Hossein M. Oloomi

Realization and canonical representation of linear systems through I/O maps

Abstract In this paper, we use input and output maps to develop simple procedures to obtain minimal realizations for linear continuous-time systems. The procedures developed are numerically efficient and yield explicit formulae for the state-space matrices of the realization in terms of the system parameters, notably the system eigenvalues. Both systems with distinct eigenvalues and repeated eigenvalues are treated. We also present a procedure for transforming a realization obtained through the input or output map to Jordan canonical form. The transformation matrices required to transform the realization to Jordan canonical form are specified entirely in terms of the system eigenvalues. We illustrate the results obtained with several examples.

H ∞ model matching problem for singularly perturbed systems

Abstract The model matching problem for single-input single-output singularly perturbed systems is considered. Two sets of sufficient conditions are obtained to guarantee the existence of a two-frequency-scale solution: one for the optimal and one for a suboptimal case. Both the minimum-phase and the non-minumum-phase cases are treated. The sub-optimal two-frequency-scale solution constructed in this paper uses the solutions of two well-defined lower-order problems, and therefore it is numerically better conditioned and computationally less demanding than the traditional optimal methods. A two-stage algorithm for the computation of the suboptimal TFS solution is presented.

High gain sampled data systems: deadbeat strategy, disturbance decoupling and cheap control

In this paper, it is shown that a sampled data system under a high gain state feedback displays a two time-scale behaviour. The two time-scale structure of the system is then used to study three seemingly different classes of problems. First, the pole placement problem is considered and a two-step design based on the theory of singular perturbation is presented. Secondly, the asymptotic disturbance decoupling problem is solved using two different methods. The first method reduces the problem to one of an exact disturbance decoupling problem for the reduced-order model, while the second method shows that the problem can be solved by means of the output deadbeat response. The third problem considered in this paper is the cheap regulator problem where a near optimal composite controller based on the optimal controllers of the slow and fast subsystems is constructed. For all three problems, it is shown that by exploiting the two time-scale property of the system and solving the problem in terms of two lower d...

Two-time-scale distributions and singular perturbations

Two-time-scale (TTS) distributions are introduced. For a class of stable systems, it is shown that every TTS distribution has a two-frequency-scale (TFS) Laplace transform. Conversely, it is shown that the impulse response of any stable TFS transfer function, and hence any stable (standard) singularly perturbed system, can be characterized in terms of a stable TTS distribution. A time domain decomposition for TTS distributions is obtained which parallels the slow and fast decomposition of singularly perturbed systems and also the frequency domain decomposition of TFS transfer functions. It is shown that every stable TTS distribution can be decomposed in terms of two simpler distributions represented in two different time scales. A composite distribution is constructed from these two which approximates the TTS distribution arbitrarily closely in the L 1 norm.

Transmission line application MATLAB Toolbox based on the graphical design methods of the Smith chart

In this article, we present a transmission line application (TLA) MATLAB Toolbox capable of solving the single‐stub and double‐stub matching problems for transmission lines using the graphical method of the Smith chart. The package handles both the short stub and open stub cases and provides an analytical and graphical solution. For each of the aforementioned problems, the software produces the corresponding Smith chart and a summary of the final results. The software provides the user with the flexibility to tackle other potential design problems that can be handled by the Smith chart techniques.

Design and Development of a Computer-Controlled Interactive Cooling System

An educational interactive cooling system (ICS) was designed, developed and constructed for instructional and demonstrative purposes. This ICSs experimental apparatus is capable of demonstrating thermodynamics and heat transfer concepts and principles. This experimental apparatus has an intuitive user interface, and it is reliable, safe for student use and portable. The interface is capable of allowing data acquisition by a computer. The unit demonstrates change phase as a refrigerant passes through a cold plate. The two-phase process is visible and can be observed through the glass cover of the cold plate. The ICS is capable of cooling heat loads between 100W and 1000W and maintains the heated surface at a temperature of less than 100°C. The unit has been used in thermodynamics classes as a demonstration unit.

A multi-loop vibration control of a torsional plant

This paper addresses the problem of suppressing torsional vibration induced by a disturbance torque in a high performance two-disk system. The plant consists of two inertia disks connected by a weakly damped link and is driven by a brushless DC motor connected to one of the disks. A distributed parameter model of the system is developed and a lumped parameter model including the dominant torsional modes is then extracted. A multi-loop controller is designed on the basis of the lumped parameter model and is shown to be capable of suppressing the vibration to a reasonable level and over a wide frequency range.

Reduced-order controller design with low sensitivity to small feedback delays

Reduced-order controller design for a class of interconnected singularly perturbed system is considered. Using the singular perturbation and sensitivity theories, a controller is designed that reduces the trajectory sensitivity to small feedback delays. A numerical algorithm for the computation of the feedback gain is presented. Application of the results to the control of a continuous stirred tank reactor is demonstrated.

Asymptotic Behavior of Zeros of Two Frequency Scale Systems

Zeros of two frequency scale systems are studied in terms of zeros of the slow and fast models. Results obtained from this study have then been used to approximate the frequency response of a two frequency scale system asymptotically in the frequency bands of interest by the frequency responses of the slow and fast models.