Methods of Ensuring Invariance with Respect to External Disturbances: Overview and New Advances

In this paper, we carry out a demonstration and comparative analysis of known methods of the synthesis of various control laws ensuring the invariance of the output (controlled) variable with respect to external disturbances under various assumptions about their type and channels of acting on the control plant. Methods of the synthesis are presented on the example of a third-order nonlinear system with single input and single output (SISO-systems), dynamic feedback synthesis is presented at a descriptive level and the focus is on procedures of static feedback synthesis. For the systems in which the matching conditions are not satisfied, it is concluded that it is expedient to introduce smooth and bounded nonlinear local feedbacks. Within the framework of the block control principle, we developed an iterative procedure of synthesis of S-shaped sigmoid feedbacks for such systems. Nonlinear local feedbacks ensure stabilization of the output variable with the given accuracy and settling time as in a system with traditionally used linear local feedbacks with high gains. However, in contrast to it, sigmoid functions do not lead to a large overshoot of state variables and control actions.

Riemannian geometric approach to optimal binocular rotation, pyramid based interpolation and bio-mimetic pan-tilt movement

Over the past several years, we have been studying the problem of optimally rotating a rigid sphere about its center, where the rotation is actuated by a triplet of external torques acting on the body. The control objective is to repeatedly direct a suitable radial vector, called the gaze vector, towards a stationary point target in IR3. The orientation of the sphere is constrained to lie in a suitable submanifold of SO(3). Historically, the constrained rotational movements were studied by physiologists in the nineteenth century, interested in eye and head movements. In this paper we revisit the gaze control problem, where two visual sensors, are tasked to simultaneously stare at a point target in the visual space. The target position changes discretely and the problem we consider is how to reorient the gaze directions of the sensors, along the optimal pathway of the human eyes, to the new location of the target. This is done by first solving an optimal control problem on the human binocular system. Next, we use these optimal control and show that a pan-tilt system can be controlled to follow the gaze trajectory of the human eye requiring a nonlinear static feedback of the pan and tilt angles and their derivatives. Our problem formulation uses a new Riemannian geometric description of the orientation space. The paper also introduces a new, pyramid based interpolation method, to implement the optimal controller.

Relationship of drain induced barrier lowering and top/bottom gate oxide thickness in asymmetric junctionless double gate MOSFET

The relationship of drain induced barrier lowering (DIBL) phenomenon and channel length, silicon thickness, and thicknesses of top and bottom gate oxide films is derived for asymmetric junctionless double gate (JLDG) MOSFETs. The characteristics between the drain current and the gate voltage is derived by using the potential distribution model to propose in this paper. In this case, the threshold voltage is defined as the corresponding gate voltage when the drain current is (W/L) × 10-7 A, and the DIBL representing the change in the threshold voltage with respect to the drain voltage is obtained. As a result, we observe the DIBL is proportional to the negative third power of the channel length and the second power of the silicon thickness and linearly proportional to the geometric mean of the top and bottom gate oxide thicknesses, and derive a relation such as DIBL =25.15ηL_g^(-3) t_si^2 √(t_ox1∙t_ox2 ), where η is a static feedback coefficients between 0 and 1. The η is found to be between 0.5 and 1.0 in this model. The DIBL model of this paper has been observed to be in good agreement with the result of other paper, so it can be used in circuit simulation such as SPICE.

Controllability and stabilization of gravity-capillary surface water waves in a basin

<p style='text-indent:20px;'>The paper concerns the controllability and stabilization of surface water waves in a two-dimensional rectangular basin under the forces of gravity and surface tension. The surface waves are generated by a wave-maker placed at the left side-boundary and it is physical relevant to see whether the surface waves are controllable or can be stabilized using appropriate motion of the wave-maker. Due to the surface tension, an edge condition must be imposed at the contact point between the free surface and a solid boundary. Two types of wave-makers are considered: "flexible" or "rigid". It is shown that the surface waves are approximately controllable, but not exactly controllable, for both "flexible" and "rigid" wave-makers. In addition, under a static feedback to control a "rigid" wave-maker, the strong stability of feedback control system is obtained.</p>

An Application of QSR-Dissipativity to the Problem of Static Output Feedback Robust Stabilization of Nonlinear Systems

In this work we deal with the asymptotic stabilization problem of polynomial (and rational) input-affine systems subject to parametric uncertainties. The problem of linear static output feedback (SOF) control synthesis is handled, having as a prerequisite a differential algebraic representation (DAR) of the plant. Using the property of strict QSR-dissipativity, theFinsler's Lemma and the notion of linear annihilators we introduce a new dissipativity-based strategy for robust stabilization which determines a static feedback gain by solving a simple linear semidenite program on a polytope. At the same time, an estimate of the closed-loop domain of attraction is given in terms of an ellipsoidal set. The novelty of the proposed approach consists in this combination of dissipativity theory and powerful semidenite programming(SDP) tools allowing for a simple solution of the challenging problem of static output feedback design for nonlinear systems. A numerical example allows the reader to verify the applicability of the proposed technique.

Distributed control of multi-agents system via static feedback controllers under directed networks

During recent years, a lot of distributed control approaches based on static feedback controllers have been proposed to realize consensus of multi-agents systems with undirected topologies. However, many of these approaches have not been generalized to systems with directed topologies yet. Therefore, in this paper, for first- and second-order multi-agents systems with directed topologies, we propose a series of new nonlinear consensus protocols based on traditional design. With integral Lyapunov functions, we can prove the stability of proposed control protocols and a group of simulation results are also given to testify our theory.

SPICE model of drain induced barrier lowering in sub-10 nm junctionless cylindrical surrounding gate MOSFET

We propose a SPICE Drain Induced Barrier Lowering (DIBL) model for sub-10 nm Junctionless Cylindrical Surrounding Gate (JLCSG) MOSFETs. The DIBL shows the proportionl relation to the -3 power of the channel length Lg and the 2 power of silicon thickness in MOSFET having a rectangular channel, but this relation cannot be used in cylindrical channel because of the difference in channel structure. The subthreshold currents, including the tunneling current from the WKB (Wentzel-Kramers-Brillouin) approximation as well as the diffusion-drift current, are used in the model. The constant current method is used to define the threshold voltage as the gate voltage at a constant current, (2πR/Lg)10-7 A for channel length and channel radius R. The central potential of the JLCSG MOSFET is determined by the Poisson equation. As a result, it can be seen that the DIBL of the JLCSG MOSFET is proportional to the –2.76 power of the channel length, to the 1.76 power of the channel radius, and linearly to the oxide film thickness. At this time, we observe that the SPICE parameter, the static feedback coefficient, has a value less than 1 1, and this model can be used to analyze the DIBL of the JLCSG MOSFET.