Design and modeling of a piezo-actuated positioning mechanism

PID control of second-order systems with hysteresis

“…In the case of (2), the operator Φ models hysteretic actuation. Such hysteretic effects arise in, for example, micro-positioning control problems using piezo-electric actuators or smart actuators, as investigated in, inter alia, [1,4,5,6,9,10,16,17,19].…”

“…The latter is a distinguishing feature of the present paper visà vis [7] (wherein constant non-zero reference signals cannot be handled). Moreover, the investigation in [7] is concerned with systems of form (1) and is focussed on one particular hysteresis component, namely the Bouc-Wen model [8,20]. By contrast, in this paper we deal with a large class of rate-independent causal hysteresis operators which includes the play operator, stop operator, backlash operator and Preisach operators.…”

“…The rapidly expanding literature (of which [1] - [20] is but a representative sample) on analysis and control of systems with hysteresis attests to the growing importance of the field to both control theorists and practitioners. The analytical framework of the present paper is based on frequency-domain conditions developed recently in [12,13] which ensure existence, regularity and certain asymptotic properties of solutions of a feedback interconnection of a linear (possibly infinite dimensional) system and a hysteresis operator Φ.…”

PID control of second-order systems with hysteresis

“…In the case of (2), the operator Φ models hysteretic actuation. Such hysteretic effects arise in, for example, micro-positioning control problems using piezo-electric actuators or smart actuators, as investigated in, among other papers in this field, [1], [4], [5], [6], [8], [10], [15], [16], [18].…”

“…of the present paper visà vis [7]. The investigation in [7] is concerned with systems of form (1) and is focussed on one particular hysteresis component, namely the Bouc-Wen model [19]. By contrast, in this paper we deal with a large class of rate-independent causal hysteresis operator Φ which includes the play operator, stop operator, backlash operator and Preisach operators.…”