Tip tracking control of a micro-cantilever Timoshenko beam via piezoelectric actuator

Abstract

In this paper, the tip tracking control problem of a Timoshenko micro-cantilever beam is investigated. The beam is actuated by a piezoelectric layer laminated on one side of the beam. Dynamic equations of the beam and piezoelectric layer are found using the Hamilton principle. By employing the Galerkin projection method, state space representation of the system is derived. Then, a cascade control loop is used for tracking control of the beam’s tip. The cascade control structure consists of an inner loop stabilizer and an outer loop proportional-integral-derivative controller. The stabilizer has a linear feedback form whose states are obtained through a linear observer which is based on the beam tip displacement measurement. Stability analysis of the inner loop stabilizer is performed to study the effects of higher un-controlled modes on performance of the controlled system. Simulation results show the effectiveness of the proposed control method.

Vibration boundary control of Timoshenko micro-cantilever using piezoelectric actuators

“…A silicon dioxide micro cantilever with a PZT layer laminated on one of its side is considered as a case study. The physical characteristics of the beam and piezoelectric layer can be found in Table 1 [2,16,37]. According to Table 1: …”

“…Partial di erential equations of Timoshenko beam with a piezoelectric layer and boundary conditions obtained from the Hamilton principle with a little modi cation are given in [16]. A modi cation is made to the equations, that is, no external force has been entered into the system.…”

“…The geometry of the piezoelectric layer and beam is given in Table 2 [16]. Using the following de nitions of parameters, the governing equation of the system will become nondimensionalized:…”

“…Such algorithms are not appropriate for continuum systems, such as beams and membranes. For this purpose, governing equations should be converted to ordinary di erential equations in the vibrational modes, and then they would be controlled [3,16]. In contrast, in boundary control algorithm, the system is considered as a Partial Di erential Equation (PDE) where the controller is applied onto the boundary of the system and can change the response by changing the boundary conditions of the system [17][18][19].…”

A Novel Micro-cantilever Based Angular Speed Sensor Controlled Piezoelectrically and Tuned by Electrostatic Actuators

“…Sadek et al [24] considered the vibration control of an Euler-Bernoulli beam via a boundary control algorithm with minimum control effort. Salarieh et al [25] via the piezoelectric actuation studied the tip tracking control of a Timoshenko beam. Schoeftner et al [26] presented single point control (SPC), in order to cancel harmonic vibrations of slender beams.…”