Pierre-Yves Richard

On the stabilisation of switching electrical power converters

This paper considers the control of switching power converters which are a particular class of hybrid systems. Such systems, which are controlled by switches, can be modeled using physical principles. Taking advantage of the energetical properties of their models, a Lyapunov function is proposed. This function, which has not to be computed but is systematically deduced from the physical model, allows to derive different stabilizing switching sequences. From a theoretical point of view, asymptotic stability can be obtained, but it requires null intervals between switching times. In order to ensure a minimum time between switchings, this Lyapunov function has to be increasing for a small duration by using a delay or a dead zone. A control law principle that guarantees the invariance of a specified domain with respect to state trajectories is proposed. Two examples are provided at the end of this paper that demonstrate the efficiency of the proposed approach.

Analysis of the bond graph model of hybrid physical systems with ideal switches

Abstract This paper deals with the modelling of hybrid physical systems. The bond graph technique is used to establish their knowledge model, based upon an ideal representation of the switches. These components are modelled either by flow or by effort sources according to their state and therefore modify the circuit topology at switching times. The paper shows the usefulness of the implicit representation to derive a unique implicit state equation with jumping parameters, to analyse the model properties, to derive an implicit state equation with nilpotency index one for each configuration and to compute the discontinuities. Also, a comparison between the chosen ideal modelling approach and the more common non-ideal approach is carried out using singular perturbations theory. After a presentation of the whole study in the most general context, its results are applied to power converters, which constitute a particular class of hybrid physical systems where switches only commutate in pairs. Finally, an example is developed.

Model-based analysis of myocardial strain data acquired by tissue Doppler imaging

OBJECTIVE Tissue Doppler imaging (TDI) is commonly used to evaluate regional ventricular contraction properties through the analysis of myocardial strain. During the clinical examination, a set of strain signals is acquired concurrently at different locations. However, the joint interpretation of these signals remains difficult. This paper proposes a model-based approach in order to assist the clinician in making an analysis of myocardial strain. METHODS AND MATERIALS The proposed method couples a model of the left ventricle, which takes into account cardiac electrical, mechanical and hydraulic activities with an adapted identification algorithm, in order to obtain patient-specific model representations. The proposed model presents a tissue-level resolution, adapted to TDI strain analysis. The method is applied in order to reproduce TDI strain signals acquired from two healthy subjects and a patient presenting with dilated cardiomyopathy (DCM). RESULTS The comparison between simulated and experimental strains for the three subjects reflects a satisfying adaptation of the model on different strain morphologies. The mean error between real and synthesized signals is equal to 2.34% and 2.09%, for the two healthy subjects and 1.30% for the patient suffering from DCM. Identified parameters show significant electrical conduction and mechanical activation delays for the pathologic case and have shown to be useful for the localization of the failing myocardial segments, which are situated on the anterior and lateral walls of the ventricular base. CONCLUSION The present study shows the feasibility of a model-based method for the analysis of TDI strain signals. The identification of delayed segments in the pathologic case produces encouraging results and may represent a way to better utilize the information included in strain signals and to improve the therapy assistance.

An autonomic nervous system model applied to the analysis of orthostatic tests

One of the clinical examinations performed to evaluate the autonomic nervous system (ANS) activity is the tilt test, which consists in studying the cardiovascular response to the change of a patients position from a supine to a head-up position. The analysis of heart rate variability signals during tilt tests has been shown to be useful for risk stratification and diagnosis on different pathologies. However, the interpretation of such signals is a difficult task. The application of physiological models to assist the interpretation of these data has already been proposed in the literature, but this requires, as a previous step, the identification of patient-specific model parameters. In this paper, a model-based approach is proposed to reproduce individual heart rate signals acquired during tilt tests. A new physiological model adapted to this problem and coupling the ANS, the cardiovascular system (CVS), and global ventricular mechanics is presented. Evolutionary algorithms are used for the identification of patient-specific parameters in order to reproduce heart rate signals obtained during tilt tests performed on eight healthy subjects and eight diabetic patients. The proposed approach is able to reproduce the main components of the observed heart rate signals and represents a first step toward a model-based interpretation of these signals.

Modelling and Passivity Based Control of switched systems from bond graph formalism: Application to multicellular converters

This paper addresses the modelling and control of switched systems with Boolean inputs. A generalization of Passivity Based Control (PBC) is proposed and fitted to bond graph formalism. The state equations of the equivalent average model are first deduced from the original bond graph using the notion of commutation cells and then interpreted according to Port Controlled Hamiltonian formalism. The whole approach is presented in a formal way. This method is then applied on a multicellular serial converter, which is widespread in power systems and of growing interest. The application of PBC associated to a modelling approach using commutation cells on a non-trivial example shows its efficiency to determine a generic controller, the number of elementary cells being considered as a parameter.

A GENERIC PASSIVITY BASED CONTROL FOR MULTICELLULAR SERIAL CONVERTERS

Abstract Multicellular converters appeared for a few years in order to palliate some drawbacks of the classical structures. Such structures allow to reduce the voltage throughout the switches and the number of discrete values of the voltage in the load is directly related to the number of commutation cells. In opposing view, the control of a multicellular converter is more complex. In this paper a generic controller for a multicellular serial converter is developed, based on a generalization of Passivity Based Control (PBC) fitted to bond graph formalism. The generic state equations are deduced from the original bond graph model using the notion of commutation cells. The whole approach is presented in a formal way and the performances of the controller realised will be tested on an example.

Extending passivity based control to dae systems with boolean inputs

Abstract This paper addresses the control of switching systems with Boolean inputs and state equations in DAE form. A generalization of Passivity Based Control is proposed and fitted to bond graph formalism in the general case where derivative causality occur in the models. The state equations deduced from the original bond graph models are first made explicit via a special variable change, then interpreted according to Port Controlled Hamiltonian formalism. The whole approach is presented in a formal way, and illustrated on the example of a power converter.

A Closed-Loop Artificial Pancreas Using a Proportional Integral Derivative with Double Phase Lead Controller Based on a New Nonlinear Model of Glucose Metabolism

Background: Most closed-loop insulin delivery systems rely on model-based controllers to control the blood glucose (BG) level. Simple models of glucose metabolism, which allow easy design of the control law, are limited in their parametric identification from raw data. New control models and controllers issued from them are needed. Methods: A proportional integral derivative with double phase lead controller was proposed. Its design was based on a linearization of a new nonlinear control model of the glucose-insulin system in type 1 diabetes mellitus (T1DM) patients validated with the University of Virginia/Padova T1DM metabolic simulator. A 36 h scenario, including six unannounced meals, was tested in nine virtual adults. A previous trial database has been used to compare the performance of our controller with their previous results. The scenario was repeated 25 times for each adult in order to take continuous glucose monitoring noise into account. The primary outcome was the time BG levels were in target (70–180 mg/dl). Results: Blood glucose values were in the target range for 77% of the time and below 50 mg/dl and above 250 mg/dl for 0.8% and 0.3% of the time, respectively. The low blood glucose index and high blood glucose index were 1.65 and 3.33, respectively. Conclusion: The linear controller presented, based on the linearization of a new easily identifiable nonlinear model, achieves good glucose control with low exposure to hypoglycemia and hyperglycemia.

Using trees to build non-singular bond graphs from electric circuit graphs

Abstract A commonly used method to build bond graphs for electric circuits can lead to causal bond graphs with unity gain causal loops. Deriving equations from such causal bond graphs is problematic. This paper shows that, for electric circuits, unity gain causal loops are not a property inherent in the system but rather are due to the nature of the causal bond graphs. A method is proposed for building an acausal bond graph to which a modified version of the sequential causality assignment procedure can be applied, in order to guarantee a non-singular causal bond graph. This approach can also be applied to the problem of joining sub-systems.

A New Model for Closed-Loop Control in Type 1 Diabetes

A new control model for T1DM is designed with the aim to represent accurately the plasma glucose-insulin dynamics. It is in the form of a nonlinear system of three timecontinuous state equations. The model includes two successive remote compartments for plasma insulin, accounting for a slow and a fast dynamics. The modeling of the action of the insulin on the glucose disappearance is in an original nonlinear form. This new model is identified and validated using data from the adult subjects of the UVa T1DM simulator training database. The parametric identification of the model provides in each case an accurate representation of the glucose-insulin dynamics of the subjects.