Noncollocated passivity-based PD control of a single-link flexible manipulator

Abstract

The passivity property of a noncollocated single-link flexible manipulator with a parameterized output is studied. The system can be characterized by either the irrational transfer function of an infinite-dimensional model or its truncated rational transfer functions. Necessary and sufficient conditions for these transfer functions to be passive are found. It is also shown that a non-passive, marginal minimum-phase, truncated transfer function can be rendered passive by using either the root strain feedback or the joint angular acceleration feedback. For the noncollocated truncated passive transfer function, a PD controller suffices to stabilize the overall system. Numerical results are given to show the efficacy of the proposed approaches.

Control of Flexible Manipulators. Theory and Practice

“…passive and robust control theories) to obtain a controller more adequate and versatile to do a determined control task, as a consequence of its easy implementation. Classic control techniques are more convenient when minimum phase systems are used (see discussions of ), which can be obtained by choosing an appropriate output ( (Gervarter, 1970), (Luo, 1993) and (Pereira et al, 2007)) or by redefining it ( (Wang & Vidyasagar 1992) and (Liu & Yuan, 2003)). …”

Neural Network Control of a Flexible Robotic Manipulator Using the Lumped Spring-Mass Model

“…In recent years, a number of techniques for vibration control of flexible structures have been used, including observer-based control [3], potential difference (PD) control [4], adaptive boundary control [5]- [8], input preshaping approach [9], and adaptive control [2]. However, these traditional control approaches mentioned above are difficult to track the desired angle and suppress the vibration simultaneously, since the flexible manipulator is assumed to be distributed into a number of units with the absence of velocity sensors for every separated mode.…”

“…[4,2] T , and = 0.001. The initial values of the observer are set as π 1 = π 2 =π 1 =π 2 = [0, 0] T .…”

Parameter estimation and stabilisation for a one-dimensional wave equation with boundary output constant disturbance and non-collocated control

“…Actually, the noncollocated design has been widely used in engineering systems control (see e.g. Cannon and Schmitz 1984;Spector and Flashner 1990;Udwadia 1991;Yang and Mote 1992;Liu and Yuan 1997;Wu 2001;de Querioz and Rhan 2002;Ryu, Kwon, and Hannsford 2003;Yuan and Liu 2003;Lacarbonara and Yabuno 2004). But non-collocated control design proposes some theoretical challenges.…”