This paper develops the theory of vibrational control of nonlinear time lag systems with arbitrarily large but bounded delay. Averaging theory for fast oscillating, differential delay equations is presented and then applied to vibrational control. Conditions are given which ensure the existence of parametric vibrations that stabilize nonlinear time lag systems. Transient behavior is also discussed. Illustrative examples are given which show 1) the feasibility of the theory to important applications and 2) the differences in the theory presented and the existing known theory for vibrational control of ordinary differential equations. >

Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior

Complexity, bifurcation and chaos in natural and man-made lumped and distributed systems

Digital simulation of industrial fluid catalytic cracking units—IV. Dynamic behaviour

We consider the problem of creating oscillations of the Furuta pendulum around the open-loop unstable equilibrium. We start with a control transformation shaping the energy of the passive link. Then, a dissipativity-based controller is designed to create oscillations, neglecting the possibility of unbounded motion of the directly actuated link. After that, an auxiliary linear feedback action is added to the control law stabilizing a desired level of the reshaped energy. Parameters of the controller are tuned to approximately keep the originally created oscillations but ensuring bounded motion of both links. The analysis is valid only for oscillations of sufficiently high frequency and is based on higher order averaging technique. The performance of the designed controller is verified using numerical simulations as well as experimentally.

Partial-Energy-Shaping Control for Orbital Stabilization of High-Frequency Oscillations of the Furuta Pendulum

A numerical-method for determining optimal parameter values in forced periodic operation

Des oscillations forcees introduites dans des debits d'entree d'un reacteur continu agite exothermique, provoquent une modification de la courbe en S de regime permanent. Cette modification rend possible d'operer a un regime asymptotiquement stable localise au voisinage d'un regime permanent instable du reacteur aux debits d'entree stationnaires. Ainsi, des vibrations dans les debits d'entree peuvent etre considerees comme un mecanisme stabilisant ce type de reacteur

Vibrational control of an exothermic reaction in a CSTR: Theory and experiments

Vibrational control of an exothermic reaction - in a cstr: theory, simulation, experiment.

Vibrational control is a method for modification of dynamic properties of linear and nonlinear systems by introduction of fast, zero-average oscillations in a system's parameters. It has been previously shown that forced oscillations introduced in the reactant flow rates to a continuous stirred tank reactor (CSTR) cause a modification of the S - shaped steady-state curve. In the present note experimental evidence is given to show that this modification leads to the operation the CSTR at an asymptotically stable periodic regime located near an unstable steady-state of the reactor system having fixed flow rates. For a given average stabilized state, such a stabilizing mechanism results in a higher production rate or lower energy expenditure compared to a steady operation with shifted input conditions.

http://ieeexplore.ieee.org/iel5/9/24253/01104598.pdf

Jian Deng

Papers

Vibrational control of an exothermic reaction in a CSTR: Theory and experiments

Vibrational control of an exothermic reaction - in a cstr: theory, simulation, experiment.

Vibrational stabilization of a chemical reactor: An experimental study