A pendulum device is provided including at least one oscillating mass, at least one proximal arm, and at least one first distal arm, The at least one proximal arm is fixed to the oscillating mass at one end and is rotatably connected to the distal arm at the other end, so that the oscillating mass can oscillate with respect to said distal arm. The distal arm is rotatably fixed to a support element fixed through a fulcrum point. Furthermore, transmission means are included between the distal arm and the proximal arm. The transmission means is configured so that oscillation of the mass causes the rotation of the distal arm around the fulcrum point and so that at least one point of said proximal arm performs at least a linear translation, the mass performing a cycloidal trajectory.

In order to eliminate control problems caused by a manipulated variable limitation in the oscillation control of an oscillatable technical system, a restriction $\left(\frac{d^{n}u}{{{\mathrm{dt}}^n}_{min}},\frac{d^{n}u}{{{\mathrm{dt}}^n}_{m\mathrm{ax}}}\right)$
of at least one time derivative of the manipulated variable (u) in a control law for calculating the manipulated variable (u) is taken into account.

In order to eliminate control problems caused by a manipulated variable limitation in the oscillation control of an oscillatable technical system, a restriction $\left(\frac{d^{n}u}{{{\mathrm{dt}}^n}_{min}},\frac{d^{n}u}{{{\mathrm{dt}}^n}_{m\mathrm{ax}}}\right)$
of at least one time derivative of the manipulated variable (u) in a control law for calculating the manipulated variable (u) is taken into account.

A pendulum device is provided including at least one oscillating mass, at least one proximal arm, and at least one first distal arm, The at least one proximal arm is fixed to the oscillating mass at one end and is rotatably connected to the distal arm at the other end, so that the oscillating mass can oscillate with respect to said distal arm. The distal arm is rotatably fixed to a support element fixed through a fulcrum point. Furthermore, transmission means are included between the distal arm and the proximal arm. The transmission means is configured so that oscillation of the mass causes the rotation of the distal arm around the fulcrum point and so that at least one point of said proximal arm performs at least a linear translation, the mass performing a cycloidal trajectory.

In order to eliminate control problems caused by a manipulated variable limitation in the oscillation control of an oscillatable technical system, a restriction

[00001]$\left(\frac{d^n.Math.u}{{{\mathrm{dt}}^n.Math.}_{m.Math..Math.i.Math..Math.n}},\frac{d^n.Math.u}{{{\mathrm{dt}}^n.Math.}_{m.Math..Math.\mathrm{ax}}}\right)$

of at least one time derivative of the manipulated variable (u) in a control law for calculating the manipulated variable (u) is taken into account.

In order to eliminate control problems caused by a manipulated variable limitation in the oscillation control of an oscillatable technical system, a restriction

[00001]$\left(\frac{d^n.Math.u}{{{\mathrm{dt}}^n.Math.}_{m.Math..Math.i.Math..Math.n}},\frac{d^n.Math.u}{{{\mathrm{dt}}^n.Math.}_{m.Math..Math.\mathrm{ax}}}\right)$

of at least one time derivative of the manipulated variable (u) in a control law for calculating the manipulated variable (u) is taken into account.

An oscillating regulator for a timepiece includes at least two resonant oscillating systems (20, 30), each one having at least one magnetic component (25, 35) suitable for exchanging magnetic energy between the oscillating systems during their oscillations. The shafts (22, 32) of at least two of the oscillating systems (20, 30) differ substantially from each other in terms of their respective orientation.

An oscillating regulator for a timepiece includes at least two resonant oscillating systems (20, 30), each one having at least one magnetic component (25, 35) suitable for exchanging magnetic energy between the oscillating systems during their oscillations. The shafts (22, 32) of at least two of the oscillating systems (20, 30) differ substantially from each other in terms of their respective orientation.