Robust pole assignment in linear state feedback

Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

Eigenstructure assignment in descriptor systems

Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

Mechanism for synchronized motion between two humans in mutual tapping experiments: Transition from alternative mode to synchronization mode

We performed mutual tapping experiments between two humans to investigate the conditions required for synchronized motion. A transition from an alternative mode to a synchronization mode was discovered under the same conditions when a subject changed from a reactive mode to an anticipation mode in single tapping experiments. Experimental results suggest that the cycle time for each tapping motion is tuned by a proportional control that is based on synchronization errors and cycle time errors. As the tapping frequency increases, the mathematical model based on the feedback control in the sensory-motor closed loop predicts a discrete mode transition as the gain factors of the proportional control decease. The conditions of the synchronization were shown as a consequence of the coupled dynamics based on the subsequent feedback loop in the sensory-motor system.

A microchannel neuroprosthesis for bladder control after spinal cord injury in rat

A severe complication of spinal cord injury is loss of bladder function (neurogenic bladder), which is characterized by loss of bladder sensation and voluntary control of micturition (urination), and spontaneous hyperreflexive voiding against a closed sphincter (detrusor-sphincter dyssynergia). A sacral anterior root stimulator at low frequency can drive volitional bladder voiding, but surgical rhizotomy of the lumbosacral dorsal roots is needed to prevent spontaneous voiding and dyssynergia. However, rhizotomy is irreversible and eliminates sexual function, and the stimulator gives no information on bladder fullness. We designed a closed-loop neuroprosthetic interface that measures bladder fullness and prevents spontaneous voiding episodes without the need for dorsal rhizotomy in a rat model. To obtain bladder sensory information, we implanted teased dorsal roots (rootlets) within the rat vertebral column into microchannel electrodes, which provided signal amplification and noise suppression. As long as they were attached to the spinal cord, these rootlets survived for up to 3 months and contained axons and blood vessels. Electrophysiological recordings showed that half of the rootlets propagated action potentials, with firing frequency correlated to bladder fullness. When the bladder became full enough to initiate spontaneous voiding, high-frequency/amplitude sensory activity was detected. Voiding was abolished using a high-frequency depolarizing block to the ventral roots. A ventral root stimulator initiated bladder emptying at low frequency and prevented unwanted contraction at high frequency. These data suggest that sensory information from the dorsal root together with a ventral root stimulator could form the basis for a closed-loop bladder neuroprosthetic. Copyright © 2013, American Association for the Advancement of Science

Control of final moisture content of food products baked in continuous tunnel ovens

There are well-known difficulties in making measurements of the moisture content of baked goods (such as bread, buns, biscuits, crackers and cake) during baking or at the oven exit; in this paper several sensing methods are discussed, but none of them are able to provide direct measurement with sufficient precision. An alternative is to use indirect inferential methods. Some of these methods involve dynamic modelling, with incorporation of thermal properties and using techniques familiar in computational fluid dynamics (CFD); a method of this class that has been used for the modelling of heat and mass transfer in one direction during baking is summarized, which may be extended to model transport of moisture within the product and also within the surrounding atmosphere. The concept of injecting heat during the baking process proportional to the calculated heat load on the oven has been implemented in a control scheme based on heat balance zone by zone through a continuous baking oven, taking advantage of the high latent heat of evaporation of water. Tests on biscuit production ovens are reported, with results that support a claim that the scheme gives more reproducible water distribution in the final product than conventional closed loop control of zone ambient temperatures, thus enabling water content to be held more closely within tolerance.

Architecture for Living Neuronal Network Control of a mobile robot

The intelligent controlling mechanism of a typical mobile robot is usually a computer system. Research is however now ongoing in which biological neural networks are being cultured and trained to act as the brain of an interactive real world robot – thereby either completely replacing or operating in a cooperative fashion with a computer system. Studying such neural systems can give a distinct insight into biological neural structures and therefore such research has immediate medical implications. The principal aims of the present research are to assess the computational and learning capacity of dissociated cultured neuronal networks with a view to advancing network level processing of artificial neural networks. This will be approached by the creation of an artificial hybrid system (animat) involving closed loop control of a mobile robot by a dissociated culture of rat neurons. This paper details the components of the overall animat closed loop system architecture and reports on the evaluation of the results from preliminary real-life and simulated robot experiments.

The solubility of gypsum in calcareous soils

Three gypsiferous-calcareous soils from the Al-Hassa Oasis in Saudi Arabia were examined to determine the conditions under which dissolution of gypsum could be hindered by the formation of coatings of calcite during leaching. Batch extraction with water of a sandy clay loam, a sandy clay and a sandy loam containing 40, 26 and 5% gypsum and 14, 12 and 13% calcite respectively was followed by chemical analysis of the extracts, SEM examination and XRD and EDX microprobe analysis. Extraction in closed centrifuge tubes for I h or 5 h showed that initially gypsum dissolved to give solutions near to equilibrium but then in the sandy clay loam, between one quarter and one third of the gypsum could not dissolve. In the sandy clay about one fifth of the gypsum could not dissolve with none remaining in the sandy loam. All the extracts were close to equilibrium with calcite. SEM and EDX examination showed that coatings of calcite had formed on the gypsum particles. The sandy clay loam was also extracted using an open system in which either air or air +1% CO2 was bubbled through the suspensions for 1 h with stirring. The gypsum dissolved more rapidly and all of the gypsum dissolved. Thus, where the rate of dissolution of gypsum was rapid, calcite did not manage to cover the gypsum surfaces probably because the surface was being continuously removed. Slower leaching conditions in the field are likely to be conducive to the formation of coatings and less dissolution of gypsum. (c) 2006 Elsevier B.V. All rights reserved.

Reconciling the electron counterstreaming and dropout occurrence rates with the heliospheric flux budget

Counterstreaming electrons (CSEs) are treated as signatures of closed magnetic flux, i.e., loops connected to the Sun at both ends. However, CSEs at 1 AU likely fade as the apex of a closed loop passes beyond some distance R, owing to scattering of the sunward beam along its continually increasing path length. The remaining antisunward beam at 1 AU would then give a false signature of open flux. Subsequent opening of a loop at the Sun by interchange reconnection with an open field line would produce an electron dropout (ED) at 1 AU, as if two open field lines were reconnecting to completely disconnect from the Sun. Thus EDs can be signatures of interchange reconnection as well as the commonly attributed disconnection. We incorporate CSE fadeout into a model that matches time-varying closed flux from interplanetary coronal mass ejections (ICMEs) to the solar cycle variation in heliospheric flux. Using the observed occurrence rate of CSEs at solar maximum, the model estimates R ∼ 8–10 AU. Hence we demonstrate that EDs should be much rarer than CSEs at 1 AU, as EDs can only be detected when the juncture points of reconnected field lines lie sunward of the detector, whereas CSEs continue to be detected in the legs of all loops that have expanded beyond the detector, out to R. We also demonstrate that if closed flux added to the heliosphere by ICMEs is instead balanced by disconnection elsewhere, then ED occurrence at 1 AU would still be rare, contrary to earlier expectations.

Controlling a mobile robot with a biological brain

The intelligent controlling mechanism of a typical mobile robot is usually a computer system. Some recent research is ongoing in which biological neurons are being cultured and trained to act as the brain of an interactive real world robot�thereby either completely replacing, or operating in a cooperative fashion with, a computer system. Studying such hybrid systems can provide distinct insights into the operation of biological neural structures, and therefore, such research has immediate medical implications as well as enormous potential in robotics. The main aim of the research is to assess the computational and learning capacity of dissociated cultured neuronal networks. A hybrid system incorporating closed-loop control of a mobile robot by a dissociated culture of neurons has been created. The system is flexible and allows for closed-loop operation, either with hardware robot or its software simulation. The paper provides an overview of the problem area, gives an idea of the breadth of present ongoing research, establises a new system architecture and, as an example, reports on the results of conducted experiments with real-life robots.

High bandwidth, large workspace haptic interaction: flying phantoms

It is well understood that for haptic interaction: free motion performance and closed-loop constrained motion performance have conflicting requirements. The difficulties for both conditions are compounded when increased workspace is required as most solutions result in a reduction of achievable impedance and bandwidth. A method of chaining devices together to increase workspace without adverse effect on performance is described and analysed. The method is then applied to a prototype, colloquially known as 'The Flying Phantom', and shown to provide high-bandwidth, low impedance interaction over the full range of horizontal movement across the front of a human user.

Architecture for neuronal cell control of a mobile robot

It is usually expected that the intelligent controlling mechanism of a robot is a computer system. Research is however now ongoing in which biological neural networks are being cultured and trained to act as the brain of an interactive real world robot - thereby either completely replacing or operating in a cooperative fashion with a computer system. Studying such neural systems can give a distinct insight into biological neural structures and therefore such research has immediate medical implications. In particular, the use of rodent primary dissociated cultured neuronal networks for the control of mobile `animals' (artificial animals, a contraction of animal and materials) is a novel approach to discovering the computational capabilities of networks of biological neurones. A dissociated culture of this nature requires appropriate embodiment in some form, to enable appropriate development in a controlled environment within which appropriate stimuli may be received via sensory data but ultimate influence over motor actions retained. The principal aims of the present research are to assess the computational and learning capacity of dissociated cultured neuronal networks with a view to advancing network level processing of artificial neural networks. This will be approached by the creation of an artificial hybrid system (animal) involving closed loop control of a mobile robot by a dissociated culture of rat neurons. This 'closed loop' interaction with the environment through both sensing and effecting will enable investigation of its learning capacity This paper details the components of the overall animat closed loop system and reports on the evaluation of the results from the experiments being carried out with regard to robot behaviour.