Siddhartha Mukhopadhyay

New class of discrete-time models for continuous-time systems

Digital computing in estimation, control or signal processing for continuous-time systems requires the use of discrete-time models. While conventional difference equation or z-transfer function models are widely popular, a class of methods exists that uses discrete approximations of continuous signals and operators, retaining the continuous-time parameters. Some important advantages of this class have been demonstrated in the contexts of parameter estimation, adaptive control and controller design. This paper proposes a new class of discrete-time models that originates from the z transfer function but which is close to continuous-time models in structure and parameters, thereby retaining its advantageous features. The recently proposed ‘delta’ model is seen to be a member of this class. The interrelations among various digital model types are brought out. Better sensitivity properties over z transfer function models are established. Finite word length properties of these models vis-a-vis the z-transfer fu...

Fault diagnosis in discrete time hybrid systems - A case study

A method of analysing diagnosability of discrete time hybrid systems (DTHS), which are similar to the simple n-rate timed automata [R. Alur, C. Courcoubetis, T.A. Henzinger, P. Ho, Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems, in: Hybrid Systems, LNCS 736, Springer Verlag, 1993, pp. 209-229], has been proposed. A state based fault modeling formalism is used. The properties of the DTHS model, under measurement limitations due to inadequacy or non-availability of sensors, are discussed. A definition of diagnosability for DTHS models has been adopted from the one proposed in [M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, D. Teneketzis, Diagnosability of discrete-event systems, IEEE Transactions on Automatic Control 40 (9) (1995) 1555-1575] for discrete-event system (DES) models. Based on the measurement limited DTHS models, an algorithm for construction of a diagnoser is presented. It is next demonstrated through an example of a chemical reaction chamber that the diagnosability condition (over the diagnoser), which has been shown to be necessary and sufficient for DES diagnosability, fails to hold for many systems. This is so because the abstraction employed in DES modeling obliterates an important feature of the transitions namely fairness. Exploiting the explicit continuous dynamics of the DTHS models, the fairness of transitions is identified and used to demonstrate diagnosability. The diagnosability condition over the diagnoser is suitably modified to encompass the situations typified by the example.

On-line tool condition monitoring in face milling using current and power signals

The vast majority of tool condition monitoring systems use the cutting force as the predictor signal. However, due to prohibitive cost to performance ratios and maintenance and operational problems, such methods are not favoured by industries. In this paper, a method for continuous on-line estimation of tool wear, based on the inexpensive spindle motor current and voltage measurements, is proposed for the complex and intermittent cutting face milling operation. Sensors for these signals are free from problems associated with the cutting forces and the vibration signals. Novel signal processing strategies have been proposed for on-line computation of useful features from the measured signals. Feature space filtering is introduced to obtain robust and improved predictors from the extracted features. A multiple linear regression model, built on the filtered features, is then used to estimate tool wear in real-time. Very accurate predictions are achieved for both laboratory and industrial experiments, surpassing earlier results using cutting forces and estimation methods based on complex methodologies such as artificial neural networks.

MVEM-Based Fault Diagnosis of Automotive Engines Using Dempster–Shafer Theory and Multiple Hypotheses Testing

Internal combustion engines exhibit fast pulsating short-time dynamics due to the reciprocating cylinder motion, around mean operating points that change comparatively slow due to inputs such as throttle and load. Comparatively, simple mean value engine models (MVEM) describe the slow changes of the averaged states for automotive control and fault diagnosis. In this paper, a bank of state estimators based on MVEMs is used for fault residual generation. Three faults: 1) throttle mass air-flow sensor fault; 2) exhaust gas recirculation valve sensor fault; and 3) exhaust leak fault are considered here. These faults are significant as they affect emission levels. Optimized thresholds for residual classification are derived for minimizing false alarm rates and missed detection rates. The diagnosis logic, based on the principles of structured residuals proposed in literature, is extended here for multiple hypotheses testing. Furthermore, the Dempster-Shafer theory is used to associate a confidence measure with the decision conclusions and this is shown to improve isolation. Performance is demonstrated with automotive engine data obtained from a four-cylinder instantaneous spark-ignition engine (gasoline) system model, developed in the simulation software AMESim.

Irreducible model estimation for MIMO systems

Abstract Estimation of the parameters of a reducible (inflated common denominator) model for the transfer function matrix of MIMO systems is well known. However, the reduction of the model to the minimal form by pole-zero cancellation is possible only in the noise-free case. This paper presents an algorithm for the estimation of the minimal continuous-time transfer function matrix model. Monte Carlo simulation results are presented for discrete-time and continuous-time models. Least-squares and generalized least-squares methods have been used in both cases. An asymptotic analysis of convergence has also been provided for these models in the noise-free case. The computation times and space complexities of different variants of the algorithm are compared. The results show that in noisy situations, obtaining a discrete-time model by discretizing an estimated continuous-time model may be a viable proposition

Tracking Reentry Ballistic Targets using Acceleration and Jerk Models

In this paper an acceleration model and a jerk model are proposed for estimation of the kinematic state of reentry ballistic targets (RBTs) using extended Kalman filters (EKF). The models proposed here use the equations of target kinematics only and do not assume any model parameterization for variation of the ballistic coefficient and air density a priori, as found in the literature. The novelty lies in estimation of the ratio (γ) of air density and ballistic coefficient and its time derivatives using a separate Kalman filter (KF) (γ-filter) which utilizes pseudo measurements of γ computed from the velocity and acceleration estimated by the EKF at each time step. The parameter γ and its derivatives estimated by the γ-filter are, in turn, used for the estimation of position, velocity, acceleration, and jerk in the EKF. The use of the pseudo measurements of γ makes the algorithms inherently adaptive to variations of the ballistic coefficient and air density during reentry. A comparative assessment of several dynamic models for reentry of ballistic targets reported in the literature and those proposed here demonstrates that the estimation errors in velocity and acceleration are significantly less for the proposed models compared with the existing ones.

A Formal Approach to On-Line Monitoring of Digital VLSI Circuits: Theory, Design and Implementation

This work is concerned with the development of algorithms and CAD tools for the design of digital circuits with on line monitoring capability. The Theory of Fault Detection and Diagnosis available in the literature on Discrete Event Systems has been adopted for on-line detection of stuck-at faults in Digital Circuits. Efficient computational techniques to deal with very large state spaces based on Ordered Binary Decision Diagrams and Abstraction have been proposed. Based on these a CAD tool has been developed that can provide a fully automated flow for design of circuits with on-line test capability without the requirement of any modification to the core. The tool can handle generic digital circuits with cell count as high as 15,000 and having the order of 2500 states. This is believed to be an improvement of an order of magnitude over results presented in the literature. This methodology enables the designer to tradeoff fault coverage and detection latency against area and power overhead. The design flow using the CAD tool developed is described and results for design of on-line detectors for various ISCAS89 benchmark circuits are provided. The methodology is further validated by design, fabrication, and testing of an ASIC in 0.18 μ technology.

Optimal slope compensation for step load in peak current controlled dc-dc buck converter

The paper comes up with the variation of slope compensation with step load and duty cycle for one cycle control in a peak current controlled dc-dc buck converter. For an optimal performance under varying load conditions and input voltage the amount of slope compensation desired, vary dynamically. A conventionally used linear slope is definitely not a solution. To meet the dynamic requirement of slope in a current controlled dc-dc buck converter a non-linear ramp generator circuit has been proposed. The primary aim of the circuit is to provide a slope which is very small for low duty cycles and increases steeply as duty cycle increases. Consequently, it proves much more efficient in low duty cycle (less than 0.5) of operation. On the higher side this achieves a similar performance as that by a linear ramp with much less p-p value of the ramp.

Fault Detection and Remedial Strategies for Inter-Turn Short Circuit Faults in a Permanent Magnet Brushless DC Motor

The paper describes Fault detection, diagnosis and remedial strategies taken against turn-to-turn fault in the phases of permanent magnet brushless dc motor drive. The basic idea of the topology considered here is to change the current references and the switching sequences as soon as the fault is detected. The topology requires the availability of neutral for preventing the capacitor midpoint voltage from drifting from the correct point. The achieved results show the feasibility of the proposed scheme for the cases where some amount of reduced performance from the nominal case is allowable.

Auxiliary Specifications for Context-Sensitive Monitoring of AMS Assertions

As research on developing assertion languages for the analog and mixed-signal (AMS) domain gains in momentum, it is increasingly being felt that extensions of existing assertion languages like property specification language and SystemVerilog assertions into the AMS domain are not adequate for expressing the analog design intent. This is largely due to the intricacy of the analog behavioral intent which cannot be captured purely in terms of logic. In this paper, we show that by using auxiliary forms of formal specifications such as abstract state machines and real-valued functions, called auxiliary functions, as references for AMS assertions, it becomes possible to model complex AMS behavioral properties. In addition, we present complexity results for the satisfiability problem of such specifications. This approach leverages the growing adoption of AMS behavioral modeling in the industry. This paper also shows that the use of auxiliary state machines allows us to separate out the scope of different analog assertions leading to significant performance gains in the assertion checking overhead.