Optimal sampling-rates of digital LQ and LQG tracking controllers with costs associated to sampling

Control Systems;Sampling;Costs;operations research

LQ-control of sampled continuous-time systems

Control Systems;controle-systemen

Emergence of the second law out of reversible dynamics

Abstract If one demystifies entropy the second law of thermodynamics comes out as an emergent property entirely based on the simple dynamic mechanical laws that govern the motion and energies of system parts on a micro-scale. The emergence of the second law is illustrated in this paper through the development of a new, very simple and highly efficient technique to compare time-averaged energies in isolated conservative linear large scale dynamical systems. Entropy is replaced by a notion that is much more transparent and more or less dual called ectropy. Ectropy has been introduced before but we further modify the notion of ectropy such that the unit in which it is expressed becomes the unit of energy. The second law of thermodynamics in terms of ectropy states that ectropy decreases with time on a large enough time-scale and has an absolute minimum equal to zero. Zero ectropy corresponds to energy equipartition. Basically we show that by enlarging the dimension of an isolated conservative linear dynamical system and the dimension of the system parts over which we consider time-averaged energy partition, the tendency towards equipartition increases while equipartition is achieved in the limit. This illustrates that the second law is an emergent property of these systems. Finally from our large scale linear dynamic model we clarify Loschmidt’s paradox concerning the irreversible behavior of ectropy obtained from the reversible dynamic laws that govern motion and energy at the micro-scal

Collision-free inverse kinematics of a 7 link cucumber picking robot

The paper presents results of research on inverse kinematics algorithms to be used in a functional model of a cucumber harvesting robot consisting of a redundant manipulator with one prismatic and six rotational joints (P6R). Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming problem and solved with a generic algorithm. Solutions were easily obtained, but the considerable calculation time needed to solve the problem prevented on line implementation. To circumvent this problem, a second, less generic approach was developed consisting of a mixed numerical-analytic solution of the inverse kinematics problem exploiting the particular structure of the P6R manipulator. This approach facilitated rapid and robust calculation of the inverse kinematics of the cucumber harvester. During the early stages of the cucumber harvesting project, this inverse kinematics algorithm was used to off-line evaluate the ability of the robot to harvest cucumbers using 3D-information of a cucumber crop obtained in a real greenhouse. Thereafter, the algorithm was employed successfully in a functional model of the cucumber harvester to determine if cucumbers were hanging within the reachable workspace of the robot and to determine a collision-free harvest posture to be used for motion control of the manipulator during harvesting

Collision-free inverse kinematics of the redundant seven-link manipulator used in a cucumber picking robot

The paper presents results of research on an inverse kinematics algorithm that has been used in a functional model of a cucumber-harvesting robot consisting of a redundant P6R manipulator. Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming problem and solved with a Genetic Algorithm (GA). Although solutions were easily obtained, the considerable calculation time needed to solve the problem prevented on-line implementation. To circumvent this problem, a second, less generic, approach was developed which consisted of a mixed numerical-analytic solution of the inverse kinematics problem exploiting the particular structure of the P6R manipulator. Using the latter approach, calculation time was considerably reduced. During the early stages of the cucumber-harvesting project, this inverse kinematics algorithm was used off-line to evaluate the ability of the robot to harvest cucumbers using 3D-information obtained from a cucumber crop in a real greenhouse. Thereafter, the algorithm was employed successfully in a functional model of the cucumber harvester to determine if cucumbers were hanging within the reachable workspace of the robot and to determine a collision-free harvest posture to be used for motion control of the manipulator during harvesting. The inverse kinematics algorithm is presented and demonstrated with some illustrative examples of cucumber harvesting, both off-line during the design phase as well as on-line during a field test

Toward optimal control of flat plate photobioreactors: the greenhouse analogy?

Abstract: The cultivation of algae in photo-bioreactors shows similarities to crop cultivation in greenhouses, especially when the reactors are driven by sun light. Advanced methodologies for dynamic optimization and optimal control for greenhouses are known from earlier research. The aim here is to extend these methodologies to microalgae cultivated in a flat plate photo-bioreactor. A one-state space model for the algal biomass in the reactor is presented. The growth rate vs. light curve is parameterized on the basis of experimental evidence. Spatial distribution of light and growth rate between the plates is also considered. The control variable is the dilution rate. Dynamic optimal control trajectories are presented for various choices of goal function and external solar irradiation trajectories over a horizon of 3 days. It was found that the algae present in the reactor at final time represent a value for the future. Numerical and theoretical results suggest that the control is bang-(singular-)bang, with a strong dependence on the weather. The optimal biomass also depends on the available light, and achieving it to reach a new optimal steady cycle after a prolonged change in weather may take several days. A preliminary theoretical analysis suggests a control law that maximizes the effective growth rate. The analysis shows that like in the greenhouse case, the co-state of the algal biomass plays a pivot role in developing on-line controllers

Modelling of spatial variation of floor eggs in an aviary house for laying hens

A problem in loose housing systems for layers is laying eggs on the floor, which need manual collection. To automate this, it is desired to know the location of floor eggs for planning a collection path. as this information is not available, we constructed a spatial model to indicate the probability on floor eggs, based on housing properties. This model is mainly determined by parameters relating probability to position in the house. Validation against floor egg locations from poultry practice indicated that underlying model assumptions match with practice, making the model a suitable start for further work in this field

Temporal and One-Step Stabilizability and Detectability of Time-Varying Discrete-Time Linear Systems

Time-varying discrete-time linear systems may be temporarily uncontrollable and unreconstructable. This is vital knowledge to both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability requires considering discrete-time systems with variable dimensions and the j-step, k-step Kalman decomposition. In this note for linear discrete-time systems with variable dimensions measures of temporal and one-step stabilizability and detectability are developed. These measures indicate to what extent the temporal loss of controllability and reconstructability may lead to temporal instability of the closed loop system when designing a static state or dynamic output feedback controller. The measures are calculated by solving specific linear quadratic cheap control problems