The concept of stability is very well known. By the term stability one implies the ability of a system to return to its original position or attain a new steady-state condition when there is some disturbance or change in the input condition of the system. Following changes in input, or any disturbance, a controlled drive system has a time response made up of steady-state and transient responses. The former is of the form of input or noise and does not reveal any information about the Stability Control Drives of the system. The nature of the system with regard to stability is revealed by the transient response. If the transients are damped out and the system successfully takes up a steady-state operating point the system is said to be stable. It is always necessary that a drive system must be stable.
The Stability Control Drives of the system is associated with its characteristic equation. For the transient to die down the roots of the characteristic equation must lie on the left hand side of the s-plane, i.e., the roots must be negative if they are real or they must have a negative real part if they are complex.
The presence of one or more positive roots or complex roots with positive real parts indicates instability, as the transient response associated with these roots increases without bounds with time. Obviously such roots lie on the right hand side of the s-plane.
One of the requirements of a controlled drive system is stability. From the above discussion, a linear control system is said to be stable if
(a) it attains a steady-state condition which is unique and repeatable for a special input and is of the form of the input,
(b) the response dies away when the input is removed.
On the other hand it is unstable if its response increases continually with time, the system is self sustained and the response does not die down when the input is removed. Sometimes the system also shows a stable oscillatory behavior, which is just the borderline case between the stable and unstable responses. This is also not desirable. Some systems are conditionally stable, i.e., the system is stable for a range of values of a parameter and for other values it is unstable.
A direct and straightforward method for ascertaining the Stability Control Drives of a system is to determine the roots of the characteristic equation and to examine them for the negative real parts. The nature of a system’s stability is also revealed by the determination of the system’s response to specified inputs.
However, these two methods are very tedious and are difficult to apply when the order of the system is large. It is, therefore, desirable to have some indirect methods leading to an investigation of the stability of a system using some criteria without needing to evaluate the roots. These save both time and labour. Two such criteria are
(a) Routh-Hurwitz criterion and
(b) Nyquist stability criterion.
The Bode frequency response plots may also be used to ascertain the nature of Stability Control Drives. Sometimes a study of the effect of variation of parameters of a drive on its stability may be required for a judicious choice of the parameters or for correcting the parameters already existing. In such cases we may use root-locus techniques, which are developed to ascertain the variation of roots of a characteristic equation when the drive parameters are varied. The parameter plane method due to Siljak, and the domain decomposition method are very powerful for this purpose. These methods give the boundary between the stable and unstable operating regions when a pair of parameters are varied at a time.
The study of absolute stability is required in the drive technology where a drive motor is controlled and the control system has several components. It is also necessary to study the effect of variation of parameters on the stability for a suitable design of controllers, to improve the performance of the system.