actions. The reset law is simplified for the reset instants to be periodic, but on the other hand a key idea is the use of a variable reset value at each instant that minimizes the error between consecutive reset actions. This variable reset value defines by itself a different controller so the system may be considered as an hybrid system that combines the base linear system and a complementary system given by the variable reset value. Simple rules for adjusting the complementary system and for the switching will be given. Simulation results show how to apply these rules to networked control systems.