Comparison of negative and positive position feedback control of a flexible structure

Abstract

Two modal control techniques, negative position feedback (NPF) and positive position feedback (PPF), are applied to reduce multi-mode vibration of a lightly damped flexible beam using a piezoelectric sensor and piezoelectric actuators. The NPF and PPF controllers are constructed by respectively feeding back the generalized displacement response from the sensor in a negative and a positive sense to the actuators through second order high pass and low pass filters. PPF is well known while NPF is new for this application and is in fact an electrical realization of a dynamic vibration absorber. The choice of the parameters for controllers of both types is made easy by a robust modal control technique that offers an optimal performance for NPF control and a near-optimal performance for PPF control. Explicit forms of the controller parameters are presented. Experiments are conducted on a cantilever beam embedded with a matched pair of PZT (lead zirconate titanate) patch actuators and a collocated PVDF (polyvinylidene fluoride) patch sensor. The experiments demonstrate that it is possible to realize an electrical dynamic absorber using the generalized displacement sensor. It is further demonstrated that NPF can be a good alternative control strategy particularly when multiple modes are to be controlled.

Topology optimization of flextensional piezoelectric actuators with active control law

“…The advantage of designing the controlled piezoelectric system through a numerical method is that it enables the modelling of the controller integrated to the structure so that the control effect within the microstructure is part of the analysis. An active vibration control scheme, defined by the extra voltage or electric charge that is supplied to the piezoceramic material (TAKEZAWA et al, 2014b), has been studied for flexible plates (TZOU; TSENG, 1990;WANG;ANG, 2001;CARUSO;GALEANI;MENINI, 2003), for cylindrical laminated composite shells (RAY;REDDY, 2003), for beams (VASQUES;RODRIGUES, 2006;WANG;BRENNAN, 2010) and for precision positioning of hard disk drives (CHOI; CHAN;LIAO, 2008). Active control schemes are often modeled for dynamic topology optimization method designs in frequency domain analysis considering either the velocity feedback control, (ZHANG; KANG; LI, 2014) and (ZHANG; TAKEZAWA; KANG, 2018), or the control of single mode from the state space representation by using the controllability Gramian (GONÇALVES; DELEON; PERONDI, 2017) and (GONCALVES; DELEON; PERONDI, 2018).…”

Narrowband feedback for narrowband control of resonant and non-resonant vibration

“…PPF is particularly suitable for controlling the fundamental mode when a strain-type sensor is used. The electrical dynamic absorber (EDA) method was then proposed as a rather general tool for resonant vibration control, which is also narrowband feedback employing a number of second order filters [8][9][10][11]. Unlike PPF, however, it is a passivity-based controller (PBC) electrically realizing a mechanical dynamic absorber [9,10].…”

“…It is further a robust-PBC that is even more robust than Karnopp's electrical damper [8]. This method is also applicable to multiple modal control in both collocated and non-collocated control configurations, regardless of the types of transducers used [10,11]. Many other methods are also available in the control society, such as, classical compensators [12], statebased optimal methods [13], and intelligent methods like fuzzy control [14].…”

Topology optimization of piezoelectric bi-material actuators with velocity feedback control

“…The active vibration control scheme in piezoelectric systems, that is stablished by the extra voltage or electric charge supplied to the piezoceramic material [9], and that is applied to the design of the controlled BPEA therein proposed, has been studied for flexible plates [10][11][12], for cylindrical laminated composite shells [13], for beams [14,15], and for precision positioning of hard disk drives [16,17]. Tzou and Tseng [10] implemented the constantgain feedback control and the constant-amplitude feedback control.…”