Experimental study on vibration control for rope-sway of elevator of high-rise building

Lyapunov-Based Control of the Sway Dynamics for Elevator Ropes

“…Remark 2: It is clear from equation (16) that the trivial choice of a constant positive damping control U , will also imply a convergence of the sway dynamics to zero. However, the controller (14) has the advantage to require less control energy comparatively to a constant damping, since by construction of the control law (14), the stabilizing damping force decreases together with the decrease of the sway.…”

“…The controller U given by (14) does not take into account the disturbance F (t) explicitly. Next, we present a controller which deals with the case of a static elevator in a building under sustained external disturbances, e.g.…”

“…The sway w(y, t) can be measured by laser displacement sensors placed at the positions y(i), i = 1, 2, ...N , along the rope, e.g. [14], subsequently q can be computed by simple algebraic inversion of (10), andq can be obtained by direct numerical differentiation of q. Next, we consider the model (12), (13) with no-zero disturbance signals: f 1 (t) = 0.2sin(2π.0.08t), and f 2 being deduced from f 1 via equation (3).…”

“…Furthermore, to make the simulation tests more challenging we added a random white noise to the states fed back to the controller (equivalent to about ±1 cm of error on the rope sway measurement from which the states are computed, see Remark 1), and we filtered the control signal with a first order filter with a cut frequency of 10 hz and a delay term of 5 sampling times, to simulate actuator dynamics and delays due to signal transmission and computation time. First, to validate Theorem 1, we present the results obtained by applying the controller (14), to the model (12), (13), with non-zero initial conditions q(0) = 20,q(0) = 5, and zero external disturbances, i.e. f 1 (t) = f 2 (t) = 0, ∀t.…”

“…We see that the sway steady state maximum amplitude is reduced from 8.4 m in the uncontrolled case to 2.4 m with control. The noisy (due to the simulated measurements noise) bounded and continuous control signals are reported onFigures 8,9. Output of controller(14) Output of controller (14)-Zoom…”