Eva H. Dulf

A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers

In this paper a fractional order (FO) controller is proposed for solving the vibration suppression problem in civil structures. A laboratory scaled steel structure, with one floor, modeled as a single degree-of-freedom system is used as a case study. Two passive control solutions are proposed: a tuned mass damper (TMD) and a viscoelastic damper (VED), the latter being modeled using fractional derivatives. The simulation results show that the VED is able to further reduce the vibrations induced as forced oscillations or due to seismic excitation inputs, as compared to the passive TMD. The FO controller is then tuned using a new approach based on imposing a magnitude condition for the closed-loop system at the structural resonance frequency. The resulting FO active control strategy, together with the VED, ensures an increased seismic mitigation. Structural modeling errors are also considered, with the proposed active FO control strategy behaving robustly in terms of vibration suppression. The novelty of the paper resides in the tuning approach, as well as in the proposed active control strategy that is based upon combing VEDs, described using an FO model, and an FO controller.

Robust Feedback Linearization Control for Reference Tracking and Disturbance Rejection in Nonlinear Systems

Most industrial processes are nonlinear systems, the control method applied consisting of a linear controller designed for the linear approximation of the nonlinear system around an operating point. However, even though the design of a linear controller is rather straightforward, the result may prove to be unsatisfactorily when applied to the nonlinear system. The natural consequence is to use a nonlinear controller. Several authors proposed the method of feedback linearization (Chou & Wu, 1995), to design a nonlinear controller. The main idea with feedback linearization is based on the fact that the system is no entirely nonlinear, which allows to transform a nonlinear system into an equivalent linear system by effectively canceling out the nonlinear terms in the closedloop (Seo et al., 2007). It provides a way of addressing the nonlinearities in the system while allowing one to use the power of linear control design techniques to address nonlinear closed loop performance specifications. Nevertheless, the classical feedback linearization technique has certain disadvantages regarding robustness. A robust linear controller designed for the linearized system may not guarantee robustness when applied to the initial nonlinear system, mainly because the linearized system obtained by feedback linearization is in the Brunovsky form, a non robust form whose dynamics is completely different from that of the original system and which is highly vulnerable to uncertainties (Franco, et al., 2006). To eliminate the drawbacks of classical feedback linearization, a robust feedback linearization method has been developed for uncertain nonlinear systems (Franco, et al., 2006; Guillard & Bourles, 2000; Franco et al., 2005) and its efficiency proved theoretically by W-stability (Guillard & Bourles, 2000). The method proposed ensures that a robust linear controller, designed for the linearized system obtained using robust feedback linearization, will maintain the robustness properties when applied to the initial nonlinear system. In this paper, a comparison between the classical approach and the robust feedback linearization method is addressed. The mathematical steps required to feedback linearize a nonlinear system are given in both approaches. It is shown how the classical approach can be altered in order to obtain a linearized system that coincides with the tangent linearized system around the chosen operating point, rather than the classical chain of integrators. Further, a robust linear controller is designed for the feedback linearized system using loop-

Feedback linearization control design for the 13C cryogenic separation column

The separation of carbon isotopes represents a major research area due to the numerous uses of the least abundant carbon isotope, 13C. One of the methods used for separating these isotopes is the cryogenic distillation, in large counter- current columns. Such industrial plants represent a difficult problem in terms of automatic control, since they are characterized by nonlinearities, large delay times and extremely severe control input constraints. The paper presents a control strategy based on a feedback linearization technique as an inner loop controller and a robust controller as the outer loop. The two are combined to result in a nonlinear robust control that achieves robust stability and robust performance for a certain amount of model uncertainties.

Microcontroller Implementation of a Multivariable Fractional Order PI Controller

Fractional order calculus has been used intensively to control various types of processes. The main approaches towards fractional order controllers focus on the single-input-single-output systems. The general design procedure consists in a frequency domain specification of various performance criteria followed by optimization routines. The implementation issues regarding fractional order controllers are based on Oustaloup approximations and are centered on SISO processes. The present paper addresses the problem of implementing on a microcontroller a fractional order multivariable controller for time delay processes. The paper presents a tuning algorithm for determining the parameters of the multivariable fractional order controller and the implementation issues. The multivariable time delay process is implemented in Matlab Simulink environment. The experimental results show that the fractional order multivariable controller implemented on a simple microcontroller provides similar results to that obtained by simulation, even under uncertainty conditions.

Design and analysis of a multivariable fractional order controller for a non-minimum phase system

Two control strategies for multivariable processes are proposed that are based on a decentralised and a steady state decoupling approach. The designed controllers are fractional order PIs. The efficiency and robustness of the proposed strategies is tested and validated using a non-minimum phase process. Previous research for the same non-minimum phase process has proven that simple decentralised or decoupling techniques do not yield satisfactorily results and a multivariable IMC controller has been proposed as an alternative solution. The simulation results presented in this paper, as well as the experimental results, show that the proposed fractional order multivariable control strategies ensure an improved closed loop performance and disturbance rejection, as well as increased robustness to modelling uncertainties, as compared to traditional multivariable IMC controllers.

Modelling and numerical simulation examples of distributed parameters processes

Abstract Continuing the papers (Abrudean et al ., 2007), (Colosi et al ., 2006), where the theoretical preliminaries of the definition and use of the M pdx matrix are presented, associated to the Taylor series, for the modelling and numerical simulation of some categories of processes with distributed parameters from power systems, thermoenergetic, electro-energetic, chemical and electromechanical processes, etc, this paper presents a number of four examples. The advantages, the limits and the disadvantages of the method applied to these examples are being underlined.

Fractional and integer order control. Application to DC motor speed control

Sustainable engineering implies the active management of engineering resources, by cutting down expenses and ensuring the premises for further development. Advanced control strategies offer increased robustness, high reliability and efficiency, but they require fast computation times and powerful numerical resources. Hence, the trend in control engineering should be directed towards developing and employing cheap, reliable and energy-efficient devices that support the implementation of the advanced control strategies. This would eventually lead to a more sustainable use of the available technological resources and a decrease of the energy consumption. The present paper offers a comparison between a fractional order control algorithm and a traditional PI controller for a DC motor. The results show that the fractional order controller has the pros of the advanced control methods, offering increased robustness, while the cons related to the computation requirements are avoided through a simple implementation technique that is similar to that of a classical PI controller.

Adaptive control in series load PWM induction heating inverters

Permanent variations of the electric properties of the load in induction heating equipment make difficult to control the plant. To overcome these disadvantages, the authors propose a new approach based on adaptive control methods. For real plants it is enough to present desired performances or start-up variables for the controller, from which the algorithms tune the controllers by itself. To present the advantages of the proposed controllers, comparisons are made to a PI controller tuned through Ziegler–Nichols method.

multivariable fractional order PI controller for time delay processes

Fractional order calculus has been used intensively to control various types of processes, with a focus on singleinput-single-output systems. A few design procedures for multivariable systems exist. This paper proposes a simple and effective method for designing a multivariable fractional order PI controller for systems with multiple time delays. The design procedure is based on a steady state decoupling of the multivariable system and on settling time and gain robustness specifications. To avoid the time consuming optimization routines for determining the controller parameters, an iterative procedure is preferred and used. The case study presented demonstrates the efficiency of the proposed control design, the closed loop system behaving robustly to significant gain variations ranging ±30%.

Study on a wave energy based power system

Huge quantities of clean energy can be obtained from the waves of the oceans and seas. As wave energy extraction technology is currently in a preliminary state of development any new results in this field should be of real interest. A direct driven wave power conversion system to be placed in the Black Sea near the Romania shores was proposed and analyzed. The paper focuses on its linear generator, respectively on its power electronic and control system.