Position tracking control of a smart flexible structure featuring a piezofilm actuator

Abstract

A position tracking control of a smart flexible structure with a piezofilm actuator is presented. A governing equation of motion for a smart cantilevered beam is derived via Hamilton's principle, and a reduced-order control model is subsequently obtained through a modal analysis. Uncertain system parameters such as frequency variations are included in the control model. A sliding-mode control theory, which has inherent robustness to system uncertainties, is adopted to design a position tracking controller for the piezofilm actuator. Using the output information from a tip displacement sensor, a full-order observer is constructed to estimate state variables of the control system. Tracking control performances for desired position trajectories represented by sinusoidal and step functions are evaluated by undertaking both simulation and experimental works. Nomenclature A i = cross-sectiona l area of the composite beam A 2 = cross-sectional area of the piezofilm b = width of the composite beam (or piezofilm) di = magnitude of the disturbance d3i = piezoelectric strain constant E = elastic modulus of the composite beam EI = elastic modulus of the piezofilm e = tracking error of the tip displacement / = external disturbance g = gradient of the sliding surface hi = thickness of the composite beam hi = thickness of the piezofilm // = generalized mass /i = area moment of inertia of the composite beam 72 = area moment of inertia of the piezofilm k = discontinuity gain of the sliding-mode controller L = length of the composite beam (or piezofilm) qi = generalized modal coordinate R = observer matrix s = sliding surface t = time variable Tk = kinetic energy V = control input voltage Vp = potential energy x = spatial variable in the axial direction Xj = state variable Xj = estimated state variable ydt = desired tip displacement yt = actual tip displacement Pi = weighting factor of the natural frequency deviation Yi = weighting factor of the damping ratio deviation s = boundary layer width of saturation function f/ = damping ratio Pi = density of the composite beam p2 = density of the piezofilm , = mode shape function o)i = natural frequency