Tm-afm nonlinear motion control with robustness analysis to parametric errors in the control signal determination

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Robust Switched Control Design for Nonlinear Systems Using Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torque

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.

Multi-task control strategy for grid-tied inverters based on conservative power theory

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

SDRE control strategy applied to a nonlinear robotic including drive motor

A robotic control design considering all the inherent nonlinearities of the robot-engine configuration is developed. The interactions between the robot and joint motor drive mechanism are considered. The proposed control combines two strategies, one feedforward control in order to maintain the system in the desired coordinate, and feedback control system to take the system into a desired coordinate. The feedback control is obtained using State-Dependent Riccati Equation (SDRE). For link positioning two cases are considered. Case I: For control positioning, it is only used motor voltage; Case II: For control positioning, it is used both motor voltage and torque between the links. Simulation results, including parametric uncertainties in control shows the feasibility of the proposed control for the considered system.

Nonlinear angle control of a sectioned airfoil by using shape memory alloys

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On nonlinear dynamics and control of a robotic arm with chaos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonlinear state estimation and control for chaos suppression in MEMS resonator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Nonlinear state estimation and control applied to a manipulator robotic including drive motor

A robotic control design considering all the inherent nonlinearities of the robot engine configuration is developed. The interactions between the robot and joint motor drive mechanism are considered. The proposed control combines two strategies, one feedforward control in order to maintain the system in the desired coordinate, and feedback control system to take the system into a desired coordinate. The feedback control is obtained using State Dependent Riccati Equation (SDRE). For link positioning two cases are considered. Case 1: For control positioning, it is only used motor voltage; Case 2: For control positioning, it is used both motor voltage and torque between the links. Simulation results, including parametric uncertainties in control shows the feasibility of the proposed control for the considered system.

Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems

The existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits. The characterizations derived in this technical note are a generalization of existing results in the theory of stability regions. A characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components, which can be equilibrium points, closed orbits, quasi-periodic solutions and even chaotic invariant sets.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

[EN] As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.