Deadbeat control and tracking of discrete-time systems

A new approach for forcing the state of a linear discrete-time system to zero in a minimum number of steps is discussed. The problem is formulated as the solution to a steady-state optimal control problem with no cost on the control. This problem in turn is set up as the solution to an associated eigenvalue problem. No special assumption on the open loop system matrix and/or the ratio of the number of states to controls is required. Stable numerical techniques are presented for solving for the feedback gain. Robust deadbeat tracking is also discussed.     

Computation of zeros of linear multivariable systems

Several algorithms have been proposed in the literature for the computation of the zeros of a linear system described by a state-space model {A, B, C, D}. In this paper we discuss the numerical properties of a new algorithm and compare it with some earlier techniques of computing zeros. The method is a modified version of Silverman's structure algorithm and is shown to be backward stable in a rigorous sense. The approach is shown to handle both nonsquare and/or degenerate systems. Several numerical examples are also provided.     

Deadbeat control of linear multivariable generalized state-spacesystems

The classic idea of deadbeat control is extended to linear multivariable discrete-time generalized state-space systems using algebraic methods. The asymptotic properties of the linear quadratic regulator theory are used to obtain the classes of deadbeat controllers using stabilizing full semistate feedback. The solution is constructed from a `cheap control' problem. Both semistate and output deadbeat control laws are considered. The main design criteria are to drive the semistate and/or outputs of the system to zero in minimum time and that the closed-loop system be internally stable. Unique properties of these types of control laws are discussed. For semistate deadbeat control, all the (dynamic) poles including the ones at infinity are moved to the origin, whereas for output deadbeat, some of the finite transmission zeros are canceled. Numerically reliable algorithms are developed to solve both problems     

A Physical Model for the Drying of Gelcast Ceramics

Gelcasting is a promising new technology for manufactur-ing advanced structural ceramic components. The process involves drying of the "green" gelcast part before densifi-cation. The physical mechanisms that control this relatively long drying process are not well understood. In this study, several controlled experiments have been performed to elu-cidate the key mechanisms. A one-dimensional drying model has been formulated, based on evaporation and gas-eous diffusion through the part. Experimental data have been used to obtain correlations for model parameters. This model predicts the instantaneous moisture content of a gelcast sample with an accuracy of better than 10% when the dryer humidity, dryer temperature, and sample thick-ness are specified.     

Design of ripple-free multivariable robust servomechanisms

The application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants, the output will normally contain ripple. In this note, the robust servomechanism theory is extended to sampled-data systems and a technique is proposed for ripple-free tracking of sinusoids and polynomials. It is shown that a continuous internal model is necessary and sufficient to provide ripple-free response.     

Comments on "On the numerical solution of the discrete-time algebraic Riccati equation"

The problem discussed in the above paper has been independently considered by the authors in [1], [2]. The purpose of this note is to point out the differences with our approach of solving the same problem, to present a solution to the eigenvalue reordering problem which is left as work to be done in the paper, and to present an extension suitable for problems with singular loss matrix on control.     

Effect of model uncertainty on failure detection: the thresholdselector

The performance of all failure detection, isolation, and accommodation (DIA) algorithms is influenced by the presence of model uncertainty. The authors present a unique framework to incorporate a knowledge of modeling error in the analysis and design of failure detection systems. A concept is introduced called the threshold selector, which is a nonlinear inequality whose solution defines the set of detectable sensor failure signals. It identifies the optimal threshold to be used in innovations-based DIA algorithms. The optimal threshold is shown to be a function of the bound on modeling errors, the noise properties, the speed of DIA filters and the classes of reference and failure signals. The size of the smallest detectable failure is also determined. The results are applied to a multivariable turbofan jet engine example, which demonstrates improvements compared to previous studies