J.A. De Abreu-Garcia

Control of lateral motion in moving webs

A partial differential equation for the lateral motion of a web conveyance system is derived by modeling the web as a viscoelastic beam under axial tension. This model treats the web position between rollers as a function of both time and space, assumes that there is no slip between the web material and the rollers, and incorporates the web materials viscoelastic damping property. A finite-difference approximation of the model is used to simulate a typical two-span web system. The finite-difference approximation is validated by comparing its frequency responses with those of an analytical frequency domain model. The analytical frequency domain model is used to design feedback compensation strategies that make the two-span web system less sensitive to upstream disturbances. The results show that, using a transverse vibration model incorporating viscoelasticity to design even simple classical controllers, it is possible to make the web system less sensitive to upstream disturbances at the sensor location.

Least squares model reduction

Abstract A model reduction method based on the least squares algorithm is derived. This method calculates a low order autoregressive moving average (ARMA) predictor equation from a high order ARMA equation. The low order ARMA equation minimizes the sum of the squares of the prediction errors when the input is white noise. This is almost equivalent to minimizing the sum of the squares of the error in the impulse response function. Transfer function models can also be used and a steady-state gain constraint can be incorporated into the procedure. The merits of this method of model order reduction are shown with three examples. In these examples, the proposed method produced results that compared favorably with highly regarded existing model reduction techniques which require many more computations.

Improved bounds for linear discrete-time systems with structured perturbations

A time-domain analysis of the stability robustness of linear discrete-time systems subject to time-varying structured perturbations is considered. The Lyapunov stability theory is used to obtain bounds on the perturbation such that the systems remain stable. It is shown that these bounds are less conservative than the existing ones. This is illustrated via two numerical examples. >

A fuzzy system cardio pulmonary bypass rotary blood pump controller

Abstract Fuzzy logic regulation of flow was investigated in simulation of a model of the Cleveland Clinic Foundation rotodynamic Cardio Pulmonary Bypass blood pump comprised of impeller model #4079 and volute model #4080. A non-linear model of the pump was derived from pump maps obtained from measurements using a custom made pump dynamometer. Pump speed and generated delta pressure were used as inputs to a fuzzy engine in charge of manipulating the pumps speed; the fuzzy controller was capable of maintaining a setpoint of 6±0.5 l/min when presented with pressure disturbances over a range of ±50 mmHg from the baseline of 100 mmHg.

On the computation of reduced order models of nonlinear systems using balancing technique

A balancing-based algorithm for obtaining nonlinear reduced-order models of nonlinear systems is presented. This is done by considering the input/output behavior of the system around its equilibrium point. The algorithm is shown to be particularly useful in the real-time simulation of stiff nonlinear systems.<<ETX>>

Multistep Matrix Integrators for Real-Time Simulation

An explicit linear multistep matrix-integration technique is presented for vector systems of ODEs which employs the stability region placement approach to permit the time-step to be chosen independently of system eigenvalues. Closed-form solutions for the general p-step method and the case where the system matrix has zero eigenvalues are given. It is shown that system mode shapes are preserved over the integration process, and that the technique remains applicable to systems with eigenvalues at their origin without need for computing a matrix inversion.

Model reduction of unstable systems

A simple and powerful method for unstable model reduction has been developed in which the approach is based on the fact that translation transformations in the s-plane preserve the input-output properties of a system. Using translation transformations in the frequency domain it is possible to change the stability of the system without losing input-output information. Although balancing requires that the model be asymptotically stable, it reduces the model depending only on the information of input to state and state to output. The stability requirement comes from the computation of the controllability and observability gramians which are used for characterizing the contribution of the states to the input-output map. It has been shown in this paper that it is possible to use balancing to reduce the models of unstable systems by transforming them into the stable models, reducing the model order, and then transforming the models back. The method has been demonstrated by case studies.

Optimization of stability robustness bounds for linear discrete-time systems

In this paper, existing stability robustness measures for the perturbation of both continuous-time and discrete-time systems are reviewed. Optimized robustness bounds for discrete-time systems are derived. These optimized bounds are obtained reducing the conservatism of existing bounds by (a) using the structural information on the perturbation and (b) changing the system coordinates via a properly chosen similarity transformation matrix. Numerical examples are used to illustrate the proposed reduced conservatism bounds.

On matrix integrators for real-time simulation

A matrix integration method is generalized to systems with zero eigenvalues. It is shown that the regression coefficients of the integrator can be determined without explicitly computing the inverse of the system Jacobian. This is done by transforming the original system into a new system whose Jacobian is in block upper triangular form. A numerical example is included for illustrative purposes. >

A simple algorithm for time scale separation

Gerschgorins circle theorem is used to develop a simple algorithm for identifying time scales in linear systems. The similarity transformation of matrices is then used to partition the system matrix A, with each diagonal block of A corresponding to a different time scale. Sufficient conditions under which this technique is applicable are given. The tractability of this algorithm in comparison to those found in the literature is discussed. The proposed algorithm is particularly useful for reducing the computational cost involved in decoupling a given system into its fast and slow subsystems. Two numerical examples are given to illustrate the use of the method. It is apparent from these examples that this algorithm is simple, computationally cheap, and reliable. However, it may require preliminary transformations of the A matrix to ensure that Gerschgorins circle theorem can be used.<<ETX>>