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.

Method for adjusting the rate of a basic oscillator of a watch arranged to oscillate at a nominal frequency N0, with a master oscillator generating an excitation frequency NE approximately equal to an integer multiple of this nominal frequency N0, the master oscillator subjecting the watch to excitation or a modulated motion during a transition phase after which the basic oscillator is stabilised at the excitation frequency NE, and a state of display correction method with a winder for mechanical or automatic watches, moving a support carrying the watch and comprising a state of display correction oscillator, having a lower variation of rate value than the initial variation of rate value DI of this basic oscillator, and oscillating at a correction frequency NC to impose oscillation or a motion on the watch, during a state of display correction phase whose duration is adjusted to exactly correct a state of display error measured at the initial moment of actuation.

Method for adjusting the rate of a basic oscillator of a watch arranged to oscillate at a nominal frequency N0, with a master oscillator generating an excitation frequency NE approximately equal to an integer multiple of this nominal frequency N0, the master oscillator subjecting the watch to excitation or a modulated motion during a transition phase after which the basic oscillator is stabilised at the excitation frequency NE, and a state of display correction method with a winder for mechanical or automatic watches, moving a support carrying the watch and comprising a state of display correction oscillator, having a lower variation of rate value than the initial variation of rate value DI of this basic oscillator, and oscillating at a correction frequency NC to impose oscillation or a motion on the watch, during a state of display correction phase whose duration is adjusted to exactly correct a state of display error measured at the initial moment of actuation.

Method for adjusting the rate of a basic oscillator of a watch arranged to oscillate at a nominal frequency N0, with a master oscillator generating an excitation frequency NE approximately equal to an integer multiple of this nominal frequency N0, the master oscillator subjecting the watch to excitation or a modulated motion during a transition phase after which the basic oscillator is stabilised at the excitation frequency NE, and a state of display correction method with a winder for mechanical or automatic watches, moving a support carrying the watch and comprising a state of display correction oscillator, having a lower variation of rate value than the initial variation of rate value DI of this basic oscillator, and oscillating at a correction frequency NC to impose oscillation or a motion on the watch, during a state of display correction phase whose duration is adjusted to exactly correct a state of display error measured at the initial moment of actuation.

Method for adjusting the rate of a basic oscillator of a watch arranged to oscillate at a nominal frequency N0, with a master oscillator generating an excitation frequency NE approximately equal to an integer multiple of this nominal frequency N0, the master oscillator subjecting the watch to excitation or a modulated motion during a transition phase after which the basic oscillator is stabilised at the excitation frequency NE, and a state of display correction method with a winder for mechanical or automatic watches, moving a support carrying the watch and comprising a state of display correction oscillator, having a lower variation of rate value than the initial variation of rate value DI of this basic oscillator, and oscillating at a correction frequency NC to impose oscillation or a motion on the watch, during a state of display correction phase whose duration is adjusted to exactly correct a state of display error measured at the initial moment of actuation.

A balance of a timepiece including an adjustment face provided with at least one recess provided for receiving a projected material for an implementation of an adjustment of the rate of the timepiece notably by the modification of the inertia and of the unbalance of the balance, the recess including an opening and a back notably a solid back or a back fully or partially forming an orifice, the back being at most partially visible from a position defined above the opening notably on a central axis of the opening.

A balance of a timepiece including an adjustment face provided with at least one recess provided for receiving a projected material for an implementation of an adjustment of the rate of the timepiece notably by the modification of the inertia and of the unbalance of the balance, the recess including an opening and a back notably a solid back or a back fully or partially forming an orifice, the back being at most partially visible from a position defined above the opening notably on a central axis of the opening.

A horological movement provided with a generator and a circuit for regulating the frequency of rotation of this generator, the regulation circuit being arranged to be able to detect the zero crossings of an induced voltage generated in the stator by the rotating rotor and to generate first braking pulses which are triggered after zero crossings and each end before the induced voltage reaches a peak value, preferably before the rectified induced voltage reaches a power supply voltage provided by a power supply capacity. In addition, the regulation circuit is arranged so as to be able to further generate second braking pulses each of which occurs after detection of the end of a charging period of the power supply capacity during which the induced voltage reaches a peak value and each end before the induced voltage crosses zero.

A horological movement provided with a generator and a circuit for regulating the frequency of rotation of this generator, the regulation circuit being arranged to be able to detect the zero crossings of an induced voltage generated in the stator by the rotating rotor and to generate first braking pulses which are triggered after zero crossings and each end before the induced voltage reaches a peak value, preferably before the rectified induced voltage reaches a power supply voltage provided by a power supply capacity. In addition, the regulation circuit is arranged so as to be able to further generate second braking pulses each of which occurs after detection of the end of a charging period of the power supply capacity during which the induced voltage reaches a peak value and each end before the induced voltage crosses zero.