Time-optimal control of a particle in a dielectrophoretic system

International audienceWe study the time-optimal control of a particle in a dielectrophoretic system. This system consists of a time-varying nonuniform electric field which acts upon the particle by creating a dipole within it. The interaction between the induced dipole and the electric field generates the motion of the particle. The control is the voltage on the electrodes which induces the electric field. Since we are considering the motion of a particle on an invariant line in a chamber filled with fluid flowing at low Reynolds number, the dynamics have a two dimensional state; one for the particle position and the other for the induced dipole moment. In regard to time-optimal control, we address the issue of existence and uniqueness of optimal trajectories, and explicitly compute the optimal control and the corresponding minimum time. Finally, we cast our analysis in the framework of symplectic reduction theory in order to provide geometric insight into the problem

Control Strategies for Multi-Controller Multi-Objective Systems

This dissertation\u27s focus is control systems controlled by multiple controllers, each having its own objective function. The control of such systems is important in many practical applications such as economic systems, the smart grid, military systems, robotic systems, and others. To reap the benefits of feedback, we consider and discuss the advantages of implementing both the Nash and the Leader-Follower Stackelberg controls in a closed-loop form. However, closed-loop controls require continuous measurements of the system\u27s state vector, which may be expensive or even impossible in many cases. As an alternative, we consider a sampled closed-loop implementation. Such an implementation requires only the state vector measurements at pre-specified instants of time and hence is much more practical and cost-effective compared to the continuous closed-loop implementation. The necessary conditions for existence of such controls are derived for the general linear-quadratic system, and the solutions developed for the Nash and Stackelberg controls in detail for the scalar case. To illustrate the results, an example of a control system with two controllers and state measurements available at integer multiples of 10% of the total control interval is presented. While both Nash and Stackelberg are important approaches to develop the controls, we then considered the advantages of the Leader-Follower Stackelberg strategy. This strategy is appropriate for control systems controlled by two independent controllers whose roles and objectives in terms of the system\u27s performance and implementation of the controls are generally different. In such systems, one controller has an advantage over the other in that it has the capability of designing and implementing its control first, before the other controller. With such a control hierarchy, this controller is designated as the leader while the other is the follower. To take advantage of its primary role, the leader\u27s control is designed by anticipating and considering the follower\u27s control. The follower becomes the sole controller in the system after the leader\u27s control has been implemented. In this study, we describe such systems and derive in detail the controls of both the leader and follower. In systems where the roles of leader and follower are negotiated, it is important to consider each controller\u27s leadership property. This property considers the question for each controller as to whether it is preferable to be a leader and let the other controller be a follower or be a follower and let the other controller be the leader. In this dissertation, we try to answer this question by considering two models, one static and the other dynamic, and illustrating the results with an example in each case. The final chapter of the dissertation considers an application in microeconomics. We consider a dynamic duopoly problem, and we derive the necessary conditions for the Stackelberg solution with one firm as a leader controlling the price in the marke

Distributed manipulation by controlling force fields through arrays of actuators

Tato práce se zaměřuje na řízení distribuované manipulace prostřednictvím fyzikálních polí vytvářených maticí akčních členů. Práce se zabývá především manipulací s objekty pomocí nehomogenního elektrického a magnetického pole - dielektroforézou a magnetoforézou. Pro oba principy jsou odvozeny matematické modely vhodné pro začlenění do zpětnovazební řídicí smyčky. Modely mají v obou doménách podobnou strukturu, která dovoluje vývoj jednotného řídicího systému. Nelineární model dynamiky systému je v každé vzorkovací periodě invertován pomocí numerického řešení optimalizačního problému. Výhodou navržené strategie řízení je, že dovoluje paralelní manipulaci - nezávislou manipulaci s několika objekty najednou. Práce vedle teoretických konceptů popisuje také technické detaily experimentálních platforem spolu s výsledky mnoha experimentů. Pro dielektroforézu je navrženo nové uspořádání elektrod, které umožňuje manipulaci s více objekty v rovině a zároveň vyžaduje pouze jednovrstvou výrobní technologii. Na algoritmické straně práce představuje nové použití fázové modulace napětí pro řízení dielektroforézy. Dále také popisuje součásti vyvinuté instrumentace, jako jsou vícekanálové generátory pro řízení dielektroforézy prostřednictvím amplitudové a fázové modulace a optické měření polohy v reálném čase pomocí senzoru bez objektivu. Pro magnetoforézu je detailně popsána modulární experimentální platforma sestávající se z pole cívek se železnými jádry. Díky modularitě může být platforma použita k ověření nejen centralizovaných, ale také distribuovaných řídicích systémů.This work focuses on the control of distributed manipulation through physical fields created by arrays of actuators. In particular, the thesis addresses manipulation of objects using non-uniform electric and magnetic fields---dielectrophoresis and magnetophoresis, respectively. In both domains, mathematical models suitable for incorporation into a feedback control loop are derived. The models in the two domains exhibit a similar structure, which encourages the development of a unified approach to control. The nonlinear model of the system dynamics is inverted by solving a numerical optimization problem in every sampling period. A powerful attribute of the proposed control strategy is that a parallel manipulation---the simultaneous and independent manipulation of several objects---can be demonstrated. Besides the theoretical concepts, the thesis also describes technical details of experimental platforms for both physical domains, together with outcomes from numerous experiments. For dielectrophoresis, a new layout of electrodes is documented that allows full planar manipulation while requiring only a one-layer fabrication technology. On the algorithmic side, work presents a novel use of phase modulation of the voltages to control dielectrophoresis. Dedicated instrumentation is also discussed in the thesis such as multichannel generators for control of dielectrophoresis through amplitude and phase modulation and optical real-time position measurements using common optics and a lensless sensor. For magnetophoresis, a modular test bed composed of a planar array of coils with iron cores is described in detail. Thanks to the modularity, the platform can be used for verification of not only the centralized but also distributed control strategies

Time-Optimal Control Of A Particle

We study the time-optimal control of a particle in a dielectrophoretic system. This system consists of a time-varying non-uniform electric field which acts upon the particle by inducing a dipole moment within it. The interaction between the dipole and the electric field generates the motion of the particle

Time-Optimal Control of a Particle in a

Abstract—We study the time-optimal control of a particle in a dielectrophoretic system. This system consists of a time-varying nonuniform electric field which acts upon the particle by creating a dipole within it. The interaction between the induced dipole and the electric field generates the motion of the particle. The control is the voltage on the electrodes which induces the electric field. Since we are considering the motion of a particle on an invariant line in a chamber filled with fluid flowing at low Reynolds number, the dynamics have a two dimensional state; one for the particle position and the other for the induced dipole moment. In regard to time-optimal control, we address the issue of existence and uniqueness of optimal trajectories, and explicitly compute the optimal control and the corresponding minimum time. Finally, we cast our analysis in the framework of symplectic reduction theory in order to provide geometric insight into the problem. Index Terms—Biotechnology, dielectrophoresis, nanotechnology, time-optimal control