AnH₂norm approach for the actuator and sensor placement in vibration control of a smart structure

Abstract

In active vibration control of smart structures, the actuator and sensor placement is a key point of the control system design. Even the most robust control logics could easily make a structure unstable if the actuators and sensors were not correctly positioned. The objective of this paper is to propose an H2 norm approach for the actuator and sensor placement. Unlike most modal H2 norm actuator and sensor placement methodologies, this work aims not only to maximize the norms of the controlled modes but also to reduce spillover problems by taking into account the residual modes and minimizing their H2 norms. It discusses the optimal actuator and sensor configuration in a finite element model of a square plate fixed on three sides with piezoelectric patch actuators and acceleration sensors. Finally, downstream of the actuator and sensor positioning, IMSC, PPF and NDF controls have been tested and discussed.

An adaptive optimal control for smart structures based on the subspace tracking identification technique

“…Three strain gauges and three accelerometers are simulated to collect data from the plate model. Only one sensor per time is used by the RST algorithm, and it is chosen to optimize the observability [11] depending on the considered frequency range. Table 1 shows the output of the ARMA model compared with an offline estimation of the structure natural frequencies and damping ratios.…”

“…Now, the SVD of R can be calculated as T ss  R U SV (10) the Hankel matrix becomes (11) and the i-th signal component can be calculated as…”

Comparison of actuator placement criteria for control of structures

“…Here, since the modes can be easily calculated, a modal approximation is used. Let ϕ i ðaÞ indicate the eigenfunctions of ∂ 4 w=∂a 4 with boundary conditions (4). For any positive integer N, define Z N to be the span of ϕ i ; i ¼ 1…N.…”

“…The placement of actuators and sensors with respect to the disturbance and with respect to each other is shown to have a significant effect on performance. In [4] an H 2 -type criterion based on a modal approximation of a structure that takes into account the neglected modes in order to avoid spillover is applied. Selection of the actuator/sensor location improved closed loop performance.…”

On the use of electrical and optical strain gauges paired to magnetostrictive patch actuators

“…One of the most efficient way to reduce vibration is to actively increase the system damping and, as a consequence, the energy dissipation associated to it [15][16][17][18][19][20][21][22]. The control forces can be designed as…”