In this paper, an electrostatic actuator linearization will be introduced, which is based on an existing hardware-efficient
iterative square root algorithm. The algorithm is solely based on add and shift operations while just
needing n/2 iterations for an n bit wide input signal. As a practical example, the nonlinear input transformation
will be utilized for the design of the primary mode controller of a capacitive MEMS gyroscope and an implementation
of the algorithm in the Verilog hardware description language will be instantiated. Finally, measurement
results will validate the feasibility of the presented control concept and its hardware implementation.
KEYWORDS: Actuators, Composites, Motion models, Control systems, Microsoft Foundation Class Library, Electrodes, Piezoelectric effects, Motion analysis, Smart structures, Adaptive optics
A systematic approach for flatness-based motion planning and feedforward control is presented for the transient shaping of
a piezo-actuated rectangular cantilevered plate modeling an adaptive wing. In the first step the consideration of an idealized
infinite-dimensional input allows to determine the state and input parametrization in terms of a flat or basic output, which
is used for a systematic motion planning approach. Subsequently, the obtained idealized input function is projected onto a
finite number of suitably placed Macro-fiber Composite (MFC) patch actuators. The tracking performance of the proposed
approach is evaluated in a simulation scenario.
In this contribution, a method will be introduced to derive an envelope model for vibratory gyroscopes capturing
the essential "slow" dynamics (envelope) of the system. The methodology will be exemplarily carried out for a
capacitive gyroscope with electrostatic actuators and sensors. The resulting envelope model can be utilized for
transient simulations with the advantage of a significantly increased simulation speed as well as for steady state
simulations. Especially for the sensor design and optimization, where usually very complex mathematical models
are used, efficient steady state simulations are of certain interest. Another great advantage of this approach is
that the steady state solutions in terms of the envelope model are constant. Thus, for the controller design,
a linearization of the nonlinear envelope model around the steady state solution yields a linear time-invariant
system allowing for the application of the powerful methods known from linear control theory.
Piezoelectric devices represent an important new group of actuators and senors for active vibration control systems. Indeed, this technology allows to construct spatially distributed devices. A mathematical model of a multilayered piezoelectric plate, which takes hysteresis and polarization of the piezoelectric laminae into account, is presented. Passive control for Lagrangian systems is used to derive a class of stabilizing control laws, which are based on the collocation of sensors and actuators. Therefore, the design of the spatial distribution of the sensors/actuators is considered as a part of the controller synthesis.
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