Observer-based state-feedback versus H-infinity output feedback control solved by LMI approach for applications in smart structures

This paper aims with the use of linear matrix inequalities approach (LMIs) for application in active vibration control problems in smart strutures. A robust controller for active damping in a panel was designed with piezoelectrical actuators in optimal locations for illustration of the main proposal. It was considered, in the simulations of the closed-loop, a model identified by eigensystem realization algorithm (ERA) and reduced by modal decomposition. We tested two differents techniques to solve the problem. The first one uses LMI approach by state-feedback based in an observer design, considering several simultaneous constraints as: a decay rate, limited input on the actuators, bounded output peak (output energy) and robustness to parametic uncertainties. The results demonstrated the vibration attenuation in the structure by controlling only the first modes and the increased damping in the bandwidth of interest. However, it is possible to occur spillover effects, because the design has not been done considering the dynamic uncertainties related with high frequencies modes. In this sense, the second technique uses the classical H. output feedback control, also solved by LMI approach, considering robustness to residual dynamic to overcome the problem found in the first test. The results are compared and discussed. The responses shown the robust performance of the system and the good reduction of the vibration level, without increase mass.

Active control in rotating machinery using magnetic actuators with linear matrix inequalities (LMI) approach

The recent years have seen the appearance of innovative system for acoustic and vibration attenuation, most of them integrating new actuator technologies. In this sense, the study of algorithms for active vibrations control in rotating machinery became an area of enormous interest, mainly due to countless demands of an optimal performance of mechanical systems in aircraft, aerospace and automotive structures. In this way, this paper presents an approach that is numerically verified for active vibration control in a rotor using Active Magnetic Bearings (AMB). The control design in a discrete state-space formulation is carried out through feedback technique and Linear Matrix Inequalities (LMI) approach. LMI is useful for system with uncertainties. The AMB uses electromagnetic forces to support a rotor without mechanical contact. By monitoring the position of the shaft and changing the dynamics of the system accordingly, the AMB keeps the rotor in a desired position. This unique feature has broadened for the applications of AMB and now they can be considered not only as a main support bearing in a machine but also as dampers for vibration control and force actuators. © 2009 Society for Experimental Mechanics Inc.

Robust controller design of a wheelchair mobile via LMI approach to SPR systems with feedback output

This article discusses the design of robust controller applied to Wheelchair Furniture via Linear Matrix Inequalities (LMI), to obtain Strictly Positive Real (SPR) systems. The contributions of this work were the choice of a mathematical model for wheelchair: mobile with uncertainty about the position of the center of gravity (CG), the decoupling of the kinematic and dynamical systems, linearization of the models, the headquarters building of parametric uncertainties, the proposal of the control loop and control law with a specified decay rate.

A controller design used in Lorenz synchronization chaotic system for secure communication based on LMI fuzzy control system

This paper describes a mathematical study about chaotic system and about the unified approach of chaos control via fuzzy control system based in Linear Matrix Inequality to design a controller which synchronizes the transmission/reception system. This system, that was based in Lorenz chaotic circuit, can be used for transmit signals in secure way.

Alocação de zeros aplicada a sistemas de controle via LMI

A systematic procedure of zero placement to design control systems is proposed. A state feedback controller with vector gain K is used to perform the pole placement. An estimator with vector gain L is also designed for output feedback control. A new systematic method of zero assignment to reduce the effect of the undesirable poles of the plant and also to increase the velocity error constant is presented. The methodology places the zeros in a specific region and it is based on Linear Matrix Inequalities (LMIs) framework, which is a new approach to solve this problem. Three examples illustrate the effectiveness of the proposed method.

Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented. © 2013 Copyright Taylor and Francis Group, LLC.

A fuzzy Lyapunov function approach for stabilization and control of switched TS fuzzy systems

In this work, sufficient conditions for the existence of switching laws for stabilizing switched TS fuzzy systems via a fuzzy Lyapunov function are proposed. The conditions are found by exploring properties of the membership functions and are formulated in terms of linear matrix inequalities (LMIs). Stabilizing switching conditions with bounds on the decay rate solution and H1 performance are also obtained. Numerical examples illustrate the effectiveness of the proposed design methods.