Investigation and Synthesis of Robust Polynomials in Uncertainty on the Basis of the Root Locus Theory

The root locus method is proposed in the chapter for searching intervals of uncertainty for coefficients of the given (source) polynomial with constant or interval coefficients under perturbations, which ensures its robust stability regardless of whether the given polynomial is Hurwitz or not. The method is based on introduction and application of the “extended root locus” notion. Polynomial adjustment is performed by setting up each one of its coefficients separately and sequentially and determining permissible values of coefficient variation intervals (intervals of uncertainty). The effect of each coefficient variation upon the polynomial root dynamics (behavior) is considered and analyzed separately, and this influence could be observed in the root locus portraits. Root locus method is thus generalized to the cases when the number of polynomial variable coefficients is arbitrary. The root locus parameter distribution diagram along the asymptotic stability bound is introduced and applied for observing the roots behavior regularities. On this basis, the stability conditions are derived, and analytical and graphic-analytical methods are worked out for calculating intervals of variation for the 4th order polynomial family parameters ensuring its robust stability. It also allows to extract Hurwitz subfamilies from the non-Hurwitz families of interval polynomials and to determine whether there exists at least one stable polynomial in the unstable polynomial family

Parametric synthesis of linear regulator in interval system with guaranteed root quality indices

Automatic control system containing proportional-plus-integral action regulator and control object which has interval specified parameters has been considered. Using robust expansion of root-locus method the technique of synthesis of proportional-plus-integral action regulator parameters guaranteeing minimal degree of stability and maximal degree of system oscillation was developed. The technique is based on vertex analysis of root quality indices applying the equation of Theodorchik-Evans. The numeric illustration is give

Evidence of neutral transcriptome evolution in plants

The transcriptome of an organism is its set of gene transcripts (mRNAs) at a defined spatial and temporal locus. Because gene expression is affected markedly by environmental and developmental perturbations, it is widely assumed that transcriptome divergence among taxa represents adaptive phenotypic selection. This assumption has been challenged by neutral theories which propose that stochastic processes drive transcriptome evolution. To test for evidence of neutral transcriptome evolution in plants, we quantified 18 494 gene transcripts in nonsenescent leaves of 14 taxa of Brassicaceae using robust cross-species transcriptomics which includes a two-step physical and in silicobased normalization procedure based on DNA similarity among taxa. Transcriptome divergence correlates positively with evolutionary distance between taxa and with variation in gene expression among samples. Results are similar for pseudogenes and chloroplast genes evolving at different rates. Remarkably, variation in transcript abundance among root-cell samples correlates positively with transcriptome divergence among root tissues and among taxa. Because neutral processes affect transcriptome evolution in plants, many differences in gene expression among or within taxa may be nonfunctional, reflecting ancestral plasticity and founder effects. Appropriate null models are required when comparing transcriptomes in space and time

Robust saturated control of human-induced floor vibrations via a proof-mass actuator

This paper is concerned with the design of a robust active vibration control system that makes use of a proof-mass actuator for the mitigation of human-induced vibrations in floor structures. Ideally, velocity feedback control (VFC) is unconditionally stable and robust to spillover effects, interlacing of poles and zeros of collocated control is then accomplished. However, the use of a proof-mass actuator influences the system dynamics and the alternating pole-zero pattern of the system formed by the actuator and structure is no longer fulfilled. However, a controlled migration of the two zeros of the root locus plot at the origin, resulting from the acceleration output, can be achieved by adding a feed-through term (FTT) to the structure acceleration output. That is, the FTT enables us to control the position of a pair of complex conjugate zeros (an anti-resonance in the frequency domain). This paper proposes the introduction of an FTT designed in such a way that the anti-resonance at the origin is located between the actuator resonance and the structure fundamental resonance. Hence, an integral controller leads to infinite gain margin and significant phase margin. Simulation and experimental results on a concrete slab strip have validated the proposed control strategy. Significant improvements in the stability properties compared with VFC are reported

Stochastic Satbility and Performance Robustness of Linear Multivariable Systems

Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters

LSS reference platform control

The long range objective of this task is to develop basic technology in the design, mechanization, and analysis of control systems for large flexible space structures. The focus of the FY'81 platform control effort was on the pointing control problems associated with multiple independently controlled experiment packages operating simultaneously on a single platform. Particular emphasis was placed on obtaining a quantitative comparison of controller performance with and without base motion compensation

An analytical approach to integral resonant control of second-order systems

Peer reviewedPostprin

Flutter suppression for the active flexible wing: Control system design and experimental validation AIAA-92-2097

The synthesis and experimental validation of a control law for13; an actiqe flutter suppression system for the Active Flexible13; Wing wind-tunnel model is presenied. The design was13; accomplished with traditional root locus and Nyquist methods13; using interactive computer graphics tools and with extensive use13; of simulation-based analysis. The design approach relied on a13; fundamental understanding of the flutter mechanism to13; formulate a simple control law structure. Experimentally, the13; flutter suppression controller succeeded in simultaneous13; suppression of two flutter modes, significantly increasing the13; flutter dynamic pressure despite errors in the design model. The13; flutter suppression controller was also successfully operated in13; combination with a rolling maneuver controller to perform13; flutter suppression during rapid rolling maneuvers