SHAPE CONTROL OF A PLATE USING PIEZOELECTRIC ACTUATORS AND LQR CONTROL
The control of shape in metallic structures has been gaining ground in aeronautical
research. Its application in aircraft wings has already shown to generate signifcant improvements in the performance of aerial vehicles. This work utilizes a linear controller of
the LQR (Linear Quadratic Regulator) type to control the shape of a simply crimpedfree-free-free plate through piezoelectric actuators. The linear plate model is used. The
plate deflection is considered sufciently small. Therefore, only the transverse component
of the deflection is considered in this work. The governing equations of motion are obtained using the extended Hamilton’s principle. The resulting partial differential equations
are discretized using the fnite difference method. The discretized closed-loop governing
equations of motion are numerically simulated using a fourth-order Runge-Kutta numerical integrator. The LQR control is applied to these equations. The investigated types
of optimal controllers are tracking and regulation, with fnite and infnite horizons, respectively. The mathematical model for the linear plate has complete controllability, and
the steady-state error in the performed simulations has been signifcantly reduced in all
scenarios. The results presented here demonstrate the feasibility of optimal control techniques for this type of dynamic system under the given conditions and create expectations
for studying more complex systems regarding nonlinearities in the mathematical model
or the addition of constraints on the control signal value, for example.