# Stabilization

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## stabilization

[‚stā·bə·lə′zā·shən]## Stabilization

## Stabilization

the attainment and fixation of a constant state or the maintenance of such a state. Examples include the maintenance of the constancy of a process, as in frequency stabilization, and increasing the stability of a substance, as in the stabilization ofpolymers.

## Stabilization

in automatic control and regulation, the maintenance of a specified value over time of one or several controlled quantities *x(t)* in such a way that the value remains unaffected by disturbing (destabilizing) effects *f*. The effects, which can be external or internal with regard to the stabilized object, tend to deflect the controlled quantity from the specified value x_{0} (t) = x_{0}*=* const. It is possible to stabilize not only any measured controlled quantity, such as the effective value of voltage, but also any given function of this quantity, including even a function of several primary measured quantities.

The efficiency of stabilization is quantitatively expressed by the dimensionless stabilization coefficient σ This coefficient is equal to the quotient obtained by dividing a small relative change in the destabilizing effect Δf/f by the resulting relatively small change in the controlled quantity *Δx/x*. At the limit, these small changes are replaced by differentials:

Ideal stabilization is attained at σ → ∞.

Several destabilizing effects may be present, in which case stabilization coefficients characterizing the influence of each of the factors are calculated. If the destabilizing effects are regular and mutually independent, their combined influence on the parameter being stabilized is equal to the algebraic sum of these effects. If the destabilizing effects are irregular (random), their combined influence on the parameter is evaluated as the geometric sum of the individual effects.

In general calculations involving stabilization systems, the coefficient σ-^{1} is frequently used; ideal stabilization of the controlled parameter is attained at σ^{1} → = ∞. Often, in place of the coefficients σ and σ^{–1}, the values of the relative (δ) or absolute (Δ) deviation of the stabilized quantity from a specified constant value are used in evaluating the operation of a stabilization system. A distinction is made between φ, φ^{-1}, δ, and Δ for instantaneous values of the controlled quantity *x(t)* (short-term stability) and for average values of the quantity over a longer period, a period characteristic of the particular stabilization system or process (long-term, or integral, stability). In addition, for a slow change in *x(t)*, a value known as drift ξ is used as a characteristic in evaluating the operational effectiveness of a stabilization system. The drift is usually calculated as the rate of departure of *x(t)* from a specified value x_{0} (during a specified characteristic time interval from O to *t*_{1},):

The two main groups of stabilizing devices, that is, stabilizers, are those with and those without feedback. Stabilizers without feedback can be parametric or can effect an automatic compensation of destabilizing effects. Stabilizers with feedback, referred to as automatic controllers, correct the deviations of the controlled quantity *x(t)* from the desired value x_{0} generated by a setting (master) device.

Parametric stabilizers utilize a nonlinear stabilizing element whose controlled output quantity in the operational range is practically independent of input values. Here, if the influence of all other destabilizing effects is small in comparison with the change in the generalized input, a nearly constant value of the controlled quantity will be obtained at the parametric stabilizer’s output. Parametric stabilizers are widely used for stabilizing electrical quantities, such as voltage.

In stabilizers with automatic compensation of a destabilizing effect, the controlling quantity is generated as a function of this sole or, at any rate, principal factor. In a number of cases, a nonlinear element is used for automatic compensation of the main destabilizing effect, just as in parametric stabilizers. If there are two or more substantial destabilizing factors in a given system, stabilization through automatic compensation of destabilizing effects becomes less effective and as such has practically no technical applications. In these cases, combined stabilizers with two control circuits are used. One circuit is actuated by the main disturbance (destabilizing effect) and thus has no feedback; the other is actuated by deviations and utilizes feedback. In this case, the provision of a circuit that compensates for destabilizing effects significantly increases the operational speed of the stabilizer; that is, it reduces time lags. The increase is achieved because control actuated by disturbances, which involves expenditure of time, is not required in arriving at the deviation of the controlled quantity from the desired value.

A stabilizer with feedback has a closed loop and compares the actual instantaneous value of the controlled quantity *x(t)* with the desired value x_{0}. The error signal e(r) = x_{0} – *x(t)*, transformed if necessary and amplified, serves as a basis for the controlling action. This action is directed, through the agency of the controller, toward decreasing ∊(t); the controlled output then again enters the comparator through the feedback loop and a new error signal is produced. This process continues until the threshold of sensitivity of any of the elements in the loop can no longer be reached.

### REFERENCES

Dusavitskii, Iu. Ia.*Magnitnye stabilizatory postoiannogo napriazheniia*. Moscow, 1970.

Lukes, J. H.

*Skhemy na poluprovodnikovykh diodakh*. Moscow, 1972. (Translated from German.)

*Teoriia avtomaticheskogo upravleniia*, part 2. Edited by A. V. Netushil. Moscow, 1972.

*Osnovy avtomaticheskogo upravleniia*, 3rd ed. Edited by V. S. Pugachev. Moscow, 1974.

Zhuravlev, A. A., and K. B. Mazel’.

*Preobrazovateli postoiannogo napriazheniia na tranzistorakh*, 3rd ed. Moscow, 1974.

M. M. MAIZEL’