Bahram Shafai

Magnetic bearing control systems and adaptive forced balancing

Active magnetic bearing (AMB) actuators support rotors without friction but require feedback control for stabilization and performance. We address the application of modern control techniques such as LQG/LTR, H/spl infin/, and QFT to AMB systems. We also introduce a novel method called adaptive forced balancing (AFB) which solves the problem of synchronous vibration caused by mass unbalance. Simulation and experimental results are included to show the performance of AFB as applied to single-end AMB suspensions (SISO systems). Finally, AFB with frequency tracking and its generalization for double-end AMB suspensions (MIMO systems) are briefly explored.<<ETX>>

Robust control system design with a proportional integral observer

A design method for a robust controller including a new type of observer called the proportional integral observer (PI observer) is proposed. The new observer differs from the conventional one by an integration path which provides additional degrees of freedom. This freedom can be used to make the observer-based controller design less sensitive to parameter variation of the system. It is shown that some of the difficulties that may arise in the exclusive pursuit of a design for the conventional observer-based controller from the point of view of system robustness are resolved in a straightforward manner using the PI observer. A systematic robustness recovery procedure is described for the PI observer-based controller design which asymptotically achieves the same loop transfer functions as the full-state feedback control implementation. A design example is included and the effectiveness of our method is illustrated by simulation results.

Simultaneous disturbance attenuation and fault detection using proportional integral observers

This paper considers the design of a proportional integral observer (PIO) for simultaneous disturbance attenuation and fault detection. Unlike the proportional observer, an integral observer alone suffices to achieve good convergence and filtering properties when sensor noise is present in the system. On the other hand, a proportional integral observer makes it possible to decouple the modeling uncertainties while estimating the states and faults with satisfactory convergence properties. We show that a generalized PIO structure, a proportional integral fading observer, facilitates the design procedure for achieving the above goal.

LTR design of discrete-time proportional-integral observers

Applies the proportional-integral (PI) observer in connection with loop-transfer recovery (LTR) design for discrete-time systems. Both the prediction and the filtering versions of the PI observer are considered. We show that a PI observer makes it possible to obtain time recovery, i.e., exact recovery for t/spl rarr//spl infin/, under mild conditions. Two systematic LTR design methods, one based on an extension of the linear quadratic Gaussian loop-transfer recovery (LQG/LTR) and the other based on linear matrix inequality (LMI), are derived for the discrete-time PI observer case, Explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given.

Design of a minimal-order observer for singular systems

This paper considers the design of an observer for generalized state-space systems using the concept of generalized inverses. In contrast to the Luenberger observer theory, a new method is proposed which does not presuppose the observer structure. It is shown that under certain conditions it is possible to construct a minimal-order observer for this class of systems. Illustrative examples are included.

Explicit formulas for stability radii of nonnegative and Metzlerian matrices

We address stability issues pertaining to uncertain nonnegative and Metzlerian matrices. The problem under consideration is the computation of the stability radius when matrix perturbations are both unstructured and structured. We show that the stability radius can be obtained in the former case by computing the largest singular value of a constant matrix and in the latter case by computing the spectral radius of a constant matrix.

Design of proportional-integral observer for linear time-varying multivariable systems

A new method for the design of proportional-integral observer for linear time-varying multivariable systems is proposed. Necessary and sufficient conditions are provided to construct full-order and reduced-order PI observers for uniformly observable systems. The design procedure is illustrated by means of an example.

Balanced realization and model reduction of singular systems

The problem of balanced realization and model reduction of a singular system of the form E[xdot] = Ax + Bu, where E is a singular matrix, is considered. Using coordinate transformation, which can be computed by performing singular value decomposition of E, we derive our first approach to the balancing of singular systems. The second approach is based on standard form decomposition of singular systems to slow and fast subsystems and performing balanced realization on the decomposed model. In this sense model reduction can be established in two steps: first, by decomposing the singular system and second, by performing balancing transformation on the decomposed subsystems.

A necessary and sufficient condition for the stability of nonnegative interval discrete systems

The stability of nonnegative discrete systems with interval uncertainty is discussed. For this class of system a necessary and sufficient condition for the stability is provided when all elements of the system matrix are assumed to be specified by intervals. An illustrative example is used as a guideline to demonstrate the effectiveness of the result. Simple computational tests are suggested, and their usefulness in this framework is discussed. The possible extension of this result to more general classes of systems is addressed. >

Robust nonnegative stabilization of interval discrete systems

The authors consider the class of nonnegative discrete-time systems and analyze the matrix theoretical results involving nonnegative maintainability with respect to the problem of robust stabilization of interval discrete systems. Using state feedback, a controller which may include an observer such that the closed-loop interval system is robustly stabilized and at the same time becomes nonnegative is designed. The procedure is to characterize the set of robust controllers by means of matrix inequalities, and to choose a suitable controller by solving an optimization algorithm.<<ETX>>