Control design for a class of nonlinear continuous-time systems

This paper addresses the control design problem for a certain class of continuous-time nonlinear systems subject to actuator saturations. The system under consideration consists of a system with two nested nonlinearities of different type: saturation nonlinearity and cone-bounded nonlinearity. The control law investigated for stabilization purposes depends on both the state and the cone-bounded nonlinearity. Constructive conditions based on LMIs are then provided to ensure the regional or global stability of the system. Different points, like other approaches issued from the literature, are quickly discussed. An illustrative example allows to show the interest of the approach proposed.     

An eigenstructure assignment approach for constrained linear continuous-time singular systems

This paper establishes necessary and sufficient algebraic conditions for positive invariance of convex polyhedra with respect to some linear continuous-time singular systems. They can be considered as an extension for linear singular systems of the classical positive invariance relations for regular linear systems. For a stabilizable and impulse controllable singular system with constrained inputs, a stabilizing state feedback control guaranteeing the closed-loop positive invariance of some polyhedral sets determined from the feedback matrix is studied. An analysis of the closed-loop positive invariance relations is thus presented in terms of eigenstructure and stability properties. An eigenstructure assignment technique is proposed depending on the number of stable finite poles of the singular system.     

A reduced-order framework applied to linear systems withconstrained controls

A major issue in the control of dynamical systems is the integration of both technological constraints and some dynamic performance requirements in the design of the control system. The authors show in this work that it is possible to solve a class of constrained control problems of linear systems by using a reduced-order system obtained by the projection of the trajectories of the original system onto a subspace associated with the undesirable open-loop eigenvalues. The class of regulation schemes considered uses full state feedback to guarantee that any trajectory emanating from a given polyhedral set of admissible initial states remains in that set. This set of admissible states is said to be positively invariant with respect to the closed-loop system. The authors also address the important issues of numerical stability and complexity of the computations     

On invariant polyhedra of continuous-time linear systems

This note presents some conditions of existence of positively invariant polyhedra for linear continuous-time systems. These conditions are first described algebraically, then interpreted on the basis of the system eigenstructure. Then, a simple state-feedback placement method is described for solving some linear regulation problems under constraints     

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

We address the design of dynamic parameter‐dependent controllers with antiwindup action to locally stabilize in the input‐to‐state sense a class of discrete‐time linear parameter‐varying (LPV) systems. Such a class consists of systems with delayed state, saturating actuators, and subject to energy bounded disturbances. Moreover, the interval time‐varying delay can have a limited variation rate between two consecutive instants allowing to achieve less conservative design conditions. Differently from other conditions in the literature, the proposed convex synthesis methods allow to design dynamic controllers of different orders. Additionally, the user can choose to feed back only the current output of the system or its delayed ones. Thanks to the embedded (parameter dependent) antiwindup action, it is possible, for instance, to enlarge the region of admissible initial conditions or the maximum admissible disturbance energy. To illustrate the efficiency of our approach, we present numerical examples to compare with other methods from the literature.     

The effect of pulsed voltages on dielectric material properties

The problem of premature failure of rotating machines fed by inverters appears to be of crucial importance. Understanding of the phenomena caused by this new type of supply on the stator insulation of motors provides enhanced reliability of the inverter/motor set. After identifying the stresses created by this type of device, a study of aging of the materials used as models, and subjected to similar stresses, is undertaken. For the voltage, rise time and frequency under study, the intrinsic part of the aging is studied. The results are presented and discussed according to the nature of the interaction existing between the electrical stress and the material properties     

A gametheoretic approach for non-uniform pole shifting and pole homothety

This paper investigates the problems of non-uniform pole shifting or pole homothety in multivariable linear systems by using a gametheoretic approach and more specifically a particular Nash strategy with an open-loop information structure for a game including a time preference rate in the quadratic criteria. Such a result is possible due to properties of non-symmetric Algebraic Riccati equations associated with an open-loop Nash strategy. Numerical examples allow to illustrate the efficiency of the proposed approach.     

Acid mine drainage wastewater photoelectrolysis for hydrogen fuel generation: Preliminary results

Acid mine drainage (AMD) occurs when sulfide composite materials are exposed to oxygen gas, water, and microorganisms present in the environment. An alternative for the treatment of this residual water is the generation of hydrogen gas by electrolysis using a photovoltaic system. In this work, an electrolytic cell with 304 stainless steel electrodes was to form hydrogen gas. After 390 minutes of hydrogen generation, it was observed that the accumulated amount of H₂ was 254 mL when PV panels were used as the current source. When using AMD, hydrogen generation was 5.5 times higher compared to that using the sulfuric acid solution under the same experimental conditions. The electrolyte AMD conductivity diminished from 3850 μS cm⁻¹ to 2960 μS cm⁻¹. The decrease in conductivity may be related to removal of metal ions from the solution by the formation of insoluble compounds. After 390 minutes of testing, electrolysis using a PV panel resulted in a 9-fold increase in the total solid content. The reduction of iron and manganese ions in AMD samples was approximately 60% and 10%, respectively. No decrease in sulfate concentration and low pH variation were observed.     

ℒ︁2‐Stabilization of continuous‐time linear systems with saturating actuators

This paper addresses the problem of controlling a linear system subject to actuator saturations and to ??₂‐bounded disturbances. Linear matrix inequality (LMI) conditions are proposed to design a state feedback gain in order to satisfy the closed‐loop input‐to‐state stability (ISS) and the closed‐loop finite gain ??₂ stability. By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition, which encompasses the classical sector‐nonlinearity condition considered in some previous works, and Finsler's Lemma, which allows to derive stabilization conditions which are adapted to treat multiple objective control optimization problems in a potentially less conservative framework. Copyright © 2006 John Wiley & Sons, Ltd.