scholarly journals Hamilton’s rule, gradual evolution, and the optimal (feedback) control of phenotypically plastic traits

2020 ◽  
Author(s):  
Piret Avila ◽  
Tadeas Priklopil ◽  
Laurent Lehmann
Keyword(s):  
Closed Loop ◽  
Expression Profiles ◽  
Open Loop ◽  
Order Conditions ◽  
Optimal Feedback Control ◽  
State Variables ◽  
First Order ◽  
Hamilton’S Rule ◽  
Gradual Evolution ◽  
Hamilton's Rule

AbstractMost traits expressed by organisms, such as gene expression profiles, developmental trajectories, behavioural sequences and reaction norms are function-valued traits (colloquially “phenotypically plastic traits”), since they vary across an individual’s age and in response to various internal and/or external factors (state variables). Furthermore, most organisms live in populations subject to limited genetic mixing and are thus likely to interact with their relatives. We here formalise selection on genetically determined function-valued traits of individuals interacting in a group-structured population, by deriving the marginal version of Hamilton’s rule for function-valued traits. This rule simultaneously gives a condition for the invasion of an initially rare mutant function-valued trait and its ultimate fixation in the population (invasion thus implies substitution). Hamilton’s rule thus underlies the gradual evolution of function-valued traits and gives rise to necessary first-order conditions for their uninvadability (evolutionary stability). We develop a novel analysis using optimal control theory and differential game theory, to simultaneously characterise and compare the first-order conditions of (i) open-loop traits - functions of time (or age) only, and (ii) closed-loop (state-feedback) traits - functions of both time and state variables. We show that closed-loop traits can be represented as the simpler open-loop traits when individuals do no interact or when they interact with clonal relatives. Our analysis delineates the role of state-dependence and interdependence between individuals for trait evolution, which has implications to both life-history theory and social evolution.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

Plans and The Structure of Target Acquisition Behavior

1981 ◽  
Vol 25 (1) ◽  
pp. 571-575
Author(s):  
R. A. Miller ◽  
R. J. Jagacinski ◽  
R. B. Nalavade ◽  
W. W. Johnson
Keyword(s):  
Closed Loop ◽  
Position Control ◽  
Open Loop ◽  
General Strategy ◽  
Velocity Control ◽  
Additional Time ◽  
First Order ◽  
Oscilloscope Screen ◽  
Activity Sequence ◽  
Event Based

Subjects manipulated a position control stick with one hand and a velocity control stick with the other hand in order to capture a moving target displayed on an oscilloscope screen. The two control sticks were additively coupled. In order to understand the coordination of the two control sticks, event-based first-order markov “activity sequence generators” were constructed for individual subjects. These discrete probabilistic structures are closely related to each subject's overall plan or general strategy for the capture task. Striking individual differences and strategic errors in performance were revealed. When combined with additional time-conditioned (open-loop) and error-conditioned (closed-loop) details, the activity sequence generators provide a basis for a hierarchic description of this perceptual-motor skill.

scholarly journals Simulation of Performance Response of State Variables of a Chemical Boiler Process

2018 ◽  
pp. 1-5
Author(s):  
Donatus O. Njoku ◽  
Asagba P. O ◽  
Chilaka U. Longinus ◽  
Amaefule I. A. ◽  
Igwe S. Onyema
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Control Process ◽  
Open Loop ◽  
The State ◽  
Feedback Gain ◽  
State Variables ◽  
Simulink Model ◽  
Performance Response ◽  
Optimal Regulator

This paper has presented simulation of performance response of state variables of a chemical boiler process. The transfer function of a boiler flow control process of a chemical plant was obtained. The transfer function was transformed into state space form to study the state variables of the system. An optimal regulator was designed using MATLAB programme. The developed optimal regulator was added to the loop of the system to form a closed loop system. A Simulink model was developed and used to study performance response of the system. Simulation was carried out for two conditions, open loop and closed loop. The simulation results indicated that the performance responses of the state variables were improved and better stability achieved with the inclusion of the designed feedback gain matrix of the optimal regulator.

scholarly journals Control-Oriented High-Frequency Turbomachinery Modeling: Single-Stage Compression System 1D Model

1993 ◽  
Author(s):  
O. O. Badmus ◽  
S. Chowdhury ◽  
K. M. Eveker ◽  
C. N. Nett
Keyword(s):  
Experimental Data ◽  
High Frequency ◽  
Closed Loop ◽  
Open Loop ◽  
Rotating Stall ◽  
Single Stage ◽  
Model Parameters ◽  
Compression System ◽  
First Order ◽  
Direct Model

In this paper, a 1D unsteady compressible viscous flow model of a generic compression system previously developed by the authors is applied to a multi-stage axial compressor experimental rig configured for single–stage operation. The required model parameters and maps are identified from experimental data. The resulting model is an explicit system of 9 first order ODE’s. The model inputs are compressor speed, nozzle area, compressor discharge bleed area, plenum bleed area, inlet total pressure and entropy, and nozzle and bleed exit static pressures. The model and experimental data are compared with respect to both open–loop uncontrolled and closed–loop controlled behaviors. These comparisons focus on i) forced transients and ii) global nonlinear dynamics and bifurcations. In all cases the comparison between the model and experimental data is excellent. Of particular interest is the ability of the model, which does not include any hysteretic maps, to predict experimentally observed hysteresis with respect to the onset and cessation of surge. This predictive capability of the model manifests itself as the coexistence of a stable equilibrium (rotating stall) and a stable periodic solution (surge) in the model at a single fixed set of system input values. Also of interest is the fact that the controllers used for closed–loop comparisons were designed directly from the model with no a posteriori tuning of controller parameters. Thus, the excellent closed–loop comparisons between the model and experimental data provide strong evidence in support of the validity of the model for use in direct model based controller design. The excellent agreement between the model and experimental data summarized above is attributed in large part to the use of effective lengths within the model, as functions of axial Mach number and nondimensional compressor rotational speed, as prescribed by the modeling technique. The use of these effective lengths proved to be far superior to the use of physical lengths. The use of these effective lengths also provided substantial improvement over the use of physical lengths coupled with fixed first order empirical lags, as proposed by other authors for the modeling of observed compressor dynamic lag. The overall success of this model is believed to represent a positive first step toward a complete experimental validation of the approach to control–oriented high–frequency turbomachinery modeling being developed by the authors.

scholarly journals A dual-loop tracking control approach to precise nanopositioning

2018 ◽  
Vol 25 (3) ◽  
pp. 666-674 ◽  
Author(s):  
Mohammed Altaher ◽  
Douglas Russell ◽  
Sumeet S. Aphale
Keyword(s):  
Closed Loop ◽  
Reference Signal ◽  
Open Loop ◽  
Performance Criteria ◽  
Control Technique ◽  
Loop Control ◽  
Control Approach ◽  
First Order ◽  
Integral Controller ◽  
Double Integrator

Nanopositioners are mechanical devices that can accurately move with a resolution in the nanometer scale. Due to their mechanical construction and the piezoelectric actuators popularly employed in nanopositioners, these devices have severe performance limitations due to resonance, hysteresis and creep. A number of techniques to control nanopositioners, both in open-loop and closed-loop, have been reported in the literature. Closed-loop techniques clearly outperform open-loop techniques due to several desirable characteristics, such as robustness, high-bandwidth, absence of the need for tuning and high stability, along with others. The most popular closed-loop control technique reported is one where a damping controller is first employed in an inner loop to damp the mechanical resonance of the nanopositioner, thereby increasing achievable bandwidth. Consequently, a tracking controller, typically an Integral controller or a proportional–integral controller, is implemented in the outer loop to enforce tracking of the reference signal, thereby reducing the positioning errors due to hysteresis and creep dynamics of the employed actuator. The most popular trajectory a nanopositioner is forced to track is a raster scan, which is generated by making one axis of the nanopositioner follow a triangular trajectory and the other follow a slow ramp or staircase. It is quite clear that a triangle wave (a finite velocity, zero acceleration signal) cannot be perfectly tracked by a first-order integrator and a double integrator is necessary to deliver error-free tracking. However, due to the phase profile of the damped closed-loop system, implementing a double integrator is difficult. This paper proposes a method by which to implement two integrators focused on the tracking performance. Criteria for gain selection, stability analysis, error analysis, simulations, and experimental results are provided. These demonstrate a reduction in positioning error by 50%, when compared to the traditional damping plus first-order integral tracking approach.

Computer Simulation of a Variable Fill Hydraulic Dynamometer Part 3: Closed-Loop Performance

1992 ◽  
Vol 206 (5) ◽  
pp. 327-336 ◽  
Author(s):  
P G Hodgson ◽  
J K Raine
Keyword(s):  
Closed Loop ◽  
Open Loop ◽  
Digital Control System ◽  
Closed Loop System ◽  
First Order ◽  
Outlet Valve ◽  
Pressure Water ◽  
Apparent Variation ◽  
Predictor Corrector ◽  
The Mathematical Model

An engine and hydraulic dynamometer system is dynamically modelled with two different control systems. The closed-loop system behaviour is studied for a hydromechanical back-pressure water outlet valve and for an electrohydraulic servo-controlled water outlet valve. This is an extension of the open-loop dynamic model of Part 2, which incorporates the mathematical model of the torque absorption processes in a variable fill Froude-type hydraulic dynamometer presented in Part 1. The models are based on a system of first-order differential equations which are solved numerically using an Adams predictor corrector method. Both the analogue hack-pressure valve and digital servo-controlled valve are accurately simulated. In both cases the influence of the dynamic dynamometer model on the transient response is apparent. Variation in digital control system parameters across the operating envelope illustrates the non-linearity of dynamometer response. The computer model and experimental results are compared and implications of the closed-loop behaviour discussed.

Closed Loop Transient Response from the Open Loop Frequency Response

1978 ◽  
Vol 11 (8) ◽  
pp. 302-308 ◽  
Author(s):  
E.C. Hind
Keyword(s):  
Frequency Response ◽  
Transient Response ◽  
Feedback Loop ◽  
Closed Loop ◽  
Full Range ◽  
Open Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Order Model ◽  
First Order

A method is shown for relating the closed loop transient response to the open loop frequency response, which is based on the use of the contour of constant closed loop phase angle, α = −90°. The method primarily yields a second order model of the closed loop system which covers the full range of relative damping (0 < ζ < +∞). A first order model is recommended when prescribed conditions apply. The method is simpler and yields better results than currently used methods. In all cases it is assumed that the negative feedback loop has a transfer function of unity and that the closed loop system is stable.

General Formulation of an Efficient Recursive Algorithm Based on Canonical Momenta for Forward Dynamics of Closed-Loop Multibody Systems

2005 ◽  
Author(s):  
Joris Naudet ◽  
Dirk Lefeber
Keyword(s):  
Multibody Systems ◽  
Closed Loop ◽  
Recursive Algorithm ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Open Loop ◽  
Forward Dynamics ◽  
Virtual Power ◽  
Generalized Coordinates ◽  
First Order

In previous work, a method for establishing the equations of motion of open-loop multibody mechanisms was introduced. The proposed forward dynamics formulation resulted in a Hamiltonian set of 2n first order ODE’s in the generalized coordinates q and the canonical momenta p. These Hamiltonian equations were derived from a recursive Newton-Euler formulation. It was shown how an O(n) formulation could be obtained in the case of a serial structure with general joints. The amount of required arithmetical operations was considerably less than comparable acceleration based formulations. In this paper, a further step is taken: the method is extended to constrained multibody systems. Using the principle of virtual power, it is possible to obtain a recursive Hamiltonian formulation for closed-loop mechanisms as well, enabling the combination of the low amount of arithmetical operations and a better evolution of the constraints violation errors, when compared with acceleration based methods.

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