Francisco Beltran-Carbajal

Sliding mode and Generalized PI control of vehicle active suspensions

In this paper the vibration attenuation problem in automotive suspension systems is presented. A robust active vibration control strategy based on sliding mode and Generalized Proportional Integral Control techniques is proposed as a solution alternative of this problem. This active vibration control scheme only requires position measurements of the wheel and car body. Integral reconstruction of state vector is used to avoid the use of sensors of acceleration and velocity. Simulation results are included to show the dynamic performance and robustness of the proposed active suspension system.

Output feedback control of a mechanical system using magnetic levitation.

This paper presents an application of a nonlinear magnetic levitation system to the problem of efficient active control of mass-spring-damper mechanical systems. An output feedback control scheme is proposed for reference position trajectory tracking tasks on the flexible mechanical system. The electromagnetically actuated system is shown to be a differentially flat nonlinear system. An extended state estimation approach is also proposed to obtain estimates of velocity, acceleration and disturbance signals. The differential flatness structural property of the system is then employed for the synthesis of the controller and the signal estimation approach presented in this work. Some experimental and simulation results are included to show the efficient performance of the control approach and the effective estimation of the unknown signals.

Active Vibration Control for a Nonlinear Mechanical System Using On-line Algebraic Identification

Many engineering systems undergo undesirable vibrations. Vibration control in mechanical systems is an important problem, by means of which vibrations are suppressed or at least attenuated. In this direction it has been common the use of passive and active dynamic vibration absorbers. A dynamic vibration absorber is an inertia member coupled to a vibrating mechanical system by suitable linear and nonlinear coupling members (e.g., springs and dampers). For the passive case, the absorber only serves for a specific excitation frequency and stable operating conditions, but it is not recommended for variable frequencies and uncertain system parameters. An active dynamic vibration absorber achieves better dynamic performance by controlling actuator forces depending on feedback and feedforward information of the system obtained from sensors. To cancel the exogenous harmonic vibrations on the primary system, the dynamic vibration absorber should apply an equivalent reaction force to the primary system equal and opposite to the exciting force causing the vibrations. This means that the vibration energy injected to the primary system is transferred to the absorber through the coupling elements. For more details about dynamic vibration absorber we refer to (Korenev & Reznikov, 1993) and references therein. This chapter deals with the attenuation problem of harmonic mechanical vibrations in nonlinear mechanical systems by using active vibration absorbers and without employing vibration measurements. On-line algebraic identification is applied for the on-line estimation of the frequency and amplitude of exogenous vibrations affecting the nonlinear vibrating mechanical system. The proposed results are strongly based on the algebraic approach to parameter identification in linear systems reported by (Fliess & Sira-Ramírez, 2003), which employs differential algebra, module theory and operational calculus. An important property of the algebraic identification is that the parameter and signal identification is not asymptotic but algebraic, that is, the parameters are computed as fast as the system dynamics is being excited by some external input or changes in its initial

Evaluation of On-Line Algebraic Modal Parameter Identification Methods

This paper describes the application of a novel time domain and on-line algebraic modal parameter identification methodology based on differential algebra, module theory and Mikusinski operational calculus for mechanical structures with multiple degrees-of-freedom. The natural frequencies and damping ratios associated to a mechanical system are estimated in an on-line fashion from transient state real-time measurements (e.g., displacements or accelerations). The proposed identification methodology can be also extended for modal parameter identification using experimental frequency response functions. A comparison with usual modal identification techniques is performed in order to evaluate and establish the main contributions of the proposed approach. Some numerical and experimental results are included to show the efficient and robust performance and fast parametric estimation of the proposed algebraic identification approach.

Active vibration absorption of multi-frequency harmonic forces on mass-spring-damper systems

In this article an active vibration absorption scheme for linear mass-spring-damper mechanical systems subject to exogenous multi-frequency harmonic excitations is presented. The proposed scheme considers an active vibration absorber as a dynamic controller, which can simultaneously be used for vibration attenuation and desired position reference trajectory tracking tasks. The differential flatness property exhibited by the mechanical system is employed to design a control law to extend the vibrating energy dissipation capacity of a dynamic vibration absorber for multi-frequency vibration. The disturbance input signal affecting the differentially flat linear system dynamics and time derivatives up to third order of the flat output, which are required for the controller implementation, are estimated by using a flat output-based high-gain dynamic observer. Some simulation results are provided to show the robust and efficient performance of the proposed active vibration absorption scheme when the primary system is submitted to resonant frequency harmonic excitations.

Control de Vibraciones en Maquinaria Rotatoria

Vibration caused by mass imbalance is a common problem in rotating machinery. In this paper, a review of the performed research work on active balancing and active vibration control for rotating machinery is presented. In addition, two solutions to this vibration attenuation problem for desired output feedback trajectory tracking tasks are proposed. The first one consists in the use of a movable bearing to modify the effective rotor length and, as an immediate consequence, the natural frequency, to avoid the higher amplitudes presented in the resonance. The second one consists in the use of an active disk mounted on the main inertia of the rotor system, which contains a balancing mass that can be positioned in any angular and radial position inside the disk to attenuate the vibration caused by the residual unbalance. Since both active vibration control strategies require information of the eccentricity, the algebraic identification method is used for the on-line estimation of its parameters.

Design of Active Vibration Absorbers Using On-Line Estimation of Parameters and Signals

Many engineering systems undergo undesirable vibrations. Vibration control in mechanical systems is an important problem by means of which vibrations are suppressed or at least attenuated. In this direction, the dynamic vibration absorbers have been widely applied in many practical situations because of their low cost/maintenance, efficiency, accuracy and easy installation (Braun et al., 2001; Preumont, 1993). Some of their applications can be found in buildings, bridges, civil structures, aircrafts, machine tools and many other engineering systems (Caetano et al., 2010; Korenev & Reznikov, 1993; Sun et al., 1995; Taniguchi et al., 2008; Weber & Feltrin, 2010; Yang, 2010). There are three fundamental control design methodologies for vibration absorbers described as passive, semi-active and active vibration control. Passive vibration control relies on the addition of stiffness and damping to the primary system in order to reduce its dynamic response, and serves for specific excitation frequencies and stable operating conditions, but is not recommended for variable excitation frequencies and/or parametric uncertainty. Semiactive vibration control deals with adaptive spring or damper characteristics, which are tuned according to the operating conditions. Active vibration control achieves better dynamic performance by adding degrees of freedom to the system and/or controlling actuator forces depending on feedback and feedforward real-time information of the system, obtained from sensors. For more details about passive, semiactive and active vibration control we refer to the books (Braun et al., 2001; Den Hartog, 1934; Fuller et al, 1997; Preumont, 1993). On the other hand, many dynamical systems exhibit a structural property called differential flatness. This property is equivalent to the existence of a set of independent outputs, called flat outputs and equal in number to the control inputs, which completely parameterizes every state variable and control input (Fliess et al., 1993; Sira-Ramirez & Agrawal, 2004). By means of differential flatness techniques the analysis and design of a controller is greatly Design of Active Vibration Absorbers Using On-Line Estimation of Parameters and Signals 2

Sliding mode based differential flatness control and state estimation of vehicle active suspensions

In this paper the vibration attenuation problem in automotive suspension systems is presented. A robust active vibration control strategy based on sliding mode and differential flatness control techniques is proposed as a solution alternative of this problem. This active vibration control scheme only requires position measurements of the wheel and car body. State algebraic on-line estimation is used to avoid the use of sensors of acceleration and velocity. Simulation results are included to show the dynamic performance and robustness of the proposed active suspension system.

Stable predictive control horizons

The stability theory of predictive and adaptive predictive control for processes of linear and stable nature is based on the hypothesis of a physically realisable driving desired trajectory (DDT). The formal theoretical verification of this hypothesis is trivial for processes with a stable inverse, but it is not for processes with an unstable inverse. The extended strategy of predictive control was developed with the purpose of overcoming methodologically this stability problem and it has delivered excellent performance and stability in its industrial applications given a suitable choice of the prediction horizon. From a theoretical point of view, the existence of a prediction horizon capable of ensuring stability for processes with an unstable inverse was proven in the literature. However, no analytical solution has been found for the determination of the prediction horizon values which guarantee stability, in spite of the theoretical and practical interest of this matter. This article presents a new method able to determine the set of prediction horizon values which ensure stability under the extended predictive control strategy formulation and a particular performance criterion for the design of the DDT generically used in many industrial applications. The practical application of this method is illustrated by means of simulation examples.

Limit Cycle Analysis in a Class of Hybrid Systems

Hybrid systems are those that inherently combine discrete and continuous dynamics. This paper considers the hybrid system model to be an extension of the discrete automata associating a continuous evolution with each discrete state. This model is called the hybrid automaton. In this work, we achieve a mathematical formulation of the steady state and we show a way to obtain the initial conditions region to reach a specific limit cycle for a class of uncoupled and coupled continuous-linear hybrid systems. The continuous-linear term is used in the sense of the system theory and, in this sense, continuous-linear hybrid automata will be defined. Thus, some properties and theorems that govern the hybrid automata dynamic behavior to evaluate a limit cycle existence have been established; this content is explained under a theoretical framework.