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@ -79,6 +79,9 @@ Controller Poles are shown by black crosses (
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** Introduce Each part of the paper :ignore:
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This paper has been published
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The Matlab code that was use to obtain the results are available in cite:dehaeze20_activ_dampin_rotat_posit_platf.
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* Dynamics of Rotating Positioning Platforms
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** Studied Rotating Positioning Platform
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# Simplest system where gyroscopic forces can be studied
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@ -86,11 +89,12 @@ Consider the rotating X-Y stage of Figure [[fig:system]].
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# Present the system, parameters, assumptions
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# Explain the frames (inertial frame x,y, rotating frame u,v)
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# iu, iv is linked to the rotating stage and supposed to be perfect
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# Small displacements
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# Constant rotating speed
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# Explain the frames (inertial frame x,y, rotating frame u,v)
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# Constant rotational speed
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- $k$: Actuator's Stiffness [N/m]
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- $m$: Payload's mass [kg]
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@ -99,7 +103,7 @@ Consider the rotating X-Y stage of Figure [[fig:system]].
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- $d_u$, $d_v$
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#+name: fig:system
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#+caption: Figure caption
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#+caption: Schematic of the studied System
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#+attr_latex: :scale 1
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[[file:figs/system.pdf]]
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@ -109,7 +113,7 @@ Consider the rotating X-Y stage of Figure [[fig:system]].
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# [[file:figs/cedrat_xy25xs.jpg]]
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** Equation of Motion
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The system has two degrees of freedom and is thus fully described by the generalized coordinates $u$ and $v$.
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The system has two degrees of freedom and is thus fully described by the generalized coordinates $u$ and $v$ (describing the position of the mass in the rotating frame).
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Let's express the kinetic energy $T$ and the potential energy $V$ of the mass $m$ (neglecting the rotational energy):
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@ -189,8 +193,8 @@ With:
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- $\xi$ damping ratio
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** Constant Rotating Speed
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To simplify, let's consider a constant rotating speed $\dot{\theta} = \Omega$ and thus $\ddot{\theta} = 0$.
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** Constant Rotational Speed
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To simplify, let's consider a constant rotational speed $\dot{\theta} = \Omega$ and thus $\ddot{\theta} = 0$.
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#+NAME: eq:coupledplant
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\begin{equation}
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@ -234,7 +238,7 @@ When the rotation speed in not null, the resonance frequency is duplicated into
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As the rotation speed increases, one of the two resonant frequency goes to lower frequencies as the other one goes to higher frequencies (Figure [[fig:campbell_diagram]]).
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#+name: fig:campbell_diagram
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#+caption: Campbell Diagram
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#+caption: Campbell Diagram : Evolution of the poles as a function of the rotational speed $\Omega$
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#+attr_latex: :environment subfigure :width 0.4\linewidth :align c
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| file:figs/campbell_diagram_real.pdf | file:figs/campbell_diagram_imag.pdf |
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| <<fig:campbell_diagram_real>> Real Part | <<fig:campbell_diagram_imag>> Imaginary Part |
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@ -249,17 +253,17 @@ As the rotation speed increases, one of the two resonant frequency goes to lower
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The magnitude of the coupling terms are increasing with the rotation speed.
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#+name: fig:plant_compare_rotating_speed
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#+caption: Bode Plots for $\bm{G}_d$
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#+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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| file:figs/plant_compare_rotating_speed_direct.pdf | file:figs/plant_compare_rotating_speed_coupling.pdf |
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| <<fig:plant_compare_rotating_speed_direct>> Direct Terms $d_u/F_u$, $d_v/F_v$ | <<fig:plant_compare_rotating_speed_coupling>> Coupling Terms $d_v/F_u$, $d_u/F_v$ |
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# #+name: fig:plant_compare_rotating_speed
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# #+caption: Caption
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# #+attr_latex: :scale 1
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# [[file:figs/plant_compare_rotating_speed.pdf]]
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#+name: fig:plant_compare_rotating_speed
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#+caption: Dynamics
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#+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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| file:figs/plant_compare_rotating_speed_direct.pdf | file:figs/plant_compare_rotating_speed_coupling.pdf |
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| <<fig:plant_compare_rotating_speed_direct>> Direct Terms $d_u/F_u$, $d_v/F_v$ | <<fig:plant_compare_rotating_speed_coupling>> Coupling Terms $d_v/F_u$, $d_u/F_v$ |
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* Integral Force Feedback
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** Control Schematic
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@ -306,12 +310,14 @@ Which then gives:
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** Plant Dynamics
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#+name: fig:plant_iff_compare_rotating_speed
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#+caption: Figure caption
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#+caption: Bode plot of $\bm{G}_f$ for several rotational speeds $\Omega$
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#+attr_latex: :scale 1
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[[file:figs/plant_iff_compare_rotating_speed.pdf]]
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# Show that the low frequency gain is no longer zero
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# Write the analytical value of the low frequency gain
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# Explain the two real zeros => change of gain but not of phase
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# Explain physically why
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@ -325,7 +331,7 @@ Which then gives:
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# Explain the circles, crosses and black crosses (poles of the controller)
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#+name: fig:root_locus_pure_iff
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#+caption: Root Locus
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#+caption: Root Locus for the Decentralized Integral Force Feedback
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#+attr_latex: :scale 1
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[[file:figs/root_locus_pure_iff.pdf]]
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@ -354,7 +360,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Explain that now the low frequency loop gain does not reach a gain more than 1 (if g not so high)
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#+name: fig:loop_gain_modified_iff
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#+caption: Figure caption
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#+caption: Bode Plot of the Loop Gain for IFF with and without the HPF
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#+attr_latex: :scale 1
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[[file:figs/loop_gain_modified_iff.pdf]]
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@ -362,7 +368,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Actually, the system becomes unstable for g > ...
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#+name: fig:root_locus_modified_iff
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#+caption: Figure caption
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#+caption: Root Locus for IFF with and without the HPF
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#+attr_latex: :scale 1
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[[file:figs/root_locus_modified_iff.pdf]]
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@ -378,7 +384,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Trade off
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#+name: fig:root_locus_wi_modified_iff
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#+caption: Figure caption
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#+caption: Root Locus for several HPF cut-off frequencies $\omega_i$
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#+attr_latex: :scale 1
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[[file:figs/root_locus_wi_modified_iff.pdf]]
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@ -391,7 +397,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# wi = 0.1 w0 is chosen
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#+name: fig:mod_iff_damping_wi
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#+caption: Figure caption
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#+caption: Attainable damping ratio $\xi_\text{cl}$ as a function of the HPF cut-off frequency. Corresponding control gain $g_\text{opt}$ and $g_\text{max}$ are also shown
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#+attr_latex: :scale 1
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[[file:figs/mod_iff_damping_wi.pdf]]
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@ -402,7 +408,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# We want to have stable zeros => add stiffnesses in parallel
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#+name: fig:system_parallel_springs
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#+caption: Figure caption
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#+caption: System with added springs $k_p$ in parallel with the actuators
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#+attr_latex: :scale 1
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[[file:figs/system_parallel_springs.pdf]]
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@ -420,7 +426,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# For kp > negative stiffness => complex conjugate zeros
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#+name: fig:plant_iff_kp
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#+caption: Figure caption
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#+caption: Bode Plot of $f_u/F_u$ without parallel spring, with parallel springs with stiffness $k_p < m \Omega^2$ and $k_p > m \Omega^2$
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#+attr_latex: :scale 1
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[[file:figs/plant_iff_kp.pdf]]
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@ -429,7 +435,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Show that it is the case on the root locus
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#+name: fig:root_locus_iff_kp
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#+caption: Figure caption
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#+caption: Root Locus for IFF without parallel spring, with parallel springs with stiffness $k_p < m \Omega^2$ and $k_p > m \Omega^2$
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#+attr_latex: :scale 1
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[[file:figs/root_locus_iff_kp.pdf]]
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@ -443,7 +449,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Large Stiffness decreases the attainable damping
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#+name: fig:root_locus_iff_kps
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#+caption: Figure caption
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#+caption: Root Locus for IFF for several parallel spring stiffnesses $k_p$
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#+attr_latex: :scale 1
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[[file:figs/root_locus_iff_kps.pdf]]
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@ -451,7 +457,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Example with kp = 5 m Omega
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#+name: fig:root_locus_opt_gain_iff_kp
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#+caption: Figure caption
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#+caption: Root Locus for IFF with $k_p = 5 m \Omega^2$. The poles of the system using the gain that yields the maximum damping ratio are shown by black crosses
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#+attr_latex: :scale 1
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[[file:figs/root_locus_opt_gain_iff_kp.pdf]]
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@ -464,7 +470,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Equation with the control law
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#+name: fig:system_dvf
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#+caption: Figure caption
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#+caption: System with relative velocity sensors and with decentralized controllers $K_V$
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#+attr_latex: :scale 1
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[[file:figs/system_dvf.pdf]]
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@ -490,7 +496,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Arbitrary Damping can be added to the poles
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#+name: fig:root_locus_dvf
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#+caption: Figure caption
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#+caption: Root Locus for Decentralized Direct Velocity Feedback for several rotational speeds $\Omega$
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#+attr_latex: :scale 1
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[[file:figs/root_locus_dvf.pdf]]
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@ -502,7 +508,7 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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** Attainable Damping
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#+name: fig:comp_root_locus
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#+caption: Figure caption
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#+caption: Root Locus for the three proposed decentralized active damping techniques: IFF with HFP, IFF with parallel springs, and relative DVF
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#+attr_latex: :scale 1
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[[file:figs/comp_root_locus.pdf]]
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@ -519,8 +525,6 @@ This means that at low frequency, the system is decoupled (the force sensor remo
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# Relative DVF degrades the transmissibility at high frequency
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# The roll-off is -1 instead of -2
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#
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#+name: fig:comp_active_damping
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#+caption: Comparison of the three proposed Active Damping Techniques
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#+attr_latex: :environment subfigure :width 0.45\linewidth :align c
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BIN
paper/paper.pdf
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paper/paper.pdf
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123
paper/paper.tex
123
paper/paper.tex
@ -1,4 +1,4 @@
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% Created 2020-06-24 mer. 15:36
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% Created 2020-06-24 mer. 16:28
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% Intended LaTeX compiler: pdflatex
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\documentclass{ISMA_USD2020}
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\usepackage[utf8]{inputenc}
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@ -37,13 +37,6 @@
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\usetikzlibrary{shapes.misc}
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\date{}
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\title{Active Damping of Rotating Positioning Platforms}
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\hypersetup{
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pdfauthor={},
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pdftitle={Active Damping of Rotating Positioning Platforms},
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pdfkeywords={},
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pdfsubject={},
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pdfcreator={Emacs 27.0.91 (Org mode 9.4)},
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pdflang={English}}
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\begin{document}
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\maketitle
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@ -53,16 +46,18 @@
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}
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\section{Introduction}
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\label{sec:orgbec19fa}
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\label{sec:org3cbd2ff}
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\label{sec:introduction}
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Controller Poles are shown by black crosses (
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\begin{tikzpicture} \node[cross out, draw=black, minimum size=1ex, line width=2pt, inner sep=0pt, outer sep=0pt] at (0, 0){}; \end{tikzpicture}
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).
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This paper has been published
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The Matlab code that was use to obtain the results are available in \cite{dehaeze20_activ_dampin_rotat_posit_platf}.
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\section{Dynamics of Rotating Positioning Platforms}
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\label{sec:org81be86a}
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\label{sec:org3cf58d1}
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\subsection{Studied Rotating Positioning Platform}
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\label{sec:orgf8fad9b}
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\label{sec:orgf321431}
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Consider the rotating X-Y stage of Figure \ref{fig:system}.
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\begin{itemize}
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@ -76,12 +71,13 @@ Consider the rotating X-Y stage of Figure \ref{fig:system}.
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1]{figs/system.pdf}
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\caption{\label{fig:system}Figure caption}
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\caption{\label{fig:system}Schematic of the studied System}
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\end{figure}
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\subsection{Equation of Motion}
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\label{sec:org926ba54}
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The system has two degrees of freedom and is thus fully described by the generalized coordinates \(u\) and \(v\).
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\label{sec:org9612ace}
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The system has two degrees of freedom and is thus fully described by the generalized coordinates \(u\) and \(v\) (describing the position of the mass in the rotating frame).
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Let's express the kinetic energy \(T\) and the potential energy \(V\) of the mass \(m\) (neglecting the rotational energy):
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@ -125,7 +121,7 @@ Thus, the term \(- m\dot{\theta}^2\) acts like a negative stiffness (due to \tex
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\subsection{Transfer Functions in the Laplace domain}
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\label{sec:org298e237}
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\label{sec:org1590670}
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\begin{subequations}
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\begin{align}
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@ -163,9 +159,9 @@ With:
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\end{itemize}
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\subsection{Constant Rotating Speed}
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\label{sec:org8d2eda6}
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To simplify, let's consider a constant rotating speed \(\dot{\theta} = \Omega\) and thus \(\ddot{\theta} = 0\).
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\subsection{Constant Rotational Speed}
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\label{sec:orgd9375df}
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To simplify, let's consider a constant rotational speed \(\dot{\theta} = \Omega\) and thus \(\ddot{\theta} = 0\).
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\begin{equation}
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\label{eq:coupledplant}
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@ -213,7 +209,7 @@ As the rotation speed increases, one of the two resonant frequency goes to lower
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\includegraphics[width=\linewidth]{figs/campbell_diagram_imag.pdf}
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\caption{\label{fig:campbell_diagram_imag} Imaginary Part}
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\end{subfigure}
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\caption{\label{fig:campbell_diagram}Campbell Diagram}
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\caption{\label{fig:campbell_diagram}Campbell Diagram : Evolution of the poles as a function of the rotational speed \(\Omega\)}
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\centering
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\end{figure}
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@ -229,14 +225,15 @@ The magnitude of the coupling terms are increasing with the rotation speed.
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\includegraphics[width=\linewidth]{figs/plant_compare_rotating_speed_coupling.pdf}
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\caption{\label{fig:plant_compare_rotating_speed_coupling} Coupling Terms \(d_v/F_u\), \(d_u/F_v\)}
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\end{subfigure}
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\caption{\label{fig:plant_compare_rotating_speed}Dynamics}
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\caption{\label{fig:plant_compare_rotating_speed}Bode Plots for \(\bm{G}_d\)}
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\centering
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\end{figure}
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\section{Integral Force Feedback}
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\label{sec:org2e8c85f}
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\label{sec:org95f47e8}
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\subsection{Control Schematic}
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\label{sec:org50b6359}
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\label{sec:org8bb26ea}
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Force Sensors are added in series with the actuators as shown in Figure \ref{fig:system_iff}.
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@ -247,7 +244,7 @@ Force Sensors are added in series with the actuators as shown in Figure \ref{fig
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\end{figure}
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\subsection{Equations}
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\label{sec:org99c13a7}
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\label{sec:orgbd9ebe0}
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The sensed forces are equal to:
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\begin{equation}
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\begin{bmatrix} f_{u} \\ f_{v} \end{bmatrix} =
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@ -279,143 +276,153 @@ Which then gives:
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\end{align}
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\subsection{Plant Dynamics}
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\label{sec:org1e476e3}
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\label{sec:org392809f}
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1]{figs/plant_iff_compare_rotating_speed.pdf}
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\caption{\label{fig:plant_iff_compare_rotating_speed}Figure caption}
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\caption{\label{fig:plant_iff_compare_rotating_speed}Bode plot of \(\bm{G}_f\) for several rotational speeds \(\Omega\)}
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\end{figure}
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\subsection{Integral Force Feedback}
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\label{sec:orga5d8887}
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\label{sec:org049877c}
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1]{figs/root_locus_pure_iff.pdf}
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\caption{\label{fig:root_locus_pure_iff}Root Locus}
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\caption{\label{fig:root_locus_pure_iff}Root Locus for the Decentralized Integral Force Feedback}
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\end{figure}
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At low frequency, the gain is very large and thus no force is transmitted between the payload and the rotating stage.
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This means that at low frequency, the system is decoupled (the force sensor removed) and thus the system is unstable.
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\section{Integral Force Feedback with High Pass Filters}
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\label{sec:org569b7db}
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\label{sec:org54452db}
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\subsection{Modification of the Control Low}
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\label{sec:org4d0c1ca}
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\label{sec:org325cdd4}
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\subsection{Feedback Analysis}
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\label{sec:org1f34d25}
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\label{sec:org5efee77}
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\begin{figure}[htbp]
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\centering
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\includegraphics[scale=1]{figs/loop_gain_modified_iff.pdf}
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\caption{\label{fig:loop_gain_modified_iff}Figure caption}
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\caption{\label{fig:loop_gain_modified_iff}Bode Plot of the Loop Gain for IFF with and without the HPF}
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\end{figure}
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||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/root_locus_modified_iff.pdf}
|
||||
\caption{\label{fig:root_locus_modified_iff}Figure caption}
|
||||
\caption{\label{fig:root_locus_modified_iff}Root Locus for IFF with and without the HPF}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Optimal Cut-Off Frequency}
|
||||
\label{sec:org04a5aa4}
|
||||
\label{sec:orgd5828e4}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/root_locus_wi_modified_iff.pdf}
|
||||
\caption{\label{fig:root_locus_wi_modified_iff}Figure caption}
|
||||
\caption{\label{fig:root_locus_wi_modified_iff}Root Locus for several HPF cut-off frequencies \(\omega_i\)}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/mod_iff_damping_wi.pdf}
|
||||
\caption{\label{fig:mod_iff_damping_wi}Figure caption}
|
||||
\caption{\label{fig:mod_iff_damping_wi}Attainable damping ratio \(\xi_\text{cl}\) as a function of the HPF cut-off frequency. Corresponding control gain \(g_\text{opt}\) and \(g_\text{max}\) are also shown}
|
||||
\end{figure}
|
||||
|
||||
\section{Integral Force Feedback with Parallel Springs}
|
||||
\label{sec:org03c54a4}
|
||||
\label{sec:org22884d6}
|
||||
\subsection{Stiffness in Parallel with the Force Sensor}
|
||||
\label{sec:orgc2d9221}
|
||||
\label{sec:orgb871bfd}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/system_parallel_springs.pdf}
|
||||
\caption{\label{fig:system_parallel_springs}Figure caption}
|
||||
\caption{\label{fig:system_parallel_springs}System with added springs \(k_p\) in parallel with the actuators}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Effect of the Parallel Stiffness on the Plant Dynamics}
|
||||
\label{sec:org8097ba5}
|
||||
\label{sec:org4d37cce}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/plant_iff_kp.pdf}
|
||||
\caption{\label{fig:plant_iff_kp}Figure caption}
|
||||
\caption{\label{fig:plant_iff_kp}Bode Plot of \(f_u/F_u\) without any parallel stiffness, with a parallel stiffness \(k_p < m \Omega^2\) and with \(k_p > m \Omega^2\)}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/root_locus_iff_kp.pdf}
|
||||
\caption{\label{fig:root_locus_iff_kp}Figure caption}
|
||||
\caption{\label{fig:root_locus_iff_kp}Root Locus for IFF without any parallel stiffness, with a parallel stiffness \(k_p < m \Omega^2\) and with \(k_p > m \Omega^2\)}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Optimal Parallel Stiffness}
|
||||
\label{sec:org1f2e167}
|
||||
\label{sec:orgd19b212}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/root_locus_iff_kps.pdf}
|
||||
\caption{\label{fig:root_locus_iff_kps}Figure caption}
|
||||
\caption{\label{fig:root_locus_iff_kps}Root Locus for IFF for several parallel spring stiffnesses \(k_p\)}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/root_locus_opt_gain_iff_kp.pdf}
|
||||
\caption{\label{fig:root_locus_opt_gain_iff_kp}Figure caption}
|
||||
\caption{\label{fig:root_locus_opt_gain_iff_kp}Root Locus for IFF with \(k_p = 5 m \Omega^2\). The poles of the system using the gain that yields the maximum damping ratio are shown by black crosses}
|
||||
\end{figure}
|
||||
|
||||
\section{Direct Velocity Feedback}
|
||||
\label{sec:orgda2e325}
|
||||
\label{sec:org6904969}
|
||||
\subsection{Control Schematic}
|
||||
\label{sec:org0e84009}
|
||||
\label{sec:org103e18b}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/system_dvf.pdf}
|
||||
\caption{\label{fig:system_dvf}Figure caption}
|
||||
\caption{\label{fig:system_dvf}System with relative velocity sensors and with decentralized controllers \(K_V\)}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Equations}
|
||||
\label{sec:org7cc244c}
|
||||
\label{sec:org793c22d}
|
||||
|
||||
|
||||
|
||||
\subsection{Relative Direct Velocity Feedback}
|
||||
\label{sec:org668d842}
|
||||
\label{sec:orgc28d518}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/root_locus_dvf.pdf}
|
||||
\caption{\label{fig:root_locus_dvf}Figure caption}
|
||||
\caption{\label{fig:root_locus_dvf}Root Locus for Decentralized Direct Velocity Feedback for several rotational speeds \(\Omega\)}
|
||||
\end{figure}
|
||||
|
||||
\section{Comparison of the Proposed Active Damping Techniques for Rotating Positioning Stages}
|
||||
\label{sec:orgade0126}
|
||||
**
|
||||
\label{sec:org6af1fdb}
|
||||
\subsection{Physical Comparison}
|
||||
\label{sec:orgdff3aa2}
|
||||
|
||||
**
|
||||
|
||||
|
||||
\subsection{Attainable Damping}
|
||||
\label{sec:org22c8f42}
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1]{figs/comp_root_locus.pdf}
|
||||
\caption{\label{fig:comp_root_locus}Figure caption}
|
||||
\caption{\label{fig:comp_root_locus}Root Locus for the three proposed decentralized active damping techniques: IFF with HFP, IFF with parallel springs, and relative DVF}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Transmissibility and Compliance}
|
||||
\label{sec:org59b0db2}
|
||||
\label{sec:org3e2cf56}
|
||||
|
||||
|
||||
\begin{figure}[htbp]
|
||||
@ -431,13 +438,13 @@ This means that at low frequency, the system is decoupled (the force sensor remo
|
||||
\centering
|
||||
\end{figure}
|
||||
|
||||
|
||||
\section{Conclusion}
|
||||
\label{sec:org4b70853}
|
||||
\label{sec:orge292803}
|
||||
\label{sec:conclusion}
|
||||
|
||||
|
||||
\section*{Acknowledgment}
|
||||
\label{sec:org7708a14}
|
||||
\label{sec:orgaf681fb}
|
||||
|
||||
\bibliography{ref.bib}
|
||||
\end{document}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user