Control of convey-crane based on passivity

Undershoot Reduction for Plants with Real Unstable Zeros by Time-Varying Controller Design

“…Therefore, we need to achieve fast and reliable responses of the load with high precision positioning by controlling the gantry. Although the system dynamics of convey crane systems are similar to those for inverted pendulums, the output vectors are different (6) and we can show that the crane system has one real unstable zero. This implies that it is not so easy to control the crane system without any undershoot.…”

Nonlinear coupling control laws for an underactuated overhead crane system

“…In (1), M (q) 2 424 , V m (q; _ q) 2 424 , and G(q) 2 4 , represent the inertia, centripetal-Coriolis, and gravity terms (for details regarding the components of these matrices see [6], [7]), respectively, q(t) 2 4 is defined as follows:…”

“…where x(t) 2 denotes the gantry position along the X-coordinate axis, y(t) 2 denotes the gantry position along the Y -coordinate axis, (t) 2 denotes the payload angle with respect to the vertical, (t) 2 denotes the projection of the payload angle along the X-coordinate axis, and u(t) 2 4 is defined as…”

“…More recently, Fantoni et al [8] and Lozano et al [17] proposed passivity-based controllers for the inverted pendulum and the pendubot (i.e., an inverted pendulum-like robot with an unactuated second link) based on the paradigm of driving the underactuated system to a homoclinic orbit using an energy-based nonlinear controller and then switching to a linear controller to stabilize the system around its unstable equilibrium point. Using similar stability-analysis techniques, Collado et al [4] proposed a proportional-derivative (PD) controller for an overhead crane problem with a 1-DOF gantry. In [15], Kiss et al developed a PD controller for a vertical crane-winch system that only requires the measurement of the winch angle and its derivative rather than a cable angle measurement.…”

A Cable-Suspended Intelligent Crane Assist Device for the Intuitive Manipulation of Large Payloads

“…Other methods include state-space control [26], [16], backstepping [27], Lyapunov stability analysis [28], passivity [29] or proportional derivative control laws [30]. These controller were designed to control the position of the cart while minimizing cable oscillations.…”