The (approximate) diagonalization of symmetric matrices has been
studied in the past in the context of distributed control of an
array of collocated smart actuators and sensors. For distributed
control using a two dimensional array of actuators and sensors, it
is more natural to describe the system transfer function as a
complex tensor rather than a complex matrix. In this paper, we study
the problem of approximately diagonalizing a transfer function
tensor via the tensor singular value decomposition (TSVD) for a
locally spatially invariant system, and study its application along
with the technique of recursive orthogonal transforms to achieve
distributed control for a smart structure.
The Preisach operator and its variants have been successfully used
in the modeling of a physical system with hysteresis. In an
application, one has to determine the density function describing
the Preisach operator from measurements. In our earlier work, we
described a regularization method to obtain an approximation to
the density function with limited measurements. In this paper, we
describe methods for recursively computing the approximate density
function. These methods can be implemented in real-time
controllers for smart actuators.
The phenomenon of hysteresis is commonly encountered in the
study of magnetic materials. The Preisach operator and its
variants have been successfully used in the modeling of a physical
system with hysteresis. In an application, one has to determine a
density function for the Preisach operator using the input-output
behavior of the system at hand. In this paper, we describe a
method for numerically determining an approximation of the density
function when there is not enough experimental data to uniquely
solve for the density function. We also present numerical results
where we estimate an approximate density function from data
published in the literature for a magnetostrictive actuator and an
Hysteresis in smart materials hinders the wider applicability of such materials in actuators. In this paper, a systematic approach for coping with hysteresis is presented. The method is illustrated through the example of controlling a commercially available magnetostrictive actuator. We utilize the low-dimensional model for the magnetostrictive actuator that was developed in earlier work. For low frequency inputs, the model approximates to a rate-independent hysteresis operator, with current as its input and magnetization as its output. Magnetostrictive strain is proportional to the square of the magnetization. In this paper, we use a classical Preisach operator for the rate-independent hysteresis operator. In this paper, we present the results of experiments conducted on a commercial magnetostrictive actuator, the purpose of which was the control of the displacement/strain output. A constrained least-squares algorithm is employed to identify a discrete approximation to the Preisach measure. We then discuss a nonlinear inversion algorithm for the resulting Preisach operator, based on the theory of strictly-increasing operators. This algorithm yields a control input signal to produce a desired magnetostrictive response. The effectiveness of the inversion scheme is demonstrated via an open-loop trajectory tracking experiment.
In previous work we had proposed a low (6) dimensional model for a thin magnetostrictive actuator that was suitable for real-time control. One of the main results of this modeling effort was the separation of the rate-independent hysteretic effects from the rate-dependent linear effects. The hysteresis phenomenon may also be captured by a (modified) Preisach operator with the magnetic field H as the input. If one can find an inverse for the Preisach operator, then the composite system can be approximately linearized. In this paper, we complete the proof of the existence of an inverse theorem due to Brokate and Sprekels and propose a new algorithm for computation of the inverse. Previous algorithms used linearization of the operating point. As numerical differentiation is involved, this approach can cause divergence. Our algorithm does not linearize the Preisach operator, but makes use of its monotone increasing property. Convergence of the algorithm is proved using the contraction mapping principle.
In this paper, we discuss a smart motor concept, in which piezoelectric and magnetostrictive actuators forming a resonance electric circuit function together to produce bidirectional motion of a steel drum. Resonance frequency is set at 4 KHz, thereby enabling operation of the motor at reasonably high frequencies.