Gain Property Research Articles

On nonlinear H ∞ sliding mode control for a class of nonlinear cascade systems

In this work two main robust control strategies, the sliding mode control (SMC) and nonlinear H ∞ control, are integrated to function in a complementary manner for tracking control tasks. The SMC handles matched L ∞[0,∞) type system uncertainties with known bounding functions. H ∞ control deals with unmatched disturbances of L 2[0,∞) type where the upper-bound knowledge is not available. The new control method is designed for a class of nonlinear uncertain systems with two cascade subsystems. Nonlinear H ∞ control is applied to the first subsystem in the presence of unmatched disturbances. Through solving a Hamilton-Jacoby inequality, the nonlinear H ∞ control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H ∞ control, the resulting sliding manifold in the sliding phase possesses the desired L 2 gain property and to a certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L 2 gain robustness in the reaching phase. Two illustrative examples are given to show the effectiveness of the proposed robust control scheme.

Gain analysis for switched systems with continuous-time and discrete-time subsystems

In this paper, we study gain property for a class of switched systems which are composed of both continuous-time LTI subsystems and discrete-time LTI subsystems. Under the assumption that all subsystems are Hurwitz/Schur stable and have the gain less than γ, we discuss the gain that the switched system could achieve. First, we consider the case where a common Lyapunov function exists for all subsystems in sense, and show that the switched system has the gain less than the same level γ under arbitrary switching. As an example in this case, we analyse switched symmetric systems and establish the common Lyapunov function explicitly. Next, we use a piecewise Lyapunov function approach to study the case where no common Lyapunov function exists in sense, and show that the switched system achieves an ultimate (or weighted) gain under an average dwell time scheme.

Formula omitted]-like control for nonlinear stochastic systems

In this paper we develop a H ∞ -type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L 2 -gain property and the solution to a certain Hamilton–Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case-based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.

Photorefractive gain property and optimization of dynamic holographic gratings in arbitrarily cut sillenite crystal

We study the influence of vectorial wave coupling on the wave eigenmodes in an arbitrarily-cut photorefractive and optically active piezo-electric sillenite cry stal, and solve the vectorial equations for weak two-wave coupling. We deal exac tly with the vectorial wave coupling in an optically inactive piezo-electric cry stal by solving the scalar equations. By doing so we calculate the signal gains in the optically active and the optically inactive crystals and discuss the cont ributions of the isotropic and the anisotropic coupling to the gain, respectivel y. We optimize the signal gain of the optically active crystal and apply the re sults to a BSO and BTO crystal. We also investigate the influence of the piezo-e lectric and elasto-optic effect on the optimum gain for (110),(111),(112) and th eir equivalent cuts.

Pressure dependence of the small-signal gain and saturation intensity of a copper vapor laser.

The small-signal gain coefficient and the saturation intensity of a copper vapor laser have been measured for both 510.6- and 578.2-nm transitions through the implementation of a discharge driven oscillator-amplifier configuration. Pressure dependence of the gain and saturation property of the laser has been investigated.

Space-Time Turbo Coded Modulation: Design and Applications

A design method for recursive space-time trellis codes and parallel-concatenated space-time turbo coded modulation is proposed that can be applied to an arbitrary existing space-time trellis code. The method enables a large, systematic increase in coding gain while preserving the maximum transmit diversity gain and bandwidth efficiency property of the considered space-time trellis code. Applying the above method to Tarokh et al. space-time trellis codes, significant performance improvements can be obtained even with extremely short input information frames. The application of space-time turbo coded modulation to the space-frequency domain is also proposed in this paper. Exploiting the bandwidth efficient orthogonal frequency division modulation (OFDM), multiple transmit antennas and large frequency selectivity offered by typical low mobility indoor environments, the proposed space-frequency turbo coded modulation performs within 2.5 dB of the outage capacity for a variety of practical wideband multiple-input multiple-output (MIMO) radio channels.

Decentralized disturbance attenuating output-feedback trackers for large-scale nonlinear systems

The problem of decentralized output-feedback tracking with disturbance attenuation is addressed for a new class of large-scale and minimum-phase nonlinear systems. Common assumptions like matching and growth conditions are not required for the underlying decentralized system with a diagonal structure. An observer-based decentralized controller design is presented. The proposed decentralized output-feedback laws achieve asymptotic tracking and internal Lagrange stability when the disturbance inputs disappear, and, guarantee external stability in the presence of disturbance inputs. These external stability properties include Sontag's ISS and iISS conditions and standard L 2 -gain property.

Worst Case Power Generating Capabilities of Nonlinear Systems

In this paper we analyze the worst case power generating capabilities of a class of nonlinear systems which exhibit a power gain property. This class of systems includes systems which exhibit persistent excitation in the absence of inputs. Examples include limit cycle systems and chaotic systems. In order to capture the power generating capability of a nonlinear system, we define a worst case average cost per unit time performance index. This performance index, called the available power, is in effect the most power that can be generated by a system via the application of any input. The main result of the paper is that the input which achieves this worst case performance is typically a persistent input whose power is given explicitly by a function of the derivative of the available power with respect to the power gain of the system. A natural corollary of this result is that the available power may be recast as an optimization over power inputs.

FINITE FREQUENCY CHARACTERIZATION OF EASILY CONTROLLABLE MECHANICAL SYSTEMS UNDER CONTROL EFFORT CONSTRAINT

This paper is concerned with the development of a new approach for integrated design of controlled mechanical systems. The contribution is three fold. We first show through a typical design example that the closed-loop bandwidth achievable with a reasonable control effort is shown to be closely related to the frequency range for which the plant is high gain and exhibits positive-realness when high gain controllers are not allowed. Secondly, we present matrix inequality characterizations of the robust finite frequency positive-real property and the finite frequency high gain property. Thirdly, we propose a systematic method for designing mechanical systems to achieve the finite frequency properties. Then, the validity is confirmed by the smart structure design using piezo-electric films.

Influence of varying N-environments on the properties of (GaIn)(NAs) vertical-cavity surface-emitting lasers

We report electromodulated reflectance studies on the band structure of a dilute-N (∼1%) (GaIn)(NAs)/GaAs/AlAs vertical-cavity surface-emitting laser (VCSEL), as a function of temperature and incidence angle. The wide range of operating temperatures observed for this type of VCSEL (∼360 K here) is due to the reduced temperature variation of the effective band gap of the active (GaIn)(NAs) quantum wells, and broad gain. By comparing lasing properties and band structure we argue that the gain broadening is not simply due to alloy disorder but arises from a recently-proposed intrinsic property of (GaIn)(NAs): the existence of different band gaps for the five possible nearest-neighbor configurations of the N substitutional impurity.

Constructive nonlinear control: a historical perspective

In the early days of nonlinear control theory most of the stability, optimality and uncertainty concepts were descriptive rather than constructive. This survey describes their ‘activation’ into design tools and constructive procedures. Structural properties of nonlinear systems , such as relative degree and zero dynamics, are connected to passivity, while dissipativity, as a finite L 2 -gain property, also appears in the disturbance attenuation problem, a nonlinear counterpart of robust linear control. Passivation-based designs exploit the connections between passivity and inverse optimality, and between Lyapunov functions and optimal value functions. Recursive design procedures, such as backstepping and forwarding, achieve certain optimal properties for important classes of nonlinear systems. The survey concludes with four representative applications. The selection of the topics and their interpretations are greatly influenced by the experience and personal views of the senior author.

Constructive nonlinear control: a historical perspective

In the early days of nonlinear control theory most of the stability, optimality and uncertainty concepts were descriptive rather than constructive. This survey describes their ‘activation’ into design tools and constructive procedures. Structural properties of nonlinear systems, such as relative degree and zero dynamics, are connected to passivity, while dissipativity, as a finite L 2 -gain property, also appears in the disturbance attenuation problem, a nonlinear counterpart of robust linear control. Passivation-based designs exploit the connections between passivity and inverse optimality, and between Lyapunov functions and optimal value functions. Recursive design procedures, such as backstepping and forwarding, achieve certain optimal properties for important classes of nonlinear systems. The survey concludes with four representative applications. The selection of the topics and their interpretations are greatly influenced by the experience and personal views of the senior author.

Force Characteristics of Slim Pickup Actuator to Improve Actuating Performances

Recently, there has been a trend to lower the tilt margin in multifunctional rewritable optical disk drives and many attempts have been made to construct a servo system to compensate the tilt in such devices as compact disk-rewritable (CD-RW) or digital versatile disk-random access memory (DVD-RAM) drives in view of rewritable disks. However, in the slim-type drives for Notebook PCs, it is very difficult to realize mechanisms for tilt servo without accompanying impairment of the gain property, due to spatial constraints. In this paper, we suggest a method of controlling the driving force to diminish the variance of mechanical tilt over the entire movable range of wire-spring-suspension-type actuators, and propose a process for precise analysis of driving force. In addition, based on the results of force analysis, we present the conditions that minimize the phase disturbance in subsidiary resonances which have adverse effects on the servo performance of slim-type pickup actuators.

Gain characteristics of codirectionally coupledsemiconductor optical amplifier for polarity-non-inverted digital wavelengthconversion

A very unique gain property of a codirectionally coupled semiconductor optical amplifier has been utilised to realise a novel cross-phase modulation device. Features such as threshold-like input-output characteristics and the incorporation of polarity-non-inverted switching make this device much more attractive for all-optical switching and digital wavelength conversion purposes than current devices.

Robust Control Based on Dissipativeness of Open-Loop Systems

This paper proposes a robust control design method by imposing dissipativeness on open-loop systems. First, it is shown that stability of nominal feedback systems is equivalent to dissipativeness of open-loop systems. This result justifies imposing dissipativeness on open-loop systems. Second, a robust stability for some class of complex perturbations guaranteed by dissipativeness of open-loop systems is shown. This explains that our method is effective for ensuring gain and phase margins of feedback systems. Third, it is shown that dissipativeness of open-loop systems is equivalent to bounded realness of certain closed-loop transfer functions. This fact implies that H∞ control which evaluates only gain property possesses the ability to take into consideration both gain and phase properties of open-loop transfer functions, as well as it gives a controller design method based on dissipativeness of open-loop systems.

Biaxial Strain Effect on Wurtzite GaN/AlGaN Quantum Well Lasers

Subband structures and optical gains of both unstrained and biaxial strained wurtzite GaN/AlGaN quantum well (QW) laser diodes (LDs) are theoretically investigated by the 8×8 k\\cdotpp theory, with the assistance of the first-principles calculations in the derivation of the required parameters such as deformation potentials. The strong electron affinity and the small spin-orbit coupling of a nitrogen yield much heavier effective masses even in the QWs. It plays an essential role in causing a higher threshold current density for any well length than GaAs/AlGaAs QW LDs. Considering a biaxial strain induced by the lattice mismatch, the optical gain property qualitatively improves for any well length. However, the effect on the reduction of the threshold current density is quantitatively not so effective as GaAs/AlGaAs QW LDs.

Quantum Point Contact Switches

Switching behavior between electron tunneling and ballistic transport states was induced by repeatedly bringing a sharpened nickel wire into contact with a gold surface. The high-conductivity ballistic state had a quantized conductance of 0.977 +/- 0.015 (2e(2)/h). Switching was accomplished by moving the electrodes with a piezoelectric actuator over a distance of 2 angstroms. The two electrodes and the actuator form a three-terminal device that is demonstrated to be a reliable digital and analog switch; it shows good discrimination between high and low states and possesses the important property of power gain. The conductance channel is most likely only one atom wide and possibly consists of a single atom.

A necessary condition for effective performance of the multiple model adaptive estimator

Effective adaptive estimation for a general linear system driven by an input modeled by a randomly switching Gaussian process is considered. The performance of the multiple model adaptive estimator (MMAE) is, in some cases, unexpectedly hampered by a necessary condition not satisfied by the linear system. This key dependency for effective MMAE performance is based on a particular property of the DC gain of the linear system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Zero Phase Error Tracking Controllers With Optimal Gain Characteristics

Recently, a digital feedforward controller, called a Zero Phase Error Tracking Controller (ZPETC), has been proposed. In this controller, the overall frequency response between the desired output and the controlled output exhibits zero phase shift for all frequencies by using a few steps of the future desired output data. In this paper, two extensions of ZPETC’s are proposed: a ZPETC with deadbeat tracking performance and an L2-Optimal ZPETC. These ZPETC’s can provide the overall control system with not only the above phase property but also the excellent tracking performance for a desired output and the superior gain property, respectively. Moreover, a ZPETC with both the excellent tracking performance for a step-type and ramp-type desired output and the superior gain property, called an L2-Optimal ZPETC with deadbeat tracking performance, is presented.

The surprising kidney-fluid mechanism for pressure control--its infinite gain!

In this short paper, I have tried to explain the elation that we felt when we first realized that the kidney-fluid mechanism for controlling the arterial pressure has an infinite feedback gain property. Because of this, all the other pressure control mechanisms, none of which has ever been shown to have a similar infinite gain property, must themselves alter the kidney-fluid mechanism if they are to succeed in causing long-term changes in the arterial pressure. We have not been able to refute this principle despite many experiments over the last 2 decades. For this reason, our first understanding of the infinite gain property of the kidney-fluid mechanism was like a light at the end of the tunnel. I hope that I can explain to the reader the excitement of those few seconds when we first recognized the principle in 1966.