scholarly journals On PID Design Constraints in Relation to Control of Strictly Metzler Linear MIMO Systems

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1589
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Pid Control ◽  
Mimo Systems ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Control Law ◽  
Matching Conditions ◽  
Time Invariant ◽  
Parameter Constraints ◽  
The Given ◽  
First Time

For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the controller and system parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with PID control law parameter representation and is formulated as a linear matrix inequality feasibility problem. Characterization of the PID control law parameters is permitted to highlight dynamical properties of the closed-loop system and the structural influence of the control derivative gain value in the design step. For the first time, the paper comprehensively sets the synthesis standard for PID control of MIMO Metzler systems because others for the given task have not been created at present.

scholarly journals PID Control Design for SISO Strictly Metzlerian Linear Systems

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1979
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Pid Control ◽  
Linear Time ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Control Law ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Parameter Constraints ◽  
Structural Influence

For linear time-invariant Metzlerian systems, this paper proposes an original approach reflecting specific structural system constraints and positiveness in solving the problem of PID control. Refining parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with the control law representation and is formulated as a linear matrix inequality feasibility problem. Taking into account structural restriction of Metzlerian positive systems, a characterization of PID control law parameters is permitted, to highlight dynamical properties of the closed-loop system solutions and the significant structural influence of derivative gain value of the control law parameters in design.

scholarly journals Mixed H2/H∞ Control Synthesis for Discrete-time Linear Positive Systems using Enhanced Set of Linear Matrix Inequalities

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Feasibility Problem ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Positive Systems ◽  
System Matrix ◽  
Parameter Constraints ◽  
Time Linear

This paper provides an idea, resulting from linear matrix inequality representation of parameter constraints of discrete-time linear positive systems, to formulate state-feedback synthesis for this class of systems. The design conditions are imposed to obtain control respecting existing strictly positivity or non-negativity in the system matrix description. Formulated as a linear matrix inequality feasibility problem it is reiterated that approach leads iteratively to estimation of norms of closed-loop system

Root with Alternation of -ravn-/-rovn- (From Materials of the Academic Description of Russian Spelling)

2020 ◽  
Vol 81 (6) ◽  
pp. 90-96
Author(s):  
E. V. Arutiunova ◽  
E. V. Beshenkova ◽  
O. E. Ivanova
Keyword(s):  
Russian Language ◽  
Study Guides ◽  
Russian Academy Of Sciences ◽  
Academy Of Sciences ◽  
The Given ◽  
First Time ◽  
The Russian Language

The study investigates the rule of spelling the root -ravn-/-rovn- and is considered to be a fragment of the academic description of Russian spelling, which is currently being under investigation at the Russian Language Institute of the Russian Academy of Sciences. The authors clarify the meanings that determine the spelling of the unstressed root, supplement the lists of exceptions, denote words with meanings not corresponding to the given values-criteria, and, for the first time in linguistics, investigate the words that can be correlated with different values-criteria, that is, they have double motivation. The rule codifies the spelling of words that have double motivation and fluctuate in usus, dictionaries, study guides and reference books. Spelling recommendations for these words correspond to the current linguistic norm and were approved by the Spelling Commission of the Russian Academy of Sciences in 2019. The linguistic commentary to the rule contains the most significant etymological facts concerning the root -ravn-/-rovn- and summarises the scientific and methodological attempts to figure out the distribution of vocabulary with root -ravn-/-rovn- based on the meanings selected in the spelling rules. In the paper it is shown that the instability in spelling of various verbs with the root -ravn-/-rovn- in modern writing and dictionaries is determined by the double motivation of words, as well as contradictory recommendations and gaps in the rules.

LUMINESCENCE OF THE BLACK SEA MICROSCOPIC FUNGI CULTURES

2017 ◽  
Author(s):  
Olga Mashukova ◽  
Olga Mashukova ◽  
Yuriy Tokarev ◽  
Yuriy Tokarev ◽  
Nadejda Kopytina ◽  
...  
Keyword(s):  
Fresh Water ◽  
Black Sea ◽  
Ethyl Alcohol ◽  
Light Emission ◽  
Sea Water ◽  
Control Culture ◽  
Chemical Stimulation ◽  
The Black Sea ◽  
The Given ◽  
First Time

We studied for the first time luminescence characteristics of the some micromycetes, isolated from the bottom sediments of the Black sea from the 27 m depth. Luminescence parameters were registered at laboratory complex “Svet” using mechanical and chemical stimulations. Fungi cultures of genera Acremonium, Aspergillus, Penicillium were isolated on ChDA medium which served as control. Culture of Penicillium commune gave no light emission with any kind of stimulation. Culture of Acremonium sp. has shown luminescence in the blue – green field of spectrum. Using chemical stimulation by fresh water we registered signals with luminescence energy (to 3.24 ± 0.11)•108 quantum•cm2 and duration up to 4.42 s, which 3 times exceeded analogous magnitudes in a group, stimulated by sea water (p < 0.05). Under chemical stimulation by ethyl alcohol fungi culture luminescence was not observed. Culture of Aspergillus fumigatus possessed the most expressed properties of luminescence. Stimulation by fresh water culture emission with energy of (3.35 ± 0.11)•108 quantum•cm2 and duration up to 4.96 s. Action of ethyl alcohol to culture also stimulated signals, but intensity of light emission was 3–4 times lower than under mechanical stimulation. For sure the given studies will permit not only to evaluate contribution of marine fungi into general bioluminescence of the sea, but as well to determine places of accumulation of opportunistic species in the sea.

scholarly journals On the formation and stability of fermionic dark matter halos in a cosmological framework

2020 ◽  
Author(s):  
Carlos R Argüelles ◽  
Manuel I Díaz ◽  
Andreas Krut ◽  
Rafael Yunis
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Space Distribution ◽  
Coarse Grained ◽  
Dark Matter Halos ◽  
The Core ◽  
The Galaxy ◽  
Gravitating Systems ◽  
The Given ◽  
First Time

Abstract The formation and stability of collisionless self-gravitating systems is a long standing problem, which dates back to the work of D. Lynden-Bell on violent relaxation, and extends to the issue of virialization of dark matter (DM) halos. An important prediction of such a relaxation process is that spherical equilibrium states can be described by a Fermi-Dirac phase-space distribution, when the extremization of a coarse-grained entropy is reached. In the case of DM fermions, the most general solution develops a degenerate compact core surrounded by a diluted halo. As shown recently, the latter is able to explain the galaxy rotation curves while the DM core can mimic the central black hole. A yet open problem is whether this kind of astrophysical core-halo configurations can form at all, and if they remain stable within cosmological timescales. We assess these issues by performing a thermodynamic stability analysis in the microcanonical ensemble for solutions with given particle number at halo virialization in a cosmological framework. For the first time we demonstrate that the above core-halo DM profiles are stable (i.e. maxima of entropy) and extremely long lived. We find the existence of a critical point at the onset of instability of the core-halo solutions, where the fermion-core collapses towards a supermassive black hole. For particle masses in the keV range, the core-collapse can only occur for Mvir ≳ E9M⊙ starting at zvir ≈ 10 in the given cosmological framework. Our results prove that DM halos with a core-halo morphology are a very plausible outcome within nonlinear stages of structure formation.

A Unified Approach to H∞ Control of Singular Markovian Jump Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guoliang Wang ◽  
Hongyi Li
Keyword(s):  
Transition Probability ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
New Approach ◽  
Control Approach ◽  
Singular Markovian Jump Systems ◽  
Jump Systems ◽  
Bounded Uncertainties ◽  
The Given

This paper considers the H∞ control problem for a class of singular Markovian jump systems (SMJSs), where the jumping signal is not always available. The main contribution of this paper introduces a new approach to a mode-independent (MI) H∞ controller by exploiting the nonfragile method. Based on the given method, a unified control approach establishing a direct connection between mode-dependent (MD) and mode-independent controllers is presented, where both existence conditions are given in terms of linear matrix inequalities. Moreover, another three cases of transition probability rate matrix (TRPM) with elementwise bounded uncertainties, being partially unknown and to be designed are analyzed, respectively. Numerical examples are used to demonstrate the effectiveness of the proposed methods.

Optimal Nonlinear Estimation of Linear Stochastic Systems: The Multivariable Extension

1996 ◽  
Vol 118 (2) ◽  
pp. 350-353 ◽  
Author(s):  
M. A. Hopkins ◽  
H. F. VanLandingham
Keyword(s):  
Stochastic Systems ◽  
Transfer Functions ◽  
Mimo Systems ◽  
Linear Time ◽  
Nonlinear Method ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output ◽  
Time Invariant ◽  
Time Systems

This paper extends to multi-input multi-output (MIMO) systems a nonlinear method of simultaneous parameter and state estimation that appeared in the ASME JDSM&C (September, 1994), for single-input single-output (SISO) systems. The method is called pseudo-linear identification (PLID), and applies to stochastic linear time-invariant discrete-time systems. No assumptions are required about pole or zero locations; nor about relative degree, except that the system transfer functions must be strictly proper. In the earlier paper, proofs of optimality and convergence were given. Extensions of those proofs to the MIMO case are also given here.

Determining Human Control Intent Using Inverse LQR Solutions

2013 ◽  
Author(s):  
M. Cody Priess ◽  
Jongeun Choi ◽  
Clark Radcliffe
Keyword(s):  
Human Subjects ◽  
Optimal Solution ◽  
Linear Matrix ◽  
Minimization Method ◽  
Human Control ◽  
Balance Task ◽  
Lqr Problem ◽  
Seated Balance ◽  
Gradient Based ◽  
Time Invariant

In this paper, we have developed a method for determining the control intention in human subjects during a prescribed motion task. Our method is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? We describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. We develop a model for an upright seated-balance task which will be suitable for identification of human control intent once experimental data is available.

scholarly journals LMI-Based Stability Criterion of Impulsive T-S Fuzzy Dynamic Equations via Fixed Point Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ruofeng Rao ◽  
Zhilin Pu
Keyword(s):  
Fixed Point ◽  
Stability Criterion ◽  
High Efficiency ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Linear Matrix ◽  
The Matrix ◽  
Matrix Exponential Function ◽  
Takagi Sugeno ◽  
First Time

By formulating a contraction mapping and the matrix exponential function, the authors apply linear matrix inequality (LMI) technique to investigate and obtain the LMI-based stability criterion of a class of time-delay Takagi-Sugeno (T-S) fuzzy differential equations. To the best of our knowledge, it is the first time to obtain the LMI-based stability criterion derived by a fixed point theory. It is worth mentioning that LMI methods have high efficiency and other advantages in largescale engineering calculations. And the feasibility of LMI-based stability criterion can efficiently be computed and confirmed by computer Matlab LMI toolbox. At the end of this paper, a numerical example is presented to illustrate the effectiveness of the proposed methods.

How Crystals Form from a Cloud of Atoms

2011 ◽  
Vol 675-677 ◽  
pp. 3-7
Author(s):  
Peter Häussler ◽  
Martin Stiehler
Keyword(s):  
Structure Formation ◽  
Fundamental Equation ◽  
Structural Features ◽  
Local Order ◽  
Total System ◽  
Angular Momenta ◽  
General Dynamics ◽  
Bloch’S Theorem ◽  
The Given ◽  
First Time

Structure formation, the condensation of a cloud of atoms to a crystal is still not well understood. Disordered sytems (amorphous/liquid) should be in the center of this research, they are the precursors of any crystal. We consider elementary systems, as well as binary, or ternary amorphous alloys, irrespective whether they are metallically, covalently or ionically bonded and describe the process of structure formation in the formal language of thermodynamics but, as far as we know for the first time, by an extended version (general dynamics), based on the complete Gibbs fundamental equation, applied to internal subsystems. Major structural features evolve from global resonances between formerly independent internal subsystems by exchanging momenta and angular momenta, both accompanied by energy. By this they adjust mutually their internal features and create spherical-periodic structural order at medium-range distances. Under the given external constraints the resonances get optimized by selforganization. Global resonances of the type considered have clearly to be distinguished from local resonances between individual ions (described by quantum chemistry) forming local order. The global resonances cause anti-bonding (non-equilibrium) as well as bonding (equilibrium) states of the coupled total system, occupying the latter to form new structurally extended order. The transition to equilibrium creates entropy which itself leaves the system together with energy. At resonance the energetical splitting between the bonding and anti-bonding state is largest, the creation of entropy and the decrease of the total energy therefore, too. The crystal, finally, evolves by additionally optimizing a resonance based on angular momentum, and the additional adjustments of the local resonances to the global ones, theoretically done by applying Bloch’s theorem.

Sign in / Sign up

Export Citation Format

Share Document