Active Control of Viscoelastic Systems by the Method of Receptance

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Kumar V. Singh ◽  
Xiaoxuan Ling

Viscoelastic materials have frequency and temperature-dependent properties and they can be used as passive controlling devices in wide range of vibration applications. In order to design active control for viscoelastic systems, an accurate mathematical modeling is needed. In practice, various material models and approximation techniques are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state-space models, which introduces several challenges such as introduction of nonphysical internal state variables and requirement of observer/state estimator design. In this paper, it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available receptance transfer functions (RTF) and hence eliminating the need for state-space modeling for control design. By using the recently developed receptance method, it is shown that active control for poles and zeros assignment of the viscoelastic systems can be achieved. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of RTF and solution of the set of linear system of equations.

Author(s):  
Kumar V. Singh ◽  
Xiaoxuan Ling

Viscoelastic materials both stores and dissipate energies and have frequency and temperature dependent properties and hence by tuning and optimizing their damping (viscous) and stiffness (elastic) properties they can be used as passive controlling devices in wide range of vibration applications. If the control of viscoelastic systems (viscoelastic structures or structures composed of viscoelastic elements) to be realized by active means, then an accurate mathematical modeling of the viscoelastic system is needed. In practice, various material models and approximation techniques such as Biot model, Golla-Hughes-McTavish (GHM) model and Anelastic Displacement Field (ADF) methods are used to model the dynamic behavior of viscoelastic systems. These models are then transformed into approximating state space models which introduces several challenges: (i) they increase the size of the related eigenvalue problems, (ii) state space realization introduces non-physical internal state variables, and, (iii) the feedback control implementation poses practical challenges such as observer and state estimator design. In this research it is shown that the active control for viscoelastic structures can be designed accurately by only utilizing the available transfer functions. These transfer functions can be obtained from dynamic experiments and the active feedback control is designed without having the knowledge of approximated state-space system matrices. The problem associated with the active control for viscoelastic system is formulated as feedback control problems in frequency domain by using the receptance method. Active control for poles and zeros assignment of the viscoelastic systems is demonstrated using numerical examples associated with the multi-degree-degree of freedom systems. It is also shown that a nested active controller can also be designed for continuous structures (beams/rods) supported by viscoelastic elements. It is highlighted that such a controller design requires modest size of transfer functions and solution of the set of linear system of equations.


2006 ◽  
Vol 3 (1) ◽  
pp. 37
Author(s):  
Razidah Ismail

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.


2006 ◽  
Vol 3 (1) ◽  
pp. 37 ◽  
Author(s):  
Razidah Ismail

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.


2022 ◽  
Author(s):  
Nirag Kadakia

Functional forms of biophysically-realistic neuron models are constrained by neurobiological and anatomical considerations, such as cell morphologies and the presence of known ion channels. Despite these constraints, neurons models still contain unknown static parameters which must be inferred from experiment. This inference task is most readily cast into the framework of state-space models, which systematically takes into account partial observability and measurement noise. Inferring only dynamical state variables such as membrane voltages is a well-studied problem, and has been approached with a wide range of techniques beginning with the well-known Kalman filter. Inferring both states and fixed parameters, on the other hand, is less straightforward. Here, we develop a method for joint parameter and state inference that combines traditional state space modeling with chaotic synchronization and optimal control. Our methods are tailored particularly to situations with considerable measurement noise, sparse observability, very nonlinear or chaotic dynamics, and highly uninformed priors. We illustrate our approach both in a canonical chaotic model and in a phenomenological neuron model, showing that many unknown parameters can be uncovered reliably and accurately from short and noisy observed time traces. Our method holds promise for estimation in larger-scale systems, given ongoing improvements in calcium reporters and genetically-encoded voltage indicators.


2006 ◽  
Vol 10 (5) ◽  
pp. 609-618 ◽  
Author(s):  
K. Beven

Abstract. Representative Elementary Watershed concepts provide a useful scale-independent framework for the representation of hydrological processes. The balance equations that underlie the concepts, however, require the definition of boundary flux closures that should be expected to be scale dependent. The relationship between internal state variables of an REW element and the boundary fluxes will be nonlinear, hysteretic and scale-dependent and may depend on the extremes of the heterogeneities within the REW. Because of the nonlinearities involved, simple averaging of local scale flux relationships are unlikely to produce an adequate decription of the closure problem at the REW scale. Hysteresis in the dynamic response is demonstrated for some small experimental catchments and it is suggested that at least some of this hysteresis can be represented by the use of simple transfer functions. The search for appropriate closure schemes is the second most important problem in hydrology of the 21st Century (the most important is providing the techniques to measure integrated fluxes and storages at useful scales). The closure problem is a scientific Holy Grail: worth searching for even if a general solution might ultimate prove impossible to find.


Author(s):  
Bernardo Restrepo ◽  
Larry E. Banta ◽  
Alex J. Tsai ◽  
David Tucker

A nonlinear steady-state thermodynamic model was coupled with linearized dynamic transfer functions to achieve a dynamic description of the NETL HyPer Fuel Cell Gas Turbine (FC/GT) power plant. Nonlinear dynamic models insure accuracy in modeling steady-state behavior over a wide range of operation, but such models are often complex and difficult to implement in real-time using conventional control systems equipment. Conversely, the linearized models provide the ability to predict transient behavior upon which dynamic control systems can be constructed, but are valid only about a narrow operating point. In systems with one or two state variables, it is relatively straightforward to construct controllers that use gain scheduling schemes. But the HyPer system contains many coupled state variables and high degrees of nonlinearity. A method called Real-Time Piecewise Linear Dynamic Modeling (RPLDM) has been implemented to provide both modeling accuracy and real-time performance for the HyPer system over a multi-dimensional hypersurface. Both the nonlinear and the linear constituent models were constructed based on experimental data collected in tests performed on the HyPer system. The models presently consider only the cathode circuit of the fuel cell and contain a recuperated gas turbine system equipped with an electric generator, a simulated fuel cell cathode and various bypass valves for thermal management and system control. The key variables of air temperature, air pressure and mass flow to the cathode of the fuel cell and the turbomachinery have been predicted to within 2% of measured values. This paper presents the modeling technique and comparisons of the model output with experimental data.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Eduard Bertran ◽  
Paula Tercero ◽  
Alex Sànchez-Cerdà

Purpose This paper aims to overcome the main obstacle to compare the merits of the different control strategies for fixed-wing unmanned aerial vehicles (UAVs) to assess autopilot performances. Up to now, the published studies of control strategies have been carried out over disperse models, thus being complicated, if not impossible, to compare the merits of each proposal. The authors present a worked benchmark for autopilots studies, consisting of generalized models obtained by merging UAVs’ parameters gathered from selected literature (journals) with other parameters directly obtained by the authors to include some relevant UAVs whose models are not provided in the literature. To obtain them it has been used a dedicated software (from U.S. Air Force). Design/methodology/approach The proposed models have been constructed by averaging both the main aircraft defining parameters (model derivatives) and pole-zero locations of longitudinal transfer functions. The suitability of the used methodologies has been checked from their capability to fit the short period and the phugoid modes. Previous analytical model arrangement has been required to match a uniform set of parameters, as the inner state variables are neither the same along the different published models nor between the additional models the authors have here contributed. Besides, moving models between the space state representation and transfer function is not just a simple averaging process, as neither the parameters nor the model orders are the same in the different published works. So, the junction of the models to a common set of parameters requires some residual’s computation and transient responses assessment (even Fourier analysis has been included to preserve the dominance of the phugoid) to keep the main properties of the models. The least mean squares technique has been used to have better fittings between SISO model parameters with state–space ones. Findings Both the SISO (Laplace) and state-space models for the longitudinal transfer function of an “averaged” fixed-wing UAV are proposed. Research limitations/implications More complicated situations, such as strong wind conditions, need another kind of models, usually based on finite element method simulation. These particular models apply fluid dynamics to study aerostructural aircraft aspects, such as flutter and other aerolastic aspects, the behavior under icing conditions or other distributed parameter problems. Even some models aim to control other aspects than the autopilot, such as the trajectory prediction. However, these models are not the most suitable for the basic UAV autopilot design (early design), so they are outside the objective of this paper. Obviously, the here-considered UAVs are not all the existing ones, but the number is large enough to consider the result as a reliable and realistic representation. The presented study may be seen as a stepping stone, allowing to include other UAVs in future works. Practical implications The proposed models can be used as benchmarks, or as a previous step to produce improved benchmarks, in order to have a common and realistic scenario the compare the benefits of the different control actions in UAV autopilots continuously presented in the published research. Originality/value A work with the scope of the presented one, merging model parameters from literature with other (often referred in papers and websites) whose parameters have been obtained by the authors has been never published.


Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1584
Author(s):  
Purushottam D. Gujrati

The review deals with a novel approach (MNEQT) to nonequilibrium thermodynamics (NEQT) that is based on the concept of internal equilibrium (IEQ) in an enlarged state space SZ involving internal variables as additional state variables. The IEQ macrostates are unique in SZ and have no memory just as EQ macrostates are in the EQ state space SX⊂SZ. The approach provides a clear strategy to identify the internal variables for any model through several examples. The MNEQT deals directly with system-intrinsic quantities, which are very useful as they fully describe irreversibility. Because of this, MNEQT solves a long-standing problem in NEQT of identifying a unique global temperature T of a system, thus fulfilling Planck’s dream of a global temperature for any system, even if it is not uniform such as when it is driven between two heat baths; T has the conventional interpretation of satisfying the Clausius statement that the exchange macroheatdeQflows from hot to cold, and other sensible criteria expected of a temperature. The concept of the generalized macroheat dQ=deQ+diQ converts the Clausius inequality dS≥deQ/T0 for a system in a medium at temperature T0 into the Clausius equalitydS≡dQ/T, which also covers macrostates with memory, and follows from the extensivity property. The equality also holds for a NEQ isolated system. The novel approach is extremely useful as it also works when no internal state variables are used to study nonunique macrostates in the EQ state space SX at the expense of explicit time dependence in the entropy that gives rise to memory effects. To show the usefulness of the novel approach, we give several examples such as irreversible Carnot cycle, friction and Brownian motion, the free expansion, etc.


2006 ◽  
Vol 3 (3) ◽  
pp. 769-792 ◽  
Author(s):  
K. Beven

Abstract. Representative Elementary Watershed concepts provide a useful scale-independent framework for the representation of hydrological processes. The balance equations that underlie the concepts, however, require the definition of boundary flux closures. The relationship between internal state variables of an REW element and the boundary fluxes will be nonlinear, hysteretic and scale-dependent. This is demonstrated for some small experimental catchments and it is shown that at least some of this hysteresis can be represented by the use of simple transfer functions. The search for appropriate closure schemes is the second most important problem in hydrology of the 21st Century (the most important is providing the techniques to measure integrated fluxes and storages at useful scales). It is a scientific Holy Grail: worth searching for even if a general solution might ultimate prove impossible to find.


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