Mathematical models are a necessary tool to quantify physiological processes the direct measure of which is not possible. Pancreatic beta-cell and liver are respectively the secreting and the major degrading site of i...
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Mathematical models are a necessary tool to quantify physiological processes the direct measure of which is not possible. Pancreatic beta-cell and liver are respectively the secreting and the major degrading site of insulin. To quantify these processes, we have conceived a mathematical model representing secretion and kinetics of C-peptide, which is equimolarly released with insulin, but which is not extracted by the liver. C-peptide flux into plasma is thus representative of that of pre-hepatic insulin. Model parameters are estimated in a single subject from data available after an intravenous glucose injection, and a quantitative description of both beta-cell secretion and liver degradation can be obtained. The model has been applied in subjects with cirrhosis and diabetes to understand the mechanisms responsible of the altered metabolic states characteristic of such diseases. Because of its non-invasiveness, this model-based method should prove useful in several clinical investigations.
Measurements of glycated haemoglobin A (HbA1c) has within the last 10 years found widespread use for assessment of long term blood glucose control in diabetes. HbA1c is formed in the red cells, where haemoglobin A rea...
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Measurements of glycated haemoglobin A (HbA1c) has within the last 10 years found widespread use for assessment of long term blood glucose control in diabetes. HbA1c is formed in the red cells, where haemoglobin A reacts with glucose to form a labile aldimine adduct (HbA1d) which subsequently rearranges to the more stable ketoamine HbA1c. The erythrocytes are continuously formed and broken down after a lifespan of about 120 days. Based on the well known chemical kinetics and the constant in vivo replacement of haemoglobin a mathematical model for prediction of HbA1c from a given preceding blood glucose profile has been developed. From the structure of the mathematical relation between HbA1c and the blood glucose it could be shown that HbA1c closely resembles an exponentially weighted average of preceding 24 hour mean blood glucose values.
Non-steady state plasma glucose dynamics are examined using a non-linear three compartment catenary structure. The glucose model is primarily used to test the hypothesis that insulin reduces endogenous glucose product...
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Non-steady state plasma glucose dynamics are examined using a non-linear three compartment catenary structure. The glucose model is primarily used to test the hypothesis that insulin reduces endogenous glucose production rate and increases the number of glucose transporters. The performance of the model is compared to the one compartment model approximation (Steele equation). The approach adopted here is fundamentally different to that of current approaches in that the tracer dynamic is used not as an integral part of the model but rather to validate the non-linear model and its controllers. The performance of the model is tested in uncontrolled diabetic patients (following 24 hour insulin withdrawal) undergoing low dose (2.6 U/hour) and high dose (10.6 U/hour) insulin infusion. It is shown that following low and high dose insulin infusion the reductions in hepatic glucose production are similar and the increase in number of glucose transporters is higher in high dose than low dose.
Recent work in artificial intelligence has produced a collection of methods for qualitative reasoning that may fill an important gap in the modeling and control toolkit. Qualitative reasoning methods provide greater e...
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Recent work in artificial intelligence has produced a collection of methods for qualitative reasoning that may fill an important gap in the modeling and control toolkit. Qualitative reasoning methods provide greater expressive power for states of incomplete knowledge than differential or difference equations, and thus make it possible to build models without incorporating assumptions of linearity or specific values for incompletely known constants. On the other hand, there is enough information in a qualitative description to support qualitative simulation, predicting the possible behaviors of an incompletely described system. We survey results from several approaches to qualitative reasoning, and provide a detailed example of the application of these methods to a simple problem. The mathematical validity of this approach is also assessed. Results with small examples have been encouraging, and we are now taking the steps toward additional mathematical power, hierarchical decomposition, and incremental quantitative constraints.
A new complete error system where the effects of the modelling error and parametric estimation error are effectively isolated, is derived in this paper. The concepts of model prediction and model prediction error are ...
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A new complete error system where the effects of the modelling error and parametric estimation error are effectively isolated, is derived in this paper. The concepts of model prediction and model prediction error are introduced as well. The new error system is more convenient for analysis of the robustness of adaptive controlsystems than the others. The analysis of a simple adaptive algorithm is given.
This paper addresses the problem of time delay modelling using rational approximations. Two classes of models are discussed based on all-pole and all-pass transfer functions. A detailed analysis is carried out compari...
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This paper addresses the problem of time delay modelling using rational approximations. Two classes of models are discussed based on all-pole and all-pass transfer functions. A detailed analysis is carried out comparing the respective merits of these approximate models. The estimation of the parameters in these models is investigated and the associated control design problem using rational models for the delay is studied. Simulation results are presented which support the theoretical analysis.
The paper reports on the modelling and control of large colour-picture-tube(CPT) glass furnace. It is a complex and highly nonlinear plant with various noises. Based on the normal operating records and some simple exp...
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The paper reports on the modelling and control of large colour-picture-tube(CPT) glass furnace. It is a complex and highly nonlinear plant with various noises. Based on the normal operating records and some simple experiments without interrupting the production, a set of rough models was obtained. Referring the models, a compound adaptive algorithm which consists of modified PID algorithm, feedforward compensation, nonlinearity compensation technique and self-tuning control was proposed to control the five-input and five-output plant. The results of a long-run operation of the on-line computer control indicate that the modelling and control are suitable for the glass furnace and are very effective.
Sensory transduction in the cockroach tactile spine can be represented as a single-input single-output nonlinear dynamic process. The major dynamic features of transduction in this receptor are produced during the enc...
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Sensory transduction in the cockroach tactile spine can be represented as a single-input single-output nonlinear dynamic process. The major dynamic features of transduction in this receptor are produced during the encoding of action potentials from the receptor current. We have used a new functional expansion method to characterize the dynamic behavior of the tactile spine. This method, which yields similar kernels to the Wiener method, is efficient enough to obtain reasonable kernels in about one hour using a personal computer. The input stimulus was band-limited white noise and the output consisted of action potentials, which were unitized to give binary values. The kernels and the system input-output were used to identify a model for transduction comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being band-pass. The static nonlinearity was fitted with a fifth-order polynomial function over the input amplitude range and had the form of a half-wave rectifier. The complete model gave a good approximation to the system output when subjected to the same input signal.
Technological Decision-Support System (TDSS) to aid industrial Production Management (PM) is an important element for the Computer Integrated Manufacturing and Production (CIMP). For control Engineers, this is a probl...
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Technological Decision-Support System (TDSS) to aid industrial Production Management (PM) is an important element for the Computer Integrated Manufacturing and Production (CIMP). For control Engineers, this is a problem of Convivial control (CC). In this paper, we analyse how to implement a Distributed Intelligence Structure in the TDSS to implement the CC. The paper contains four parts: 1: Structuring of the systems to understand the problems. 2: Identification of the problem elements in each specific application. 3: modelling and formalising of the knowledge. 4: Implementation of the knowledge into computers.
The research in robotics requires efficient and flexible software tools, which supports the user in modelling and simulating the robot dynamics. In order to design a decoupled control of any robot, the exact dynamic m...
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The research in robotics requires efficient and flexible software tools, which supports the user in modelling and simulating the robot dynamics. In order to design a decoupled control of any robot, the exact dynamic models of these robots have to be obtained. This paper presents a computer-aided method, to achieve the dynamic model of any robot. The software first evaluates the basic data of the robot kinematics and dynamics, which are fundamental for the equation of motion and for the digital simulation of the robot dynamics. Then the tasks of an industrial controller for any robots are simulated to achieve realistic input values for the evaluation of forces/torques with the equation of motion and for the digital simulation of the robot dynamics. Finally the equation of motion is generated in a numerical-symbolical form.
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